MPQC 3.0.0-alpha
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sr_r12intermediates_VXB_diag.h
1//
2// sr_r12intermediates_VXB_diag.h
3//
4// Copyright (C) 2013 Edward Valeev
5//
6// Author: Edward Valeev <evaleev@vt.edu>
7// Maintainer: EV
8//
9// This file is part of the SC Toolkit.
10//
11// The SC Toolkit is free software; you can redistribute it and/or modify
12// it under the terms of the GNU Library General Public License as published by
13// the Free Software Foundation; either version 2, or (at your option)
14// any later version.
15//
16// The SC Toolkit is distributed in the hope that it will be useful,
17// but WITHOUT ANY WARRANTY; without even the implied warranty of
18// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19// GNU Library General Public License for more details.
20//
21// You should have received a copy of the GNU Library General Public License
22// along with the SC Toolkit; see the file COPYING.LIB. If not, write to
23// the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
24//
25// The U.S. Government is granted a limited license as per AL 91-7.
26//
27
28#ifndef _mpqc_src_lib_chemistry_qc_mbptr12_srr12intermediatesVXBdiag_h
29#define _mpqc_src_lib_chemistry_qc_mbptr12_srr12intermediatesVXBdiag_h
30
31#include <tiledarray.h>
32#include <cmath>
33
34namespace sc {
35 inline double get_element(const TA::TArrayD& array, const std::vector<std::size_t>& ele_idx)
36 {
37 const auto tile_idx = array.trange().element_to_tile(ele_idx);
38 return (array.find(tile_idx).get()[ele_idx]);
39 }
40
41 template <typename T>
42 typename SingleReference_R12Intermediates<T>::TArray2
43 SingleReference_R12Intermediates<T>::XaiAddToXam(const TA::Array<double, 2 >& Xam,
44 const TA::Array<double, 2 >& Xai) {
45// MPQC_ASSERT(Xam.size() == 1);
46//
47// typename TArray2::value_type tile_X =
48// static_cast<const typename TArray2::value_type&>(Xam.find(0)).clone();
49// typename TArray2::value_type tile_Xai = Xai.find(0);
50// const std::size_t zero_cols = tile_X.range().extent()[1] - tile_Xai.range().extent()[1];
51//
52// std::array<std::size_t, 2> i = {{0, 0}};
53// std::size_t ix = 0;
54// for(i[0] = tile_X.range().lobound()[0];
55// i[0] < tile_X.range().upbound()[0]; ++i[0]) {
56// for(i[1] = zero_cols + tile_X.range().lobound()[1];
57// i[1] < tile_X.range().upbound()[1]; ++i[1], ++ix) {
58// tile_X[i] += tile_Xai[ix];
59// }
60// }
61//
62// TArray2 X(Xam.world(), Xam.trange());
63// X.set(0, tile_X);
64 TArray2 X;
65 X("a,m") = Xam("a,m") + Xai("a,i") * _2("<i|I|m>");
66 return X;
67 }
68
69 // compute F^A'_C' R^Pk_A'B' R^Qk_C'B' (P & Q in alpha or beta space)
70 template <typename T>
71 typename SingleReference_R12Intermediates<T>::TArray2
72 SingleReference_R12Intermediates<T>::BPk_Qk(const char* p, const char* q,
73 const double C_0, const double C_1) {
74
75 const double B_C1 = 0.5 * C_0 * C_0 + 1.5 * C_1 * C_1;
76 const double B_C2 = 0.5 * C_0 * C_0 - 1.5 * C_1 * C_1;
77
78 std::string rTr_pkql = std::string("<") + p + " k|rTr|" + q + " l>";
79 std::string rTr_kpql = std::string("<k ") + p + "|rTr|" + q + " l>";
80
81 std::string r2_phJk_ql = std::string("<") + p + "_hJ(p') k|r2|" + q + " l>";
82 std::string r2_pkhJ_ql = std::string("<") + p + " k_hJ(p')|r2|" + q + " l>";
83 //
84 std::string r2_kphJ_ql = std::string("<k ") + p + "_hJ(p')|r2|" + q + " l>";
85 std::string r2_khJp_ql = std::string("<k_hJ(p') ") + p + "|r2|" + q + " l>";
86 //
87 std::string r2_pk_qhJl = std::string("<") + p + " k|r2|" + q + "_hJ(p') l>";
88 std::string r2_pk_qlhJ = std::string("<") + p + " k|r2|" + q + " l_hJ(p')>";
89 //
90 std::string r2_pk_lqhJ = std::string("<") + p + " k|r2|l " + q + "_hJ(p')>";
91 std::string r2_pk_lhJq = std::string("<") + p + " k|r2|l_hJ(p') " + q + ">";
92
93 std::string pk_PQ = std::string("<") + p + " k|r|p' q'>";
94 std::string kp_PQ = std::string("<k ") + p + "|r|p' q'>";
95 std::string qk_PKQ = std::string("<") + q + " k|r|p'_K(r') q'>";
96 std::string kq_PKQ = std::string("<k ") + q + "|r|p'_K(r') q'>";
97
98 std::string pk_Pn = std::string("<") + p + " k|r|p' n>";
99 std::string kp_Pn = std::string("<k ") + p + "|r|p' n>";
100 std::string qk_PFn = std::string("<") + q + " k|r|p'_F(r') n>";
101 std::string kq_PFn = std::string("<k ") + q + "|r|p'_F(r') n>";
102
103 std::string pk_mA = std::string("<") + p + " k|r|m a'>";
104 std::string kp_mA = std::string("<k ") + p + "|r|m a'>";
105 std::string qk_mFA = std::string("<") + q + " k|r|m_F(n) a'>";
106 std::string kq_mFA = std::string("<k ") + q + "|r|m_F(n) a'>";
107
108 std::string pk_pq = std::string("<") + p + " k|r|p b>";
109 std::string kp_pq = std::string("<k ") + p + "|r|p b>";
110 std::string qk_pFb = std::string("<") + q + " k|r|p_F(r) b>";
111 std::string kq_pFb = std::string("<k ") + q + "|r|p_F(r) b>";
112
113 std::string qk_mFPA = std::string("<") + q + " k|r|m_F(p') a'>";
114 std::string kq_mFPA = std::string("<k ") + q + "|r|m_F(p') a'>";
115 //
116 std::string qk_mA = std::string("<") + q + " k|r|m a'>";
117 std::string kq_mA = std::string("<k ") + q + "|r|m a'>";
118 std::string pk_mFPA = std::string("<") + p + " k|r|m_F(p') a'>";
119 std::string kp_mFPA = std::string("<k ") + p + "|r|m_F(p') a'>";
120
121 std::string pk_Ab = std::string("<") + p + " k|r|a' b>";
122 std::string kp_Ab = std::string("<k ") + p + "|r|a' b>";
123 std::string qk_AFb = std::string("<") + q + " k|r|a'_F(q) b>";
124 std::string kq_AFb = std::string("<k ") + q + "|r|a'_F(q) b>";
125 //
126 std::string qk_Ab = std::string("<") + q + " k|r|a' b>";
127 std::string kq_Ab = std::string("<k ") + q + "|r|a' b>";
128 std::string pk_AFb = std::string("<") + p + " k|r|a'_F(q) b>";
129 std::string kp_AFb = std::string("<k ") + p + "|r|a'_F(q) b>";
130
131 std::string pq = p + std::string(",") + q;
132
133 TArray2 B_pq;
134 B_pq(pq.c_str()) =
135 // diag
136 ( B_C1 * _4(rTr_pkql.c_str()) + B_C2 * _4(rTr_kpql.c_str())
137 // Q
138 + 0.5 * (
139 B_C1 * (_4(r2_phJk_ql.c_str()) + _4(r2_pkhJ_ql.c_str()))
140 + B_C2 * (_4(r2_kphJ_ql.c_str()) + _4(r2_khJp_ql.c_str()))
141
142 + B_C1 * (_4(r2_pk_qhJl.c_str()) + _4(r2_pk_qlhJ.c_str()))
143 + B_C2 * (_4(r2_pk_lqhJ.c_str()) + _4(r2_pk_lhJq.c_str()))
144 )
145 ) * _2("<k|I|l>")
146 // rKr_p'q'
147 - ( B_C1 * (_4(pk_PQ.c_str()) * _4(qk_PKQ.c_str())
148 + _4(kp_PQ.c_str()) * _4(kq_PKQ.c_str()))
149 + B_C2 * (_4(kp_PQ.c_str()) * _4(qk_PKQ.c_str())
150 + _4(pk_PQ.c_str()) * _4(kq_PKQ.c_str()))
151 )
152 // rFr_p'n
153 - ( B_C1 * (_4(pk_Pn.c_str()) * _4(qk_PFn.c_str())
154 + _4(kp_Pn.c_str()) * _4(kq_PFn.c_str()))
155 + B_C2 * (_4(kp_Pn.c_str()) * _4(qk_PFn.c_str())
156 + _4(pk_Pn.c_str()) * _4(kq_PFn.c_str()))
157 )
158 // rFr_mA
159 + ( B_C1 * (_4(pk_mA.c_str()) * _4(qk_mFA.c_str())
160 + _4(kp_mA.c_str()) * _4(kq_mFA.c_str()))
161 + B_C2 * (_4(kp_mA.c_str()) * _4(qk_mFA.c_str())
162 + _4(pk_mA.c_str()) * _4(kq_mFA.c_str()))
163 )
164 // rFr_pb
165 - ( B_C1 * (_4(pk_pq.c_str()) * _4(qk_pFb.c_str())
166 + _4(kp_pq.c_str()) * _4(kq_pFb.c_str()))
167 + B_C2 * (_4(kp_pq.c_str()) * _4(qk_pFb.c_str())
168 + _4(pk_pq.c_str()) * _4(kq_pFb.c_str()))
169 )
170 //
171 - ( B_C1 * (_4(pk_mA.c_str()) * _4(qk_mFPA.c_str())
172 + _4(kp_mA.c_str()) * _4(kq_mFPA.c_str()))
173 + B_C2 * (_4(kp_mA.c_str()) * _4(qk_mFPA.c_str())
174 + _4(pk_mA.c_str()) * _4(kq_mFPA.c_str()))
175
176 + B_C1 * (_4(qk_mA.c_str()) * _4(pk_mFPA.c_str())
177 + _4(kq_mA.c_str()) * _4(kp_mFPA.c_str()))
178 + B_C2 * (_4(kq_mA.c_str()) * _4(pk_mFPA.c_str())
179 + _4(qk_mA.c_str()) * _4(kp_mFPA.c_str()))
180 )
181 //
182 - ( B_C1 * (_4(pk_Ab.c_str()) * _4(qk_AFb.c_str())
183 + _4(kp_Ab.c_str()) * _4(kq_AFb.c_str()))
184 + B_C2 * (_4(kp_Ab.c_str()) * _4(qk_AFb.c_str())
185 + _4(pk_Ab.c_str()) * _4(kq_AFb.c_str()))
186
187 + B_C1 * (_4(qk_Ab.c_str()) * _4(pk_AFb.c_str())
188 + _4(kq_Ab.c_str()) * _4(kp_AFb.c_str()))
189 + B_C2 * (_4(kq_Ab.c_str()) * _4(pk_AFb.c_str())
190 + _4(qk_Ab.c_str()) * _4(kp_AFb.c_str()))
191 );
192 return B_pq;
193 }
194
195 template <typename T>
196 typename SingleReference_R12Intermediates<T>::TArray4
197 SingleReference_R12Intermediates<T>::Bpr_qs(const char* p, const char* q)
198 {
199
200 const double C_0 = 0.5;
201 const double C_1 = 0.25;
202 const double B_C1 = 0.5 * C_0 * C_0 + 1.5 * C_1 * C_1;
203 const double B_C2 = 0.5 * C_0 * C_0 - 1.5 * C_1 * C_1;
204
205 std::string rTr_pkql = std::string("<") + p + " k|rTr|" + q + " l>";
206 std::string rTr_kpql = std::string("<k ") + p + "|rTr|" + q + " l>";
207
208 std::string r2_phJk_ql = std::string("<") + p + "_hJ(p') k|r2|" + q + " l>";
209 std::string r2_pkhJ_ql = std::string("<") + p + " k_hJ(p')|r2|" + q + " l>";
210 //
211 std::string r2_kphJ_ql = std::string("<k ") + p + "_hJ(p')|r2|" + q + " l>";
212 std::string r2_khJp_ql = std::string("<k_hJ(p') ") + p + "|r2|" + q + " l>";
213 //
214 std::string r2_pk_qhJl = std::string("<") + p + " k|r2|" + q + "_hJ(p') l>";
215 std::string r2_pk_qlhJ = std::string("<") + p + " k|r2|" + q + " l_hJ(p')>";
216 //
217 std::string r2_pk_lqhJ = std::string("<") + p + " k|r2|l " + q + "_hJ(p')>";
218 std::string r2_pk_lhJq = std::string("<") + p + " k|r2|l_hJ(p') " + q + ">";
219
220 std::string pk_PQ = std::string("<") + p + " k|r|p' q'>";
221 std::string kp_PQ = std::string("<k ") + p + "|r|p' q'>";
222 std::string ql_PKQ = std::string("<") + q + " l|r|p'_K(r') q'>";
223 std::string lq_PKQ = std::string("<l ") + q + "|r|p'_K(r') q'>";
224
225 std::string pk_Pn = std::string("<") + p + " k|r|p' n>";
226 std::string kp_Pn = std::string("<k ") + p + "|r|p' n>";
227 std::string ql_PFn = std::string("<") + q + " l|r|p'_F(r') n>";
228 std::string lq_PFn = std::string("<l ") + q + "|r|p'_F(r') n>";
229
230 std::string pk_mA = std::string("<") + p + " k|r|m a'>";
231 std::string kp_mA = std::string("<k ") + p + "|r|m a'>";
232 std::string ql_mFA = std::string("<") + q + " l|r|m_F(n) a'>";
233 std::string lq_mFA = std::string("<l ") + q + "|r|m_F(n) a'>";
234
235 std::string pk_pq = std::string("<") + p + " k|r|p b>";
236 std::string kp_pq = std::string("<k ") + p + "|r|p b>";
237 std::string ql_pFb = std::string("<") + q + " l|r|p_F(r) b>";
238 std::string lq_pFb = std::string("<l ") + q + "|r|p_F(r) b>";
239
240 std::string ql_mFPA = std::string("<") + q + " l|r|m_F(p') a'>";
241 std::string lq_mFPA = std::string("<l ") + q + "|r|m_F(p') a'>";
242 //
243 std::string ql_mA = std::string("<") + q + " l|r|m a'>";
244 std::string lq_mA = std::string("<l ") + q + "|r|m a'>";
245 std::string pk_mFPA = std::string("<") + p + " k|r|m_F(p') a'>";
246 std::string kp_mFPA = std::string("<k ") + p + "|r|m_F(p') a'>";
247
248 std::string pk_Ab = std::string("<") + p + " k|r|a' b>";
249 std::string kp_Ab = std::string("<k ") + p + "|r|a' b>";
250 std::string ql_AFb = std::string("<") + q + " l|r|a'_F(q) b>";
251 std::string lq_AFb = std::string("<l ") + q + "|r|a'_F(q) b>";
252 //
253 std::string ql_Ab = std::string("<") + q + " l|r|a' b>";
254 std::string lq_Ab = std::string("<l ") + q + "|r|a' b>";
255 std::string pk_AFb = std::string("<") + p + " k|r|a'_F(q) b>";
256 std::string kp_AFb = std::string("<k ") + p + "|r|a'_F(q) b>";
257
258 TArray4 Bpr_qs;
259 Bpr_qs("p,r,q,s") =
260 // diag
261 B_C1 * _4(rTr_pkql.c_str()) + B_C2 * _4(rTr_kpql.c_str())
262 // Q
263 + 0.5 * (
264 B_C1 * (_4(r2_phJk_ql.c_str()) + _4(r2_pkhJ_ql.c_str()))
265 + B_C2 * (_4(r2_kphJ_ql.c_str()) + _4(r2_khJp_ql.c_str()))
266
267 + B_C1 * (_4(r2_pk_qhJl.c_str()) + _4(r2_pk_qlhJ.c_str()))
268 + B_C2 * (_4(r2_pk_lqhJ.c_str()) + _4(r2_pk_lhJq.c_str()))
269 )
270 // rKr_p'q'
271 - ( B_C1 * (_4(pk_PQ.c_str()) * _4(ql_PKQ.c_str())
272 + _4(kp_PQ.c_str()) * _4(lq_PKQ.c_str()))
273 + B_C2 * (_4(kp_PQ.c_str()) * _4(ql_PKQ.c_str())
274 + _4(pk_PQ.c_str()) * _4(lq_PKQ.c_str()))
275 )
276 // rFr_p'n
277 - ( B_C1 * (_4(pk_Pn.c_str()) * _4(ql_PFn.c_str())
278 + _4(kp_Pn.c_str()) * _4(lq_PFn.c_str()))
279 + B_C2 * (_4(kp_Pn.c_str()) * _4(ql_PFn.c_str())
280 + _4(pk_Pn.c_str()) * _4(lq_PFn.c_str()))
281 )
282 // rFr_mA
283 + ( B_C1 * (_4(pk_mA.c_str()) * _4(ql_mFA.c_str())
284 + _4(kp_mA.c_str()) * _4(lq_mFA.c_str()))
285 + B_C2 * (_4(kp_mA.c_str()) * _4(ql_mFA.c_str())
286 + _4(pk_mA.c_str()) * _4(lq_mFA.c_str()))
287 )
288 // rFr_pb
289 - ( B_C1 * (_4(pk_pq.c_str()) * _4(ql_pFb.c_str())
290 + _4(kp_pq.c_str()) * _4(lq_pFb.c_str()))
291 + B_C2 * (_4(kp_pq.c_str()) * _4(ql_pFb.c_str())
292 + _4(pk_pq.c_str()) * _4(lq_pFb.c_str()))
293 )
294 //
295 - ( B_C1 * (_4(pk_mA.c_str()) * _4(ql_mFPA.c_str())
296 + _4(kp_mA.c_str()) * _4(lq_mFPA.c_str()))
297 + B_C2 * (_4(kp_mA.c_str()) * _4(ql_mFPA.c_str())
298 + _4(pk_mA.c_str()) * _4(lq_mFPA.c_str()))
299
300 + B_C1 * (_4(ql_mA.c_str()) * _4(pk_mFPA.c_str())
301 + _4(lq_mA.c_str()) * _4(kp_mFPA.c_str()))
302 + B_C2 * (_4(lq_mA.c_str()) * _4(pk_mFPA.c_str())
303 + _4(ql_mA.c_str()) * _4(kp_mFPA.c_str()))
304 )
305 //
306 - ( B_C1 * (_4(pk_Ab.c_str()) * _4(ql_AFb.c_str())
307 + _4(kp_Ab.c_str()) * _4(lq_AFb.c_str()))
308 + B_C2 * (_4(kp_Ab.c_str()) * _4(ql_AFb.c_str())
309 + _4(pk_Ab.c_str()) * _4(lq_AFb.c_str()))
310
311 + B_C1 * (_4(ql_Ab.c_str()) * _4(pk_AFb.c_str())
312 + _4(lq_Ab.c_str()) * _4(kp_AFb.c_str()))
313 + B_C2 * (_4(lq_Ab.c_str()) * _4(pk_AFb.c_str())
314 + _4(ql_Ab.c_str()) * _4(kp_AFb.c_str()))
315 );
316 return Bpr_qs;
317 }
318
319 // compute V^PQ_RS = 1/2 R^PQ_A'B' g^A'B'_RS (all indices in alpha or beta space)
320 // do not use p1, q1, a1', or n1 as argument
321 template <typename T>
322 typename SingleReference_R12Intermediates<T>::TArray4
323 SingleReference_R12Intermediates<T>::VPQ_RS(const char* p, const char* q,
324 const char* r, const char* s)
325 {
326
327 std::string gr_pqrs = std::string("<") + p + " " + q + "|gr|" + r + " " + s + ">";
328
329 std::string rpq_pq = std::string("<") + p + " " + q + "|r|p1 q1>";
330 std::string grs_pq = std::string("<p1 q1|g|") + r + " " + s + ">";
331
332 std::string rpq_apn = std::string("<") + p + " " + q + "|r|a1' n1>";
333 std::string grs_apn = std::string("<a1' n1|g|") + r + " " + s + ">";
334
335 std::string rpq_nap = std::string("<") + p + " " + q + "|r|n1 a1'>";
336 std::string grs_nap = std::string("<n1 a1'|g|") + r + " " + s + ">";
337
338 std::string pqrs = p + std::string(",") + q + std::string(",")
339 + r + std::string(",") + s;
340
341 TArray4 Vpq_rs;
342 Vpq_rs(pqrs.c_str()) = _4(gr_pqrs.c_str())
343 - _4(rpq_pq.c_str()) * _4(grs_pq.c_str())
344 - _4(rpq_apn.c_str()) * _4(grs_apn.c_str())
345 - _4(rpq_nap.c_str()) * _4(grs_nap.c_str())
346 ;
347 return Vpq_rs;
348 }
349
350 // compute V^Pq_Rs = 1/2 bar{R}^Pq_A'B' bar{g}^A'B'_Rs (P, R in alpha or beta space)
351 // do not use p1, q1, a1', or n1 as argument
352 template <typename T>
353 typename SingleReference_R12Intermediates<T>::TArray4
354 SingleReference_R12Intermediates<T>::VPq_Rs(const char* p, const char* q,
355 const char* r, const char* s,
356 const double C_0, const double C_1)
357 {
358 const double V_C1 = (0.5 * C_0 + 1.5 * C_1);
359 const double V_C2 = (0.5 * C_0 - 1.5 * C_1);
360
361 std::string gr_pqrs = std::string("<") + p + " " + q + "|gr|" + r + " " + s + ">";
362 std::string gr_qprs = std::string("<") + q + " " + p + "|gr|" + r + " " + s + ">";
363
364 std::string rpq_pq = std::string("<") + p + " " + q + "|r|p1 q1>";
365 std::string rqp_pq = std::string("<") + q + " " + p + "|r|p1 q1>";
366 std::string grs_pq = std::string("<p1 q1|g|") + r + " " + s + ">";
367
368 std::string rpq_apn = std::string("<") + p + " " + q + "|r|a1' n1>";
369 std::string rqp_apn = std::string("<") + q + " " + p + "|r|a1' n1>";
370 std::string grs_apn = std::string("<a1' n1|g|") + r + " " + s + ">";
371
372 std::string rpq_nap = std::string("<") + p + " " + q + "|r|n1 a1'>";
373 std::string rqp_nap = std::string("<") + q + " " + p + "|r|n1 a1'>";
374 std::string grs_nap = std::string("<n1 a1'|g|") + r + " " + s + ">";
375
376 std::string pqrs = p + std::string(",") + q + std::string(",")
377 + r + std::string(",") + s;
378
379 TArray4 Vpq_rs;
380 Vpq_rs(pqrs.c_str()) = V_C1 * _4(gr_pqrs.c_str()) + V_C2 * _4(gr_qprs.c_str())
381 - (V_C1 * _4(rpq_pq.c_str()) + V_C2 * _4(rqp_pq.c_str()))
382 * _4(grs_pq.c_str())
383 - (V_C1 * _4(rpq_apn.c_str()) + V_C2 * _4(rqp_apn.c_str()))
384 * _4(grs_apn.c_str())
385 - (V_C1 * _4(rpq_nap.c_str()) + V_C2 * _4(rqp_nap.c_str()))
386 * _4(grs_nap.c_str())
387 ;
388 return Vpq_rs;
389 }
390
391 // compute V^Rk_Sk = 1/2 bar{R}^Rk_A'B' bar{g}^A'B'_Sk
392 // can not use k1 l2 n1 a1' for arguments
393 template <typename T>
394 typename SingleReference_R12Intermediates<T>::TArray2
395 SingleReference_R12Intermediates<T>::VRk_Sk(const char* r, const char* s,
396 const double C_0, const double C_1)
397 {
398 const double V_C1 = (0.5 * C_0 + 1.5 * C_1);
399 const double V_C2 = (0.5 * C_0 - 1.5 * C_1);
400
401 std::string gr_rksk = std::string("<") + r + " k1|gr|" + s + " l1>";
402 std::string gr_krsk = std::string("<k1 ") + r + "|gr|" + s + " l1>";
403
404 std::string r_rkpq = std::string("<") + r + " k1|r|p1 q1>";
405 std::string r_krpq = std::string("<k1 ") + r + "|r|p1 q1>";
406 std::string g_skpq = std::string("<p1 q1|g|") + s + " k1>";
407
408 std::string r_rkapn = std::string("<") + r + " k1|r|a1' n1>";
409 std::string r_krapn = std::string("<k1 ") + r + "|r|a1' n1>";
410 std::string g_skapn = std::string("<a1' n1|g|") + s + " k1>";
411
412 std::string r_rknap = std::string("<") + r + " k1|r|n1 a1'>";
413 std::string r_krnap = std::string("<k1 ") + r + "|r|n1 a1'>";
414 std::string g_sknap = std::string("<n1 a1'|g|") + s + " k1>";
415
416 std::string rs = r + std::string(",") + s;
417 TArray2 Vrk_sk;
418 Vrk_sk(rs.c_str()) = (V_C1 * _4(gr_rksk.c_str()) + V_C2 * _4(gr_krsk.c_str()))
419 * _2("<l1|I|k1")
420 - (V_C1 * _4(r_rkpq.c_str()) + V_C2 * _4(r_krpq.c_str()))
421 * _4(g_skpq.c_str())
422 - (V_C1 * _4(r_rkapn.c_str()) + V_C2 * _4(r_krapn.c_str()))
423 * _4(g_skapn.c_str())
424 - (V_C1 * _4(r_rknap.c_str()) + V_C2 * _4(r_krnap.c_str()))
425 * _4(g_sknap.c_str())
426 ;
427 return Vrk_sk;
428 }
429
430 template <typename T>
431 std::pair<typename SingleReference_R12Intermediates<T>::TArray2,
432 typename SingleReference_R12Intermediates<T>::TArray2>
433 SingleReference_R12Intermediates<T>::V_diag() {
434
435 TArray2 V_ij_ij_cabs; V_ij_ij_cabs("i,j") = dotket(ij_xy("<i j|g|m a'>"), ij_xy("<i j|r|m a'>"));
436 // don't need this in closed shell!
437 //TArray2 V_ij_ij_cabs1 = dotket(ij_xy("<i j|g|a' m>"), ij_xy("<i j|r|a' m>"));
438
439 TArray2 V_ij_ij; V_ij_ij("i,j") = take(ij_xy("<i j|gr|p q>"), ij) - dotket(ij_xy("<i j|g|p q>"), ij_xy("<i j|r|p q>"))
440 - V_ij_ij_cabs("i,j") - V_ij_ij_cabs("j,i");
441
442 TArray2 V_ij_ji_cabs = dotket(ij_xy("<i j|g|m a'>"), ij_xy("<i j|r|m a'>"), true);
443 TArray2 V_ij_ji = take(ij_xy("<i j|gr|p q>"), ji) - dotket(ij_xy("<i j|g|p q>"), ij_xy("<i j|r|p q>"), true)
444 - V_ij_ji_cabs("i,j") - V_ij_ji_cabs("j,i");
445
446 return std::make_pair(V_ij_ij,V_ij_ji);
447
448 }
449
450 template <typename T>
451 std::pair<typename SingleReference_R12Intermediates<T>::TArray2,
452 typename SingleReference_R12Intermediates<T>::TArray2>
453 SingleReference_R12Intermediates<T>::X_diag() {
454
455 TArray2 X_ij_ij_cabs = dotket(ij_xy("<i j|r|m a'>"), ij_xy("<i j|r|m a'>"));
456 // don't need this in closed shell!
457 //TArray2 X_ij_ij_cabs1 = dotket(ij_xy("<i j|r|a' m>"), ij_xy("<i j|r|a' m>"));
458
459 TArray2 X_ij_ij = take(ij_xy("<i j|r2|p q>"), ij) - dotket(ij_xy("<i j|r|p q>"), ij_xy("<i j|r|p q>"))
460 - X_ij_ij_cabs("i,j") - X_ij_ij_cabs("j,i");
461
462 TArray2 X_ij_ji_cabs = dotket(ij_xy("<i j|r|m a'>"), ij_xy("<i j|r|m a'>"), true);
463 TArray2 X_ij_ji = take(ij_xy("<i j|r2|p q>"), ji) - dotket(ij_xy("<i j|r|p q>"), ij_xy("<i j|r|p q>"), true)
464 - X_ij_ji_cabs("i,j") - X_ij_ji_cabs("j,i");
465
466 return std::make_pair(X_ij_ij,X_ij_ji);
467
468 }
469
470 template <typename T>
471 std::pair<typename SingleReference_R12Intermediates<T>::TArray2,
472 typename SingleReference_R12Intermediates<T>::TArray2>
473 SingleReference_R12Intermediates<T>::B_diag() {
474
476 TArray2 B_ij_ij = take(ij_xy("<i j|rTr|p q>"), ij) + take(ij_xy("<i_hJ(p') j|r2|p q>"), ij)
477 - dotket(ij_xy("<i j|r|p' q'>"), ij_xy("<i j|r|p' q'_K(r')>"));
478
479 TArray2 B_ij_ji = take(ij_xy("<i j|rTr|p q>"), ji) + take(ij_xy("<i_hJ(p') j|r2|p q>"), ji);
480
481 return std::make_pair(B_ij_ij,B_ij_ji);
482
483 }
484
485 namespace detail {
486
490 template<typename T>
491 struct selfenergy_denom {
492 typedef Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> EigenMatrixX;
493 selfenergy_denom(const T& E,
494 const EigenMatrixX& Y_mat,
495 const EigenMatrixX& X1_mat,
496 const EigenMatrixX& X2_mat) :
497 E_(E), Y_mat_(Y_mat), X1_mat_(X1_mat), X2_mat_(X2_mat) {
498 }
499 template<typename Index> T operator()(const Index& i) {
500 return 1.0 / ( E_ + Y_mat_(i[1], i[1]) - X1_mat_(i[2], i[2]) - X2_mat_(i[3], i[3]) );
501 }
502
503 private:
504 T E_;
505 EigenMatrixX Y_mat_;
506 EigenMatrixX X1_mat_;
507 EigenMatrixX X2_mat_;
508 };
509 }; // namespace sc::detail
510
511 template <typename T>
512 void
513 SingleReference_R12Intermediates<T>::gf2_r12(int orbital) {
514
515 enum CalcType {
516 IP, EA
517 };
518
519 MPQC_ASSERT(orbital != 0);
520 const CalcType type = (orbital < 0) ? IP : EA;
521
522 const std::string X_label = (type == IP) ? "i1" : "a1"; // active orbital label
523 const Ref<OrbitalSpace>& X_space = (type == IP) ? this->r12world()->refwfn()->occ_act()
524 : this->r12world()->refwfn()->uocc_act();
525
526 TArray2 fij = xy("<j|F|j>");
527 TArray2 fab = xy("<a|F|b>");
528
529 // use the diagonal element of the Fock matrix as the guess (only HOMO/LUMO supported);
530 const double E = (type == IP) ? X_space->evals()(X_space->rank() + orbital) : X_space->evals()(orbital - 1);
531
532 // compute Delta_ijaE = 1 / (- E - <a|F|a> + <i|F|i> + <j|F|j>)
533 typedef detail::selfenergy_denom<double> sedenom_eval_type;
534 sedenom_eval_type Delta_jab_gen(E,
535 TA::array_to_eigen(fij),
536 TA::array_to_eigen(fab),
537 TA::array_to_eigen(fab) );
538 sedenom_eval_type Delta_ajk_gen(E,
539 TA::array_to_eigen(fab),
540 TA::array_to_eigen(fij),
541 TA::array_to_eigen(fij) );
542
543 std::ostringstream Xjab; Xjab << "<" << X_label << " j|g|a b>";
544 TArray4d g_Xjab = ijxy(Xjab.str());
545 typedef TA::Array<T, 4, LazyTensor<T, 4, sedenom_eval_type > > TArray4dLazy;
546 TArray4dLazy Delta_Xjab(g_Xjab.world(), g_Xjab.trange());
547
548 // construct local tiles
549 for(auto t = Delta_Xjab.trange().tiles_range().begin();
550 t != Delta_Xjab.trange().tiles_range().end(); ++t)
551 if (Delta_Xjab.is_local(*t)) {
552 std::array<std::size_t, 4> index;
553 std::copy(t->begin(), t->end(), index.begin());
554 madness::Future < typename TArray4dLazy::value_type >
555 tile((LazyTensor<T, 4, sedenom_eval_type >(&Delta_Xjab, index, &Delta_jab_gen)
556 ));
557
558 // Insert the tile into the array
559 Delta_Xjab.set(*t, tile);
560 }
561
562 std::ostringstream Xajk; Xajk << "<" << X_label << " a|g|j k>";
563 TArray4d g_Xajk = ijxy(Xajk.str());
564 typedef TA::Array<T, 4, LazyTensor<T, 4, sedenom_eval_type > > TArray4dLazy;
565 TArray4dLazy Delta_Xajk(g_Xajk.world(), g_Xajk.trange());
566
567 // construct local tiles
568 for(auto t = Delta_Xajk.trange().tiles_range().begin();
569 t != Delta_Xajk.trange().tiles_range().end(); ++t)
570 if (Delta_Xajk.is_local(*t)) {
571 std::array<std::size_t, 4> index;
572 std::copy(t->begin(), t->end(), index.begin());
573 madness::Future < typename TArray4dLazy::value_type >
574 tile((LazyTensor<T, 4, sedenom_eval_type >(&Delta_Xajk, index, &Delta_ajk_gen)
575 ));
576
577 // Insert the tile into the array
578 Delta_Xajk.set(*t, tile);
579 }
580
581 TArray4 dg_Xjab; dg_Xjab("Y,j,a,b") = Delta_Xjab("Y,j,a,b") * (4 * g_Xjab("Y,j,a,b") - 2 * g_Xjab("Y,j,b,a"));
582 TArray4 dg_Xajk; dg_Xajk("Y,a,j,m") = Delta_Xajk("Y,a,j,m") * (4 * g_Xajk("Y,a,j,m") - 2 * g_Xajk("Y,a,m,j"));
583
584 // second-order self-energy, Eq. 11.16 in Dickoff-VanNeck, with spin integrated out
585 // \sigma_{X}^{Y} =
586// TArray2 sigma2; sigma2("X,Y") = (1./2) * ( g_Xjab("X,j,a,b") * dg_Xjab("Y,j,a,b") +
587// g_Xajk("X,a,j,m") * dg_Xajk("Y,a,j,m") );
588 TArray2 sigma2_hpp; sigma2_hpp("X,Y") = (1./2) * g_Xjab("X,j,a,b") * dg_Xjab("Y,j,a,b");
589 TArray2 sigma2_phh; sigma2_phh("X,Y") = (1./2) * g_Xajk("X,a,j,m") * dg_Xajk("Y,a,j,m");
590
591 ExEnv::out0() << "Fock:" << std::endl << fij << std::endl;
592 ExEnv::out0() << "SE2_hpp(e=" << E << "):" << std::endl << sigma2_hpp << std::endl;
593 ExEnv::out0() << "SE2_phh(e=" << E << "):" << std::endl << sigma2_phh << std::endl;
594 }
595
596 namespace detail {
599 template<typename T>
600 struct _CABS_singles_h0t1 {
601
602 typedef TiledArray::Array<T, 2> Array;
603
608 _CABS_singles_h0t1(const Array& h0_AB, const Array& h0_ij) :
609 H0_AB(h0_AB), H0_IJ(h0_ij) {
610 }
611
612 const Array& H0_AB;
613 const Array& H0_IJ;
614
619 void operator()(const Array& T1, Array& R1) {
620 R1 = T1("i,b") * H0_AB("b,a") - H0_IJ("i,j") * T1("j,a");
621 }
622 };
623
626 template<typename T>
627 struct _OrbResponse {
628
629 typedef TiledArray::Array<T, 2> Array2;
630 typedef TiledArray::Array<T, 4> Array4;
631
638 _OrbResponse(const Array2& f_AB, const Array2& f_ij,
639 const Array4& g_ij_ab, const Array4& g_ia_jb) :
640 F_AB(f_AB), F_IJ(f_ij), G_IJ_AB(g_ij_ab), G_IA_JB(g_ia_jb) {
641 }
642
643 const Array2& F_AB;
644 const Array2& F_IJ;
645 const Array4& G_IJ_AB;
646 const Array4& G_IA_JB;
647
652 void operator()(const Array2& kappa, Array2& residual) {
653 residual = kappa("i,b") * F_AB("b,a") - F_IJ("i,j") * kappa("j,a")
654 + 4.0 * G_IJ_AB("i,j,a,b") * kappa("j,b")
655 - G_IJ_AB("i,j,b,a") * kappa("j,b")
656 - G_IA_JB("i,a,j,b") * kappa("j,b");
657 }
658 };
659
661 template <typename T>
662 struct diag_precond2 {
663 typedef Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> EigenMatrixX;
664 diag_precond2(const EigenMatrixX& O1_mat,
665 const EigenMatrixX& O2_mat) :
666 O1_mat_(O1_mat), O2_mat_(O2_mat) {
667 }
668 template <typename Index> T operator()(const Index& i) {
669 return 1.0 / (- O1_mat_(i[0], i[0]) + O2_mat_(i[1], i[1]));
670 }
671
672 private:
673 EigenMatrixX O1_mat_;
674 EigenMatrixX O2_mat_;
675 };
676
678 template <typename T>
679 struct diag_precond4 {
680 typedef Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> EigenMatrixX;
681 diag_precond4(const EigenMatrixX& O1_mat,
682 const EigenMatrixX& O2_mat,
683 const EigenMatrixX& O3_mat,
684 const EigenMatrixX& O4_mat) :
685 O1_mat_(O1_mat), O2_mat_(O2_mat),
686 O3_mat_(O3_mat), O4_mat_(O4_mat) {
687 }
688 template <typename Index> T operator()(const Index& i) {
689 return 1.0 / (- O1_mat_(i[0], i[0]) - O2_mat_(i[1], i[1]) + O3_mat_(i[2], i[2]) + O4_mat_(i[3], i[3]));
690 }
691
692 private:
693 EigenMatrixX O1_mat_;
694 EigenMatrixX O2_mat_;
695 EigenMatrixX O3_mat_;
696 EigenMatrixX O4_mat_;
697 };
698
699 template<typename T>
700 struct Orbital_relaxation_Abjai {
701
702 typedef TiledArray::Array<T, 2> Array2;
703 typedef TiledArray::Array<T, 4> Array4;
704
708 Orbital_relaxation_Abjai(const Array4& a_bjai) :
709 A_bjai(a_bjai) {
710 }
711
712 const Array4& A_bjai;
713
718 void operator()(const Array2& K_bj, Array2& R1) {
719 R1("a,i") = K_bj("b,j") * A_bjai("b,j,a,i");
720 }
721 };
722
723 // e_ij = (e_i + e_j)
724 template <typename T>
725 struct e_ij {
726 typedef Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> EigenMatrixX;
727 e_ij(const EigenMatrixX& O1_mat, const EigenMatrixX& O2_mat):
728 O1_mat_(O1_mat), O2_mat_(O2_mat) {}
729
730 template <typename Index> T operator()(const Index& i) {
731 return (O1_mat_(i[0], i[0]) + O2_mat_(i[1], i[1]));
732 }
733
734 private:
735 EigenMatrixX O1_mat_;
736 EigenMatrixX O2_mat_;
737 };
738
739 } // namespace sc::detail
740
741 // Xam contribution from CABS Singles
742 template <typename T>
743 typename SingleReference_R12Intermediates<T>::TArray2
744 SingleReference_R12Intermediates<T>::Xam_CabsSingles(const TArray2& TmA,
745 const TArray2& Tma) {
746 // density from CABS Singles contribution
747 TArray2 D_e2_mn, D_e2_AB;
748 // D^m_n = t^m_A' * t^A'_n
749 D_e2_mn("m,n")= TmA("m,A'") * TmA("n,A'");
750 // D^A'_B' = t^A'_m * t^m_B'
751 D_e2_AB("A',B'") = TmA("m,A'") * TmA("m,B'");
752
753 // compute intermediate to reduce memory consumption
754 TArray4 g_aAmB;
755 g_aAmB("a,A',m,B'") = 2.0 * _4("<a A'|g|m B'>") - _4("<a A'|g|B' m>");
756 TArray4::wait_for_lazy_cleanup(g_aAmB.world());
757
758 TArray4d g_aAmn = ijxy("<a A'|g|m n>");
759 TArray4d g_ammn = ijxy("<a m|g|m1 n>");
760
761 TArray2 Xam_E2;
762 Xam_E2("a,m") = 2.0 * (
763 - _2("<A'|F|a>") * TmA("m,A'")
764 + Tma("n,a") * _2("<m|F|n>")
765 + (TmA("n,A'") * Tma("n,a")) * _2("<m|F|A'>")
766 //
767 - ( 2.0 * _4("<a n|g|m A'>") - _4("<a n|g|A' m>")
768 + 2.0 * g_aAmn("a,A',m,n") - g_aAmn("a,A',n,m")
769 ) * TmA("n,A'")
770 //
771 - g_aAmB("a,A',m,B'") * D_e2_AB("A',B'")
772 //
773 + (2.0 * g_ammn("a,n1,m,n2") - g_ammn("a,n1,n2,m"))
774 * D_e2_mn("n1,n2")
775 );
776 return Xam_E2;
777 }
778
779 // Xam contribution from MP2 correlation
780 template <typename T>
781 typename SingleReference_R12Intermediates<T>::TArray2
782 SingleReference_R12Intermediates<T>::Xam_mp2(const TArray4& T2_ijab,
783 const TArray2& Dij,
784 const TArray2& Dab) {
785 TArray2 Xai_mp2, Xam_mp2;
786 Xai_mp2("a,i") = 2.0 * (
787 // derivatives of 1/4 g^kl_cd T^cd_kl
788 // g^al_cd T^cd_il
789 - _4("<a l|g|c d>")
790 * (2.0 * T2_ijab("i,l,c,d") - T2_ijab("l,i,c,d"))
791 );
792 Xam_mp2("a,m") = 2.0 * (
793 // derivatives of 1/4 g^kl_cd T^cd_kl
794 // g_mc^kl T^ac_kl
795 (2.0 * T2_ijab("k,l,a,c") - T2_ijab("k,l,c,a"))
796 * _4("<m c|g|k l>")
797
798 // derivatives of 1/2 F^c_d D^d_c - 1/2 F^l_k D^k_l
799 // g^ac_md D^d_c
800 - (2.0 * _4("<a c|g|m d>") - _4("<a c|g|d m>"))
801 * Dab("d,c")
802 // g^al_mk D^k_l
803 + (2.0 * _4("<a l|g|m k>") - _4("<a l|g|k m>"))
804 * Dij("k,l")
805 );
806
807 // test code: print out I intermediates
808// TArray2 Iam, Iia, Ima;
809// Iam("a,m") = - (2.0 * T2_ijab("k,l,a,c") - T2_ijab("k,l,c,a"))
810// * _4("<m c|g|k l>")
811// ;
812// Iia("a,i") = _4("<a l|g|c d>")
813// * (2.0 * T2_ijab("i,l,c,d") - T2_ijab("l,i,c,d"));
814// Ima("a,m") = (2.0 * _4("<a c|g|m d>") - _4("<a c|g|d m>"))
815// * Dab("d,c")
816// - (2.0 * _4("<a l|g|m k>") - _4("<a l|g|k m>"))
817// * Dij("k,l")
818// ;
819// TArray2 Iima = XaiAddToXam(Ima, Iia);
820// std::cout << "MP2 Iam: " << std::endl << Iam << std::endl;
821// std::cout << "MP2 Ima: " << std::endl << Iima << std::endl;
822
823 return XaiAddToXam(Xam_mp2, Xai_mp2);
824 }
825
826 // Xai contribution from MP2 F12 coupling part
827 template <typename T>
828 typename SingleReference_R12Intermediates<T>::TArray2
829 SingleReference_R12Intermediates<T>::Xam_Cmp2f12(const double C_0, const double C_1,
830 const TArray4& T2_ijab, const TArray4& A_ijab,
831 const TArray2& Dij, const TArray2& Dab,
832 const TArray2& RT_apb) {
833 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
834 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
835 const double RR_C1 = 0.5 * C_0 * C_0 + 1.5 * C_1 * C_1;
836 const double RR_C2 = 0.5 * C_0 * C_0 - 1.5 * C_1 * C_1;
837
838 TArray4 T2pA_temp;
839 T2pA_temp("i,j,a,b") = R_C1 * T2_ijab("i,j,a,b") + R_C2 * T2_ijab("j,i,a,b")
840 + RR_C1 * A_ijab("i,j,a,b") + RR_C2 * A_ijab("j,i,a,b");
841
842 TArray2 Xai_mp2f12, Xam_mp2f12;
843 // Xai
844 Xai_mp2f12("a,i") = // derivatives of 1/4 g^kl_cd \tilde{T}^cd_kl
845 // g^al_cd \tilde{T}^cd_il
846 - _4("<a l|g|c d>")
847 * (R_C1 * A_ijab("i,l,c,d") + R_C2 * A_ijab("l,i,c,d"));
848 Xai_mp2f12("a,i") = Xai_mp2f12("a,i")
849 // F^a'_b R^al_a'c \tilde{T}^bc_il
850 // 1st part
851 - _4("<a l|r|b_F(a') c>") * T2pA_temp("i,l,b,c");
852 Xai_mp2f12("a,i") = Xai_mp2f12("a,i")
853 // 2nd part
854 - _4("<a l|r|c b_F(a')>") * T2pA_temp("i,l,c,b");
855
856 // Xam
857 Xam_mp2f12("a,m") = // derivatives of 1/4 g^kl_cd \tilde{T}^cd_kl
858 // g_ic^kl \tilde{T}^Ac_kl
859 (R_C1 * A_ijab("k,l,a,c") + R_C2 * A_ijab("k,l,c,a"))
860 * _4("<m c|g|k l>")
861
862 // derivatives of 1/2 F^c_d D^d_c - 1/2 F^l_k D^k_l
863 // g^ac_md D^d_c
864 - (2.0 * _4("<a c|g|m d>") - _4("<a c|g|d m>"))
865 * Dab("d,c")
866 // g^al_mk D^k_l
867 + (2.0 * _4("<a l|g|m k>") - _4("<a l|g|k m>"))
868 * Dij("k,l");
869 Xam_mp2f12("a,m") = Xam_mp2f12("a,m")
870 // derivatives of 1/2 F^a'_b R^kl_a'c \tilde{T}^bc_kl
871 // 1/2 F^a'_m R^kl_a'b \tilde{T}^ab_kl
872 // & 1/2 F^a'_b R^kl_ma' \tilde{T}^ab_kl
873 + T2pA_temp("k,l,a,b")
874 * (_4("<k l|r|m_F(a') b>") + _4("<k l|r|m b_F(a')>"));
875 TArray4 g_temp;
876 {
877 TArray4d gab_map = ijxy("<a b|g|m a'>");
878 g_temp("a,a',m,b") = 2.0 * _4("<a a'|g|m b>") - _4("<a a'|g|b m>")
879 + 2.0 * gab_map("a,b,m,a'") - gab_map("b,a,m,a'");
880 }
881 Xam_mp2f12("a,m") = Xam_mp2f12("a,m")
882 // g^aa'_mb 1/2 R^kl_a'c \tilde{T}^bc_kl
883 // & g^ab_ma' 1/2 R^kl_a'c \tilde{T}^bc_kl
884 - g_temp("a,a',m,b") * RT_apb("a',b");
885
886 return XaiAddToXam(Xam_mp2f12, Xai_mp2f12);
887 }
888
889 // compute F12 density from X and B terms
890 template <typename T>
891 void SingleReference_R12Intermediates<T>::compute_Df12_XB(const double C_0, const double C_1,
892 TArray2& D_f12_ij, TArray2& D_f12_ab,
893 TArray2& D_f12_apbp, TArray2& D_f12_apb) {
894
895 const double RR_C1 = 0.5 * C_0 * C_0 + 1.5 * C_1 * C_1;
896 const double RR_C2 = 0.5 * C_0 * C_0 - 1.5 * C_1 * C_1;
897
898 // Dij = 1/2 R^ik_A'B' R^A'B'_kl (A': all virtual)
899 {
900 TArray4d r2_ijkl = ijxy("<i j|r2|k l>");
901 TArray4d r_ijpq = ijxy("<i j|r|p q>");
902 TArray4d r_ijapn = ijxy("<i j|r|a' n>");
903 D_f12_ij("i,j") = (RR_C1 * r2_ijkl("i,k,j,l") + RR_C2 * r2_ijkl("k,i,j,l"))
904 * _2("<k|I|l>")
905 - (RR_C1 * r_ijpq("i,k,p,q") + RR_C2 * r_ijpq("k,i,p,q"))
906 * r_ijpq("j,k,p,q")
907 - (RR_C1 * r_ijapn("i,k,a',n") + RR_C2 * r_ijapn("k,i,a',n"))
908 * r_ijapn("j,k,a',n")
909 - (RR_C1 * r_ijapn("k,i,a',n") + RR_C2 * r_ijapn("i,k,a',n"))
910 * r_ijapn("k,j,a',n");
911 }
912 TArray4d::wait_for_lazy_cleanup(D_f12_ij.world());
913
914 // DA'B' = 1/2 R^A'C'_kl R^kl_B'C' (A': all virtual)
915 TArray4d r_acpkl = ijxy("<a c'|r|k l>");
916 {
917 TArray4d r_apcpkl = ijxy("<a' c'|r|k l>");
918 D_f12_apb("a',b") = (RR_C1 * r_apcpkl("a',c',k,l") + RR_C2 * r_apcpkl("a',c',l,k"))
919 * r_acpkl("b,c',k,l");
920
921 D_f12_apbp("a',b'") = (RR_C1 * r_acpkl("c,a',l,k") + RR_C2 * r_acpkl("c,a',k,l"))
922 * r_acpkl("c,b',l,k")
923 + (RR_C1 * r_apcpkl("a',c',k,l") + RR_C2 * r_apcpkl("a',c',l,k"))
924 * r_apcpkl("b',c',k,l");
925// D_f12_apbp("a',b'") = (RR_C1 * _4("<a' p'|r|k l>") + RR_C2 * _4("<a' p'|r|l k>"))
926// * _4("<b' p'|r|k l>")
927// - (RR_C1 * _4("<a' m|r|k l>") + RR_C2 * _4("<a' m|r|l k>"))
928// * _4("<b' m|r|k l>");
929 }
930 TArray4d::wait_for_lazy_cleanup(D_f12_ij.world());
931
932 D_f12_ab("a,b") = (RR_C1 * r_acpkl("a,c',k,l") + RR_C2 * r_acpkl("a,c',l,k"))
933 * r_acpkl("b,c',k,l");
934 }
935
936 // compute X and B density contribution to Xam
937 template <typename T>
938 typename SingleReference_R12Intermediates<T>::TArray2
939 SingleReference_R12Intermediates<T>::Xam_Df12_XB(const double C_0, const double C_1,
940 const TArray2& Df12_ij, const TArray2& Df12_ab,
941 const TArray2& Df12_apbp, const TArray2& Df12_apb) {
942 TArray2 gdf12_am;
943 gdf12_am("a,m") = // X related contribution
944 (2.0 * _4("<a k|g|m l>") - _4("<a k|g|l m>"))
945 * Df12_ij("k,l");
946
947 TArray4d g_abmc = ijxy("<a b|g|m c>");
948 gdf12_am("a,m") = gdf12_am("a,m")
949 // B related contribution
950 // 1st part
951 - (2.0 * g_abmc("a,b,m,c") - g_abmc("b,a,m,c"))
952 * Df12_ab("b,c");
953 {
954 TArray4 g_temp;
955 g_temp("a,b',m,c'") = 2.0 * _4("<a b'|g|m c'>") - _4("<a b'|g|c' m>");
956 TArray4d::wait_for_lazy_cleanup(g_temp.world());
957
958 gdf12_am("a,m") = gdf12_am("a,m")
959 // 2nd part
960 - g_temp("a,b',m,c'") * Df12_apbp("b',c'");
961 }
962 {
963 TArray4 g_temp;
964 g_temp("a,b',m,c") = 2.0 * _4("<a b'|g|m c>") - _4("<a b'|g|c m>");
965 gdf12_am("a,m") = gdf12_am("a,m")
966 // 3rd part
967 - g_temp("a,b',m,c") * Df12_apb("b',c");
968 }
969 TArray4d g_abmcp = ijxy("<a b|g|m c'>");
970 gdf12_am("a,m") = gdf12_am("a,m")
971 // 4th part
972 - (2.0 * g_abmcp("a,b,m,c'") - g_abmcp("b,a,m,c'"))
973 * Df12_apb("c',b");
974 return gdf12_am;
975 }
976
977 // Xam contribution from F12 V part
978 template <typename T>
979 typename SingleReference_R12Intermediates<T>::TArray2
980 SingleReference_R12Intermediates<T>::Xam_V(const double C_0, const double C_1) {
981
982 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
983 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
984
985 TArray2 Xai_V, Xam_V;
986 {
987 TArray4d gr_ak_ij = ijxy("<a k|gr|i j>");
988 TArray4d rpq_kl = ijxy("<p q|r|k l>");
989 TArray4d rapn_kl = ijxy("<a' n|r|k l>");
990 TArray4d rpq_ak = ijxy("<p q|r|a k>");
991
992 TArray4d gij_apm = ijxy("<i j|g|a' m>");
993 TArray4d rapn_ak = ijxy("<a' n|r|a k>");
994 TArray4d rapn_ka = ijxy("<a' n|r|k a>");
995
996 TArray2 Ikl = xy("<k|I|l>");
997
998 Xai_V("a,i") = // 1/2 R^ik_AC g^AC_ak
999 - ( (R_C1 * gr_ak_ij("a,k,i,l") + R_C2 * gr_ak_ij("a,k,l,i"))
1000 * Ikl("k,l")
1001 - _4("<a k|g|p q>")
1002 * ( R_C1 * rpq_kl("p,q,i,k") + R_C2 * rpq_kl("p,q,k,i") )
1003 - _4("<a k|g|a' n>")
1004 * ( R_C1 * rapn_kl("a',n,i,k") + R_C2 * rapn_kl("a',n,k,i"))
1005 - _4("<k a|g|a' n>")
1006 * ( R_C1 * rapn_kl("a',n,k,i") + R_C2 * rapn_kl("a',n,i,k"))
1007 )
1008 // 1/2 R^ak_AC g^AC_ik
1009 - ( (R_C1 * gr_ak_ij("a,l,i,k") + R_C2 * gr_ak_ij("a,l,k,i"))
1010 * Ikl("k,l")
1011 - _4("<i k|g|p q>")
1012 * ( R_C1 * rpq_ak("p,q,a,k") + R_C2 * rpq_ak("q,p,a,k"))
1013 - gij_apm("i,k,a',n")
1014 * ( R_C1 * rapn_ak("a',n,a,k") + R_C2 * rapn_ka("a',n,k,a"))
1015 - gij_apm("k,i,a',n")
1016 * ( R_C1 * rapn_ka("a',n,k,a") + R_C2 * rapn_ak("a',n,a,k"))
1017 );
1018 }
1019 TArray4d::wait_for_lazy_cleanup(Xai_V.world());
1020
1021 TArray4d raap_kl = ijxy("<a a'|r|k l>");
1022 TArray4d rmap_kl = ijxy("<m a'|r|k l>");
1023
1024 Xam_V("a,m") = // 1/2 R^kl_ac' g^mc'_kl
1025 ( R_C1 * raap_kl("a,a',k,l") + R_C2 * raap_kl("a,a',l,k"))
1026 * _4("<k l|g|m a'>")
1027 // 1/2 R^kl_mc' g^ac'_kl
1028 + ( R_C1 * rmap_kl("m,a',k,l") + R_C2 * rmap_kl("m,a',l,k"))
1029 * _4("<k l|g|a a'>");
1030
1031 return XaiAddToXam(Xam_V, Xai_V);
1032 }
1033
1034 // Xam contribution from F12 X part
1035 template <typename T>
1036 typename SingleReference_R12Intermediates<T>::TArray2
1037 SingleReference_R12Intermediates<T>::Xam_X(const double C_0, const double C_1) {
1038
1039 const double RR_C1 = 0.5 * C_0 * C_0 + 1.5 * C_1 * C_1;
1040 const double RR_C2 = 0.5 * C_0 * C_0 - 1.5 * C_1 * C_1;
1041
1042 TArray4d r2_akjl = ijxy("<a k|r2|j l>");
1043 TArray4d r2_kajl = ijxy("<k a|r2|j l>");
1044 TArray2 F_ij = xy("<i|F|j>");
1045
1046 TArray4d r_pqjk = ijxy("<p q|r|j k>");
1047 TArray4d r_apnjk = ijxy("<a' n|r|j k>");
1048 TArray4d r_napjk = ijxy("<n a'|r|j k>");
1049
1050 TArray2 X_ai, X_am;
1051
1052 // - 1/2 (F^i_i + F^k_k) R^ak_alpha beta R_ik^alpha beta
1053 X_ai("a,i") = - (RR_C1 * r2_akjl("a,k,j,l") + RR_C2 * r2_kajl("k,a,j,l"))
1054 * _2("<l|I|k>") * F_ij("j,i")
1055
1056 - (RR_C1 * r2_akjl("a,k,i,l") + RR_C2 * r2_kajl("k,a,i,l"))
1057 * F_ij("l,k")
1058
1059 + (RR_C1 * _4("<a k|r|p q>") + RR_C2 * _4("<k a|r|p q>"))
1060 * ( r_pqjk("p,q,j,k") * F_ij("j,i")
1061 + r_pqjk("p,q,i,l") * F_ij("l,k"))
1062
1063 + (RR_C1 * _4("<a k|r|a' n>") + RR_C2 * _4("<k a|r|a' n>"))
1064 * ( r_apnjk("a',n,j,k") * F_ij("j,i")
1065 + r_apnjk("a',n,i,l") * F_ij("l,k"))
1066
1067 + (RR_C1 * _4("<a k|r|n a'>") + RR_C2 * _4("<k a|r|n a'>"))
1068 * ( r_napjk("n,a',j,k") * F_ij("j,i")
1069 + r_napjk("n,a',i,l") * F_ij("l,k"));
1070
1071 // 1/2 (F^k_k + F^l_l) R^ab'_kl R_mb'^kl
1072 TArray4d r_aapkl = ijxy("<a a'|r|k l>");
1073 TArray4d r_klmap = ijxy("<k l|r|m a'>");
1074 X_am("a,m") = (RR_C1 * r_aapkl("a,b',k,l") + RR_C2 * r_aapkl("a,b',l,k"))
1075 * ( r_klmap("j,l,m,b'") * F_ij("j,k")
1076 + r_klmap("k,j,m,b'") * F_ij("j,l"));
1077
1078 return XaiAddToXam(X_am, X_ai);
1079 }
1080
1081 // Xam contribution from F12 B part
1082 template <typename T>
1083 typename SingleReference_R12Intermediates<T>::TArray2
1084 SingleReference_R12Intermediates<T>::Xam_B(const double C_0, const double C_1) {
1085
1086 const double B_C1 = 0.5 * C_0 * C_0 + 1.5 * C_1 * C_1;
1087 const double B_C2 = 0.5 * C_0 * C_0 - 1.5 * C_1 * C_1;
1088
1089 TArray2 B_ai, B_am;
1090
1091 // 1st parts of B_am:
1092 // - R^ak_A'B' F^A'_C' R^ik_C'B' (A': all virtual orbital index)
1093 TArray4d r_akPQ = ijxy("<a k|r|p' q'>");
1094 TArray4d r_kaPQ = ijxy("<k a|r|p' q'>");
1095 TArray4d rik_PKQ = ijxy("<i k|r|p'_K(r') q'>");
1096
1097 TArray4d r_akPn = ijxy("<a k|r|p' n>");
1098 TArray4d r_kaPn = ijxy("<k a|r|p' n>");
1099 TArray4d rik_PFn = ijxy("<i k|r|p'_F(r') n>");
1100
1101 TArray4d r_akmA = ijxy("<a k|r|m a'>");
1102 TArray4d r_kamA = ijxy("<k a|r|m a'>");
1103 TArray4d rik_mFA = ijxy("<i k|r|m_F(n) a'>");
1104
1105 TArray4d r_akpq = ijxy("<a k|r|p b>");
1106 TArray4d r_kapq = ijxy("<k a|r|p b>");
1107 TArray4d rik_pFb = ijxy("<i k|r|p_F(r) b>");
1108
1109 TArray4d rik_nFA = ijxy("<i k|r|n_F(p') a'>");
1110 //
1111 TArray4d r_ikmA = ijxy("<i k|r|m a'>");
1112 TArray4d rak_nFA = ijxy("<a k|r|n_F(p') a'>");
1113 TArray4d rka_nFA = ijxy("<k a|r|n_F(p') a'>");
1114 TArray4d r_akAb = ijxy("<a k|r|a' b>");
1115 TArray4d r_kaAb = ijxy("<k a|r|a' b>");
1116 TArray4d rik_AFb = ijxy("<i k|r|a'_F(q) b>");
1117 //
1118 TArray4d r_ikAb = ijxy("<i k|r|a' b>");
1119 TArray4d rak_AFb = ijxy("<a k|r|a'_F(q) b>");
1120 TArray4d rka_AFb = ijxy("<k a|r|a'_F(q) b>");
1121
1122 B_ai("a,i") = // diag
1123 - ( B_C1 * _4("<a k|rTr|i l>") + B_C2 * _4("<k a|rTr|i l>")
1124 // Q
1125 + ( B_C1 * (_4("<a_hJ(p') l|r2|i k>") + _4("<a l_hJ(p')|r2|i k>")
1126 + _4("<a l|r2|i_hJ(p') k>") + _4("<a l|r2|i k_hJ(p')>"))
1127
1128 + B_C2 * (_4("<l a_hJ(p')|r2|i k>") + _4("<l_hJ(p') a|r2|i k>")
1129 + _4("<l a|r2|i_hJ(p') k>") + _4("<l a|r2|i k_hJ(p')>"))
1130 ) * 0.5
1131 ) * _2("<k|I|l>")
1132 // rKr_p'q'
1133 + ( B_C1 * (r_akPQ("a,k,p',q'") * rik_PKQ("i,k,p',q'")
1134 + r_kaPQ("k,a,p',q'") * rik_PKQ("k,i,p',q'"))
1135
1136 + B_C2 * (r_kaPQ("k,a,p',q'") * rik_PKQ("i,k,p',q'")
1137 + r_akPQ("a,k,p',q'") * rik_PKQ("k,i,p',q'"))
1138 )
1139 // rFr_p'n
1140 + ( B_C1 * (r_akPn("a,k,p',n") * rik_PFn("i,k,p',n")
1141 + r_kaPn("k,a,p',n") * rik_PFn("k,i,p',n"))
1142
1143 + B_C2 * (r_kaPn("k,a,p',n") * rik_PFn("i,k,p',n")
1144 + r_akPn("a,k,p',n") * rik_PFn("k,i,p',n"))
1145 )
1146 // rFr_mA
1147 - ( B_C1 * (r_akmA("a,k,m,a'") * rik_mFA("i,k,m,a'")
1148 + r_kamA("k,a,m,a'") * rik_mFA("k,i,m,a'"))
1149
1150 + B_C2 * (r_kamA("k,a,m,a'") * rik_mFA("i,k,m,a'")
1151 + r_akmA("a,k,m,a'") * rik_mFA("k,i,m,a'"))
1152 )
1153 // rFr_pb
1154 + ( B_C1 * (r_akpq("a,k,p,b") * rik_pFb("i,k,p,b")
1155 + r_kapq("k,a,p,b") * rik_pFb("k,i,p,b"))
1156
1157 + B_C2 * (r_kapq("k,a,p,b") * rik_pFb("i,k,p,b")
1158 + r_akpq("a,k,p,b") * rik_pFb("k,i,p,b"))
1159 )
1160 //
1161 + ( B_C1 * (r_akmA("a,k,n,a'") * rik_nFA("i,k,n,a'")
1162 + r_kamA("k,a,n,a'") * rik_nFA("k,i,n,a'"))
1163
1164 + B_C2 * (r_kamA("k,a,n,a'") * rik_nFA("i,k,n,a'")
1165 + r_akmA("a,k,n,a'") * rik_nFA("k,i,n,a'"))
1166
1167 + B_C1 * (r_ikmA("i,k,n,a'") * rak_nFA("a,k,n,a'")
1168 + r_ikmA("k,i,n,a'") * rka_nFA("k,a,n,a'"))
1169
1170 + B_C2 * (r_ikmA("k,i,n,a'") * rak_nFA("a,k,n,a'")
1171 + r_ikmA("i,k,n,a'") * rka_nFA("k,a,n,a'"))
1172 )
1173 //
1174 + ( B_C1 * (r_akAb("a,k,a',b") * rik_AFb("i,k,a',b")
1175 + r_kaAb("k,a,a',b") * rik_AFb("k,i,a',b"))
1176
1177 + B_C2 * (r_kaAb("k,a,a',b") * rik_AFb("i,k,a',b")
1178 + r_akAb("a,k,a',b") * rik_AFb("k,i,a',b"))
1179
1180 + B_C1 * (r_ikAb("i,k,a',b") * rak_AFb("a,k,a',b")
1181 + r_ikAb("k,i,a',b") * rka_AFb("k,a,a',b"))
1182
1183 + B_C2 * (r_ikAb("k,i,a',b") * rak_AFb("a,k,a',b")
1184 + r_ikAb("i,k,a',b") * rka_AFb("k,a,a',b"))
1185 );
1186
1187// // test codes for computing B_ai for H2O molecule
1188// const char* a = "a";
1189// const char* i = "i";
1190// TArray2 B_ia = Bpk_qk(i,a);
1191// TArray2 B_ai = Bpk_qk(a,i);
1192// TArray2 B_ai2 = B_ai("a,i") + B_ia("i,a");
1193//
1194// TArray4 B_akil = Bpr_qs(a,i);
1195// TArray2 B_ai2 = B_akil("a,k,i,l") * _2("<k|I|l");
1196//
1197// const char* i = "i";
1198// const char* j = "j";
1199// TArray4 B_ijkl = Bpr_qs(i,j);
1200//
1201// double sum_Bijij = 0;
1202// std::cout << "B_ijkl" << std::endl;
1203// for (std::size_t i = 0; i < 5; ++i) {
1204// for (std::size_t j = 0; j < 5; ++j) {
1205// std::vector<std::size_t> indices(4);
1206// indices[0] = indices[2] = i;
1207// indices[1] = indices[3] = j;
1208// sum_Bijij += get_element(B_ijkl, indices);
1209// }
1210// }
1211// std::cout << "Bijkl sum: " << sum_Bijij << std::endl;
1212
1213 // 2nd parts of B_am:
1214 // 1/2 R^ab'_kl F^c'_m R^c'b'_kl
1215 // + (1/2 R^mb'_kl F^C'_a R^C'b'_kl + 1/2 R^mb'_kl F^c'_b' R^ab'_kl)
1216 TArray4d r_abpkl = ijxy("<a b'|r|k l>");
1217 TArray4d raFpbp_kl = ijxy("<a_F(c') b'|r|k l>");
1218 TArray4d raFbp_kl = ijxy("<a_F(c) b'|r|k l>");
1219 TArray4d rabpFp_kl = ijxy("<a b'_F(c')|r|k l>") ;
1220
1221 B_am("a,m") = (B_C1 * r_abpkl("a,b',k,l") + B_C2 * r_abpkl("a,b',l,k"))
1222 * _4("<k l|r|m_F(c') b'>")
1223 //
1224 //+ (B_C1 * _4("<a_F(C') b'|r|k l>") + B_C2 *_4("<b' a_F(C')|r|k l>"))
1225 // * _4("<k l|r|i b'>") // do not work for CCR12
1226 + ( B_C1 * raFpbp_kl("a,b',k,l") + B_C2 * raFpbp_kl("a,b',l,k")
1227 + B_C1 * raFbp_kl("a,b',k,l") + B_C2 * raFbp_kl("a,b',l,k"))
1228 * _4("<k l|r|m b'>")
1229 //
1230 + (B_C1 * rabpFp_kl("a,b',k,l") + B_C2 * rabpFp_kl("a,b',l,k"))
1231 * _4("<k l|r|m b'>")
1232 ;
1233
1234 return XaiAddToXam(B_am, B_ai);
1235 }
1236
1237 // frozen-core F12 Xii' contribution
1238 template <typename T>
1239 typename SingleReference_R12Intermediates<T>::TArray2
1240 SingleReference_R12Intermediates<T>::Xiip_VBX(const double C_0, const double C_1) {
1241
1242 const double RR_C1 = 0.5 * C_0 * C_0 + 1.5 * C_1 * C_1;
1243 const double RR_C2 = 0.5 * C_0 * C_0 - 1.5 * C_1 * C_1;
1244
1245 TArray2 Xiip_V;
1246 const char* ip = "i'";
1247 const char* i = "i";
1248 TArray2 V_ipi = VRk_Sk(ip,i,C_0, C_1);
1249 TArray2 V_iip = VRk_Sk(i,ip,C_0, C_1);
1250 Xiip_V("i,i'") = // 2 * (1/2 R^i'k_A'C' g^A'C'_ik + 1/2 R^ik_A'C' g^A'C'_i'k)
1251 2.0 * (V_ipi("i',i") + V_iip("i,i'"));
1252 // test
1253// TArray4d gr_ipk_ij = ijxy("<i' k|gr|i j>");
1254// TArray4d rpq_kl = ijxy("<p q|r|k l>");
1255// TArray4d rapn_kl = ijxy("<a' n|r|k l>");
1256// TArray4d rnap_kl = ijxy("<n a'|r|k l>");
1257// TArray4d rpq_ipk = ijxy("<p q|r|i' k>");
1258// TArray2 Ikl = xy("<k|I|l>");
1259// Xiip_V("i,i'") = // 1/2 R^ik_AC g^AC_i'k
1260// ( (R_C1 * gr_ipk_ij("i',k,i,l") + R_C2 * gr_ipk_ij("i',k,l,i"))
1261// * Ikl("k,l")
1262// - _4("<i' k|g|p q>")
1263// * ( R_C1 * rpq_kl("p,q,i,k") + R_C2 * rpq_kl("p,q,k,i") )
1264// - _4("<i' k|g|a' n>")
1265// * ( R_C1 * rapn_kl("a',n,i,k") + R_C2 * rapn_kl("a',n,k,i"))
1266// - _4("<i' k|g|n a'>")
1267// * ( R_C1 * rnap_kl("n,a',i,k") + R_C2 * rnap_kl("n,a',k,i"))
1268// ) * 2.0
1269// // 1/2 R^i'k_AC g^AC_ik
1270// + ( (R_C1 * gr_ipk_ij("i',l,i,k") + R_C2 * gr_ipk_ij("i',l,k,i"))
1271// * Ikl("k,l")
1272// - _4("<i k|g|p q>")
1273// * ( R_C1 * rpq_ipk("p,q,i',k") + R_C2 * rpq_ipk("q,p,i',k"))
1274// - _4("<i k|g|a' n>")
1275// * ( R_C1 * _4("<a' n|r|i' k>") + R_C2 * _4("<a' n|r|k i'>"))
1276// - _4("<i k|g|n a'>")
1277// * ( R_C1 * _4("<n a'|r|i' k>") + R_C2 * _4("<n a'|r|k i'>"))
1278// ) * 2.0;
1279
1280 TArray2 Xiip_X;
1281 TArray2 F_ij = xy("<i|F|j>");
1282 TArray4d r2_ipk_jl = ijxy("<i' k|r2|j l>");
1283 TArray4d r_ipk_pq = ijxy("<i' k|r|p q>");
1284 TArray4d r_pqkl = ijxy("<p q|r|k l>");
1285 TArray4d r_ipk_apn = ijxy("<i' k|r|a' n>");
1286 TArray4d r_apn_kl = ijxy("<a' n|r|k l>");
1287 TArray4d r_kip_apn = ijxy("<k i'|r|a' n>");
1288 Xiip_X("i,i'") = // 2 * (F^i_i + F^k_k) 1/2 R^i'k_A'B' R_ik^A'B'
1289 2.0 * ( (RR_C1 * r2_ipk_jl("i',k,j,l") + RR_C2 * r2_ipk_jl("i',k,l,j"))
1290 * _2("<l|I|k>") * F_ij("j,i")
1291 + (RR_C1 * r2_ipk_jl("i',k,i,l") + RR_C2 * r2_ipk_jl("i',k,l,i"))
1292 * F_ij("l,k")
1293
1294 - (RR_C1 * r_ipk_pq("i',k,p,q") + RR_C2 * r_ipk_pq("i',k,q,p"))
1295 * ( r_pqkl("p,q,j,k") * F_ij("j,i")
1296 + r_pqkl("p,q,i,l") * F_ij("l,k"))
1297
1298 - (RR_C1 * r_ipk_apn("i',k,a',n") + RR_C2 * r_kip_apn("k,i',a',n"))
1299 * ( r_apn_kl("a',n,j,k") * F_ij("j,i")
1300 + r_apn_kl("a',n,i,l") * F_ij("l,k"))
1301
1302 - (RR_C1 * r_kip_apn("k,i',a',n") + RR_C2 * r_ipk_apn("i',k,a',n"))
1303 * ( r_apn_kl("a',n,k,j") * F_ij("j,i")
1304 + r_apn_kl("a',n,l,i") * F_ij("l,k"))
1305 );
1306
1307 TArray2 Xiip_B;
1308 TArray2 B_ipi = BPk_Qk(ip,i,C_0,C_1);
1309 Xiip_B("i,i'") = // 2 R^i'k_A'B' F^A'_C' R^ik_C'B'
1310 2.0 * B_ipi("i',i");
1311
1312 TArray2 Xiip_f12;
1313 Xiip_f12("i,i'") = Xiip_V("i,i'") - Xiip_X("i,i'") + Xiip_B("i,i'");
1314 return Xiip_f12;
1315 }
1316
1317 // frozen-core Xii' contribution from CCSD F12 coupling
1318 template <typename T>
1319 typename SingleReference_R12Intermediates<T>::TArray2
1320 SingleReference_R12Intermediates<T>::Xiip_CVT(const double C_0, const double C_1,
1321 const TArray2& T1, const TArray4& T2){
1322
1323 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
1324 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
1325
1326 TArray2 Xiip_CT2;
1327 Xiip_CT2("i,i'") = // 2 F^a'_b R^i'l_a'c T2^bc_il
1328 2.0 * ( _4("<i' l|r|b_F(a') c>")
1329 * (R_C1 * T2("b,c,i,l") + R_C2 * T2("b,c,l,i"))
1330 + _4("<i' l|r|c b_F(a')>")
1331 * (R_C1 * T2("c,b,i,l") + R_C2 * T2("c,b,l,i"))
1332 );
1333
1334 TArray2 Xiip_VT2;
1335 const char* ip = "i'";
1336 const char* i = "i";
1337 const char* l = "l";
1338 const char* c = "c";
1339 const char* d = "d";
1340 TArray4 V_ipl_cd = VPq_Rs(ip,l,c,d,C_0, C_1);
1341 Xiip_VT2("i,i'") = // 2 * 1/4 R^i'l_A'B' g^A'B'_cd T^cd_il
1342 2.0 * V_ipl_cd("i',l,c,d") * T2("c,d,i,l");
1343
1344 TArray2 Xiip_VT1;
1345 TArray4 V_ipl_ic = VPq_Rs(ip,l,i,c, C_0, C_1);
1346 TArray4 V_il_ipc = VPq_Rs(i,l,ip,c,C_0, C_1);
1347 TArray2 V_ipc = VRk_Sk(ip,c,C_0, C_1);
1348 Xiip_VT1("i,i'") = // 2 *
1349 2.0 * ( // 1/2 R^i'l_A'B' g^A'B'_ic t1^c_l
1350 // 1/2 R^il_A'B' g^A'B'_i'c t1^c_l
1351 (V_ipl_ic("i',l,i,c") + V_il_ipc("i,l,i',c")) * T1("c,l")
1352
1353 // 1/2 R^i'k_A'B' g^A'B'_ck t1^c_i
1354 + V_ipc("i',c") * T1("c,i")
1355 );
1356
1357 TArray2 Xiip_C;
1358 Xiip_C("i,i'") = Xiip_CT2("i,i'") + Xiip_VT2("i,i'") + Xiip_VT1("i,i'");
1359 return Xiip_C;
1360 }
1361
1362 // Xam contribution of CT2 part resulted from CCSD F12 coupling
1363 template <typename T>
1364 typename SingleReference_R12Intermediates<T>::TArray2
1365 SingleReference_R12Intermediates<T>::Xam_CT2_ccsd(const double C_0, const double C_1,
1366 const TArray4& T2, const TArray2& RT2_aPb) {
1367 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
1368 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
1369
1370 TArray4d g_abmaP = ijxy("<a b|g|m a'>");
1371 TArray2 Xam_CT2, Xai_CT2;
1372 Xam_CT2("a,m") = 2.0 * ( // + 1/2 F^a'_m R^kl_a'b T2^ab_kl
1373 // + 1/2 F^a'_b R^kl_ma' T2^ab_kl
1374 (R_C1 * T2("a,b,k,l") + R_C2 * T2("b,a,k,l"))
1375 * (_4("<k l|r|m_F(a') b>") + _4("<k l|r|m b_F(a')>"))
1376 //RT2_aPb("a',a") * _2("<a'|F|m>")
1377
1378 // - g^aa'_mb 1/2 R^kl_a'c T2^bc_kl
1379 // - g^ab_ma' 1/2 R^kl_a'c T2^bc_kl
1380 - ( 2.0 * _4("<a a'|g|m b>") - _4("<a a'|g|b m>")
1381 + 2.0 * g_abmaP("a,b,m,a'") - g_abmaP("b,a,m,a'")
1382 ) * RT2_aPb("a',b")
1383 );
1384 Xai_CT2("a,i") = 2.0 * ( // - F^a'_b R^al_a'c T2^bc_il
1385 - _4("<a l|r|b_F(a') c>")
1386 * (R_C1 * T2("b,c,i,l") + R_C2 * T2("b,c,l,i"))
1387 - _4("<a l|r|c b_F(a')>")
1388 * (R_C1 * T2("c,b,i,l") + R_C2 * T2("c,b,l,i"))
1389 );
1390
1391 return XaiAddToXam(Xam_CT2, Xai_CT2);
1392 }
1393
1394 // Xam contribution of VT(T1&T2) part resulted from CCSD F12 coupling
1395 template <typename T>
1396 typename SingleReference_R12Intermediates<T>::TArray2
1397 SingleReference_R12Intermediates<T>::Xam_VT_ccsd(const double C_0, const double C_1,
1398 const TArray2& T1, const TArray4& T2) {
1399
1400 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
1401 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
1402
1403 const char* i = "i";
1404 const char* j = "j";
1405 const char* k = "k";
1406 const char* l = "l";
1407 const char* m = "m";
1408
1409 const char* a = "a";
1410 const char* c = "c";
1411 const char* d = "d";
1412
1413 TArray4 V_alic = VPq_Rs(a,l,i,c, C_0, C_1);
1414 TArray4 V_ilac = VPq_Rs(i,l,a,c,C_0, C_1);
1415 TArray2 V_ac = VRk_Sk(a,c,C_0, C_1);
1416 TArray2 V_jm = VRk_Sk(j,m,C_0, C_1);
1417 TArray4d r_klmaP = ijxy("<k l|r|m a'>");
1418 TArray4d r_abPkl = ijxy("<a b'|r|k l>");
1419 TArray2 Xam_VT1, Xai_VT1;
1420 Xam_VT1("a,m") = 2.0 * ( // + 1/2 R^jk_A'B' g^A'B'_mk t1^a_j
1421 T1("a,j") * V_jm("j,m")
1422// // test
1423// ( (R_C1 * _4("<j k|gr|m l>") + R_C2 * _4("<k j|gr|m l>"))
1424// * _2("<k|I|l>")
1425// - (R_C1 * _4("<j k|r|p q>") + R_C2 * _4("<k j|r|p q>"))
1426// * _4("<p q|g|m k>")
1427// - (R_C1 * _4("<j k|r|a' n>") + R_C2 * _4("<k j|r|a' n>"))
1428// * _4("<a' n|g|m k>")
1429// - (R_C1 * _4("<j k|r|n a'>") + R_C2 * _4("<k j|r|n a'>"))
1430// * _4("<n a'|g|m k>")
1431// )
1432
1433 + ( // + R^kl_mb' g^ab'_kc t1^c_l
1434 _4("<a b'|g|k c>")
1435 * (R_C1 * r_klmaP("k,l,m,b'") + R_C2 * r_klmaP("l,k,m,b'"))
1436 + _4("<a b'|g|c k>")
1437 * (R_C1 * r_klmaP("l,k,m,b'") + R_C2 * r_klmaP("k,l,m,b'"))
1438 // + R^kl_ab' g^mb'_kc t1^c_l
1439 + (R_C1 * r_abPkl("a,b',k,l") + R_C2 * r_abPkl("a,b',l,k"))
1440 * _4("<k c|g|m b'>")
1441 + (R_C1 * r_abPkl("a,b',l,k") + R_C2 * r_abPkl("a,b',k,l"))
1442 * _4("<c k|g|m b'>")
1443 ) * T1("c,l")
1444 );
1445 Xai_VT1("a,i") = 2.0 * ( // - 1/2 R^al_A'B' g^A'B'_ic t1^c_l
1446 // - 1/2 R^il_A'B' g^A'B'_ac t1^c_l
1447 - (V_alic("a,l,i,c") + V_ilac("i,l,a,c")) * T1("c,l")
1448
1449 // - 1/2 R^ak_A'B' g^A'B'_ck t1^c_i
1450 - V_ac("a,c") * T1("c,i")
1451// // test
1452// ( (R_C1 * _4("<a k|gr|c l>") + R_C2 * _4("<k a|gr|c l>"))
1453// * _2("<k|I|l>")
1454// - (R_C1 * _4("<a k|r|p q>") + R_C2 * _4("<k a|r|p q>"))
1455// * _4("<p q|g|c k>")
1456// - (R_C1 * _4("<a k|r|a' n>") + R_C2 * _4("<k a|r|a' n>"))
1457// * _4("<a' n|g|c k>")
1458// - (R_C1 * _4("<a k|r|n a'>") + R_C2 * _4("<k a|r|n a'>"))
1459// * _4("<n a'|g|c k>")
1460// )
1461 );
1462 TArray2 Xam_VT1_tot = XaiAddToXam(Xam_VT1, Xai_VT1);
1463
1464 TArray4 V_alcd = VPq_Rs(a,l,c,d,C_0, C_1);
1465 TArray4 V_klmd = VPq_Rs(k,l,m,d,C_0, C_1);
1466 TArray2 Xam_VT2, Xai_VT2;
1467 Xam_VT2("a,m") = 2.0 * ( // 1/4 R^kl_A'B' g^A'B'_md T^ad_kl
1468 T2("a,d,k,l") * V_klmd("k,l,m,d")
1469
1470 + ( // + 1/4 R^kl_ab' g^mb'_cd T^cd_kl
1471 (R_C1 * r_abPkl("a,b',k,l") + R_C2 * r_abPkl("a,b',l,k"))
1472 * _4("<c d|g|m b'>")
1473 // + 1/4 R^kl_mb' g^ab'_cd T^cd_kl
1474 + _4("<a b'|g|c d>")
1475 * (R_C1 * r_klmaP("k,l,m,b'") + R_C2 * r_klmaP("l,k,m,b'"))
1476 ) * T2("c,d,k,l")
1477 );
1478 Xai_VT2("a,i") = 2.0 * ( // - 1/4 R^al_A'B' g^A'B'_cd T^cd_il
1479 - V_alcd("a,l,c,d") * T2("c,d,i,l")
1480 );
1481 TArray2 Xam_VT2_tot = XaiAddToXam(Xam_VT2, Xai_VT2);
1482
1483 TArray2 Xam_VT_tot;
1484 Xam_VT_tot("a,m") = Xam_VT1_tot("a,m") + Xam_VT2_tot("a,m");
1485 return Xam_VT_tot;
1486 }
1487
1488 // compute T1 & T2 amplitudes of CC2
1489 template <typename T>
1490 void SingleReference_R12Intermediates<T>::compute_T_cc2(TArray2& t1, TArray4& t2) {
1491
1492 TArray2 fij = xy("<j|F|j>");
1493 TArray2 fab = xy("<a|F|b>");
1494 TArray2 fai = xy("<a|F|i>");
1495
1496 // compute Delta_ai = 1 / (- <a|F|a> + <i|F|i>)
1497 typedef detail::diag_precond2<double> pceval_type;
1498 pceval_type Delta_ai_gen(TA::array_to_eigen(fab), TA::array_to_eigen(fij));
1499
1500 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2dLazy;
1501 TArray2dLazy Delta_ai(fai.world(), fai.trange());
1502
1503 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2d;
1504 // construct local tiles
1505 for(auto t = Delta_ai.trange().tiles_range().begin();
1506 t != Delta_ai.trange().tiles_range().end(); ++t)
1507 if (Delta_ai.is_local(*t)) {
1508 std::array<std::size_t, 2> index;
1509 std::copy(t->begin(), t->end(), index.begin());
1510 madness::Future < typename TArray2dLazy::value_type >
1511 tile((LazyTensor<T, 2, pceval_type >(&Delta_ai, index, &Delta_ai_gen)
1512 ));
1513
1514 // Insert the tile into the array
1515 Delta_ai.set(*t, tile);
1516 }
1517
1518 // compute Delta_ijab = 1 / (- <a|F|a> - <b|F|b> + <i|F|i> + <j|F|j>)
1519 typedef detail::diag_precond4<double> pc4eval_type;
1520 pc4eval_type Delta_abij_gen(TA::array_to_eigen(fab), TA::array_to_eigen(fab),
1521 TA::array_to_eigen(fij),TA::array_to_eigen(fij));
1522
1523 TArray4d g_abij = ijxy("<a b|g|i j>");
1524 typedef TA::Array<T, 4, LazyTensor<T, 4, pc4eval_type > > TArray4dLazy;
1525 TArray4dLazy Delta_abij(g_abij.world(), g_abij.trange());
1526
1527 // construct local tiles
1528 for(auto t = Delta_abij.trange().tiles_range().begin();
1529 t != Delta_abij.trange().tiles_range().end(); ++t)
1530 if (Delta_abij.is_local(*t)) {
1531 std::array<std::size_t, 4> index;
1532 std::copy(t->begin(), t->end(), index.begin());
1533 madness::Future < typename TArray4dLazy::value_type >
1534 tile((LazyTensor<T, 4, pc4eval_type >(&Delta_abij, index, &Delta_abij_gen)
1535 ));
1536
1537 // Insert the tile into the array
1538 Delta_abij.set(*t, tile);
1539 }
1540
1541 // compute initial T1 & T2 amplitudes and energy
1542 t1("a,i") = fai("a,i") * Delta_ai("a,i");
1543 t2("a,b,i,j") = g_abij("a,b,i,j") * Delta_abij("a,b,i,j");
1544 TArray4 tau;
1545 tau("a,b,i,j") = t2("a,b,i,j") + t1("a,i") * t1("b,j");
1546
1547 double E_0 = 0.0;
1548 double E_1 = 2.0 * dot(fai("a,i"), t1("a,i"))
1549 + dot((2.0 * g_abij("a,b,i,j") - g_abij("b,a,i,j")), tau("a,b,i,j") );
1550 double Delta_E = std::abs(E_0 - E_1);
1551
1552 TArray2 Iij = xy("<i|I|j>");
1553 TArray2 Iab = xy("<a|I|b>");
1554
1555 TArray4d g_iabj = ijxy("<i a|g|b j>");
1556 TArray4d g_iajb = ijxy("<i a|g|j b>");
1557 TArray4d g_iacd = ijxy("<i a|g|c d>");
1558 TArray4d g_aicd = ijxy("<a i|g|c d>");
1559 TArray4d g_klai = ijxy("<k l|g|a i>");
1560 TArray4d g_klia = ijxy("<k l|g|i a>");
1561 TArray4d g_ijkl = ijxy("<i j|g|k l>");
1562 TArray4d g_abcd = ijxy("<a b|g|c d>");
1563
1564 TArray2 hac, hki, hck;
1565 TArray4 a_klij, b_abcd;
1566
1567 double iter = 0;
1568 std::cout << indent << scprintf("%-5s", "Iter") << scprintf("%-20s", "Delta_E")
1569 << scprintf("%-20s", "E(CC2)") << std::endl;
1570 std::cout << indent << scprintf("%-5.0f", iter) << scprintf("%-20.10f", Delta_E)
1571 << scprintf("%-15.10f", E_1) << std::endl;
1572
1573 while (Delta_E >= 1.0e-12) {
1574
1575 // recompute T1 and T2 amplitudes
1576 hac("a,c") = //- fab("a,c") * (Iab("a,c") - 1.0)
1577 - (2.0 * g_abij("c,d,k,l") - g_abij("c,d,l,k")) * tau("a,d,k,l");
1578 hki("k,i") = //fij("k,i") * (1.0 - Iab("k,i"))
1579 //+
1580 (2.0 * g_abij("c,d,k,l") - g_abij("d,c,k,l")) * tau("c,d,i,l");
1581 hck("c,k") = fai("c,k")
1582 + (2.0 * g_abij("c,d,k,l") - g_abij("d,c,k,l")) * t1("d,l");
1583
1584 t1("a,i") = Delta_ai("a,i") * (
1585 //
1586 fai("a,i") - 2.0 * fai("c,k") * t1("a,k") * t1("c,i")
1587 //
1588 + t1("c,i") * hac("a,c") - t1("a,k") * hki("k,i")
1589 //
1590 + hck("c,k")
1591 * (2.0 * t2("c,a,k,i") - t2("c,a,i,k") + t1("c,i") * t1("a,k"))
1592 //
1593 + (2.0 * g_iabj("k,a,c,i") - g_iajb("k,a,i,c")) * t1("c,k")
1594 //
1595 + (2.0 * g_iacd("k,a,c,d") - g_iacd("k,a,d,c")) * tau("c,d,k,i")
1596 //
1597 - (2.0 * g_klai("k,l,c,i") - g_klai("l,k,c,i")) * tau("c,a,k,l")
1598 );
1599
1600 a_klij("k,l,i,j") = g_ijkl("k,l,i,j")
1601 + g_klia("k,l,i,c") * t1("c,j") + g_klai("k,l,c,j") * t1("c,i")
1602 + g_abij("c,d,k,l") * t1("c,i") * t1("d,j");
1603 b_abcd("a,b,c,d") = g_abcd("a,b,c,d")
1604 - g_aicd("a,k,c,d") * t1("b,k") - g_iacd("k,b,c,d") * t1("a,k");
1605
1606 t2("a,b,i,j") = Delta_abij("a,b,i,j") * (
1607 //
1608 g_abij("a,b,i,j")
1609 //
1610 + a_klij("k,l,i,j") * t1("a,k") * t1("b,l")
1611 //
1612 + b_abcd("a,b,c,d") * t1("c,i") * t1("d,j")
1613 //
1614 //+ (fab("a,c") * t2("c,b,i,j") + fab("b,c") * t2("a,c,i,j"))
1615 // * (1.0 - Iab("a,c"))
1616 //+ (fij("k,i") * t2("a,b,k,j") + fij("k,j") * t2("a,c,i,k"))
1617 // * (1 - Iij("k,i"))
1618 //
1619 + (g_iacd("i,c,a,b") - g_iajb("k,b,i,c") * t1("a,k")) * t1("c,j")
1620 + (g_iacd("j,c,b,a") - g_iajb("k,a,j,c") * t1("b,k")) * t1("c,i")
1621 //
1622 - (g_klai("i,j,a,k") + g_iabj("i,c,a,k") * t1("c,j")) * t1("b,k")
1623 - (g_klai("j,i,b,k") + g_iabj("j,c,b,k") * t1("c,i")) * t1("a,k")
1624 );
1625 tau("a,b,i,j") = t2("a,b,i,j") + t1("a,i") * t1("b,j");
1626
1627 // recompute energy
1628 E_0 = E_1;
1629 E_1 = 2.0 * dot(fai("a,i"), t1("a,i"))
1630 + dot((2.0 * g_abij("a,b,i,j") - g_abij("b,a,i,j")), tau("a,b,i,j") );
1631 Delta_E = std::abs(E_0 - E_1);
1632 iter += 1;
1633 std::cout << indent << scprintf("%-5.0f", iter) << scprintf("%-20.10f", Delta_E)
1634 << scprintf("%-15.10f", E_1) << std::endl;
1635 }
1636 //std::cout << "CC2 T1 amplitudes: " << std::endl << t1 << std::endl;
1637
1638 }
1639
1640 // compute lambda amplitudes of CC2
1641 // using formula from JCP 87, 5361 (1987)
1642 template <typename T>
1643 void SingleReference_R12Intermediates<T>::compute_lambda_cc2(const TArray2& t1, const TArray4& t2,
1644 TArray2& L1, TArray4& L2) {
1645
1646 TArray2 fij = xy("<j|F|j>");
1647 TArray2 fab = xy("<a|F|b>");
1648 TArray2 fai = xy("<a|F|i>");
1649
1650 // compute Delta_ai = 1 / (- <a|F|a> + <i|F|i>)
1651 typedef detail::diag_precond2<double> pceval_type;
1652 pceval_type Delta_ai_gen(TA::array_to_eigen(fab), TA::array_to_eigen(fij));
1653
1654 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2dLazy;
1655 TArray2dLazy Delta_ai(fai.world(), fai.trange());
1656
1657 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2d;
1658 // construct local tiles
1659 for(auto t = Delta_ai.trange().tiles_range().begin();
1660 t != Delta_ai.trange().tiles_range().end(); ++t)
1661 if (Delta_ai.is_local(*t)) {
1662 std::array<std::size_t, 2> index;
1663 std::copy(t->begin(), t->end(), index.begin());
1664 madness::Future < typename TArray2dLazy::value_type >
1665 tile((LazyTensor<T, 2, pceval_type >(&Delta_ai, index, &Delta_ai_gen)
1666 ));
1667
1668 // Insert the tile into the array
1669 Delta_ai.set(*t, tile);
1670 }
1671
1672 // compute Delta_ijab = 1 / (- <a|F|a> - <b|F|b> + <i|F|i> + <j|F|j>)
1673 typedef detail::diag_precond4<double> pc4eval_type;
1674 pc4eval_type Delta_abij_gen(TA::array_to_eigen(fab), TA::array_to_eigen(fab),
1675 TA::array_to_eigen(fij),TA::array_to_eigen(fij));
1676
1677 TArray4d g_abij = ijxy("<a b|g|i j>");
1678 typedef TA::Array<T, 4, LazyTensor<T, 4, pc4eval_type > > TArray4dLazy;
1679 TArray4dLazy Delta_abij(g_abij.world(), g_abij.trange());
1680
1681 // construct local tiles
1682 for(auto t = Delta_abij.trange().tiles_range().begin();
1683 t != Delta_abij.trange().tiles_range().end(); ++t)
1684 if (Delta_abij.is_local(*t)) {
1685 std::array<std::size_t, 4> index;
1686 std::copy(t->begin(), t->end(), index.begin());
1687 madness::Future < typename TArray4dLazy::value_type >
1688 tile((LazyTensor<T, 4, pc4eval_type >(&Delta_abij, index, &Delta_abij_gen)
1689 ));
1690
1691 // Insert the tile into the array
1692 Delta_abij.set(*t, tile);
1693 }
1694
1695 L1("a,i") = t1("a,i");
1696 L2("a,b,i,j") = t2("a,b,i,j");
1697
1698 TArray4 tau;
1699 tau("a,b,i,j") = t2("a,b,i,j") + t1("a,i") * t1("b,j");
1700
1701 // pseudo energy
1702 double E_0_L = 0.0;
1703 double E_1_L = dot((2.0 * g_abij("a,b,i,j") - g_abij("b,a,i,j")), L2("a,b,i,j") );
1704 double Delta_E_L = std::abs(E_0_L - E_1_L);
1705
1706
1707 TArray4d g_abci = ijxy("<a b|g|c i>"); // g_aicd = ijxy("<a i|g|c d>");
1708 TArray4d g_aikl = ijxy("<a i|g|k l>"); // g_klia = ijxy("<k l|g|i a>");
1709 TArray4d g_aibj = ijxy("<a i|g|b j>"); // g_iajb = ijxy("<i a|g|j b>");
1710 TArray4d g_aijb = ijxy("<a i|g|j b>"); // g_iabj = ijxy("<i a|g|b j>");
1711 TArray4d g_ijkl = ijxy("<i j|g|k l>");
1712 TArray4d g_abcd = ijxy("<a b|g|c d>");
1713
1714 double iter = 0;
1715 std::cout << indent << scprintf("%-5s", "Iter") << scprintf("%-20s", "Delta_E_L")
1716 << scprintf("%-20s", "E_L(CC2)") << std::endl;
1717 std::cout << indent << scprintf("%-5.0f", iter) << scprintf("%-20.10f", Delta_E_L)
1718 << scprintf("%-15.10f", E_1_L) << std::endl;
1719
1720 // intermediates for L1 & L2
1721 TArray2 Iai, Gac, Kki, Iai_L2;
1722 TArray4 R_akic, Q_akic, A_klim, E_klic, B_aecd, F_akcd;
1723 TArray4 H_abcj, J_kbij;
1724
1725 Iai("a,i") = fai("a,i")
1726 + (2.0 * g_abij("a,c,i,k") - g_abij("a,c,k,i")) * t1("c,k");
1727 //TArray4 I_abij; I_abij("a,b,i,j") = g_abij("a,b,i,j");
1728
1729 Gac("a,c") = //- fab("a,c") * (1.0 - Iab("a,c")) +
1730 // fai("a,k") * t1("c,k")
1731 - (2.0 * g_abci("a,d,c,k") - g_abci("d,a,c,k")) * t1("d,k")
1732 + (2.0 * g_abij("a,d,k,l") - g_abij("a,d,l,k")) * tau("c,d,k,l");
1733
1734 Kki("k,i") = //fij("k,i") * (1.0 - Iij("k,i")) +
1735 fai("c,i") * t1("c,k")
1736 + (2.0 * g_aikl("c,k,l,i") - g_aikl("c,k,i,l")) * t1("c,l")
1737 + (2.0 * g_abij("c,d,i,l") - g_abij("c,d,l,i")) * tau("c,d,k,l");
1738
1739 R_akic("a,k,i,c") = g_aibj("a,k,c,i") + g_abci("a,d,c,i") * t1("d,k")
1740 - g_aikl("a,k,l,i") * t1("c,l")
1741 - g_abij("a,d,l,i") * tau("c,d,l,k")
1742 ;
1743
1744 Q_akic("a,k,i,c") = g_aijb("a,k,i,c") + g_abci("d,a,c,i") * t1("d,k")
1745 - g_aikl("a,k,i,l") * t1("c,l")
1746 - g_abij("a,d,l,i") * t2("c,d,k,l")
1747 + g_abij("a,d,i,l") * (2.0 * t2("c,d,k,l") - tau("c,d,l,k"))
1748 ;
1749
1750 A_klim("k,l,i,m") = - (2.0 * g_ijkl("k,l,i,m") - g_ijkl("k,l,m,i"))
1751 - (2.0 * g_abij("c,d,i,m") - g_abij("c,d,m,i")) * t1("c,k") * t1("d,l")
1752 - (2.0 * g_aikl("c,l,i,m") - g_aikl("c,l,m,i")) * t1("c,k")
1753 - (2.0 * g_aikl("c,k,m,i") - g_aikl("c,k,i,m")) * t1("c,l");
1754
1755 E_klic("k,l,i,c") = 2.0 * g_aikl("c,i,l,k") - g_aikl("c,i,k,l")
1756 // a^kl_im tcm
1757 + A_klim("k,l,i,m") * t1("c,m")
1758 //
1759 + (2.0 * g_abci("e,d,c,i") - g_abci("d,e,c,i")) * t1("d,k") * t1("e,l")
1760 //
1761 + (2.0 * g_aijb("d,l,i,c") - g_aibj("d,l,c,i")) * t1("d,k")
1762 + (2.0 * g_aibj("d,k,c,i") - g_aijb("d,k,i,c")) * t1("d,l")
1763 ;
1764
1765 B_aecd("a,e,c,d") = - (2.0 * g_abcd("a,e,c,d") - g_abcd("e,a,c,d"))
1766 - (2.0 * g_abij("a,e,k,l") - g_abij("e,a,k,l")) * t1("c,k") * t1("d,l")
1767 + (2.0 * g_abci("e,a,d,k") - g_abci("a,e,d,k")) * t1("c,k")
1768 + (2.0 * g_abci("a,e,c,k") - g_abci("e,a,c,k")) * t1("d,k");
1769
1770 F_akcd("a,k,c,d") = - (2.0 * g_abci("c,d,a,k") - g_abci("d,c,a,k"))
1771 // b^ae_cd tek
1772 + B_aecd("a,e,c,d") * t1("e,k")
1773 //
1774 - (2.0 * g_aikl("a,k,m,l") - g_aikl("a,k,l,m")) * t1("d,l") * t1("c,m")
1775 //
1776 + (2.0 * g_aibj("a,k,c,l") - g_aijb("a,k,l,c")) * t1("d,l")
1777 + (2.0 * g_aijb("a,k,l,d") - g_aibj("a,k,d,l")) * t1("c,l")
1778 ;
1779
1780 H_abcj("a,b,c,j") = - g_abci("a,b,c,j")
1781 + g_abij("a,b,k,j") * t1("c,k");
1782
1783 J_kbij("k,b,i,j") = g_aikl("b,k,j,i")
1784 + g_abij("b,c,j,i") * t1("c,k");
1785
1786 while (Delta_E_L >= 1.0e-12) {
1787
1788 // close-shell L^a_i & alpha-beta case L^ab_ij
1789 L1("a,i") = Delta_ai("a,i") * (
1790 // Iai
1791 Iai("a,i")
1792 // Gac Lci
1793 - Gac("a,c") * L1("c,i")
1794 // Kki Lak
1795 - Kki("k,i") * L1("a,k")
1796 // (R - 2Q)ak_ic Lck
1797 - (R_akic("a,k,i,c") - 2.0 * Q_akic("a,k,i,c")) * L1("c,k")
1798 // E^kl_ic L2^ac_kl
1799 - E_klic("k,l,i,c") * L2("a,c,k,l")
1800 // F^ak_cd L2^cd_ik
1801 - F_akcd("a,k,c,d") * L2("c,d,i,k")
1802 );
1803
1804 L2("a,b,i,j") = Delta_abij("a,b,i,j") * (
1805 // I^ab_ij
1806 g_abij("a,b,i,j")
1807
1808 // Ibi Laj + Iaj Lbi
1809 //- L1("a,j") * Iai("b,i")
1810 //- L1("b,i") * Iai("a,j")
1811
1812 // Ibj Lai + Iai Lbj
1813 + L1("a,i") * Iai("b,j")
1814 + L1("b,j") * Iai("a,i")
1815
1816 // Gbc L^ac_ij + Gac L^bc_ji
1817 // CC2: Gbc = - fbc (1 - delta_bc) = 0
1818 //+ fab("b,c") * (1.0 - Iab("b,c")) * L2("a,c,i,j")
1819 //+ fab("a,c") * (1.0 - Iab("a,c")) * L2("b,c,j,i")
1820
1821 // Kkj L^ab_ik + Kki L^ba_jk
1822 // CC2: Kkj = fkj (1 - delta_kj) = 0
1823 //- fij("k,j") * (1.0 - Iij("k,j")) * L2("a,b,i,k")
1824 //- fij("k,i") * (1.0 - Iij("k,i")) * L2("b,a,j,k")
1825
1826 // H^ab_cj Lci + H^ba_ci Lcj
1827 - H_abcj("a,b,c,j") * L1("c,i")
1828 - H_abcj("b,a,c,i") * L1("c,j")
1829
1830 // J^kb_ij Lak - j^ka_ji Lbk
1831 - J_kbij("k,b,i,j") * L1("a,k")
1832 - J_kbij("k,a,j,i") * L1("b,k")
1833 );
1834
1835#if 0 // close-shell L^a_i & alpha-beta case L^ab_ij in explicit form
1836
1837 L1("a,i") = Delta_ai("a,i") * (
1838 // Iai
1839 fai("a,i")
1840 + (2.0 * g_abij("a,b,i,j") - g_abij("a,b,j,i")) * t1("b,j")
1841
1842 // Gac Lci
1843 - ( fai("a,j") * t1("c,j")
1844 - (2.0 * g_abci("a,b,c,j") - g_abci("b,a,c,j")) * t1("b,j")
1845 + (2.0 * g_abij("a,d,k,l") - g_abij("a,d,l,k")) * tau("c,d,k,l"))
1846 * L1("c,i")
1847
1848 // Kki Lak
1849 - ( fai("c,i") * t1("c,k")
1850 + (2.0 * g_aikl("b,k,j,i") - g_aikl("b,k,i,j")) * t1("b,j")
1851 + (2.0 * g_abij("c,d,i,l") - g_abij("c,d,l,i")) * tau("c,d,k,l"))
1852 * L1("a,k")
1853
1854 // (R - 2Q)ak_ic Lck
1855 + ( 2.0 * g_aijb("a,k,i,c") - g_aibj("a,k,c,i")
1856 + (2.0 * g_abci("b,a,c,i") - g_abci("a,b,c,i")) * t1("b,k")
1857 - (2.0 * g_aikl("a,k,i,l") - g_aikl("a,k,l,i")) * t1("c,l")
1858 - (2.0 * g_abij("a,b,i,j") - g_abij("a,b,j,i")) * t1("c,j") * t1("b,k")
1859 + (2.0 * g_abij("a,b,i,j") - g_abij("a,b,j,i"))
1860 * (2.0 * t2("c,b,k,j") - t2("c,b,j,k"))
1861 ) * L1("c,k")
1862
1863 // E^kl_ic L2^ac_kl
1864 - ( 2.0 * g_aikl("b,i,l,k") - g_aikl("b,i,k,l")
1865 // a^kl_im tcm
1866 + ( - (2.0 * g_ijkl("k,l,i,j") - g_ijkl("k,l,j,i"))
1867 - (2.0 * g_abij("c,d,i,j") - g_abij("c,d,j,i")) * t1("c,k") * t1("d,l")
1868
1869 - (2.0 * g_aikl("c,l,i,j") - g_aikl("c,l,j,i")) * t1("c,k")
1870 - (2.0 * g_aikl("c,k,j,i") - g_aikl("c,k,i,j")) * t1("c,l")
1871 ) * t1("b,j")
1872 //
1873 + (2.0 * g_abci("d,c,b,i") - g_abci("c,d,b,i")) * t1("d,l") * t1("c,k")
1874 //
1875 + (2.0 * g_aijb("c,l,i,b") - g_aibj("c,l,b,i")) * t1("c,k")
1876 + (2.0 * g_aibj("c,k,b,i") - g_aijb("c,k,i,b")) * t1("c,l")
1877 ) * L2("a,b,k,l")
1878
1879 // F^ak_cd L2^cd_ik
1880 - ( - 2.0 * g_abci("c,d,a,j") - g_abci("d,c,a,j")
1881 // b^ae_cd tek
1882 + ( - (2.0 * g_abcd("a,b,c,d") - g_abcd("b,a,c,d"))
1883 - (2.0 * g_abij("a,b,k,l") - g_abij("b,a,k,l")) * t1("c,k") * t1("d,l")
1884
1885 + (2.0 * g_abci("b,a,d,k") - g_abci("a,b,d,k")) * t1("c,k")
1886 + (2.0 * g_abci("a,b,c,k") - g_abci("b,a,c,k")) * t1("d,k")
1887 ) * t1("b,j")
1888 //
1889 - (2.0 * g_aikl("a,j,k,l") - g_aikl("a,j,l,k")) * t1("d,l") * t1("c,k")
1890 //
1891 + (2.0 * g_aibj("a,j,c,k") - g_aijb("a,j,k,c")) * t1("d,k")
1892 + (2.0 * g_aijb("a,j,k,d") - g_aibj("a,j,d,k")) * t1("c,k")
1893 ) * L2("c,d,i,j")
1894 );
1895
1896 L2("a,b,i,j") = Delta_abij("a,b,i,j") * (
1897 // I^ab_ij
1898 g_abij("a,b,i,j")
1899
1900 // Ibi Laj + Iaj Lbi
1901 // Ibj Lai + Iai Lbj
1902
1903 + ( fai("a,i")
1904 + (2.0 * g_abij("a,f,i,n") - g_abij("a,f,n,i")) * t1("f,n"))
1905 * L1("b,j")
1906
1907 + ( fai("b,j")
1908 + (2.0 * g_abij("b,f,j,n") - g_abij("b,f,n,j")) * t1("f,n"))
1909 * L1("a,i")
1910
1911 // H^ab_cj Lci + H^ba_ci Lcj
1912 - (- g_abci("a,b,e,j")
1913 + g_abij("a,b,n,j") * t1("e,n")) * L1("e,i")
1914 - (- g_abci("b,a,e,i")
1915 + g_abij("b,a,n,i") * t1("e,n")) * L1("e,j")
1916
1917 // J^kb_ij Lak - j^ka_ji Lbk
1918 - ( g_aikl("b,m,j,i")
1919 + g_abij("b,f,j,i") * t1("f,m")) * L1("a,m")
1920 - ( g_aikl("a,m,i,j")
1921 + g_abij("a,f,i,j") * t1("f,m")) * L1("b,m")
1922 );
1923#endif
1924
1925 E_0_L = E_1_L;
1926 E_1_L = dot((2.0 * g_abij("a,b,i,j") - g_abij("b,a,i,j")), L2("a,b,i,j") );
1927 Delta_E_L = std::abs(E_0_L - E_1_L);
1928
1929 iter += 1;
1930 std::cout << indent << scprintf("%-5.0f", iter) << scprintf("%-20.10f", Delta_E_L)
1931 << scprintf("%-15.10f", E_1_L) << std::endl;
1932 }
1933 //std::cout << "CC2 L1 amplitudes: " << std::endl << L1 << std::endl;
1934 }
1935
1936 // compute lambda amplitudes of CC2
1937 // use formula from Gauss and Stanton, JCP, 103 (1995)
1938 template <typename T>
1939 void SingleReference_R12Intermediates<T>::compute_lambda_cc2_2(const TArray2& t1, const TArray4& t2,
1940 TArray2& L1, TArray4& L2) {
1941
1942 TArray2 fij = xy("<j|F|j>");
1943 TArray2 fab = xy("<a|F|b>");
1944 TArray2 fai = xy("<a|F|i>");
1945
1946 // compute Delta_ai = 1 / (- <a|F|a> + <i|F|i>)
1947 typedef detail::diag_precond2<double> pceval_type;
1948 pceval_type Delta_ai_gen(TA::array_to_eigen(fab), TA::array_to_eigen(fij));
1949
1950 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2dLazy;
1951 TArray2dLazy Delta_ai(fai.world(), fai.trange());
1952
1953 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2d;
1954 // construct local tiles
1955 for(auto t = Delta_ai.trange().tiles_range().begin();
1956 t != Delta_ai.trange().tiles_range().end(); ++t)
1957 if (Delta_ai.is_local(*t)) {
1958 std::array<std::size_t, 2> index;
1959 std::copy(t->begin(), t->end(), index.begin());
1960 madness::Future < typename TArray2dLazy::value_type >
1961 tile((LazyTensor<T, 2, pceval_type >(&Delta_ai, index, &Delta_ai_gen)
1962 ));
1963
1964 // Insert the tile into the array
1965 Delta_ai.set(*t, tile);
1966 }
1967
1968 // compute Delta_ijab = 1 / (- <a|F|a> - <b|F|b> + <i|F|i> + <j|F|j>)
1969 typedef detail::diag_precond4<double> pc4eval_type;
1970 pc4eval_type Delta_abij_gen(TA::array_to_eigen(fab), TA::array_to_eigen(fab),
1971 TA::array_to_eigen(fij),TA::array_to_eigen(fij));
1972
1973 TArray4d g_abij = ijxy("<a b|g|i j>");
1974 typedef TA::Array<T, 4, LazyTensor<T, 4, pc4eval_type > > TArray4dLazy;
1975 TArray4dLazy Delta_abij(g_abij.world(), g_abij.trange());
1976
1977 // construct local tiles
1978 for(auto t = Delta_abij.trange().tiles_range().begin();
1979 t != Delta_abij.trange().tiles_range().end(); ++t)
1980 if (Delta_abij.is_local(*t)) {
1981 std::array<std::size_t, 4> index;
1982 std::copy(t->begin(), t->end(), index.begin());
1983 madness::Future < typename TArray4dLazy::value_type >
1984 tile((LazyTensor<T, 4, pc4eval_type >(&Delta_abij, index, &Delta_abij_gen)
1985 ));
1986
1987 // Insert the tile into the array
1988 Delta_abij.set(*t, tile);
1989 }
1990
1991 // pseudo energy
1992 L1("a,i") = t1("a,i");
1993 L2("a,b,i,j") = t2("a,b,i,j");
1994
1995 double E_0_L = 0.0;
1996 double E_1_L = dot((2.0 * g_abij("a,b,i,j") - g_abij("b,a,i,j")), L2("a,b,i,j") );
1997 double Delta_E_L = std::abs(E_0_L - E_1_L);
1998
1999 double iter = 0;
2000 std::cout << indent << scprintf("%-5s", "Iter") << scprintf("%-20s", "Delta_E_L")
2001 << scprintf("%-20s", "E_L(CC2)") << std::endl;
2002 std::cout << indent << scprintf("%-5.0f", iter) << scprintf("%-20.10f", Delta_E_L)
2003 << scprintf("%-15.10f", E_1_L) << std::endl;
2004
2005 // intermediates for computing L1 & L2
2006 TArray4d g_abci = ijxy("<a b|g|c i>");
2007 TArray4d g_aikl = ijxy("<a i|g|k l>");
2008 TArray4d g_aibj = ijxy("<a i|g|b j>");
2009 TArray4d g_aijb = ijxy("<a i|g|j b>");
2010 TArray4d g_ijkl = ijxy("<i j|g|k l>");
2011 TArray4d g_abcd = ijxy("<a b|g|c d>");
2012
2013 TArray4 tau2_aa, tau2_ab, Ttau_aa, Ttau_ab;
2014 tau2_aa("a,b,i,j") = t2("a,b,i,j") - t2("b,a,i,j")
2015 + (t1("a,i") * t1("b,j") - t1("b,i") * t1("a,j"));
2016 tau2_ab("a,b,i,j") = t2("a,b,i,j")
2017 + (t1("a,i") * t1("b,j"));
2018
2019 Ttau_aa("a,b,i,j") = t2("a,b,i,j") - t2("b,a,i,j")
2020 + 0.5 * (t1("a,i") * t1("b,j") - t1("b,i") * t1("a,j"));
2021 Ttau_ab("a,b,i,j") = t2("a,b,i,j")
2022 + 0.5 * t1("a,i") * t1("b,j");
2023
2024 TArray4 tau2t1_aa, tau2t1_ab, Ttaut1_aa, Ttaut1_ab;
2025 tau2t1_aa("a,b,i,j") = t1("a,i") * t1("b,j") - t1("b,i") * t1("a,j");
2026 tau2t1_ab("a,b,i,j") = t1("a,i") * t1("b,j");
2027 Ttaut1_aa("a,b,i,j") = 0.5 * t1("a,i") * t1("b,j") - t1("b,i") * t1("a,j");
2028 Ttaut1_ab("a,b,i,j") = 0.5 * t1("a,i") * t1("b,j");
2029
2030 TArray2 TFme, TFae, TFmi;
2031 TFme("m,e") = // fme
2032 // + t^f_n g^mn_ef
2033 (2.0 * g_abij("e,f,m,n") - g_abij("e,f,n,m")) * t1("f,n");
2034 TFae("a,e") = // fae - 1/2 fme t^a_m
2035 // + t^f_m g^am_ef
2036 t1("f,m") * (2.0 * g_abci("e,f,a,m") - g_abci("f,e,a,m"))
2037 // - 1/2 Ttau^af_mn g^mn_ef
2038 - 0.5 * Ttau_aa("a,f,m,n") * (g_abij("e,f,m,n") - g_abij("f,e,m,n"))
2039 - Ttau_ab("a,f,m,n") * g_abij("e,f,m,n")
2040 ;
2041 TFmi("m,i") = // fmi + 1/2 fme t^e_i
2042 // + t^e_n g^mn_ie
2043 t1("e,n") * (2.0 * g_aikl("e,i,n,m") - g_aikl("e,i,m,n"))
2044 // + 1/2 Ttau^ef_in g^mn_ef
2045 + 0.5 * Ttau_aa("e,f,i,n") * (g_abij("e,f,m,n") - g_abij("e,f,n,m"))
2046 + Ttau_ab("e,f,i,n") * g_abij("e,f,m,n")
2047 ;
2048
2049 TArray2 CFme, CFae, CFmi;
2050 CFme("m,e") = TFme("m,e");
2051 CFae("a,e") = TFae("a,e") - 0.5 * t1("a,m") * TFme("m,e");
2052 CFmi("m,i") = TFmi("m,i") + 0.5 * t1("e,i") * TFme("m,e");
2053
2054 // compute \cal{W}mbej
2055 TArray4 TW_MBEJ_aa, TW_MbEj_ab,CW_MBEJ_aa, CW_MbEj_ab;
2056
2057 // \tilde{W}mbej:
2058 // alpha-alpha case
2059 TW_MBEJ_aa("m,b,e,j") = // g^mb_ej
2060 g_aijb("e,j,m,b") - g_aibj("e,j,b,m")
2061
2062 // + t^f_j g^mb_ef
2063 + t1("f,j") * (g_abci("f,e,b,m") - g_abci("e,f,b,m"))
2064
2065 // - t^b_n g^mn_ej
2066 - t1("b,n") * (g_aikl("e,j,m,n") - g_aikl("e,j,n,m"))
2067
2068 // - 1/2 (t^fb_jn + 2 t^f_j t^b_n) g^mn_ef:
2069 // + 1/2 t^bf_jn g^mn_ef
2070 + 0.5 * ( (2.0 * t2("b,f,j,n") - t2("f,b,j,n"))
2071 * g_abij("e,f,m,n")
2072 - (t2("b,f,j,n") - t2("f,b,j,n"))
2073 * g_abij("f,e,m,n")
2074 )
2075 // - t^f_j t^b_n g^mn_ef
2076 - t1("f,j") * t1("b,n")
2077 * (g_abij("e,f,m,n") - g_abij("f,e,m,n"))
2078 ;
2079 // alpha-beta case
2080 TW_MbEj_ab("m,b,e,j") = // g^mb_ej
2081 g_aijb("e,j,m,b")
2082 // + t^f_j g^mb_ef
2083 + t1("f,j") * g_abci("f,e,b,m")
2084 // - t^b_n g^mn_ej
2085 - t1("b,n") * g_aikl("e,j,m,n")
2086
2087 // - 1/2 (t^fb_jn + 2 t^f_j t^b_n) g^mn_ef:
2088 // + 1/2 t^bf_jn g^mn_ef
2089 + 0.5 * ( (2.0 * t2("b,f,j,n") - t2("f,b,j,n"))
2090 * g_abij("e,f,m,n")
2091 - t2("b,f,j,n") * g_abij("f,e,m,n")
2092 )
2093 // - t^f_j t^b_n g^mn_ef
2094 - t1("f,j") * t1("b,n") * g_abij("e,f,m,n")
2095 ;
2096
2097 // \cal{W}mbej
2098 CW_MBEJ_aa("m,b,e,j") = // \tilde{W}mbej
2099 TW_MBEJ_aa("m,b,e,j")
2100
2101 // - 1/2 t^fb_jn g^mn_ef = + 1/2 t^fb_nj g^mn_ef
2102 + 0.5 * (t2("f,b,n,j") - t2("b,f,n,j"))
2103 * (g_abij("e,f,m,n") - g_abij("f,e,m,n"))
2104 + 0.5 * t2("f,b,n,j") * g_abij("e,f,m,n")
2105 ;
2106 CW_MbEj_ab("m,b,e,j") = // \tilde{W}mbej
2107 TW_MbEj_ab("m,b,e,j")
2108
2109 // - 1/2 t^fb_jn g^mn_ef = + 1/2 t^fb_nj g^mn_ef
2110 + 0.5 * (t2("f,b,n,j") - t2("b,f,n,j"))
2111 * g_abij("e,f,m,n")
2112 + 0.5 * t2("f,b,n,j")
2113 * (g_abij("e,f,m,n") - g_abij("f,e,m,n"))
2114 ;
2115
2116
2117 // compute \cal{W}abei
2118 TArray4 TW_ABEF_aa, TW_AbEf_ab, CW_ABEF_aa, CW_AbEf_ab, CW_ABEI_aa, CW_AbEi_ab;
2119
2120 // \tilde{W}abef
2121 TW_ABEF_aa("a,b,e,f") = // g^ab_ef
2122 g_abcd("a,b,e,f") - g_abcd("b,a,e,f")
2123
2124 // - P(ab) t^b_m g^am_ef:
2125 // - t^b_m g^am_ef
2126 - t1("b,m") * (g_abci("e,f,a,m") - g_abci("f,e,a,m"))
2127 // + t^a_m g^bm_ef
2128 + t1("a,m") * (g_abci("e,f,b,m") - g_abci("f,e,b,m"))
2129
2130 // + 1/4 tau^ab_mn g^mn_ef
2131 + 0.25 * tau2t1_aa("a,b,m,n") * (g_abij("e,f,m,n") - g_abij("f,e,m,n"))
2132 ;
2133
2134 TW_AbEf_ab("a,b,e,f") = // g^ab_ef
2135 g_abcd("a,b,e,f")
2136
2137 // - P(ab) t^b_m g^am_ef:
2138 // - t^b_m g^am_ef
2139 - t1("b,m") * g_abci("e,f,a,m")
2140 // - t^a_m g^mb_ef
2141 - t1("a,m") * g_abci("f,e,b,m")
2142
2143 // + 1/4 tau^ab_mn g^mn_ef
2144 + 0.5 * tau2t1_ab("a,b,m,n") * g_abij("e,f,m,n")
2145 ;
2146
2147 // \cal{W}abef
2148 CW_ABEF_aa("a,b,e,f") = // \tilde{W}abef
2149 TW_ABEF_aa("a,b,e,f")
2150 // + 1/4 tau^ab_mn g^mn_ef
2151 + 0.25 * tau2t1_aa("a,b,m,n") * (g_abij("e,f,m,n") - g_abij("f,e,m,n"));
2152
2153 CW_AbEf_ab("a,b,e,f") = // \tilde{W}abef
2154 TW_AbEf_ab("a,b,e,f")
2155 // + 1/4 tau^ab_mn g^mn_ef
2156 + 0.5 * tau2t1_ab("a,b,m,n") * g_abij("e,f,m,n");
2157
2158 // \cal{W}abei
2159 CW_ABEI_aa("a,b,e,i") = // g^ab_ei
2160 g_abci("a,b,e,i") - g_abci("b,a,e,i")
2161
2162 // - \cal{F}me t^ab_mi
2163 //- CFme("m,e") * (t2("a,b,m,i") - t2("b,a,m,i"))
2164
2165 // + t^f_i \cal{W}abef
2166 + t1("f,i") * CW_ABEF_aa("a,b,e,f")
2167
2168 // + 1/2 g^mn_ei tau^ab_mn
2169 + 0.5 * (g_aikl("e,i,m,n") - g_aikl("e,i,n,m")) * tau2t1_aa("a,b,m,n")
2170
2171 // - P(ab) g^mb_ef t^af_mi (=> 0 for cc2):
2172 // - g^mb_ef t^af_mi = - g^bm_ef t^fa_mi
2173 //- (g_abci("f,e,b,m") - g_abci("e,f,b,m")) * (t2("a,f,m,i") - t2("f,a,m,i")) // m,f in alpha space
2174 //- g_abci("e,f,b,m") * t2("f,a,m,i") // m,f in beta space
2175 // + g^ma_ef t^bf_mi = + g^am_ef t^fb_mi
2176 //+ g_abci("f,e,a,m") * t2("b,f,m,i") - g_abci("e,f,a,m") * t2("b,f,m,i")
2177 //- g_abci("f,e,a,m") * t2("f,b,m,i") + 2.0 * g_abci("e,f,a,m") * t2("f,b,m,i")
2178
2179 // - P(ab) t^a_m (g^mb_ei - t^bf_ni g^mn_ef):
2180 // - t^a_m (g^mb_ei - t^bf_ni g^mn_ef) = - t^a_m (g^mb_ei + t^fb_ni g^mn_ef)
2181 - t1("a,m")
2182 * ( g_aijb("b,m,i,e") - g_aibj("b,m,e,i")
2183 //- ( t2("b,f,n,i") * g_abij("e,f,m,n") - 2.0 * t2("f,b,n,i") * g_abij("e,f,m,n")
2184 // - t2("b,f,n,i") * g_abij("f,e,m,n") + t2("f,b,n,i") * g_abij("f,e,m,n"))
2185 )
2186 // + t^b_m (g^ma_ei - t^af_ni g^mn_ef) = + t^b_m (- g^am_ei + t^af_in g^mn_ef)
2187 + t1("b,m")
2188 * (- g_aibj("a,m,e,i") + g_aijb("a,m,i,e")
2189 //+ ( 2.0 * t2("f,a,n,i") * g_abij("e,f,m,n") - t2("a,f,n,i") * g_abij("e,f,m,n")
2190 // - t2("f,a,n,i") * g_abij("f,e,m,n") + t2("a,f,n,i") * g_abij("f,e,m,n")
2191 // )
2192 )
2193 ;
2194
2195 CW_AbEi_ab("a,b,e,i") = // g^ab_ei
2196 g_abci("a,b,e,i")
2197
2198 // - \cal{F}me t^ab_mi
2199 //- CFme("m,e") * t2("a,b,m,i")
2200
2201 // + t^f_i \cal{W}abef
2202 + t1("f,i") * CW_AbEf_ab("a,b,e,f")
2203
2204 // + 1/2 g^mn_ei tau^ab_mn
2205 + g_aikl("e,i,m,n") * tau2t1_ab("a,b,m,n")
2206
2207 // - P(ab) g^mb_ef t^af_mi (=> 0 for cc2):
2208 // - g^mb_ef t^af_mi
2209 //- g_abci("f,e,b,m") * t2("a,f,m,i")
2210 // + g^ma_ef t^bf_mi = + g^am_ef t^fb_mi
2211 //+ (g_abci("e,f,a,m") - g_abci("f,e,a,m")) * t2("f,b,m,i")
2212 //+ g_abci("e,f,a,m") * (t2("f,b,m,i") - t2("b,f,m,i"))
2213
2214 // - P(ab) t^a_m (g^mb_ei - t^bf_ni g^mn_ef):
2215 // - t^a_m (g^mb_ei - t^bf_ni g^mn_ef) = - t^a_m (g^mb_ei + t^fb_ni g^mn_ef)
2216 - t1("a,m")
2217 * ( g_aijb("b,m,i,e")
2218 //+ t2("f,b,n,i") * (g_abij("e,f,m,n") - g_abij("f,e,m,n"))
2219 //+ (t2("f,b,n,i") - t2("b,f,n,i")) * g_abij("e,f,m,n")
2220 )
2221 // + t^b_m (g^ma_ei - t^af_ni g^mn_ef) = + t^b_m (- g^am_ei + t^af_ni g^nm_ef)
2222 + t1("b,m")
2223 * (- g_aibj("a,m,e,i")
2224 //+ t2("a,f,n,i") * g_abij("e,f,n,m")
2225 )
2226 ;
2227
2228 // compute \cal{W}mbij
2229 TArray4 TW_MNIJ_aa, TW_MnIj_ab, CW_MNIJ_aa, CW_MnIj_ab, CW_MBIJ_aa, CW_MbIj_ab;
2230
2231 // \tilde{W}mnij
2232 TW_MNIJ_aa("m,n,i,j") = // g^mn_ij
2233 g_ijkl("m,n,i,j") - g_ijkl("n,m,i,j")
2234
2235 // + P(ij) t^e_j g^mn_ie:
2236 // + t^e_j g^mn_ie
2237 + t1("e,j") * (g_aikl("e,i,n,m") - g_aikl("e,i,m,n"))
2238 // + t^e_i g^mn_ej
2239 + t1("e,i") * (g_aikl("e,j,m,n") - g_aikl("e,j,n,m"))
2240
2241 // + 0.25 * tau^ef_ij * g^mn_ef
2242 + 0.25 * tau2t1_aa("e,f,i,j") * (g_abij("e,f,m,n") - g_abij("e,f,n,m"))
2243 ;
2244 TW_MnIj_ab("m,n,i,j") = // g^mn_ij
2245 g_ijkl("m,n,i,j")
2246
2247 // + P(ij) t^e_j g^mn_ie:
2248 // + t^e_j g^mn_ie
2249 + t1("e,j") * g_aikl("e,i,n,m")
2250 // + t^e_i g^mn_ej
2251 + t1("e,i") * g_aikl("e,j,m,n")
2252
2253 // + 0.25 * tau^ef_ij * g^mn_ef
2254 + 0.5 * tau2t1_ab("e,f,i,j") * g_abij("e,f,m,n")
2255 ;
2256
2257 // \cal{W}mnij
2258 CW_MNIJ_aa("m,n,i,j") = // \tilde{W}mnij
2259 TW_MNIJ_aa("m,n,i,j")
2260 // + 1/4 tau^ef_ij g^mn_ef
2261 + 0.25 * tau2t1_aa("e,f,i,j") * (g_abij("e,f,m,n") - g_abij("e,f,n,m"))
2262 ;
2263 CW_MnIj_ab("m,n,i,j") = // \tilde{W}mnij
2264 TW_MnIj_ab("m,n,i,j")
2265 // + 1/4 tau^ef_ij g^mn_ef
2266 + 0.5 * tau2t1_ab("e,f,i,j") * g_abij("e,f,m,n")
2267 ;
2268
2269 // \cal{W}mbij
2270 CW_MBIJ_aa("m,b,i,j") = // g^mb_ij
2271 g_aikl("b,m,j,i") - g_aikl("b,m,i,j")
2272
2273 // - \cal{F}me t^be_ij = + CFme t^eb_ij
2274 //+ CFme("m,e") * (t2("e,b,i,j") - t2("b,e,i,j"))
2275
2276 // - t^b_n \cal{W}mnij
2277 - t1("b,n") * CW_MNIJ_aa("m,n,i,j")
2278
2279 // + 0.5 g^mb_ef tau^ef_ij
2280 + 0.5 * (g_abci("f,e,b,m") - g_abci("e,f,b,m")) * tau2t1_aa("e,f,i,j")
2281
2282 // + P(ij) g^mn_ie t^be_jn (=> 0 for cc2)：
2283 // + g^mn_ie t^be_jn
2284 //+ 2.0 * g_aikl("e,i,n,m") * t2("b,e,j,n") - g_aikl("e,i,m,n") * t2("b,e,j,n")
2285 //- g_aikl("e,i,n,m") * t2("b,e,n,j") + g_aikl("e,i,m,n") * t2("b,e,n,j")
2286 // - g^mn_je t^be_in
2287 //+ 2.0 * g_aikl("e,j,n,m") * t2("b,e,i,n") - g_aikl("e,j,m,n") * t2("b,e,i,n")
2288 //- g_aikl("e,j,n,m") * t2("e,b,i,n") + g_aikl("e,j,m,n") * t2("e,b,i,n")
2289
2290 // + P(IJ) t^e_i (g^mb_ej - t^bf_nj g^mn_ef)
2291 // + t^e_i (g^mb_ej - t^bf_nj g^mn_ef) = + t^e_i (g^mb_ej + t^bf_jn g^mn_ef)
2292 + t1("e,i")
2293 * ( g_aijb("e,j,m,b") - g_aibj("e,j,b,m")
2294
2295 //+ 2.0 * t2("b,f,j,n") * g_abij("e,f,m,n") - t2("f,b,j,n") * g_abij("e,f,m,n")
2296 //- t2("b,f,j,n") * g_abij("f,e,m,n") + t2("f,b,j,n") * g_abij("f,e,m,n")
2297 )
2298 // - t^e_j (g^mb_ei - t^bf_ni g^mn_ef) = - t^e_j (g^mb_ei + t^bf_in g^mn_ef)
2299 - t1("e,j")
2300 * ( g_aijb("e,i,m,b") - g_aibj("e,i,b,m")
2301
2302 //+ 2.0 * t2("b,f,i,n") * g_abij("e,f,m,n") - t2("f,b,i,n") * g_abij("e,f,m,n")
2303 //- t2("b,f,i,n") * g_abij("f,e,m,n") + t2("f,b,i,n") * g_abij("f,e,m,n")
2304 )
2305 ;
2306
2307 CW_MbIj_ab("m,b,i,j") = // g^mb_ij
2308 g_aikl("b,m,j,i")
2309
2310 // - \cal{F}me t^be_ij = + CFme t^eb_ij
2311 //+ CFme("m,e") * t2("e,b,i,j")
2312
2313 // - t^b_n \cal{W}mnij
2314 - t1("b,n") * CW_MnIj_ab("m,n,i,j")
2315
2316 // + 0.5 g^mb_ef tau^ef_ij
2317 + g_abci("f,e,b,m") * tau2t1_ab("e,f,i,j")
2318
2319 // + P(ij) g^mn_ie t^be_jn (=> 0 for cc2):
2320 // + g^mn_ie t^be_jn
2321 //+ 2.0 * g_aikl("e,i,n,m") * t2("b,e,j,n") - g_aikl("e,i,n,m") * t2("b,e,n,j")
2322 //- g_aikl("e,i,m,n") * t2("b,e,j,n")
2323 // - g^mn_je t^be_in = - g^nm_je t^eb_in
2324 //+ g_aikl("e,j,m,n") * t2("e,b,i,n")
2325
2326 // + P(IJ) t^e_i (g^mb_ej - t^bf_nj g^mn_ef)
2327 // + t^e_i (g^mb_ej - t^bf_nj g^mn_ef) = + t^e_i (g^mb_ej + t^bf_jn g^mn_ef)
2328 + t1("e,i")
2329 * ( g_aijb("e,j,m,b")
2330
2331 //+ 2.0 * t2("b,f,j,n") * g_abij("e,f,m,n") - t2("f,b,j,n") * g_abij("e,f,m,n")
2332 //- t2("b,f,j,n") * g_abij("f,e,m,n")
2333 )
2334 // - t^e_j (g^mb_ei - t^bf_ni g^mn_ef) = - t^e_j (- g^mb_ie + t^bf_ni g^mn_fe)
2335 - t1("e,j")
2336 * (- g_aibj("e,i,b,m")
2337 //+ t2("b,f,n,i") * g_abij("f,e,m,n")
2338 )
2339 ;
2340
2341 // intermediates for L2
2342 TArray4 CW_MnIe_ab, CW_MniE_ab, CW_AmEf_ab, CW_aMEf_ab;
2343
2344 CW_MnIe_ab("m,n,i,e") = // g^mn_ie
2345 g_aikl("e,i,n,m")
2346 // + t^f_i g^mn_fe
2347 + t1("f,i") * g_abij("f,e,m,n")
2348 ;
2349 CW_MniE_ab("m,n,i,e") = // g^mn_ie
2350 - g_aikl("e,i,m,n")
2351 // + t^f_i g^mn_fe
2352 - t1("f,i") * g_abij("f,e,n,m")
2353 ;
2354
2355 CW_AmEf_ab("a,m,e,f") = // g^am_ef
2356 g_abci("e,f,a,m")
2357 // - t^a_n g^nm_ef
2358 - t1("a,n") * g_abij("e,f,n,m")
2359 ;
2360 CW_aMEf_ab("a,m,e,f") = // g^am_ef
2361 - g_abci("f,e,a,m")
2362 // - t^a_n g^nm_ef
2363 + t1("a,n") * g_abij("f,e,n,m")
2364 ;
2365
2366 while (Delta_E_L >= 1.0e-9) {
2367
2368 L1("a,i") = Delta_ai("a,i") * (
2369 // \cal{F}ia
2370 CFme("i,a")
2371 // + \lambda^i_e \cal{F}ea
2372 + L1("e,i") * CFae("e,a")
2373 // - \lambda^m_a \cal{F}im
2374 - L1("a,m") * CFmi("i,m")
2375 // + \lambda^m_e \cal{W}ieam
2376 + L1("e,m") * (CW_MBEJ_aa("i,e,a,m") + CW_MbEj_ab("i,e,a,m"))
2377 // + 1/2 \lambda^im_ef \cal{W}efam
2378 + 0.5 * (L2("e,f,i,m") - L2("e,f,m,i") ) * CW_ABEI_aa("e,f,a,m")
2379 + L2("e,f,i,m") * CW_AbEi_ab("e,f,a,m")
2380 // - 1/2 \lambda^mn_ae \cal{W}iemn
2381 - 0.5 * (L2("a,e,m,n") - L2("e,a,m,n") ) * CW_MBIJ_aa("i,e,m,n")
2382 - L2("a,e,m,n") * CW_MbIj_ab("i,e,m,n")
2383 );
2384
2385 L2("a,b,i,j") = Delta_abij("a,b,i,j") * (
2386 // g^ij_ab
2387 g_abij("a,b,i,j")
2388
2389 // + P(ab) \lambda^ij_ae \cal{F}eb
2390 //+ L2("a,e,i,j") * CFae("e,b")
2391 //+ L2("e,b,i,j") * CFae("e,a")
2392
2393 // - P(ij) \lambda^im_ab \cal{F}jm
2394 //- L2("a,b,i,m") * CFmi("j,m")
2395 //- L2("a,b,m,j") * CFmi("i,m")
2396
2397 // + P(ij) \lambda^i_e \cal{W}ejab
2398 + L1("e,i") * CW_AmEf_ab("e,j,a,b")
2399 - L1("e,j") * CW_aMEf_ab("e,i,a,b")
2400
2401 // - P(ab) \lambda^m_a \cal{W}ijmb
2402 - L1("a,m") * CW_MnIe_ab("i,j,m,b")
2403 + L1("b,m") * CW_MniE_ab("i,j,m,a")
2404
2405 // + P(ij) P(ab) \lambda^i_a \cal{F}jb
2406 + L1("a,i") * CFme("j,b")
2407 //- L1("b,i") * CFme("j,a")
2408 //- L1("a,j") * CFme("i,b")
2409 + L1("b,j") * CFme("i,a")
2410 );
2411
2412 E_0_L = E_1_L;
2413 E_1_L = dot((2.0 * g_abij("a,b,i,j") - g_abij("b,a,i,j")), L2("a,b,i,j") );
2414 Delta_E_L = std::abs(E_0_L - E_1_L);
2415
2416 iter += 1;
2417 std::cout << indent << scprintf("%-5.0f", iter) << scprintf("%-20.10f", Delta_E_L)
2418 << scprintf("%-15.10f", E_1_L) << std::endl;
2419 }
2420 //std::cout << "CC2 L1 amplitudes: " << std::endl << L1 << std::endl;
2421 }
2422
2423 // compute CC2 one-electron density from amplitudes
2424 template <typename T>
2425 void SingleReference_R12Intermediates<T>::compute_cc2_1rdm_amp(
2426 const TArray2& T1_cc2, const TArray4& T2_cc2,
2427 const TArray2& L1_cc2, const TArray4& L2_cc2,
2428 TArray2& Dij_cc2, TArray2& Dab_cc2,
2429 TArray2& Dia_cc2, TArray2& Dai_cc2) {
2430
2431 Dij_cc2("i,j") = // - 1/4 P+(ij) t^ef_im lambda^jm_ef
2432 - 0.5 * ( (2.0 * T2_cc2("c,d,i,k") - T2_cc2("c,d,k,i"))
2433 * L2_cc2("c,d,j,k")
2434 + (2.0 * T2_cc2("c,d,j,k") - T2_cc2("c,d,k,j"))
2435 * L2_cc2("c,d,i,k")
2436 )
2437 // - 1/2 P+(ij) t^e_i lambda^j_e
2438 - 0.5 * ( T1_cc2("c,i") * L1_cc2("c,j")
2439 + T1_cc2("c,j") * L1_cc2("c,i")
2440 )
2441 ;
2442 //std::cout << "Dij_cc2: " << std::endl << Dij_cc2 << std::endl;
2443
2444 Dab_cc2("a,b") = // 1/4 P+(ab) t^mn_ae lambda^be_mn
2445 0.5 * ( (2.0 * T2_cc2("a,c,k,l") - T2_cc2("c,a,k,l"))
2446 * L2_cc2("b,c,k,l")
2447 + (2.0 * T2_cc2("b,c,k,l") - T2_cc2("c,b,k,l"))
2448 * L2_cc2("a,c,k,l")
2449 )
2450 // + 1/2 P+(ab) lambda^m_a t^b_m
2451 + 0.5 * ( L1_cc2("a,k") * T1_cc2("b,k")
2452 + L1_cc2("b,k") * T1_cc2("a,k")
2453 )
2454 ;
2455
2456 Dia_cc2("i,a") = // t^a_i
2457 T1_cc2("a,i")
2458 // + (t^ae_im - t^e_i t^a_m) \lambda^m_e
2459 + (2.0 * T2_cc2("a,c,i,k") - T2_cc2("a,c,k,i")
2460 - T1_cc2("c,i") * T1_cc2("a,k"))
2461 * L1_cc2("c,k")
2462 // CCSD term
2463 // - 1/2 lambda^mn_ef (t^ef_in t^a_m + t^e_i t^af_mn)
2464// - (2.0 * L2_cc2("c,d,k,l") - L2_cc2("d,c,k,l"))
2465// * ( T2_cc2("c,d,i,l") * T1_cc2("a,k")
2466// + T2_cc2("a,d,k,l") * T1_cc2("c,i")
2467// )
2468 ;
2469
2470 Dai_cc2("a,i") = // lambda^i_a
2471 L1_cc2("a,i");
2472 }
2473
2474 // compute lambda amplitudes of CCSD
2475 // use formula from Gauss and Stanton, JCP, 103 (1995)
2476 // compute Delta_ai = 1 / (- <a|F|a> + <i|F|i>)
2477 // & Delta_ijab = 1 / (- <a|F|a> - <b|F|b> + <i|F|i> + <j|F|j>)
2478 template <typename T>
2479 void SingleReference_R12Intermediates<T>::compute_Delta_cc(const TA::TiledRange& TR_ai,
2480 const TA::TiledRange& TR_abij,
2481 TArray2& D_ai, TArray4& D_abij) {
2482 TArray2 fij = xy("<j|F|j>");
2483 TArray2 fab = xy("<a|F|b>");
2484
2485 // compute Delta_ai = 1 / (- <a|F|a> + <i|F|i>)
2486 typedef detail::diag_precond2<double> pceval_type;
2487 pceval_type Delta_ai_gen(TA::array_to_eigen(fab), TA::array_to_eigen(fij));
2488
2489 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2dLazy;
2490 TArray2dLazy Delta_ai(fij.world(), TR_ai);
2491
2492 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2d;
2493 // construct local tiles
2494 for(auto t = Delta_ai.trange().tiles_range().begin();
2495 t != Delta_ai.trange().tiles_range().end(); ++t)
2496 if (Delta_ai.is_local(*t)) {
2497 std::array<std::size_t, 2> index;
2498 std::copy(t->begin(), t->end(), index.begin());
2499 madness::Future < typename TArray2dLazy::value_type >
2500 tile((LazyTensor<T, 2, pceval_type >(&Delta_ai, index, &Delta_ai_gen)
2501 ));
2502
2503 // Insert the tile into the array
2504 Delta_ai.set(*t, tile);
2505 }
2506 D_ai("a,i") = Delta_ai("a,i");
2507
2508 // compute Delta_ijab = 1 / (- <a|F|a> - <b|F|b> + <i|F|i> + <j|F|j>)
2509 typedef detail::diag_precond4<double> pc4eval_type;
2510 pc4eval_type Delta_abij_gen(TA::array_to_eigen(fab), TA::array_to_eigen(fab),
2511 TA::array_to_eigen(fij),TA::array_to_eigen(fij));
2512
2513 typedef TA::Array<T, 4, LazyTensor<T, 4, pc4eval_type > > TArray4dLazy;
2514 TArray4dLazy Delta_abij(fij.world(), TR_abij);
2515
2516 // construct local tiles
2517 for(auto t = Delta_abij.trange().tiles_range().begin();
2518 t != Delta_abij.trange().tiles_range().end(); ++t)
2519 if (Delta_abij.is_local(*t)) {
2520 std::array<std::size_t, 4> index;
2521 std::copy(t->begin(), t->end(), index.begin());
2522 madness::Future < typename TArray4dLazy::value_type >
2523 tile((LazyTensor<T, 4, pc4eval_type >(&Delta_abij, index, &Delta_abij_gen)
2524 ));
2525
2526 // Insert the tile into the array
2527 Delta_abij.set(*t, tile);
2528 }
2529 D_abij("a,b,i,j") = Delta_abij("a,b,i,j");
2530 fij.world().gop.fence();
2531 }
2532
2533 // compute intermediates needed for T amplitudes
2534 template <typename T>
2535 void SingleReference_R12Intermediates<T>::compute_intermediates_TFW_ccsd(
2536 const TArray2& t1, const TArray4& t2,
2537 const TArray4d& g_abij, const TArray4d& g_aikl,
2538 const TArray4d& g_aibj, const TArray4d& g_aijb,
2539 const TArray4d& g_abci,
2540 const TArray4d& g_ijkl, const TArray4d& g_abcd,
2541 TArray2& TFkc, TArray2& TFac, TArray2& TFki,
2542 TArray4& TW_KbCj_ab,TArray4& TW_KbcJ_ba,
2543 TArray4& TW_AbCd_ab, TArray4& TW_KlIj_ab) {
2544 TArray4 tau_ab, Ttau_ab;
2545 tau_ab("a,b,i,j") = t2("a,b,i,j") + (t1("a,i") * t1("b,j"));
2546 Ttau_ab("a,b,i,j") = t2("a,b,i,j") + 0.5 * t1("a,i") * t1("b,j");
2547
2548 TArray4 gabij_temp;
2549 gabij_temp("a,b,i,j") = 2.0 * g_abij("a,b,i,j") - g_abij("a,b,j,i");
2550
2551 TFkc("k,c") = // fkc
2552 // + t^d_l g^kl_cd
2553 gabij_temp("c,d,k,l") * t1("d,l");
2554 TFac("a,c") = // fac (1 - delta_ac) - 1/2 fkc t^a_k
2555 // + t^d_k g^ak_cd
2556 t1("d,k") * (2.0 * g_abci("c,d,a,k") - g_abci("d,c,a,k"))
2557 // - 1/2 Ttau^ad_kl g^kl_cd
2558 - Ttau_ab("a,d,k,l") * gabij_temp("c,d,k,l")
2559 ;
2560 TFki("k,i") = // fki (1 - delta_ki) + 1/2 fkc t^c_i
2561 // + t^c_l g^kl_ic
2562 t1("c,l") * (2.0 * g_aikl("c,i,l,k") - g_aikl("c,i,k,l"))
2563 // + 1/2 Ttau^cd_il g^kl_cd
2564 + Ttau_ab("c,d,i,l") * gabij_temp("c,d,k,l")
2565 ;
2566
2567 // \tilde{W}mbej:
2568 // alpha-beta case
2569 TW_KbCj_ab("k,b,c,j") = // g^kb_cj
2570 g_aijb("c,j,k,b")
2571 // + t^d_j g^kb_cd
2572 + t1("d,j") * g_abci("d,c,b,k")
2573 // - t^b_l g^kl_cj
2574 - t1("b,l") * g_aikl("c,j,k,l")
2575
2576 // - 1/2 (t^db_jl + 2 t^d_j t^b_l) g^kl_cd:
2577 // + 1/2 t^bd_jl g^kl_cd
2578 + 0.5 * ( t2("b,d,j,l") * gabij_temp("c,d,k,l")
2579 - t2("d,b,j,l") * g_abij("c,d,k,l")
2580 )
2581 // - t^d_j t^b_l g^kl_cd
2582 - t1("d,j") * (t1("b,l") * g_abij("c,d,k,l"))
2583 ;
2584
2586 TW_KbcJ_ba("k,b,c,j") = // g^kb_cj
2587 - g_aibj("c,j,b,k")
2588 // + t^d_j g^kb_cd
2589 - t1("d,j") * g_abci("c,d,b,k")
2590 // - t^b_l g^kl_cj
2591 + t1("b,l") * g_aikl("c,j,l,k")
2592
2593 // - 1/2 (t^db_jl + 2 t^d_j t^b_l) g^kl_cd:
2594 // + 1/2 t^bd_jl g^kl_cd
2595 + 0.5 * t2("d,b,j,l") * g_abij("d,c,k,l")
2596 // - t^d_j t^b_l g^kl_cd
2597 + t1("d,j") * (t1("b,l") * g_abij("d,c,k,l"))
2598 ;
2599
2600 // \tilde{W}abef
2601 TW_AbCd_ab("a,b,c,d") = // g^ab_cd
2602 g_abcd("a,b,c,d")
2603
2604 // - P(ab) t^b_k g^ak_cd:
2605 // - t^b_k g^ak_cd
2606 - t1("b,k") * g_abci("c,d,a,k")
2607 // - t^a_k g^kb_cd
2608 - t1("a,k") * g_abci("d,c,b,k")
2609
2610
2611 // + 1/4 tau^ab_kl g^kl_cd
2612 + 0.5 * tau_ab("a,b,k,l") * g_abij("c,d,k,l")
2613 ;
2614
2615 // \tilde{W}mnij
2616 TW_KlIj_ab("k,l,i,j") = // g^kl_ij
2617 g_ijkl("k,l,i,j")
2618
2619 // + P(ij) t^c_j g^kl_ic:
2620 // + t^c_j g^kl_ic
2621 + t1("c,j") * g_aikl("c,i,l,k")
2622 // + t^e_i g^mn_ej
2623 + t1("c,i") * g_aikl("c,j,k,l")
2624
2625
2626 // + 0.25 * tau^cd_ij * g^kl_cd
2627 + 0.5 * tau_ab("c,d,i,j") * g_abij("c,d,k,l")
2628 ;
2629 }
2630
2631 // compute intermediates for lambda amplitudes
2632 template <typename T>
2633 void SingleReference_R12Intermediates<T>::compute_intermediates_CW_ccsd(
2634 const TArray2& t1, const TArray4& t2,
2635 TArray2& CFkc, TArray2& CFac, TArray2& CFki,
2636 TArray4& CW_KbCj_ab, TArray4& CW_KbcJ_ba,
2637 TArray4& CW_AbCd_ab, TArray4& CW_AbCi_ab,
2638 TArray4& CW_KlIj_ab, TArray4& CW_KbIj_ab,
2639 TArray4& CW_KlIc_ab, TArray4& CW_KliC_ab,
2640 TArray4& CW_AkCd_ab) {
2641
2642 TArray4 tau_ab, Ttau_ab;
2643 tau_ab("a,b,i,j") = t2("a,b,i,j") + (t1("a,i") * t1("b,j"));
2644
2645 Ttau_ab("a,b,i,j") = t2("a,b,i,j") + 0.5 * t1("a,i") * t1("b,j");
2646
2647 TArray4d g_abij = ijxy("<a b|g|i j>");
2648 TArray4d g_abci = ijxy("<a b|g|c i>");
2649 TArray4d g_aikl = ijxy("<a i|g|k l>");
2650 TArray4d g_aibj = ijxy("<a i|g|b j>");
2651 TArray4d g_aijb = ijxy("<a i|g|j b>");
2652 TArray4d g_ijkl = ijxy("<i j|g|k l>");
2653 TArray4d g_abcd = ijxy("<a b|g|c d>");
2654
2655 // compute intermediates
2656 TArray2 TFkc, TFac, TFki;
2657 TArray4 TW_KbCj_ab,
2659 TW_KbcJ_ba,
2660 TW_AbCd_ab, TW_KlIj_ab;
2661
2662 compute_intermediates_TFW_ccsd(t1, t2,
2663 g_abij, g_aikl,
2664 g_aibj, g_aijb, g_abci,
2665 g_ijkl, g_abcd,
2666 TFkc, TFac, TFki,
2667 TW_KbCj_ab, TW_KbcJ_ba,
2668 TW_AbCd_ab, TW_KlIj_ab);
2669
2670 // \cal{F}
2671 CFkc("k,c") = TFkc("k,c");
2672 CFac("a,c") = TFac("a,c") - 0.5 * t1("a,k") * TFkc("k,c");
2673 CFki("k,i") = TFki("k,i") + 0.5 * t1("c,i") * TFkc("k,c");
2674
2675 // \cal{W}mbej
2676 CW_KbCj_ab("k,b,c,j") = // \tilde{W}kbcj
2677 TW_KbCj_ab("k,b,c,j")
2678
2679 // - 1/2 t^db_jl g^kn_cd = + 1/2 t^db_lj g^kl_cd
2680 + 0.5 * (t2("d,b,l,j") - t2("b,d,l,j"))
2681 * g_abij("c,d,k,l")
2682 + 0.5 * t2("d,b,l,j")
2683 * (g_abij("c,d,k,l") - g_abij("d,c,k,l"))
2684 ;
2685
2686 CW_KbcJ_ba("k,b,c,j") = // \tilde{W}kbcj
2687 TW_KbcJ_ba("k,b,c,j")
2688
2689 // - 1/2 t^db_jl g^kn_cd = + 1/2 t^db_lj g^kl_cd
2690 + 0.5 * t2("b,d,l,j") * g_abij("d,c,k,l")
2691 ;
2692
2693 // \cal{W}abef
2694 CW_AbCd_ab("a,b,c,d") = // \tilde{W}abcd
2695 TW_AbCd_ab("a,b,c,d")
2696
2697
2698 // + 1/4 tau^ab_kl g^kl_cd
2699 + 0.5 * tau_ab("a,b,k,l") * g_abij("c,d,k,l");
2700
2701 TArray4 t2_temp;
2702 t2_temp("a,b,i,j") = 2.0 * t2("a,b,i,j") - t2("a,b,j,i");
2703 // \cal{W}abei
2704 CW_AbCi_ab("a,b,c,i") = // g^ab_ci
2705 g_abci("a,b,c,i")
2706
2707 // - \cal{F}kc t^ab_ki
2708 - CFkc("k,c") * t2("a,b,k,i")
2709
2710 // + t^d_i \cal{W}abcd
2711 + t1("d,i") * CW_AbCd_ab("a,b,c,d")
2712
2713
2714 // + 1/2 g^kl_ci tau^ab_kl
2715 + g_aikl("c,i,k,l") * tau_ab("a,b,k,l")
2716
2717
2718 // - P(ab) g^kb_cd t^ad_ki:
2719 // - g^kb_cd t^ad_ki
2720 - g_abci("d,c,b,k") * t2("a,d,k,i")
2721 // + g^ka_cd t^bd_ki = + g^ak_cd t^db_ki
2722 + ( g_abci("c,d,a,k") * t2_temp("b,d,i,k")
2723 - g_abci("d,c,a,k") * t2("b,d,i,k"))
2724
2725 // - P(ab) t^a_k (g^kb_ci - t^bd_li g^kl_cd):
2726 // - t^a_k (g^kb_ci - t^bd_li g^kl_cd) = - t^a_k (g^kb_ci + t^db_li g^kl_cd)
2727 - t1("a,k")
2728 * ( g_aijb("b,k,i,c")
2730 + ( t2_temp("d,b,l,i") * g_abij("c,d,k,l")
2731 - t2("d,b,l,i") * g_abij("d,c,k,l"))
2732 )
2733 // + t^b_k (g^ka_ci - t^ad_li g^kl_cd) = + t^b_k (- g^ak_ci + t^ad_li g^lk_cd)
2734 + t1("b,k")
2735 * (- g_aibj("a,k,c,i")
2737 + t2("a,d,l,i") * g_abij("c,d,l,k")
2738 )
2739 ;
2740
2741 // \cal{W}mnij
2742 CW_KlIj_ab("k,l,i,j") = // \tilde{W}klij
2743 TW_KlIj_ab("k,l,i,j")
2745 // + 1/4 tau^cd_ij g^kl_cd
2746 + 0.5 * tau_ab("c,d,i,j") * g_abij("c,d,k,l")
2747 ;
2748
2749 // \cal{W}mbij
2750 CW_KbIj_ab("k,b,i,j") = // g^kb_ij
2751 g_aikl("b,k,j,i")
2752
2753 // - \cal{F}kc t^bc_ij = + CFkc t^cb_ij
2754 + CFkc("k,c") * t2("c,b,i,j")
2755
2756 // - t^b_l \cal{W}klij
2757 - t1("b,l") * CW_KlIj_ab("k,l,i,j")
2758
2759
2760 // + 0.5 g^kb_cd tau^cd_ij
2761 + g_abci("d,c,b,k") * tau_ab("c,d,i,j")
2762
2763
2764 // + P(ij) g^kl_ic t^bc_jl
2765 // + g^kl_ic t^bc_jl
2766 + g_aikl("c,i,l,k") * t2_temp("b,c,j,l")
2767 - g_aikl("c,i,k,l") * t2("b,c,j,l")
2768 // - g^kl_jc t^bc_il = - g^lk_jc t^cb_il
2769 - g_aikl("c,j,k,l") * t2("c,b,i,l")
2770
2771 // + P(IJ) t^c_i (g^kb_cj - t^bd_lj g^kl_cd)
2772 // + t^c_i (g^kb_cj - t^bd_lj g^kl_cd) = + t^c_i (g^kb_cj + t^bd_jl g^kl_cd)
2773 + t1("c,i")
2774 * ( g_aijb("c,j,k,b")
2776 + t2_temp("b,d,j,l") * g_abij("c,d,k,l")
2777 - t2("b,d,j,l") * g_abij("d,c,k,l")
2778 )
2779 // - t^c_j (g^kb_ci - t^bd_li g^kl_cd) = - t^c_j (- g^kb_ic + t^bd_li g^kl_dc)
2780 - t1("c,j")
2781 * (- g_aibj("c,i,b,k")
2783 + t2("b,d,l,i") * g_abij("d,c,k,l")
2784 )
2785 ;
2786
2787 // CCSD only term: CW_MNIE_ab
2788 CW_KlIc_ab("k,l,i,c") = // g^kl_ic
2789 g_aikl("c,i,l,k")
2790 // + t^d_i g^kl_dc
2791 + t1("d,i") * g_abij("d,c,k,l")
2792 ;
2793 CW_KliC_ab("k,l,i,c") = // g^kl_ic
2794 - g_aikl("c,i,k,l")
2795 // + t^d_i g^kl_dc
2796 - t1("d,i") * g_abij("d,c,l,k")
2797 ;
2798
2799 // CCSD only term: CW_AMEF_aa
2800 CW_AkCd_ab("a,k,c,d") = // g^ak_cd
2801 g_abci("c,d,a,k")
2802 // - t^a_l g^lk_cd
2803 - t1("a,l") * g_abij("c,d,l,k")
2804 ;
2805
2806 }
2807
2808 // compute T1 & T2 amplitudes of CCSD
2809 template <typename T>
2810 void SingleReference_R12Intermediates<T>::compute_T_ccsd(TArray2& t1, TArray4& t2,
2811 const std::string method) {
2812
2813 // compute Delta_ai = 1 / (- <a|F|a> + <i|F|i>)
2814 // & Delta_ijab = 1 / (- <a|F|a> - <b|F|b> + <i|F|i> + <j|F|j>)
2815 TArray2 fai = xy("<a|F|i>");
2816 TArray4d g_abij = ijxy("<a b|g|i j>");
2817
2818 TArray2 Delta_ai;
2819 TArray4 Delta_abij;
2820 compute_Delta_cc(fai.trange(), g_abij.trange(), Delta_ai, Delta_abij);
2821
2822 // compute initial T1 & T2 amplitudes and energy
2823 t1("a,i") = fai("a,i") * Delta_ai("a,i");
2824 t2("a,b,i,j") = g_abij("a,b,i,j") * Delta_abij("a,b,i,j");
2825
2826 TArray2 T1_f12contri;
2827 TArray4 T2_f12contri,
2828 T2_f12contri_T1, V_KLAJ_temp, V_IJKL_temp; // F12 contributions involing T1
2829 if (method == "f12b" || method == "F12b") {
2830 const double C_0 = 1.0 / 2.0;
2831 const double C_1 = 1.0 / 4.0;
2832 const double RC1 = 0.5 * (C_0 + C_1);
2833 const double RC2 = 0.5 * (C_0 - C_1);
2834
2835 const char* i = "i";
2836 const char* j = "j";
2837 const char* k = "k";
2838 const char* l = "l";
2839 const char* a = "a";
2840 const char* b = "b";
2841
2842 // F12 contributions to amplitude equations
2843 //
2844 // contributions to T1 equation
2845 TArray2 Via = VRk_Sk(i, a, C_0, C_1);
2846 T1_f12contri("a,i") = Delta_ai("a,i") * Via("i,a"); // 1/2 R^ik_AB g^AB_ak
2847 t1("a,i") = t1("a,i") + T1_f12contri("a,i");
2848
2849 // contributions to T2 equation
2850 TArray4d r_ijaFb = ijxy("<i j|r|a_F(c') b>");
2851 TArray4 V_IJAB = VPQ_RS(i, j, a, b);
2852 T2_f12contri("a,b,i,j") = Delta_abij("a,b,i,j") * (
2853 // F^a'_a R^ij_a'b + F^a'_b R^ij_aa'
2854 RC1 * r_ijaFb("i,j,a,b") + RC2 * r_ijaFb("j,i,a,b")
2855 + RC1 * r_ijaFb("j,i,b,a") + RC2 * r_ijaFb("i,j,b,a")
2856 // + 1/2 R^ij_AB g^AB_ab
2857 + RC1 * V_IJAB("i,j,a,b") + RC2 * V_IJAB("j,i,a,b")
2858 );
2859 // compute terms needed for constructing contributions that depends on T amplitudes
2860 // - 1/2 R^ij_AB g^AB_ak t^k_b - 1/2 R^ij_AB g^AB_kb t^k_a
2861 // + 1/2 R^ij_AB g^AB_kl t^k_a t^l_b
2862 TArray4 V_KLAJ = VPQ_RS(k, l, a, j);
2863 TArray4 V_IJKL = VPQ_RS(i, j, k, l);
2864 V_KLAJ_temp("i,j,a,k") = RC1 * V_KLAJ("i,j,a,k") + RC2 * V_KLAJ("j,i,a,k");
2865 V_IJKL_temp("i,j,k,l") = RC1 * V_IJKL("i,j,k,l") + RC2 * V_IJKL("j,i,k,l");
2866
2867 t2("a,b,i,j") = t2("a,b,i,j")
2868 + T2_f12contri("a,b,i,j")
2869 ;
2870 }
2871
2872 TArray4 tau_ab;
2873 tau_ab("a,b,i,j") = t2("a,b,i,j") + t1("a,i") * t1("b,j");
2874
2875 TArray4 gabij_temp;
2876 gabij_temp("a,b,i,j") = 2.0 * g_abij("a,b,i,j") - g_abij("b,a,i,j");
2877
2878 double E_0 = 0.0;
2879 double E_1 = //2.0 * dot(fai("a,i"), t1("a,i")) +
2880 dot(gabij_temp("a,b,i,j"), tau_ab("a,b,i,j") );
2881 double Delta_E = std::abs(E_0 - E_1);
2882
2883 double iter = 0;
2884 std::cout << indent << scprintf("%-5s", "Iter") << scprintf("%-20s", "Delta_E")
2885 << scprintf("%-20s", "E(CCSD)") << std::endl;
2886 std::cout << indent << scprintf("%-5.0f", iter) << scprintf("%-15.12f", Delta_E)
2887 << scprintf("%-15.12f", E_1) << std::endl;
2888
2889 TArray2 TFkc, TFac, TFki;
2890 TArray4 TW_KbCj_ab,
2892 TW_KbcJ_ba,
2893 TW_AbCd_ab, TW_KlIj_ab;
2894
2895 TArray4d g_aikl = ijxy("<a i|g|k l>");
2896 TArray4d g_aibj = ijxy("<a i|g|b j>");
2897 TArray4d g_aijb = ijxy("<a i|g|j b>");
2898 TArray4d g_abci = ijxy("<a b|g|c i>");
2899 TArray4d g_ijkl = ijxy("<i j|g|k l>");
2900 TArray4d g_abcd = ijxy("<a b|g|c d>");
2901
2902 TArray4 t2_unsymm, t2_interim;
2903
2904 while (Delta_E >= 1.0e-12) {
2905 // compute intermediates
2906 compute_intermediates_TFW_ccsd(t1, t2,
2907 g_abij, g_aikl,
2908 g_aibj, g_aijb, g_abci,
2909 g_ijkl, g_abcd,
2910 TFkc, TFac, TFki,
2911 TW_KbCj_ab, TW_KbcJ_ba,
2912 TW_AbCd_ab, TW_KlIj_ab);
2913
2914 t2_interim("a,b,i,j") = 2.0 * t2("a,b,i,j") - t2("b,a,i,j");
2915
2916 auto t1_temp = Delta_ai("a,i") * (
2917 // fai
2918 //fai("a,i")
2919 // + TFac t^c_i
2920 TFac("a,c") * t1("c,i")
2921 // - TFki t^a_k
2922 - TFki("k,i") * t1("a,k")
2923 // + TFkc t^ac_ik
2924 + TFkc("k,c") * t2_interim("a,c,i,k")
2925 // + t^c_k g^ak_ic
2926 + t1("c,k") * (2.0 * g_aijb("a,k,i,c") - g_aibj("a,k,c,i"))
2927 // - 1/2 t^ac_kl g^kl_ic
2928 - t2_interim("c,a,k,l") * g_aikl("c,i,k,l")
2929 // + 1/2 t^cd_ik g^ak_cd
2930 + t2_interim("c,d,i,k") * g_abci("c,d,a,k")
2931 );
2932
2933 auto t2_temp = Delta_abij("a,b,i,j") * (
2934 // g^ab_ij
2935 g_abij("a,b,i,j")
2936
2937 // + P_(ab) t^ac_ij (TFbc - 1/2 t^b_k TFkc)
2938 + t2("a,c,i,j") * (TFac("b,c") - 0.5 * t1("b,k") * TFkc("k,c"))
2939 + t2("c,b,i,j") * (TFac("a,c") - 0.5 * t1("a,k") * TFkc("k,c"))
2940
2941 // - P_(ij) T^ab_ik (TFkj + 1/2 t^c_j TFkc)
2942 - t2("a,b,i,k") * (TFki("k,j") + 0.5 * t1("c,j") * TFkc("k,c"))
2943 - t2("a,b,k,j") * (TFki("k,i") + 0.5 * t1("c,i") * TFkc("k,c"))
2944
2945 // + 1/2 tau^ab_kl TW_klij
2946 + tau_ab("a,b,k,l") * TW_KlIj_ab("k,l,i,j")
2947
2948 // + 1/2 tau^cd_ij TW_abcd
2949 + tau_ab("c,d,i,j") * TW_AbCd_ab("a,b,c,d")
2950
2951 // + P_(ij) P_(ab) (t^ac_ik TW_kbcj - t^c_i t^a_k g^kb_cj)
2952 + ( t2("a,c,i,k") * TW_KbcJ_ba("k,b,c,j")
2953 + t2_interim("a,c,i,k") * TW_KbCj_ab("k,b,c,j")
2954 //
2955 - t1("c,i") * (t1("a,k") * g_aijb("b,k,j,c"))
2956 )
2957 // - P(ab)
2958 - (- t2("c,b,i,k") * TW_KbcJ_ba("k,a,c,j") // TW_kBCj_ba => TW_KbcJ_ba
2959 + t1("c,i") * (t1("b,k") * g_aibj("a,k,c,j"))
2960 )
2961 // - P(ij)
2962 - (- t2("a,c,k,j") * TW_KbcJ_ba("k,b,c,i")
2963 + t1("c,j") * (t1("a,k") * g_aibj("b,k,c,i"))
2964 )
2965 // + P_(ij) P_(ab)
2966 + ( t2("b,c,j,k") * TW_KbcJ_ba("k,a,c,i")
2967 + t2_interim("b,c,j,k") * TW_KbCj_ab("k,a,c,i")
2968 //
2969 - t1("c,j") * (t1("b,k") * g_aijb("a,k,i,c"))
2970 )
2971
2972 // + P(ij) t^c_i g^ab_cj
2973 + t1("c,i") * g_abci("a,b,c,j")
2974 + t1("c,j") * g_abci("b,a,c,i")
2975
2976 // - P(ab) t^a_k g^kb_ij
2977 - t1("a,k") * g_aikl("b,k,j,i")
2978 - t1("b,k") * g_aikl("a,k,i,j")
2979 );
2980
2981 if (method == "f12b" || method == "F12b") {
2982 t1("a,i") = t1_temp
2983 + T1_f12contri("a,i")
2984 ;
2985
2986 // recompute F12 contributions to T2 which depend on T amplitudes
2987 T2_f12contri_T1("a,b,i,j") = Delta_abij("a,b,i,j") * (
2988 // - 1/2 R^ij_AB g^AB_ak t^k_b - 1/2 R^ij_AB g^AB_kb t^k_a
2989 - V_KLAJ_temp("i,j,a,k") * t1("b,k")
2990 - V_KLAJ_temp("j,i,b,k") * t1("a,k")
2991 // + 1/2 R^ij_AB g^AB_kl t^k_a t^l_b
2992 + V_IJKL_temp("i,j,k,l") * t1("a,k") * t1("b,l")
2993 );
2994
2995 t2_unsymm("a,b,i,j") = t2_temp
2996 + T2_f12contri("a,b,i,j")
2997 + T2_f12contri_T1("a,b,i,j")
2998 ;
2999 } else {
3000 t1("a,i") = t1_temp;
3001 t2_unsymm("a,b,i,j") = t2_temp;
3002 }
3003
3004 t2("a,b,i,j") = 0.5 * (t2_unsymm("a,b,i,j") + t2_unsymm("b,a,j,i"));
3005 tau_ab("a,b,i,j") = t2("a,b,i,j") + t1("a,i") * t1("b,j");
3006
3007 // recompute energy
3008 E_0 = E_1;
3009 E_1 = //2.0 * dot(fai("a,i"), t1("a,i")) +
3010 dot(gabij_temp("a,b,i,j"), tau_ab("a,b,i,j") );
3011 Delta_E = std::abs(E_0 - E_1);
3012 iter += 1;
3013 std::cout << indent << scprintf("%-5.0f", iter) << scprintf("%-15.12f", Delta_E)
3014 << scprintf("%-15.12f", E_1) << std::endl;
3015 }
3016 //std::cout << "CCSD T1 amplitudes: " << std::endl << t1 << std::endl;
3017
3018 }
3019
3020 template <typename T>
3021 void SingleReference_R12Intermediates<T>::compute_lambda_ccsd(const TArray2& t1, const TArray4& t2,
3022 TArray2& L1, TArray4& L2,
3023 const std::string method) {
3024
3025 TArray4d g_abij = ijxy("<a b|g|i j>");
3026 TArray4d g_abci = ijxy("<a b|g|c i>");
3027 TArray2 fai = xy("<a|F|i>");
3028
3029 // compute Delta_ai = 1 / (- <a|F|a> + <i|F|i>)
3030 // & Delta_ijab = 1 / (- <a|F|a> - <b|F|b> + <i|F|i> + <j|F|j>)
3031 TArray2 Delta_ai;
3032 TArray4 Delta_abij;
3033 compute_Delta_cc(fai.trange(), g_abij.trange(), Delta_ai, Delta_abij);
3034
3035 // initial guess for L1 and L2
3036 TArray2 L1_f12contri, L1_f12b, L1_f12b_L2;
3037 TArray4 L2_f12contri, Vijab, Vklib, Vklij;
3038 if (method == "ccsd" || method == "CCSD") {
3039 L1("a,i") = t1("a,i");
3040 L2("a,b,i,j") = t2("a,b,i,j");
3041
3042 } else {
3043 const double C_0 = 1.0 / 2.0;
3044 const double C_1 = 1.0 / 4.0;
3045 const double RC1 = 0.5 * (C_0 + C_1);
3046 const double RC2 = 0.5 * (C_0 - C_1);
3047
3048 TArray2 V_ia;
3049 const char* i = "i";
3050 const char* a = "a";
3051 V_ia = VRk_Sk(i,a, C_0, C_1);
3052
3053 L1_f12contri("a,i") = Delta_ai("a,i") * V_ia("i,a");
3054
3055 TArray4 rg_ijab;
3056 TArray4d r_ijaPn = ijxy("<i j|r|a' n>");
3057 TArray4d g_aPnab = ijxy("<a' n|g|a b>");
3058 rg_ijab("i,j,a,b") = _4("<i j|gr|a b>")
3059 - _4("<i j|r|p q>") * _4("<p q|g|a b>")
3060 - r_ijaPn("i,j,a',n") * g_aPnab("a',n,a,b")
3061 - r_ijaPn("j,i,a',n") * g_aPnab("a',n,b,a");
3062
3063 TArray4d r_ijaFb = ijxy("<i j|r|a_F(c') b>");
3064
3065 L2_f12contri("a,b,i,j") = Delta_abij("a,b,i,j")
3066 * ( RC1 * r_ijaFb("i,j,a,b") + RC2 * r_ijaFb("j,i,a,b")
3067 + RC1 * r_ijaFb("j,i,b,a") + RC2 * r_ijaFb("i,j,b,a")
3068 + RC1 * rg_ijab("i,j,a,b") + RC2 * rg_ijab("j,i,a,b")
3069 );
3070
3071 if (method == "f12" || method == "F12") {
3072 L1("a,i") = t1("a,i") + L1_f12contri("a,i") * 2.0;
3073 L2("a,b,i,j") = t2("a,b,i,j") + L2_f12contri("a,b,i,j") * 2.0;
3074
3075 } else if (method == "f12b" || method == "F12b") {
3076
3077 // contributions to L1 equation
3078 const char* j = "j";
3079 const char* k = "k";
3080 const char* l = "l";
3081 const char* b = "b";
3082
3083 // 1st contribution
3084 Vijab = VPq_Rs(i, j, a, b, C_0, C_1);
3085 L1_f12b("a,i") = Delta_ai("a,i")
3086 * (Vijab("i,j,a,b") * t1("b,j")); // 1/2 R_ij^AB g_AB^ab t^j_b
3087
3088 // 2nd contribution that depends on L2 amplitudes
3089 Vklib = VPq_Rs(k, l, i, b, C_0, C_1);
3090 Vklij = VPq_Rs(k, l, i, j, C_0, C_1);
3091 //TArray4 V_KLAJ = VPQ_RS(k, l, a, j);
3092 //TArray4 V_IJKL = VPQ_RS(i, j, k, l);
3093// L1_f12b_L2("a,i") = Delta_ai("a,i") * (
3094// // - 1/4 l^ab_kl R^kl_AB g^AB_ib
3095// - Vklib("k,l,i,b") * L2("a,b,k,l")
3096//
3097// // + 1/4 l^ab_kl R^kl_AB g^AB_ij t^j_b
3098// + Vklij("k,l,i,j") * L2("a,b,k,l") * t1("b,j")
3099// );
3100
3101 L1("a,i") = t1("a,i")
3102 + L1_f12contri("a,i")
3103 + L1_f12b("a,i")// + L1_f12b_L2("a,i")
3104 ;
3105 L2("a,b,i,j") = t2("a,b,i,j")
3106 + L2_f12contri("a,b,i,j")
3107 ;
3108 }
3109 }
3110
3111 TArray4 gabij_temp;
3112 gabij_temp("a,b,i,j") = 2.0 * g_abij("a,b,i,j") - g_abij("b,a,i,j");
3113
3114 // pseudo energy
3115 double E_0_L = 0.0;
3116 double E_1_L = dot(gabij_temp("a,b,i,j"), L2("a,b,i,j") );
3117 double Delta_E_L = std::abs(E_0_L - E_1_L);
3118
3119 double iter = 0;
3120 std::cout << indent << scprintf("%-5s", "Iter") << scprintf("%-20s", "Delta_E_L")
3121 << scprintf("%-20s", "E_L(CCSD)") << std::endl;
3122 std::cout << indent << scprintf("%-5.0f", iter) << scprintf("%-15.12f", Delta_E_L)
3123 << scprintf("%-15.12f", E_1_L) << std::endl;
3124
3125 // compute intermediates
3126 TArray2 CFkc, CFac, CFki;
3127 // \cal{W}mbej
3128 TArray4 CW_KbCj_ab,
3130 CW_KbcJ_ba,
3131 // \cal{W}abei
3132 CW_AbCd_ab, CW_AbCi_ab,
3133 // \cal{W}mbij
3134 CW_KlIj_ab, CW_KbIj_ab,
3135 // intermediates for L2
3136 CW_KlIc_ab, CW_KliC_ab, CW_AkCd_ab;
3137
3138 compute_intermediates_CW_ccsd(t1, t2, CFkc, CFac, CFki,
3139 CW_KbCj_ab, CW_KbcJ_ba,
3140 CW_AbCd_ab, CW_AbCi_ab,
3141 CW_KlIj_ab, CW_KbIj_ab,
3142 CW_KlIc_ab, CW_KliC_ab, CW_AkCd_ab);
3143
3144 TArray2 CGac, CGki;
3145
3146 TArray4 L2_unsymm, L2abij_temp;
3147
3148 while (Delta_E_L >= 1.0e-12) {
3149
3150 L2abij_temp("a,b,i,j") = 2.0 * L2("a,b,i,j") - L2("b,a,i,j");
3151
3152 CGac("a,c") = // - 1/2 t^cd_kl lambda^kl_ad
3153 - t2("c,d,k,l") * L2abij_temp("a,d,k,l");
3154 CGki("k,i") = // 1/2 t^cd_kl lambda^il_cd
3155 t2("c,d,k,l") * L2abij_temp("c,d,i,l");
3156
3157 auto L1_temp = Delta_ai("a,i") * (
3158 // \cal{F}ia
3159 CFkc("i,a")
3160 // + \lambda^i_c \cal{F}ca
3161 + L1("c,i") * CFac("c,a")
3162 // - \lambda^k_a \cal{F}ik
3163 - L1("a,k") * CFki("i,k")
3164 // + \lambda^k_c \cal{W}icak
3165 + L1("c,k") * (2.0 * CW_KbCj_ab("i,c,a,k") + CW_KbcJ_ba("i,c,a,k"))
3166 // + 1/2 \lambda^ik_cd \cal{W}cdak
3167 + L2abij_temp("c,d,i,k") * CW_AbCi_ab("c,d,a,k")
3168 // - 1/2 \lambda^kl_ac \cal{W}ickl
3169 - L2abij_temp("a,c,k,l") * CW_KbIj_ab("i,c,k,l")
3170
3171 // CCSD only terms:
3172 // - cal{G}cd cal{W}cida
3173 - CGac("c,d") * (2.0 * CW_AkCd_ab("c,i,d,a") - CW_AkCd_ab("c,i,a,d")) // CW_aKcD => CW_AkCd_ab
3174 // - cal{G}kl cal{W}kila
3175 - CGki("k,l") * (2.0 * CW_KlIc_ab("k,i,l,a") + CW_KliC_ab("k,i,l,a"))
3176 );
3177
3178 auto L2_temp = Delta_abij("a,b,i,j") * (
3179 // g^ij_ab
3180 g_abij("a,b,i,j")
3181
3182 // + P(ij) \lambda^i_c \cal{W}cjab
3183 + L1("c,i") * CW_AkCd_ab("c,j,a,b")
3184 + L1("c,j") * CW_AkCd_ab("c,i,b,a")
3185
3186 // - P(ab) \lambda^k_a \cal{W}ijkb
3187 - L1("a,k") * CW_KlIc_ab("i,j,k,b")
3188 + L1("b,k") * CW_KliC_ab("i,j,k,a")
3189
3190 // + P(ij) P(ab) \lambda^i_a \cal{F}jb
3191 + L1("a,i") * CFkc("j,b")
3192 //- L1("b,i") * CFkc("j,a")
3193 //- L1("a,j") * CFkc("i,b")
3194 + L1("b,j") * CFkc("i,a")
3195
3196 // CCSD term
3197 // + P(ab) \lambda^ij_ac \cal{F}cb
3198 + L2("a,c,i,j") * CFac("c,b")
3199 + L2("c,b,i,j") * CFac("c,a")
3200
3201 // CCSD term
3202 // - P(ij) \lambda^ik_ab \cal{F}jk
3203 - L2("a,b,i,k") * CFki("j,k")
3204 - L2("a,b,k,j") * CFki("i,k")
3205
3206
3207 // + 1/2 \lambda^kl_ab \cal{W}ijkl
3208 + L2("a,b,k,l") * CW_KlIj_ab("i,j,k,l")
3209
3210 // + 1/2 \lambda^ij_cd \cal{W}cdab
3211 + L2("c,d,i,j") * CW_AbCd_ab("c,d,a,b")
3212
3213 // + P(ij) P(ab) \lambda^ik_ac \cal{W}jcbk
3214 + ( L2abij_temp("a,c,i,k") * CW_KbCj_ab("j,c,b,k")
3215 + L2("a,c,i,k") * CW_KbcJ_ba("j,c,b,k")) // CW_kbcj => CW_KBCJ_aa
3216 // P(ab)
3217 + L2("c,b,i,k") * CW_KbcJ_ba("j,c,a,k") // CW_kBCj => CW_KbcJ_ab
3218 // P(ij)
3219 + L2("a,c,k,j") * CW_KbcJ_ba("i,c,b,k")
3220 // P(ij) P(ab)
3221 + ( L2abij_temp("b,c,j,k") * CW_KbCj_ab("i,c,a,k")
3222 + L2("b,c,j,k") * CW_KbcJ_ba("i,c,a,k"))
3223
3224 // + P(ab) g^ij_ac Gbc
3225 + g_abij("a,c,i,j") * CGac("b,c")
3226 + g_abij("c,b,i,j") * CGac("a,c")
3227
3228 // - P(ij) g^ik_ab Gkj
3229 - g_abij("a,b,i,k") * CGki("k,j")
3230 - g_abij("a,b,k,j") * CGki("k,i")
3231 );
3232
3233 if (method == "ccsd" || method == "CCSD") {
3234 L1("a,i") = L1_temp;
3235 L2_unsymm("a,b,i,j") = L2_temp;
3236
3237 } else if (method == "f12" || method == "F12") {
3238 L1("a,i") = L1_temp + L1_f12contri("a,i") * 2.0;
3239 L2_unsymm("a,b,i,j") = L2_temp + L2_f12contri("a,b,i,j") * 2.0;
3240
3241 } else if (method == "f12b" || method == "F12b") {
3242
3243 L1_f12b_L2("a,i") = Delta_ai("a,i") * (
3244 // - 1/4 l^ab_kl R^kl_AB g^AB_ib
3245 - Vklib("k,l,i,b") * L2("a,b,k,l")
3246
3247 // + 1/4 l^ab_kl R^kl_AB g^AB_ij t^j_b
3248 + Vklij("k,l,i,j") * L2("a,b,k,l") * t1("b,j")
3249 );
3250
3251 L1("a,i") = L1_temp
3252 + L1_f12contri("a,i")
3253 + L1_f12b("a,i") + L1_f12b_L2("a,i")
3254 ;
3255 L2_unsymm("a,b,i,j") = L2_temp
3256 + L2_f12contri("a,b,i,j")
3257 ;
3258
3259 }
3260
3261 L2("a,b,i,j") = 0.5 * (L2_unsymm("a,b,i,j") + L2_unsymm("b,a,j,i"));
3262
3263 E_0_L = E_1_L;
3264 E_1_L = dot(gabij_temp("a,b,i,j"), L2("a,b,i,j") );
3265 Delta_E_L = std::abs(E_0_L - E_1_L);
3266
3267 iter += 1;
3268 std::cout << indent << scprintf("%-5.0f", iter) << scprintf("%-15.12f", Delta_E_L)
3269 << scprintf("%-15.12f", E_1_L) << std::endl;
3270 }
3271 //std::cout << "CC2 L1 amplitudes: " << std::endl << L1 << std::endl;
3272 }
3273
3274 // compute intermediates for CCSD Xam (Xai)
3275 template <typename T>
3276 void SingleReference_R12Intermediates<T>::compute_Gamma_ijab_ccsd(const TArray2& T1, const TArray4& T2,
3277 const TArray4& tau_ab,
3278 const TArray2& L1, const TArray4& L2,
3279 TArray4& Gamma_IjAb_ab) {
3280// // i,j,a,b in alpha or beta space
3281// Gamma_IJAB_aa("i,j,a,b") = // 1/4 tau^ab_ij
3282// 0.25 * tau_aa("a,b,i,j")
3283//
3284// // CCSD modified term
3285// // + 1/16 tau^cd_ij lambda^kl_cd tau^ab_kl
3286// + 0.0625 * tau_aa("c,d,i,j")
3287// * (L2("c,d,k,l") - L2("c,d,l,k"))
3288// * tau_aa("a,b,k,l")
3289//
3290// // CCSD terms only
3291// // - 1/8 P-(ij) t^cd_il lambda^kl_cd tau^ab_kj
3292// - 0.125 * (T2("c,d,i,l") - T2("c,d,l,i"))
3293// * (L2("c,d,k,l") - L2("c,d,l,k")) * tau_aa("a,b,k,j")
3294// - 0.25 * T2("c,d,i,l") * L2("c,d,k,l") * tau_aa("a,b,k,j")
3295// // - P(ij)
3296// + 0.125 * (T2("c,d,j,l") - T2("c,d,l,j"))
3297// * (L2("c,d,k,l") - L2("c,d,l,k")) * tau_aa("a,b,k,i")
3298// + 0.25 * T2("c,d,j,l") * L2("c,d,k,l") * tau_aa("a,b,k,i")
3299//
3300//
3301// // - 1/4 P-(ij) t^c_i lambda^k_c tau^ab_kj
3302// - 0.25 * ( T1("c,i") * tau_aa("a,b,k,j")
3303// - T1("c,j") * tau_aa("a,b,k,i")
3304// ) * L1("c,k")
3305//
3306// // CCSD only term
3307// // - 1/8 P-(ab) t^ad_kl lambda^kl_cd tau^cb_ij
3308// - 0.125 * (T2("a,d,k,l") - T2("d,a,k,l"))
3309// * (L2("c,d,k,l") - L2("c,d,l,k")) * tau_aa("c,b,i,j")
3310// - 0.25 * T2("a,d,k,l") * L2("c,d,k,l") * tau_aa("c,b,i,j")
3311// // - P(ab)
3312// + 0.125 * (T2("b,d,k,l") - T2("d,b,k,l"))
3313// * (L2("c,d,k,l") - L2("c,d,l,k")) * tau_aa("c,a,i,j")
3314// + 0.25 * T2("b,d,k,l") * L2("c,d,k,l") * tau_aa("c,a,i,j")
3315//
3316// // - 1/4 P-(ab) t^a_k lambda^k_c tau^cb_ij
3317// - 0.25 * ( T1("a,k") * tau_aa("c,b,i,j")
3318// - T1("b,k") * tau_aa("c,a,i,j")
3319// ) * L1("c,k")
3320//
3321// // CCSD only term
3322// // - 1/8 P-(ij) P-(ab) (t^ac_ki + 2 t^c_i t^a_k) lambda^kl_cd t^bd_jl
3323// // + 1/8 P-(ij) P-(ab) t^ac_ik lambda^kl_cd t^bd_jl
3324// + 0.125 * ( (T2("a,c,i,k") - T2("c,a,i,k"))
3325// * (L2("c,d,k,l") - L2("d,c,k,l"))
3326// * (T2("b,d,j,l") - T2("d,b,j,l"))
3327// + (T2("a,c,i,k") - T2("c,a,i,k")) * L2("c,d,k,l") * T2("b,d,j,l")
3328// + T2("a,c,i,k") * (L2("c,d,k,l") - L2("d,c,k,l")) * T2("b,d,j,l")
3329// + T2("a,c,i,k") * L2("c,d,k,l") * (T2("b,d,j,l") - T2("d,b,j,l"))
3330//
3331// // P(ab)
3332// - (T2("b,c,i,k") - T2("c,b,i,k"))
3333// * (L2("c,d,k,l") - L2("d,c,k,l"))
3334// * (T2("a,d,j,l") - T2("d,a,j,l"))
3335// - (T2("b,c,i,k") - T2("c,b,i,k")) * L2("c,d,k,l") * T2("a,d,j,l")
3336// - T2("b,c,i,k") * (L2("c,d,k,l") - L2("d,c,k,l")) * T2("a,d,j,l")
3337// - T2("b,c,i,k") * L2("c,d,k,l") * (T2("a,d,j,l") - T2("d,a,j,l"))
3338//
3339// // P(ij)
3340// - (T2("a,c,j,k") - T2("c,a,j,k"))
3341// * (L2("c,d,k,l") - L2("d,c,k,l"))
3342// * (T2("b,d,i,l") - T2("d,b,i,l"))
3343// - (T2("a,c,j,k") - T2("c,a,j,k")) * L2("c,d,k,l") * T2("b,d,i,l")
3344// - T2("a,c,j,k") * (L2("c,d,k,l") - L2("d,c,k,l")) * T2("b,d,i,l")
3345// - T2("a,c,j,k") * L2("c,d,k,l") * (T2("b,d,i,l") - T2("d,b,i,l"))
3346//
3347// // P(ij)P(ab)
3348// + (T2("b,c,j,k") - T2("c,b,j,k"))
3349// * (L2("c,d,k,l") - L2("d,c,k,l"))
3350// * (T2("a,d,i,l") - T2("d,a,i,l"))
3351// + (T2("b,c,j,k") - T2("c,b,j,k")) * L2("c,d,k,l") * T2("a,d,i,l")
3352// + T2("b,c,j,k") * (L2("c,d,k,l") - L2("d,c,k,l")) * T2("a,d,i,l")
3353// + T2("b,c,j,k") * L2("c,d,k,l") * (T2("a,d,i,l") - T2("d,a,i,l"))
3354// )
3355// // - 1/4 P-(ij) P-(ab) t^c_i t^a_k lambda^kl_cd t^bd_jl
3356// - 0.25 * ( ( T1("c,i") * T1("a,k") * (T2("b,d,j,l") - T2("d,b,j,l"))
3357// - T1("c,i") * T1("b,k") * (T2("a,d,j,l") - T2("d,a,j,l"))
3358// - T1("c,j") * T1("a,k") * (T2("b,d,i,l") - T2("d,b,i,l"))
3359// + T1("c,j") * T1("b,k") * (T2("a,d,i,l") - T2("d,a,i,l"))
3360// ) * (L2("c,d,k,l") - L2("d,c,k,l"))
3361//
3362// + ( T1("c,i") * T1("a,k") * T2("b,d,j,l")
3363// - T1("c,i") * T1("b,k") * T2("a,d,j,l")
3364// - T1("c,j") * T1("a,k") * T2("b,d,i,l")
3365// + T1("c,j") * T1("b,k") * T2("a,d,i,l")
3366// ) * L2("c,d,k,l")
3367// )
3368//
3369// // - 1/4 P-(ij) P-(ab) (t^ac_ki + 2 t^c_i t^a_k) lambda^k_c t^b_j
3370// // => - 1/4 P-(ij) P-(ab) (- t^ac_ik + 2 t^c_i t^a_k) t^b_j
3371// - 0.25 * ( (- 2.0 * T2("a,c,i,k") + T2("c,a,i,k")
3372// + 2.0 * T1("c,i") * T1("a,k")
3373// ) * T1("b,j")
3374// // P(ab)
3375// - (- 2.0 * T2("b,c,i,k") + T2("c,b,i,k")
3376// + 2.0 * T1("c,i") * T1("b,k")
3377// ) * T1("a,j")
3378// // P(ij)
3379// - (- 2.0 * T2("a,c,j,k") + T2("c,a,j,k")
3380// + 2.0 * T1("c,j") * T1("a,k")
3381// ) * T1("b,i")
3382// // P(ij) P(ab)
3383// + (- 2.0 * T2("b,c,j,k") + T2("c,b,j,k")
3384// + 2.0 * T1("c,j") * T1("b,k")
3385// ) * T1("a,i")
3386// ) * L1("c,k")
3387//
3388// // + 3/4 P-(ij) P-(ab) t^a_i t^c_j lambda^k_c t^b_k
3389// + 0.75 * ( T1("a,i") * T1("c,j") * T1("b,k")
3390// - T1("b,i") * T1("c,j") * T1("a,k")
3391// - T1("a,j") * T1("c,i") * T1("b,k")
3392// + T1("b,j") * T1("c,i") * T1("a,k")
3393// ) * L1("c,k")
3394//
3395// ;
3396
3397 // a,i in alpha space, b,j in beta space
3398 Gamma_IjAb_ab("i,j,a,b") = // 1/4 tau^ab_ij
3399 0.25 * tau_ab("a,b,i,j")
3400
3401 // CCSD modified term
3402 // + 1/16 tau^cd_ij lambda^kl_cd tau^ab_kl
3403 + 0.25 * tau_ab("c,d,i,j") * L2("c,d,k,l")
3404 * tau_ab("a,b,k,l")
3405
3406 // CCSD terms only
3407 // - 1/8 P-(ij) t^cd_il lambda^kl_cd tau^ab_kj
3408 - 0.125 * (T2("c,d,i,l") - T2("c,d,l,i"))
3409 * (L2("c,d,k,l") - L2("c,d,l,k")) * tau_ab("a,b,k,j")
3410 - 0.25 * T2("c,d,i,l") * L2("c,d,k,l") * tau_ab("a,b,k,j")
3411 // - P(ij)
3412 - 0.125 * (T2("c,d,j,l") - T2("c,d,l,j"))
3413 * (L2("c,d,k,l") - L2("c,d,l,k")) * tau_ab("a,b,i,k")
3414 - 0.25 * T2("c,d,j,l") * L2("c,d,k,l") * tau_ab("a,b,i,k")
3415
3416 // - 1/4 P-(ij) t^c_i lambda^k_c tau^ab_kj
3417 - 0.25 * ( T1("c,i") * tau_ab("a,b,k,j")
3418 + T1("c,j") * tau_ab("a,b,i,k")
3419 ) * L1("c,k")
3420
3421 // CCSD only term
3422 // - 1/8 P-(ab) t^ad_kl lambda^kl_cd tau^cb_ij
3423 - 0.125 * (T2("a,d,k,l") - T2("d,a,k,l"))
3424 * (L2("c,d,k,l") - L2("c,d,l,k")) * tau_ab("c,b,i,j")
3425 - 0.25 * T2("a,d,k,l") * L2("c,d,k,l") * tau_ab("c,b,i,j")
3426 // - P(ab)
3427 - 0.125 * (T2("b,d,k,l") - T2("d,b,k,l"))
3428 * (L2("c,d,k,l") - L2("c,d,l,k")) * tau_ab("a,c,i,j")
3429 - 0.25 * T2("b,d,k,l") * L2("c,d,k,l") * tau_ab("a,c,i,j")
3430
3431 // - 1/4 P-(ab) t^a_k lambda^k_c tau^cb_ij
3432 - 0.25 * ( T1("a,k") * tau_ab("c,b,i,j")
3433 + T1("b,k") * tau_ab("a,c,i,j")
3434 ) * L1("c,k")
3435
3436 // - 1/8 P-(ij) P-(ab) (t^ac_ki + 2 t^c_i t^a_k) lambda^kl_cd t^bd_jl
3437 // + 1/8 P-(ij) P-(ab) t^ac_ik lambda^kl_cd t^bd_jl
3438 + 0.125 * ( (T2("a,c,i,k") - T2("c,a,i,k"))
3439 * (L2("c,d,k,l") - L2("d,c,k,l")) * T2("b,d,j,l")
3440 + (T2("a,c,i,k") - T2("c,a,i,k"))
3441 * L2("c,d,k,l") * (T2("b,d,j,l") - T2("d,b,j,l"))
3442 + T2("a,c,i,k") * (L2("c,d,k,l") - L2("d,c,k,l"))
3443 * (T2("b,d,j,l") - T2("d,b,j,l"))
3444 + T2("a,c,i,k") * L2("c,d,k,l") * T2("b,d,j,l")
3445
3446 // P(ab)
3447 + T2("c,b,i,k") * L2("c,d,l,k") * T2("a,d,l,j")
3448
3449 // P(ij)
3450 + T2("a,c,k,j") * L2("d,c,k,l") * T2("d,b,i,l")
3451
3452 //P(ij)P(ab)
3453 + T2("b,c,j,k") * (L2("c,d,k,l") - L2("d,c,k,l"))
3454 * (T2("a,d,i,l") - T2("d,a,i,l"))
3455 + T2("b,c,j,k") * L2("c,d,k,l") * T2("a,d,i,l")
3456 + (T2("b,c,j,k") - T2("c,b,j,k"))
3457 * L2("c,d,k,l") * (T2("a,d,i,l") - T2("d,a,i,l"))
3458 + (T2("b,c,j,k") - T2("c,b,j,k"))
3459 * (L2("c,d,k,l") - L2("d,c,k,l"))
3460 * T2("a,d,i,l")
3461 )
3462 // - 1/4 P-(ij) P-(ab) t^c_i t^a_k lambda^kl_cd t^bd_jl
3463 - 0.25 * ( T1("c,i") * T1("a,k")
3464 * ( (L2("c,d,k,l") - L2("d,c,k,l")) * T2("b,d,j,l")
3465 + L2("c,d,k,l") * (T2("b,d,j,l") - T2("d,b,j,l"))
3466 )
3467 // P(ab)
3468 - T1("c,i") * T1("b,k") * L2("c,d,l,k") * T2("a,d,l,j")
3469 // P(ij)
3470 - T1("c,j") * T1("a,k") * L2("d,c,k,l") * T2("d,b,i,l")
3471 // P(ij) P(ab)
3472 + T1("c,j") * T1("b,k")
3473 * ( (L2("c,d,k,l") - L2("d,c,k,l")) * T2("a,d,i,l")
3474 + L2("c,d,k,l") * (T2("a,d,i,l") - T2("d,a,i,l"))
3475 )
3476 )
3477
3478 // - 1/4 P-(ij) P-(ab) (t^ac_ki + 2 t^c_i t^a_k) lambda^k_c t^b_j
3479 - 0.25 * ( (- 2.0 * T2("a,c,i,k") + T2("c,a,i,k")
3480 + 2.0 * T1("c,i") * T1("a,k")
3481 ) * T1("b,j")
3482 //
3483 + (- 2.0 * T2("b,c,j,k") + T2("c,b,j,k")
3484 + 2.0 * T1("c,j") * T1("b,k")
3485 ) * T1("a,i")
3486 ) * L1("c,k")
3487
3488 // + 3/4 P-(ij) P-(ab) t^a_i t^c_j lambda^k_c t^b_k
3489 + 0.75 * ( T1("a,i") * T1("c,j") * T1("b,k")
3490 + T1("b,j") * T1("c,i") * T1("a,k")
3491 ) * L1("c,k")
3492 ;
3493
3494 }
3495
3496 // compute Gamma intermediates following JCP, 95, 2623(1991)
3497 template <typename T>
3498 void SingleReference_R12Intermediates<T>::compute_Gamma2_ccsd(const TArray2& T1, const TArray4& T2,
3499 const TArray2& L1, const TArray4& L2,
3500 const TArray4& tau_aa, const TArray4& tau_ab,
3501 TArray4& Gamma_IjKa_ab,
3502 TArray4& Gamma_AbCi_ab,
3503 TArray4& Gamma_iBjA_ab, TArray4& Gamma_iBJa_ba,
3504 TArray4& Gamma_AbCd_ab, TArray4& Gamma_IjKl_ab,
3505 TArray4& Gamma_IjAb_ab) {
3506
3507 TArray2 CGac, CGki;
3508 CGac("a,c") = - 0.5 * (T2("c,d,k,l") - T2("d,c,k,l"))
3509 * (L2("a,d,k,l") - L2("d,a,k,l"))
3510 - T2("c,d,k,l") * L2("a,d,k,l");
3511
3512 CGki("k,i") = 0.5 * (T2("c,d,k,l") - T2("c,d,l,k"))
3513 * (L2("c,d,i,l") - L2("c,d,l,i"))
3514 + T2("c,d,k,l") * L2("c,d,i,l");
3515
3516 TArray4 VKlIj_ab, VIBJA_aa, VIbJa_ab, ViBJa_ba, VAbCd_ab;
3517
3518 VKlIj_ab("k,l,i,j") = tau_ab("c,d,k,l") * L2("c,d,i,j");
3519
3520 VIBJA_aa("i,b,j,a") = 0.5 * (T2("a,c,i,k") - T2("a,c,k,i"))
3521 * (L2("b,c,j,k") - L2("b,c,k,j"))
3522 + 0.5 * T2("a,c,i,k") * L2("b,c,j,k");
3523 VIbJa_ab("i,b,j,a") = 0.5 * T2("c,a,i,k") * L2("c,b,j,k");
3524 ViBJa_ba("i,b,j,a") = 0.5 * (T2("a,c,i,k") - T2("a,c,k,i")) * L2("b,c,j,k")
3525 + 0.5 * T2("a,c,i,k") * (L2("b,c,j,k") - L2("b,c,k,j"));
3526 // VIbjA_ba("i,b,j,a") = ViBJa_ba("i,b,j,a")
3527 // ViBjA_ab("i,b,j,a") = VIbJa_ab("i,b,j,a")
3528 // ViBjA_ab("i,b,j,a") = 0.5 * T2("a,c,k,i") * L2("b,c,k,j");
3529 // VIBja_ba("i,b,j,a") = VIbJa_ab("i,b,j,a")
3530 //VIBja_ba("i,b,j,a") = 0.5 * T2("c,a,i,k") * L2("b,c,k,j");
3531
3532 VAbCd_ab("a,b,c,d") = tau_ab("c,d,k,l") * L2("a,b,k,l");
3533 // V_aBCd = - tau_ab("d,c,k,l") * L2("a,b,k,l")
3534
3535 Gamma_IjKa_ab("i,j,k,a") = // - 1/8 tau^Ca_Ij lambda^K_C
3536 - 0.125 * tau_ab("c,a,i,j") * L1("c,k")
3537
3538 // - 1/8 lambda^Ca_Ij t^K_C
3539 - 0.125 * L2("c,a,i,j") * T1("c,k")
3540
3541 // + 1/8 V_IjKl t^a_l
3542 + 0.125 * VKlIj_ab("i,j,k,l") * T1("a,l")
3543
3544 //*** + 1/4 P-(ij) V_kcia (V_icka ???) t^c_j
3545 // + 1/4 V_IcKa t^c_j
3546 + 0.25 * VIbJa_ab("i,c,k,a") * T1("c,j")
3547 // - 1/4 V_jCKa t^C_I
3548 - 0.25 * ViBJa_ba("j,c,k,a") * T1("c,i")
3549
3550 // - 1/8 P-(ij) CG_IK t^a_j
3551 - 0.125 * CGki("i,k") * T1("a,j")
3552 ;
3553
3554// Gamma_iJkA_ab("i,j,k,a") = // - 1/8 tau^cA_iJ lambda^k_c
3555// - 0.125 * tau_ab("c,a,i,j") * L1("c,k")
3556//
3557// // - 1/8 lambda^cA_iJ t^k_c
3558// - 0.125 * L2("c,a,i,j") * T1("c,k")
3559//
3560// // + 1/8 V_iJkL t^A_L
3561// + 0.125 * VKlIj_ab("i,j,k,l") * T1("a,l")
3562//
3565//
3566// // - 1/8 P-(ij) CG_ik t^A_J
3567// - 0.125 * CGki("i,k") * T1("a,j")
3568// ;
3569
3570 Gamma_AbCi_ab("a,b,c,i") = // 1/8 tau^ab_ki lambda^k_c
3571 0.125 * tau_ab("a,b,k,i") * L1("c,k")
3572
3573 // 1/8 lambda^Ki_Ab t^C_K
3574 + 0.125 * L2("a,b,k,i") * T1("c,k")
3575
3576 // - 1/8 t^d_i V_CdAb
3577 - 0.125 * T1("d,i") * VAbCd_ab("c,d,a,b")
3578
3579 //*** + 1/4 P-(ab) V_kcib (V_ickb ???) t^a_k
3580 // + 1/4 V_iCKb t^A_K
3581 + 0.25 * ViBJa_ba("i,c,k,b") * T1("a,k")
3582 // - 1/4 V_iCkA t^b_k
3583 - 0.25 * VIbJa_ab("i,c,k,a") * T1("b,k")
3584
3585 // - 1/8 P-(ab) t^b_i CG_ca
3586 // - 1/8 t^b_i CG_CA
3587 - 0.125 * CGac("c,a") * T1("b,i")
3588 ;
3589
3590 // Gamma_AbcI_ab("a,b,c,i") = - Gamma_AbcI_ab("b,a,c,i")
3591// Gamma_AbcI_ab("a,b,c,i") = // 1/8 tau^Ab_kI lambda^k_c
3592// - 0.125 * tau_ab("a,b,i,k") * L1("c,k") // tau_ab("b,a,k,i")
3593//
3594// // 1/8 lambda^kI_Ab t^c_k
3595// - 0.125 * L2("b,a,k,i") * T1("c,k")
3596//
3597// // - 1/8 t^D_I V_cDAb (- V_DcAb or - V_cDbA)
3598// + 0.125 * T1("d,i") * VAbCd_ab("c,d,b,a")
3599//
3600// // + 1/4 P-(ab) V_kcib t^a_k
3601// // + 1/4 V_KCib t^A_K
3602// // - 1/4 V_kCiA t^b_k
3603//
3604// // - 1/8 P-(ab) t^b_i CG_ca
3605// // + 1/8 t^A_I CG_cb
3606// + 0.125 * CGac("c,b") * T1("a,i")
3607// ;
3608
3609 // Gamma_IBJA_aa = Gamma_IbJa_ab + Gamma_iBJa_ab
3610
3611 Gamma_iBJa_ba("i,b,j,a") = // -?? 1/4 P+(ia,jb) Vibja
3612 // - 1/4 ViBJa
3613 - 0.25 * ViBJa_ba("i,b,j,a")
3614 // 1/4 VJaiB (ViBJa)
3615 - 0.25 * ViBJa_ba("j,a,i,b")
3616
3617 // + 1/8 P+(ia,jb) t^c_i t^a_k lambda^jk_bc
3618 // + 1/8 t^c_i t^a_k lambda^Jk_Bc
3619 + 0.125 * T1("c,i") * T1("a,k") * L2("b,c,j,k")
3620 // + 1/8 t^C_J t^B_K lambda^iK_aC
3621 + 0.125 * T1("c,j") * T1("b,k") * L2("a,c,i,k")
3622
3623 // - 1/8 P+(ia,jb) t^a_i lambda^j_b
3624 // - 1/8 t^a_i lambda^J_B
3625 - 0.125 * L1("b,j") * T1("a,i")
3626 // - 1/8 t^B_J lambda^i_a
3627 - 0.125 * L1("a,i") * T1("b,j")
3628 ;
3629
3630 // Gamma_iBjA_ab = Gamma_IbJa_ab
3631 Gamma_iBjA_ab("i,b,j,a") = // - ?? 1/4 P+(ia,jb) Vibja
3632 // - 1/4 ViBjA (VIbJa)
3633 - 0.25 * VIbJa_ab("i,b,j,a")
3634 // - 1/4 VjAiB
3635 - 0.25 * VIbJa_ab("j,a,i,b")
3636
3637 // + 1/8 P+(ia,jb) t^c_i t^a_k lambda^jk_bc
3638 // + 1/8 t^c_i t^A_K lambda^jK_Bc
3639 - 0.125 * T1("c,i") * T1("a,k") * L2("c,b,j,k")
3640 // + 1/8 t^c_j t^B_K lambda^iK_Ac
3641 - 0.125 * T1("c,j") * T1("b,k") * L2("c,a,i,k")
3642
3643 // - 1/8 P+(ia,jb) t^a_i lambda^j_b
3644 ;
3645
3646 // Gamma_IJKL_aa("i,j,k,l") = Gamma_IjKl_ab("i,j,k,l") - Gamma_IjKl_ab("j,i,k,l")
3647 Gamma_IjKl_ab("i,j,k,l") = // 1/8 P+(ij,kl) Vijkl
3648 0.125 * VKlIj_ab("k,l,i,j")
3649 + 0.125 * VKlIj_ab("i,j,k,l");
3650
3651 // Gamma_ABCD_ab("a,b,c,d") = Gamma_AbCd_ab("a,b,c,d") - Gamma_AbCd_ab("b,a,c,d")
3652 Gamma_AbCd_ab("a,b,c,d") = // 1/8 P+(ij,kl) Vabcd
3653 0.125 * VAbCd_ab("a,b,c,d")
3654 + 0.125 * VAbCd_ab("c,d,a,b");
3655
3656 Gamma_IjAb_ab("i,j,a,b") = // 1/8 tau^Ab_Ij
3657 0.125 * tau_ab("a,b,i,j")
3658
3659 // 1/8 lambda^Ab_Ij
3660 + 0.125 * L2("a,b,i,j")
3661
3662 // + 1/16 VIjkl tau^Ab_kl
3663 + 0.125 * VKlIj_ab("i,j,k,l") * tau_ab("a,b,k,l")
3664
3665 // - 1/8 P-(ij) (Gik + t^c_i lambda^k_c) tau^ab_kj
3666 // - 1/8 (GIk + t^c_i lambda^k_c) tau^Ab_kj
3667 - 0.125 * (CGki("i,k") + T1("c,i") * L1("c,k")) * tau_ab("a,b,k,j")
3668 // + 1/8 (Gjk + t^c_j lambda^k_c) tau^Ab_kI
3669 - 0.125 * (CGki("j,k") + T1("c,j") * L1("c,k")) * tau_ab("a,b,i,k")
3670
3671 // + 1/8 P-(ab) (Gca - t^a_k lambda^k_c) tau^cb_ij
3672 // + 1/8 (GCA - t^A_K lambda^K_C) tau^Cb_Ij
3673 + 0.125 * (CGac("c,a") - T1("a,k") * L1("c,k")) * tau_ab("c,b,i,j")
3674 // - 1/8 (Gcb - t^b_k lambda^k_c) tau^cA_Ij
3675 + 0.125 * (CGac("c,b") - T1("b,k") * L1("c,k")) * tau_ab("a,c,i,j")
3676
3677 //*** - 1/8 P-(ij) P-(ab) (t^ac_ki + 2 t^c_i t^a_k) Vjckb
3678 // - 1/8 t^Ac_kI Vjkcb = + 1/8 t^AC_IK VjCKb + 1/8 t^Ac_Ik Vjckb
3679 + 0.125 * (T2("a,c,i,k") - T2("c,a,i,k")) * ViBJa_ba("j,c,k,b")
3680 + 0.125 * T2("a,c,i,k") * VIBJA_aa("j,c,k,b")
3681 // + 1/8 t^bC_kI VjCkA
3682 + 0.125 * T2("b,c,k,i") * VIbJa_ab("j,c,k,a")
3683 // + 1/8 t^Ac_Kj VIcKb
3684 + 0.125 * T2("a,c,k,j") * VIbJa_ab("i,c,k,b")
3685 // - 1/8 t^bc_kj VIkcA = + 1/8 t^bC_jK VICKA + 1/8 t^bc_jk VIckA
3686 + 0.125 * T2("b,c,j,k") * VIBJA_aa("i,c,k,a")
3687 + 0.125 * (T2("b,c,j,k") - T2("c,b,j,k")) * ViBJa_ba("i,c,k,a")
3688
3689 //*** - 1/4 t^C_I t^A_K VjCKb
3690 - 0.25 * T1("c,i") * T1("a,k") * ViBJa_ba("j,c,k,b")
3691 // + 1/4 t^C_I t^b_k VjCkA
3692 + 0.25 * T1("c,i") * T1("b,k") * VIbJa_ab("j,c,k,a")
3693 // + 1/4 t^c_j t^A_K VIcKb
3694 + 0.25 * T1("c,j") * T1("a,k") * VIbJa_ab("i,c,k,b")
3695 // - 1/4 t^c_j t^b_k VIckA
3696 - 0.25 * T1("c,j") * T1("b,k") * ViBJa_ba("i,c,k,a")
3697
3698
3699 // - 1/8 P-(ij) P-(ab) (t^ac_ki + 2 t^c_i t^a_k) lambda^k_c t^b_j
3700 - 0.125 * (
3701 // (t^Ac_kI + 2 t^c_I t^A_k) lambda^k_c t^b_j
3702 (- 2.0 * T2("a,c,i,k") + T2("c,a,i,k")
3703 + 2.0 * T1("c,i") * T1("a,k")
3704 ) * T1("b,j")
3705 // (t^bc_kj + 2 t^c_j t^b_k) lambda^k_c t^A_I
3706 + (- 2.0 * T2("b,c,j,k") + T2("c,b,j,k")
3707 + 2.0 * T1("c,j") * T1("b,k")
3708 ) * T1("a,i")
3709 ) * L1("c,k")
3710
3711 // *** + 3/2 (3/8 ???) P-(ij) P-(ab) t^a_i t^c_j lambda^k_c t^b_k
3712 + 0.375 * ( // t^A_I t^c_j lambda^k_c t^b_k
3713 T1("a,i") * T1("c,j") * T1("b,k")
3714 // t^b_j t^C_I lambda^K_C t^A_K
3715 + T1("b,j") * T1("c,i") * T1("a,k")
3716 ) * L1("c,k")
3717 ;
3718
3719
3720 }
3721
3722 // compute CCSD one-electron density from amplitudes
3723 template <typename T>
3724 void SingleReference_R12Intermediates<T>::compute_ccsd_1rdm_amp(const TArray2& T1, const TArray4& T2,
3725 const TArray2& L1, const TArray4& L2,
3726 TArray2& Dij, TArray2& Dab,
3727 TArray2& Dia, TArray2& Dai) {
3728
3729 TArray4 T2_temp;
3730 T2_temp("a,b,i,j") = 2.0 * T2("a,b,i,j") - T2("a,b,j,i");
3731
3732 Dij("i,j") = // - 1/4 P+(ij) t^cd_ik lambda^jk_cd
3733 - 0.5 * ( T2_temp("c,d,i,k") * L2("c,d,j,k")
3734 + T2_temp("c,d,j,k") * L2("c,d,i,k")
3735 )
3736 // - 1/2 P+(ij) t^c_i lambda^j_c
3737 - 0.5 * ( T1("c,i") * L1("c,j")
3738 + T1("c,j") * L1("c,i")
3739 )
3740 ;
3741
3742 Dab("a,b") = // 1/4 P+(ab) t^kl_ac lambda^bc_kl
3743 0.5 * ( T2_temp("a,c,k,l") * L2("b,c,k,l")
3744 + T2_temp("b,c,k,l") * L2("a,c,k,l")
3745 )
3746 // + 1/2 P+(ab) lambda^k_a t^b_k
3747 + 0.5 * ( L1("a,k") * T1("b,k")
3748 + L1("b,k") * T1("a,k")
3749 )
3750 ;
3751
3752 Dia("i,a") = // t^a_i
3753 T1("a,i")
3754 // + (t^ac_ik - t^c_i t^a_k) \lambda^k_c
3755 + (T2_temp("a,c,i,k") - T1("c,i") * T1("a,k")) * L1("c,k")
3756 // CCSD term
3757 // - 1/2 lambda^kl_cd (t^cd_il t^a_k + t^c_i t^ad_kl)
3758 - (2.0 * L2("c,d,k,l") - L2("d,c,k,l"))
3759 * ( T2("c,d,i,l") * T1("a,k")
3760 + T2("a,d,k,l") * T1("c,i")
3761 )
3762 ;
3763
3764 Dai("a,i") = // lambda^i_a
3765 L1("a,i");
3766 }
3767
3768 // compute CCSD Xam (the right-hand side of Z-vector equations)
3769 // following formula from JCP, 103, 3561 (1995)
3770 template <typename T>
3771 void SingleReference_R12Intermediates<T>::compute_Xam_ccsd(const TArray2& T1, const TArray4& T2,
3772 const TArray2& L1, const TArray4& L2,
3773 TArray2& Xam_tot, TArray2& Xiip) {
3774
3775 TArray4 tau_ab;
3776 tau_ab("a,b,i,j") = T2("a,b,i,j") + (T1("a,i") * T1("b,j"));
3777
3778 // compute \Gamma(pq,rs) intermediates
3779
3780 TArray4 Gamma_IjAb_ab;
3781 compute_Gamma_ijab_ccsd(T1, T2, tau_ab, L1, L2,
3782 Gamma_IjAb_ab);
3783
3784 TArray4 Gamma_AbIj_ab;
3785 Gamma_AbIj_ab("a,b,i,j") = // 1/4 lambda^ij_ab
3786 0.25 * L2("a,b,i,j");
3787// TArray4 Gamma_ABIJ_aa;
3788// Gamma_ABIJ_aa("a,b,i,j") = // 1/4 lambda^ij_ab
3789// 0.25 * (L2("a,b,i,j") - L2("b,a,i,j"));
3790// TArray4 Gamma_aa_1, diff_1;
3791// Gamma_aa_1("a,b,i,j") = Gamma_AbIj_ab("a,b,i,j") - Gamma_AbIj_ab("a,b,j,i");
3792// diff_1("a,b,i,j") = Gamma_ABIJ_aa("a,b,i,j") - Gamma_aa_1("a,b,i,j");
3793// std::cout << std::endl << "Diff 1: " << std::endl
3794// << "norm = " << static_cast<double>(diff_1("a,b,i,j").norm())
3795// << " max = " << static_cast<double>(diff_1("a,b,i,j").max())
3796// << " min = " << static_cast<double>(diff_1("a,b,i,j").min()) << std::endl;
3797
3798 TArray4 Gamma_AbCd_ab;
3799 Gamma_AbCd_ab("a,b,c,d") = // 1/8 lambda^kl_ab tau^cd_kl (CCSD modified term)
3800 0.25 * L2("a,b,k,l") * tau_ab("c,d,k,l");
3801
3802 TArray4 Gamma_IjKl_ab;
3803 Gamma_IjKl_ab("i,j,k,l") = // 1/8 tau^cd_ij lambda^kl_cd
3804 0.25 * tau_ab("c,d,i,j") * L2("c,d,k,l");
3805// TArray4 Gamma_IJKL_aa;
3806// Gamma_IJKL_aa("i,j,k,l") = // 1/8 tau^cd_ij lambda^kl_cd
3807// 0.125 * tau_aa("c,d,i,j") * (L2("c,d,k,l") - L2("c,d,l,k"));
3808// TArray4 Gamma_aa_1, diff_1, Gamma_aa_2, diff_2;
3809// Gamma_aa_1("i,j,k,l") = Gamma_IjKl_ab("i,j,k,l") - Gamma_IjKl_ab("j,i,k,l");
3810// diff_1("i,j,k,l") = Gamma_IJKL_aa("i,j,k,l") - Gamma_aa_1("i,j,k,l");
3811// std::cout << std::endl << "Diff 1: " << std::endl
3812// << "norm = " << static_cast<double>(diff_1("i,j,k,l").norm())
3813// << " max = " << static_cast<double>(diff_1("i,j,k,l").max())
3814// << " min = " << static_cast<double>(diff_1("i,j,k,l").min()) << std::endl;
3815//
3816// Gamma_aa_2("i,j,k,l") = Gamma_IjKl_ab("i,j,k,l") - Gamma_IjKl_ab("i,j,l,k");
3817// diff_2("i,j,k,l") = Gamma_IJKL_aa("i,j,k,l") - Gamma_aa_2("i,j,k,l");
3818// std::cout << std::endl << "Diff 2: " << std::endl
3819// << "norm = " << static_cast<double>(diff_2("i,j,k,l").norm())
3820// << " max = " << static_cast<double>(diff_2("i,j,k,l").max())
3821// << " min = " << static_cast<double>(diff_2("i,j,k,l").min()) << std::endl;
3822
3823 TArray4 Gamma_IjKa_ab;
3824 Gamma_IjKa_ab("i,j,k,a") = // - 1/4 tau^ca_ij lambda^k_c
3825 - 0.25 * tau_ab("c,a,i,j") * L1("c,k")
3826
3827 // + 1/8 tau^cd_ij lambda^kl_cd t^a_l
3828 + 0.25 * tau_ab("c,d,i,j") * L2("c,d,k,l") * T1("a,l")
3829
3830 // + 1/4 P-(ij) t^ac_il lambda^lk_cd t^d_j
3831 + 0.25 * T2("a,c,l,i") * L2("c,d,k,l") * T1("d,j")
3832 //
3833 - 0.25 * ( (T2("a,c,j,l") - T2("a,c,l,j")) * L2("c,d,l,k")
3834 + T2("a,c,j,l") * (L2("c,d,l,k") - L2("c,d,k,l"))
3835 ) * T1("d,i")
3836
3837 // - 1/8 P-(ij) t^cd_il lambda^kl_cd t^a_j
3838 - 0.125 * ( (T2("c,d,i,l") - T2("c,d,l,i")) * (L2("c,d,k,l") - L2("c,d,l,k"))
3839 + 2.0 * T2("c,d,i,l") * L2("c,d,k,l")
3840 ) * T1("a,j")
3841 ;
3842
3843 TArray4 Gamma_AKIJ_aa, Gamma_AkIj_ab;
3844 Gamma_AkIj_ab("a,k,i,j") = // -1/4 t^c_k lambda^Ij_Ac
3845 - 0.25 * T1("c,k") * L2("a,c,i,j");
3846
3847 TArray4 Gamma_CiAb_ab;
3848 Gamma_CiAb_ab("c,i,a,b") = // 1/4 tau^ab_ki lambda^k_c
3849 0.25 * tau_ab("a,b,k,i") * L1("c,k")
3850
3851 // - 1/8 t^d_i lambda^kl_cd tau^ab_kl
3852 - 0.25 * T1("d,i") * L2("c,d,k,l") * tau_ab("a,b,k,l")
3853
3854 // - 1/4 P-(ab) t^ad_il lambda^kl_cd t^b_k
3855 - 0.25 * T2("a,d,l,i") * L2("c,d,l,k") * T1("b,k")
3856 //
3857 + 0.25 * ( (T2("b,d,i,l") - T2("b,d,l,i")) * L2("c,d,k,l")
3858 + T2("b,d,i,l") * (L2("c,d,k,l") - L2("c,d,l,k"))
3859 ) * T1("a,k")
3860
3861 // + 1/8 P-(ab) t^b_i t^ad_kl lambda^kl_cd
3862 + 0.125 * T1("b,i") * (T2("a,d,k,l") - T2("d,a,k,l"))
3863 * (L2("c,d,k,l") - L2("c,d,l,k"))
3864 + 0.25 * T1("b,i") * T2("a,d,k,l") * L2("c,d,k,l")
3865 ;
3866
3867 TArray4 Gamma_AbCi_ab;
3868 Gamma_AbCi_ab("a,b,c,i") = // 1/4 lambda^ki_ab t^c_k
3869 0.25 * L2("a,b,k,i") * T1("c,k");
3870
3871 TArray4 Gamma_aJiB_ab, Gamma_AjiB_ba;
3872 Gamma_aJiB_ab("a,j,i,b") = // 1/4 lambda^ik_ac t^c_j t^cb_kj
3873 0.25 * (L2("a,c,i,k") - L2("c,a,i,k")) * T2("c,b,k,j")
3874 + 0.25 * L2("a,c,i,k") * (T2("c,b,k,j") - T2("b,c,k,j"))
3875
3876 // - 1/4 lambda^ik_ac t^c_j t^b_k
3877 - 0.25 * L2("a,c,i,k") * T1("c,j") * T1("b,k")
3878 // + 1/4 lambda^i_a t^b_j
3879 + 0.25 * L1("a,i") * T1("b,j")
3880 ;
3881
3882 Gamma_AjiB_ba("a,j,i,b") = // 1/4 lambda^ik_ac t^c_j t^cb_kj
3883 0.25 * L2("c,a,i,k") * T2("b,c,k,j")
3884
3885 // - 1/4 lambda^ik_ac t^c_j t^b_k
3886 + 0.25 * L2("a,c,k,i") * T1("c,j") * T1("b,k")
3887 // + 1/4 lambda^i_a t^b_j
3888 ;
3889
3890 // compute CCSD density from amplitudes
3891 TArray2 Dij, Dab, Dia, Dai;
3892 compute_ccsd_1rdm_amp(T1, T2, L1, L2, Dij, Dab, Dia, Dai);
3893
3894 TArray4d g_ijma = ijxy("<i j|g|m a>");
3895 TArray4d g_mabc = ijxy("<m a|g|b c>");
3896 TArray4d g_mabi = ijxy("<m a|g|b i>");
3897 TArray4d g_maib = ijxy("<m a|g|i b>");
3898
3899 TArray4d g_imkl = ijxy("<i m|g|k l>");
3900 TArray4d g_miab = ijxy("<m i|g|a b>");
3901 TArray4d g_imbj = ijxy("<i m|g|b j>");
3902 TArray4d g_imjb = ijxy("<i m|g|j b>");
3903
3904 TArray4d g_ijak = ijxy("<i j|g|a k>");
3905 TArray4d g_abci = ijxy("<a b|g|c i>");
3906 TArray4d g_aibj = ijxy("<a i|g|b j>");
3907 TArray4d g_iabj = ijxy("<i a|g|b j>");
3908
3909 TArray4d g_ijab = ijxy("<i j|g|a b>");
3910 TArray4d g_abcd = ijxy("<a b|g|c d>");
3911
3912 TArray2 Xam, Xai;
3913 Xam("a,m") = (Dai("a,j") + Dia("j,a")) * _2("<j|F|m>")
3914 + (Dab("a,c") + Dab("c,a")) * _2("<c|F|m>")
3915
3916 - (2.0 * g_mabc("m,c,a,d") - g_mabc("m,c,d,a"))
3917 * (Dab("c,d") + Dab("d,c"))
3918 - (2.0 * g_imjb("l,m,k,a") - g_imbj("l,m,a,k"))
3919 * (Dij("k,l") + Dij("l,k"))
3920 - ( 2.0 * g_miab("m,j,a,b") - g_miab("m,j,b,a")
3921 + 2.0 * g_mabi("m,b,a,j") - g_maib("m,b,j,a")
3922 ) * (Dia("j,b") + Dai("b,j"))
3923
3924 + 4.0 * (
3925 //
3926 // (Gamma(kl,ab) + Gamma(ab,kl)) g^kl_mb
3927 (Gamma_IjAb_ab("k,l,a,b") + Gamma_AbIj_ab("a,b,k,l"))
3928 * (g_ijma("k,l,m,b") * 2.0 - g_ijma("l,k,m,b"))
3929
3930 // (Gamma(cd,ab) + Gamma(ab, cd)) g^cd_mb
3931 + (Gamma_AbCd_ab("c,d,a,b") + Gamma_AbCd_ab("a,b,c,d"))
3932 * (g_mabc("m,b,c,d") * 2.0 - g_mabc("m,b,d,c"))
3933
3934 // 2 (Gamma(ck,ab) - Gamma(ba,ck)) g^ck_mb
3935 + ( Gamma_CiAb_ab("c,k,a,b") - Gamma_CiAb_ab("c,k,b,a")
3936 - Gamma_AbCi_ab("b,a,c,k") + Gamma_AbCi_ab("a,b,c,k"))
3937 * (g_mabi("m,b,c,k") - g_maib("m,b,k,c"))
3938 + (Gamma_CiAb_ab("c,k,a,b") + Gamma_AbCi_ab("a,b,c,k"))
3939 * g_mabi("m,b,c,k")
3940 - (- Gamma_CiAb_ab("c,k,b,a") - Gamma_AbCi_ab("b,a,c,k"))
3941 * g_maib("m,b,k,c")
3942
3943 //
3944 // (Gamma(lk, ja) + Gamma(aj, kl)) g^kl_mj
3945 + (Gamma_IjKa_ab("l,k,j,a") + Gamma_AkIj_ab("a,j,k,l"))
3946 * (g_imkl("j,m,l,k") * 2.0 - g_imkl("j,m,k,l"))
3947
3948 // (Gamma(cd, aj) + Gamma(aj, cd) g^mj_cd) g^cd_mj
3949 + (Gamma_AbCi_ab("c,d,a,j") + Gamma_CiAb_ab("a,j,c,d"))
3950 * (g_miab("m,j,c,d") * 2.0 - g_miab("m,j,d,c"))
3951
3952 // * (Gamma(ck, ja) + Gamma(aj,kc)) g^kc_mj
3953 + ( Gamma_aJiB_ab("c,k,j,a") + Gamma_AjiB_ba("c,k,j,a")
3954 + Gamma_aJiB_ab("a,j,k,c") + Gamma_AjiB_ba("a,j,k,c"))
3955 * (g_imbj("j,m,c,k") - g_imjb("j,m,k,c"))
3956 + (Gamma_aJiB_ab("c,k,j,a") + Gamma_aJiB_ab("a,j,k,c"))
3957 * g_imbj("j,m,c,k")
3958 - (Gamma_AjiB_ba("c,k,j,a") + Gamma_AjiB_ba("a,j,k,c"))
3959 * g_imjb("j,m,k,c")
3960 )
3961 ;
3962
3963 Xai("a,i") = - _2("<a|F|b>") * (Dai("b,i") + Dia("i,b"))
3964 - _2("<a|F|l>") * (Dij("l,i") + Dij("i,l"))
3965
3966 - 4.0 * (
3967 //
3968 // (Gamma(kl,ij) + Gamma(ij, kl)) g^kl_aj
3969 (Gamma_IjKl_ab("k,l,i,j") + Gamma_IjKl_ab("i,j,k,l"))
3970 * (g_ijak("k,l,a,j") * 2.0 - g_ijak("l,k,a,j"))
3971
3972 // (Gamma(cd,ij) + Gamma(ij, cd)) g^cd_aj
3973 + (Gamma_AbIj_ab("c,d,i,j") + Gamma_IjAb_ab("i,j,c,d"))
3974 * (g_abci("c,d,a,j") * 2.0 - g_abci("d,c,a,j"))
3975
3976 // (- Gamma(ck,ij) + Gamma(ij,kc)) g^kc_aj
3977 + (- (Gamma_AkIj_ab("c,k,i,j") - Gamma_AkIj_ab("c,k,j,i"))
3978 + Gamma_IjKa_ab("i,j,k,c") - Gamma_IjKa_ab("j,i,k,c"))
3979 * (g_iabj("j,a,c,k") - g_aibj("a,j,c,k"))
3980 // - Gamma_aKIj_ba("c,k,i,j") = Gamma_AkIj_ab("c,k,j,i")
3981 + ( Gamma_AkIj_ab("c,k,j,i") + Gamma_IjKa_ab("i,j,k,c"))
3982 * g_iabj("j,a,c,k")
3983 - ( - Gamma_AkIj_ab("c,k,i,j") - Gamma_IjKa_ab("j,i,k,c"))
3984 * g_aibj("a,j,c,k")
3985
3986 //
3987 // (Gamma(kl,ib) - Gamma(bi,kl)) g^kl_ab
3988 + (Gamma_IjKa_ab("k,l,i,b") + Gamma_AkIj_ab("b,i,l,k"))
3989 * (g_ijab("k,l,a,b") * 2.0 - g_ijab("l,k,a,b"))
3990
3991 // (- Gamma(cd,bi) + Gamma(bi,dc)) g^cd_ab
3992 + (Gamma_AbCi_ab("d,c,b,i") + Gamma_CiAb_ab("b,i,d,c"))
3993 * (g_abcd("c,d,a,b") * 2.0 - g_abcd("d,c,a,b"))
3994
3995 // (Gamma(ck,ib) + Gamma(bi,kc)) g^ck_ab
3996 + ( Gamma_aJiB_ab("c,k,i,b") + Gamma_AjiB_ba("c,k,i,b")
3997 + Gamma_aJiB_ab("b,i,k,c") + Gamma_AjiB_ba("b,i,k,c"))
3998 * (g_abci("a,b,c,k") - g_abci("b,a,c,k"))
3999 + (Gamma_aJiB_ab("c,k,i,b") + Gamma_aJiB_ab("b,i,k,c"))
4000 * g_abci("a,b,c,k")
4001 - (Gamma_AjiB_ba("c,k,i,b") + Gamma_AjiB_ba("b,i,k,c"))
4002 * g_abci("b,a,c,k")
4003
4004 )
4005 ;
4006 Xam_tot = XaiAddToXam(Xam, Xai);
4007
4008 // *** test code: print out Iam & Ima ***
4009// TArray4d g_iabc = ijxy("<i a|g|b c>");
4010// TArray4d g_ikbj = ijxy("<i k|g|b j>");
4011// TArray4d g_ikjb = ijxy("<i k|g|j b>");
4012// TArray4d g_kabi = ijxy("<k a|g|b i>");
4013// TArray4d g_kaib = ijxy("<k a|g|i b>");
4014// TArray4d g_ijkl = ijxy("<i j|g|k l>");
4015//
4016// TArray2 Iam;
4017// Iam("a,m") = 2.0 * (
4018// //
4019// // (Gamma(kl,ab) + Gamma(ab,kl)) g^kl_mb
4020// (Gamma_IjAb_ab("k,l,a,b") + Gamma_AbIj_ab("a,b,k,l"))
4021// * (g_ijma("k,l,m,b") * 2.0 - g_ijma("l,k,m,b"))
4022//
4023// // (Gamma(cd,ab) + Gamma(ab, cd)) g^cd_mb
4024// + (Gamma_AbCd_ab("c,d,a,b") + Gamma_AbCd_ab("a,b,c,d"))
4025// * (g_mabc("m,b,c,d") * 2.0 - g_mabc("m,b,d,c"))
4026//
4027// // 2 (Gamma(ck,ab) - Gamma(ba,ck)) g^ck_mb
4028// + ( Gamma_CiAb_ab("c,k,a,b") - Gamma_CiAb_ab("c,k,b,a")
4029// - Gamma_AbCi_ab("b,a,c,k") + Gamma_AbCi_ab("a,b,c,k"))
4030// * (g_mabi("m,b,c,k") - g_maib("m,b,k,c"))
4031// + (Gamma_CiAb_ab("c,k,a,b") + Gamma_AbCi_ab("a,b,c,k"))
4032// * g_mabi("m,b,c,k")
4033// - (- Gamma_CiAb_ab("c,k,b,a") - Gamma_AbCi_ab("b,a,c,k"))
4034// * g_maib("m,b,k,c")
4035//
4036// //
4037// // (Gamma(lk, ja) + Gamma(aj, kl)) g^kl_mj
4038// + (Gamma_IjKa_ab("l,k,j,a") + Gamma_AkIj_ab("a,j,k,l"))
4039// * (g_imkl("j,m,l,k") * 2.0 - g_imkl("j,m,k,l"))
4040//
4041// // (Gamma(cd, aj) + Gamma(aj, cd) g^mj_cd) g^cd_mj
4042// + (Gamma_AbCi_ab("c,d,a,j") + Gamma_CiAb_ab("a,j,c,d"))
4043// * (g_miab("m,j,c,d") * 2.0 - g_miab("m,j,d,c"))
4044//
4045// // * (Gamma(ck, ja) + Gamma(aj,kc)) g^kc_mj
4046// + ( Gamma_aJiB_ab("c,k,j,a") + Gamma_AjiB_ba("c,k,j,a")
4047// + Gamma_aJiB_ab("a,j,k,c") + Gamma_AjiB_ba("a,j,k,c"))
4048// * (g_imbj("j,m,c,k") - g_imjb("j,m,k,c"))
4049// + (Gamma_aJiB_ab("c,k,j,a") + Gamma_aJiB_ab("a,j,k,c"))
4050// * g_imbj("j,m,c,k")
4051// - (Gamma_AjiB_ba("c,k,j,a") + Gamma_AjiB_ba("a,j,k,c"))
4052// * g_imjb("j,m,k,c")
4053// )
4054// ;
4055//
4056// TArray2 Ima, Iia;
4057// Ima("a,m") = - (2.0 * g_mabc("m,c,a,d") - g_mabc("m,c,d,a"))
4058// * (Dab("c,d") + Dab("d,c")) * 0.5
4059// - (2.0 * g_imjb("l,m,k,a") - g_imbj("l,m,a,k"))
4060// * (Dij("k,l") + Dij("l,k")) * 0.5
4061// ;
4062// Iia("a,i") = - 2.0 * (
4063// //
4064// // (Gamma(kl,ij) + Gamma(ij, kl)) g^kl_aj
4065// (Gamma_IjKl_ab("k,l,i,j") + Gamma_IjKl_ab("i,j,k,l"))
4066// * (g_ijak("k,l,a,j") * 2.0 - g_ijak("l,k,a,j"))
4067//
4068// // (Gamma(cd,ij) + Gamma(ij, cd)) g^cd_aj
4069// + (Gamma_AbIj_ab("c,d,i,j") + Gamma_IjAb_ab("i,j,c,d"))
4070// * (g_abci("c,d,a,j") * 2.0 - g_abci("d,c,a,j"))
4071//
4072// // (- Gamma(ck,ij) + Gamma(ij,kc)) g^kc_aj
4073// + (- (Gamma_AkIj_ab("c,k,i,j") - Gamma_AkIj_ab("c,k,j,i"))
4074// + Gamma_IjKa_ab("i,j,k,c") - Gamma_IjKa_ab("j,i,k,c"))
4075// * (g_iabj("j,a,c,k") - g_aibj("a,j,c,k"))
4076// // - Gamma_aKIj_ba("c,k,i,j") = Gamma_AkIj_ab("c,k,j,i")
4077// + ( Gamma_AkIj_ab("c,k,j,i") + Gamma_IjKa_ab("i,j,k,c"))
4078// * g_iabj("j,a,c,k")
4079// - ( - Gamma_AkIj_ab("c,k,i,j") - Gamma_IjKa_ab("j,i,k,c"))
4080// * g_aibj("a,j,c,k")
4081//
4082// //
4083// // (Gamma(kl,ib) - Gamma(bi,kl)) g^kl_ab
4084// + (Gamma_IjKa_ab("k,l,i,b") + Gamma_AkIj_ab("b,i,l,k"))
4085// * (g_ijab("k,l,a,b") * 2.0 - g_ijab("l,k,a,b"))
4086//
4087// // (- Gamma(cd,bi) + Gamma(bi,dc)) g^cd_ab
4088// + (Gamma_AbCi_ab("d,c,b,i") + Gamma_CiAb_ab("b,i,d,c"))
4089// * (g_abcd("c,d,a,b") * 2.0 - g_abcd("d,c,a,b"))
4090//
4091// // (Gamma(ck,ib) + Gamma(bi,kc)) g^ck_ab
4092// + ( Gamma_aJiB_ab("c,k,i,b") + Gamma_AjiB_ba("c,k,i,b")
4093// + Gamma_aJiB_ab("b,i,k,c") + Gamma_AjiB_ba("b,i,k,c"))
4094// * (g_abci("a,b,c,k") - g_abci("b,a,c,k"))
4095// + (Gamma_aJiB_ab("c,k,i,b") + Gamma_aJiB_ab("b,i,k,c"))
4096// * g_abci("a,b,c,k")
4097// - (Gamma_AjiB_ba("c,k,i,b") + Gamma_AjiB_ba("b,i,k,c"))
4098// * g_abci("b,a,c,k")
4099//
4100// )
4101// ;
4102// TArray2 I_ima = XaiAddToXam(Ima, Iia);
4103//
4104// std::cout << "Ii/m a : " << std::endl << I_ima << std::endl;
4105// std::cout << "Iam : " << std::endl << Iam << std::endl;
4106
4107 // frozen-core contribution
4108 const std::size_t nocc = Xam.trange().elements_range().extent()[1];
4109 const std::size_t naocc = Xai.trange().elements_range().extent()[1];
4110 if (nocc != naocc) {
4111 TArray4d g_ijipk = ijxy("<i j|g|i' k>");
4112 TArray4d g_abipi = ijxy("<a b|g|i' i>");
4113 TArray4d g_ipibj = ijxy("<i' i|g|b j>");
4114 TArray4d g_iipbj = ijxy("<i i'|g|b j>");
4115 TArray4d g_ijipb = ijxy("<i j|g|i' b>");
4116 TArray4d g_abipd = ijxy("<a b|g|i' d>");
4117 TArray4d g_aipbi = ijxy("<a i'|g|b i>");
4118
4119 Xiip("i,i'") = - 4.0 * (
4120 //
4121 // (Gamma(kl,ij) + Gamma(ij, kl)) g^kl_i'j
4122 (Gamma_IjKl_ab("k,l,i,j") + Gamma_IjKl_ab("i,j,k,l"))
4123 * (g_ijipk("k,l,i',j") * 2.0 - g_ijipk("l,k,i',j"))
4124
4125 // (Gamma(cd,ij) + Gamma(ij, cd)) g^cd_i'j
4126 + (Gamma_AbIj_ab("c,d,i,j") + Gamma_IjAb_ab("i,j,c,d"))
4127 * (g_abipi("c,d,i',j") * 2.0 - g_abipi("d,c,i',j"))
4128
4129 // (- Gamma(ck,ij) + Gamma(ij,kc)) g^kc_i'j
4130 + (- (Gamma_AkIj_ab("c,k,i,j") - Gamma_AkIj_ab("c,k,j,i"))
4131 + Gamma_IjKa_ab("i,j,k,c") - Gamma_IjKa_ab("j,i,k,c"))
4132 * (g_iipbj("j,i',c,k") - g_ipibj("i',j,c,k"))
4133 + ( Gamma_AkIj_ab("c,k,j,i") + Gamma_IjKa_ab("i,j,k,c"))
4134 * g_iipbj("j,i',c,k")
4135 - ( - Gamma_AkIj_ab("c,k,i,j") - Gamma_IjKa_ab("j,i,k,c"))
4136 * g_ipibj("i',j,c,k")
4137
4138 //
4139 // (Gamma(kl,ib) - Gamma(bi,kl)) g^kl_i'b
4140 + (Gamma_IjKa_ab("k,l,i,b") + Gamma_AkIj_ab("b,i,l,k"))
4141 * (g_ijipb("k,l,i',b") * 2.0 - g_ijipb("l,k,i',b"))
4142
4143 // (- Gamma(cd,bi) + Gamma(bi,dc)) g^cd_i'b
4144 + (Gamma_AbCi_ab("d,c,b,i") + Gamma_CiAb_ab("b,i,d,c"))
4145 * (g_abipd("c,d,i',b") * 2.0 - g_abipd("d,c,i',b"))
4146
4147 // (Gamma(ck,ib) + Gamma(bi,kc)) g^ck_i'b
4148 + ( Gamma_aJiB_ab("c,k,i,b") + Gamma_AjiB_ba("c,k,i,b")
4149 + Gamma_aJiB_ab("b,i,k,c") + Gamma_AjiB_ba("b,i,k,c"))
4150 * (g_abipi("c,b,i',k") - g_aipbi("b,i',c,k"))
4151 + (Gamma_aJiB_ab("c,k,i,b") + Gamma_aJiB_ab("b,i,k,c"))
4152 * g_abipi("c,b,i',k")
4153 - (Gamma_AjiB_ba("c,k,i,b") + Gamma_AjiB_ba("b,i,k,c"))
4154 * g_aipbi("b,i',c,k")
4155 )
4156 ;
4157
4158 }
4159
4160 }
4161
4162 template <typename T>
4163 void SingleReference_R12Intermediates<T>::compute_multipole() {
4164
4165 ExEnv::out0() << std::endl << indent
4166 << "Compute dipole and quadrupole moments" << std::endl;
4167
4168 bool compute_dipole = true;
4169 bool compute_quadrupole = true;
4170 bool compute_EFG = false;
4171
4172 #define INCLUDE_CABS_Singles_CONTRI 1
4173 #define INCLUDE_MP2_CONTRI 1
4174 #define INCLUDE_MP2F12C_CONTRI 1
4175 #define INCLUDE_F12_CONTRI 1
4176
4177 #define INCLUDE_CCSD_CONTRI 1
4178 #define INCLUDE_CCSDF12C_CONTRI 1
4179
4180 double conv_target = 1e-10;
4181
4182 // Obtain property integrals which is needed in multiple places
4183
4184 // dipole integrals
4185 TArray2 mu_z_mn, mu_z_am;
4186 if (compute_dipole) {
4187 mu_z_mn = xy("<m|mu_z|n>");
4188 mu_z_am = xy("<a|mu_z|m>");
4189 }
4190
4191 // quadrupole integrals
4192 TArray2 q_xx_mn, q_yy_mn, q_zz_mn;
4193 TArray2 Qxx_mn, Qyy_mn, Qzz_mn, Qxz_mn, Qxy_mn, Qyz_mn;
4194 TArray2 q_xx_am, q_yy_am, q_zz_am;
4195 TArray2 Qxx_am, Qyy_am, Qzz_am, Qxy_am, Qxz_am, Qyz_am;
4196 if (compute_quadrupole) {
4197 q_xx_mn = xy("<m|q_xx|n>");
4198 q_yy_mn = xy("<m|q_yy|n>");
4199 q_zz_mn = xy("<m|q_zz|n>");
4200 Qxx_mn("m,n") = q_xx_mn("m,n") - (q_zz_mn("m,n") + q_yy_mn("m,n")) * 0.5;
4201 Qyy_mn("m,n") = q_yy_mn("m,n") - (q_zz_mn("m,n") + q_xx_mn("m,n")) * 0.5;
4202 Qzz_mn("m,n") = q_zz_mn("m,n") - (q_xx_mn("m,n") + q_yy_mn("m,n")) * 0.5;
4203 Qxz_mn("m,n") = _2("<m|q_xz|n>") * 1.5;
4204 Qxy_mn("m,n") = _2("<m|q_xy|n>") * 1.5;
4205 Qyz_mn("m,n") = _2("<m|q_yz|n>") * 1.5;
4206
4207 q_xx_am = xy("<a|q_xx|m>");
4208 q_yy_am = xy("<a|q_yy|m>");
4209 q_zz_am = xy("<a|q_zz|m>");
4210 Qxx_am("a,m") = q_xx_am("a,m") - (q_zz_am("a,m") + q_yy_am("a,m")) * 0.5;
4211 Qyy_am("a,m") = q_yy_am("a,m") - (q_zz_am("a,m") + q_xx_am("a,m")) * 0.5;
4212 Qzz_am("a,m") = q_zz_am("a,m") - (q_xx_am("a,m") + q_yy_am("a,m")) * 0.5;
4213 Qxy_am("a,m") = _2("<a|q_xy|m>") * 1.5;
4214 Qxz_am("a,m") = _2("<a|q_xz|m>") * 1.5;
4215 Qyz_am("a,m") = _2("<a|q_yz|m>") * 1.5;
4216 }
4217
4218 // electric field gradient integrals
4219 TArray2 v_xx_mn, v_yy_mn, v_zz_mn, v_xy_mn, v_xz_mn, v_yz_mn;
4220 TArray2 v_xx_am, v_yy_am, v_zz_am, v_xy_am, v_xz_am, v_yz_am;
4221 if (compute_EFG) {
4222 v_xx_mn = xy("<m|ddphi_xx|n>");
4223 v_yy_mn = xy("<m|ddphi_yy|n>");
4224 v_zz_mn = xy("<m|ddphi_zz|n>");
4225 v_xy_mn = xy("<m|ddphi_xy|n>");
4226 v_xz_mn = xy("<m|ddphi_xz|n>");
4227 v_yz_mn = xy("<m|ddphi_yz|n>");
4228
4229 v_xx_am = xy("<a|ddphi_xx|m>");
4230 v_yy_am = xy("<a|ddphi_yy|m>");
4231 v_zz_am = xy("<a|ddphi_zz|m>");
4232 v_xy_am = xy("<a|ddphi_xy|m>");
4233 v_xz_am = xy("<a|ddphi_xz|m>");
4234 v_yz_am = xy("<a|ddphi_yz|m>");
4235 }
4236
4237 // compute HF contribution
4238 Ref<Molecule> mol = r12world_->basis()->molecule();
4239 const int natom = mol->natom();
4240
4241 TArray2 Imn = xy("<m|I|n>");
4242
4243 // HF eletric dipole
4244 double mu_z_n = 0.0, mu_z_scf = 0.0;
4245 if (compute_dipole) {
4246 // Nuclear contribution to dipole
4247 for(int a = 0; a < natom; ++a) {
4248 const double x = mol->r(a, 0);
4249 const double y = mol->r(a, 1);
4250 const double z = mol->r(a, 2);
4251 const double Z = mol->Z(a);
4252 mu_z_n += Z * z;
4253 }
4254
4255 // SCF contribution to electronic electric dipole
4256 mu_z_scf = dot(mu_z_mn("m,n"), Imn("m,n"));
4257 }
4258
4259 // HF eletric quadrupole
4260 double q_xx_n = 0.0, q_yy_n = 0.0, q_zz_n = 0.0;
4261 double q_xy_n = 0.0, q_xz_n = 0.0, q_yz_n = 0.0;
4262 double q_xx_scf = 0.0, q_yy_scf = 0.0, q_zz_scf = 0.0,
4263 q_xy_scf = 0.0, q_xz_scf = 0.0, q_yz_scf = 0.0;
4264 if (compute_quadrupole) {
4265 // Nuclear electric quadrupole (traceless)
4266 for(int a = 0; a < natom; ++a) {
4267 const double x = mol->r(a, 0);
4268 const double y = mol->r(a, 1);
4269 const double z = mol->r(a, 2);
4270 const double Z = mol->Z(a);
4271
4272 q_xx_n += Z * (x * x - (z * z + y * y) * 0.5); // traceless form of the quadrupole
4273 q_yy_n += Z * (y * y - (z * z + x * x) * 0.5); // traceless form of the quadrupole
4274 q_zz_n += Z * (z * z - (x * x + y * y) * 0.5); // traceless form of the quadrupole
4275 q_xy_n += Z * (x * y * 1.5); // traceless form of the quadrupole
4276 q_xz_n += Z * (x * z * 1.5); // traceless form of the quadrupole
4277 q_yz_n += Z * (y * z * 1.5); // traceless form of the quadrupole
4278 }
4279
4280 // SCF contribution to electronic electric quadrupoles
4281 q_xx_scf = dot(Qxx_mn("m,n"), Imn("m,n"));
4282 q_yy_scf = dot(Qyy_mn("m,n"), Imn("m,n"));
4283 q_zz_scf = dot(Qzz_mn("m,n"), Imn("m,n"));
4284 q_xy_scf = dot(Qxy_mn("m,n"), Imn("m,n"));
4285 q_xz_scf = dot(Qxz_mn("m,n"), Imn("m,n"));
4286 q_yz_scf = dot(Qyz_mn("m,n"), Imn("m,n"));
4287 }
4288
4289 // HF electric field gradient near the 1st nucleus
4290 if (compute_EFG) {
4291 // Nuclear contribution to electric field gradient near the 1st nucleus
4292 double v_xx_n = 0.0, v_yy_n = 0.0, v_zz_n = 0.0;
4293 double v_xy_n = 0.0, v_xz_n = 0.0, v_yz_n = 0.0;
4294 for(int i = 1; i < natom; i++) {
4295 const double x = mol->r(0, 0) - mol->r(i, 0);
4296 const double y = mol->r(0, 1) - mol->r(i, 1);
4297 const double z = mol->r(0, 2) - mol->r(i, 2);
4298 const double r2 = x * x + y * y + z * z;
4299 const double r = pow(r2, 0.5);
4300 const double Z = mol->Z(i);
4301
4302 v_xx_n += - Z * (3.0 * x * x - r2) / (r * r2 * r2);
4303 v_yy_n += - Z * (3.0 * y * y - r2) / (r * r2 * r2);
4304 v_zz_n += - Z * (3.0 * z * z - r2) / (r * r2 * r2);
4305
4306 v_xy_n += - Z * (3.0 * x * y) / (r * r2 * r2);
4307 v_xz_n += - Z * (3.0 * x * z) / (r * r2 * r2);
4308 v_yz_n += - Z * (3.0 * y * z) / (r * r2 * r2);
4309 }
4310
4311 // Electric field gradient near the 1st nucleus
4312 const double v_xx_scf = dot(v_xx_mn("m,n"), Imn("m,n"));
4313 const double v_yy_scf = dot(v_yy_mn("m,n"), Imn("m,n"));
4314 const double v_zz_scf = dot(v_zz_mn("m,n"), Imn("m,n"));
4315 const double v_xy_scf = dot(v_xy_mn("m,n"), Imn("m,n"));
4316 const double v_xz_scf = dot(v_xz_mn("m,n"), Imn("m,n"));
4317 const double v_yz_scf = dot(v_yz_mn("m,n"), Imn("m,n"));
4318
4319 std::cout << std::endl << indent
4320 << "electric gradient (HF=SCF+N)" << std::endl
4321 << indent << "v_xx (HF) = " << scprintf("%12.10f", v_xx_n + v_xx_scf * 2.0)
4322 << indent << " v_yy (HF) = " << scprintf("%12.10f", v_yy_n + v_yy_scf * 2.0)
4323 << indent << " v_zz (HF) = " << scprintf("%12.10f", v_zz_n + v_zz_scf * 2.0)
4324 << std::endl
4325 << indent << "v_xy (HF) = " << scprintf("%12.10f", v_xy_n + v_xy_scf * 2.0)
4326 << indent << " v_xz (HF) = " << scprintf("%12.10f", v_xz_n + v_xz_scf * 2.0)
4327 << indent << " v_yz (HF) = " << scprintf("%12.10f", v_yz_n + v_yz_scf * 2.0)
4328 << std::endl;
4329 }
4330
4331 // compute integrals needed for orbital relaxation
4332 // i.e. solve Abnam Dbn = Xam (close-shell formula)
4333 TArray4d g_mnab = ijxy("<m n|g|a b>");
4334 TArray4 A_bnam;
4335 A_bnam("b,n,a,m") = - _4("<b n|g|a m>") - g_mnab("m,n,b,a") + 4.0 * g_mnab("n,m,b,a")
4336 + _2("<b|F|a>") * Imn("m,n") - _2("<a|I|b>") * _2("<m|F|n>");
4337
4338 // Make preconditioner: Delta_am = 1 / (<a|F|a> - <m|F|m>) for
4339 // solving k_bn A_bnam = X_am
4340 TArray2 mFmn, mFab;
4341 mFmn("m,n") = - _2("<m|F|n>");
4342 mFab("a,b") = - _2("<a|F|b>");
4343 typedef detail::diag_precond2<double> pceval_type;
4344 pceval_type Delta_am_gen(TA::array_to_eigen(mFab), TA::array_to_eigen(mFmn));
4345
4346 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2d;
4347 TArray2 Iam = xy("<a|I|m>");
4348 TArray2d Delta_am(Iam.world(), Iam.trange());
4349
4350 // construct local tiles
4351 for(auto t = Delta_am.trange().tiles_range().begin();
4352 t != Delta_am.trange().tiles_range().end(); ++t)
4353 if (Delta_am.is_local(*t)) {
4354 std::array<std::size_t, 2> index;
4355 std::copy(t->begin(), t->end(), index.begin());
4356 madness::Future < typename TArray2d::value_type >
4357 tile((LazyTensor<T, 2, pceval_type >(&Delta_am, index, &Delta_am_gen)
4358 ));
4359
4360 // Insert the tile into the array
4361 Delta_am.set(*t, tile);
4362 }
4363 TArray2 preconditioner;
4364 preconditioner("a,m") = Delta_am("a,m");
4365
4366 detail::Orbital_relaxation_Abjai<double> Orbital_relaxation_Abnam(A_bnam);
4367 TA::ConjugateGradientSolver<TiledArray::Array<T,2>,
4368 detail::Orbital_relaxation_Abjai<double> > cg_solver2;
4369
4370 // compute CABS singles contribution
4371 double mu_z_e2 = 0.0, mu_z_e2or = 0.0;
4372 double q_xx_e2 = 0.0, q_yy_e2 = 0.0, q_zz_e2 = 0.0;
4373 double q_xx_e2or = 0.0, q_yy_e2or = 0.0, q_zz_e2or = 0.0;
4374#if INCLUDE_CABS_Singles_CONTRI
4375 {
4376 ExEnv::out0() << std::endl << indent
4377 << "Compute CABS_singles contributions" << std::endl;
4378 TArray2 TmA = xy("<m|T1|A'>");
4379 TArray2 Tma = xy("<m|T1|a>");
4380
4381 // density from CABS Singles contribution
4382 // D^m_n = t^m_A' * t^A'_n
4383 // D^A'_B' = t^A'_m * t^m_B'
4384 // D^A'_m = t^A'_m
4385 ExEnv::out0() << indent
4386 << "Compute CABS_singles D" << std::endl;
4387 TArray2 D_e2_mn, D_e2_AB;
4388 D_e2_mn("m,n") = TmA("m,A'") * TmA("n,A'");
4389 D_e2_AB("A',B'") = TmA("m,A'") * TmA("m,B'");
4390
4391 // CABS singles orbital response
4392 ExEnv::out0() << indent
4393 << "Compute CABS_singles Xam" << std::endl;
4394 TArray2 Xam_E2 = Xam_CabsSingles(TmA, Tma);
4395 TArray2 Dbn_E2(Xam_E2.world(), Xam_E2.trange());
4396 // solve k_bn A_bnam = X_am
4397 auto resnorm_E2 = cg_solver2(Orbital_relaxation_Abnam,
4398 Xam_E2,
4399 Dbn_E2,
4400 preconditioner,
4401 conv_target);
4402
4403 // compute CABS singles contribution to dipole
4404 if (compute_dipole) {
4405 TArray2 mu_z_AB = xy("<A'|mu_z|B'>");
4406 TArray2 mu_z_mA = xy("<m|mu_z|A'>");
4407
4408 mu_z_e2 = - dot(mu_z_mn("m,n"), D_e2_mn("m,n"))
4409 + dot(mu_z_AB("A',B'"), D_e2_AB("A',B'"))
4410 + dot(mu_z_mA("m,A'"), TmA("m,A'")) * 2.0;
4411
4412 // CABS singles orbital response contribution to dipole
4413 mu_z_e2or = dot(mu_z_am("a,m"), Dbn_E2("a,m"));
4414 }
4415
4416 // CABS singles contribution to quadrupoles
4417 if (compute_quadrupole) {
4418 TArray2 q_xx_AB = xy("<A'|q_xx|B'>");
4419 TArray2 q_yy_AB = xy("<A'|q_yy|B'>");
4420 TArray2 q_zz_AB = xy("<A'|q_zz|B'>");
4421 TArray2 Qxx_AB, Qyy_AB, Qzz_AB;
4422 Qxx_AB("A',B'") = q_xx_AB("A',B'") - (q_zz_AB("A',B'") + q_yy_AB("A',B'")) * 0.5;
4423 Qyy_AB("A',B'") = q_yy_AB("A',B'") - (q_xx_AB("A',B'") + q_zz_AB("A',B'")) * 0.5;
4424 Qzz_AB("A',B'") = q_zz_AB("A',B'") - (q_xx_AB("A',B'") + q_yy_AB("A',B'")) * 0.5;
4425
4426 TArray2 q_xx_mA = xy("<m|q_xx|A'>");
4427 TArray2 q_yy_mA = xy("<m|q_yy|A'>");
4428 TArray2 q_zz_mA = xy("<m|q_zz|A'>");
4429 TArray2 Qxx_mA, Qyy_mA, Qzz_mA;
4430 Qxx_mA("m,A'") = q_xx_mA("m,A'") - (q_zz_mA("m,A'") + q_yy_mA("m,A'") ) * 0.5;
4431 Qyy_mA("m,A'") = q_yy_mA("m,A'") - (q_xx_mA("m,A'") + q_zz_mA("m,A'") ) * 0.5;
4432 Qzz_mA("m,A'") = q_zz_mA("m,A'") - (q_xx_mA("m,A'") + q_yy_mA("m,A'") ) * 0.5;
4433
4434 q_xx_e2 = - dot(Qxx_mn("m,n"), D_e2_mn("m,n"))
4435 + dot(Qxx_AB("A',B'"), D_e2_AB("A',B'"))
4436 + dot(Qxx_mA("m,A'"), TmA("m,A'")) * 2.0;
4437 q_yy_e2 = - dot(Qyy_mn("m,n"), D_e2_mn("m,n"))
4438 + dot(Qyy_AB("A',B'"), D_e2_AB("A',B'"))
4439 + dot(Qyy_mA("m,A'"), TmA("m,A'")) * 2.0;
4440 q_zz_e2 = - dot(Qzz_mn("m,n"), D_e2_mn("m,n"))
4441 + dot(Qzz_AB("A',B'"), D_e2_AB("A',B'"))
4442 + dot(Qzz_mA("m,A'"), TmA("m,A'")) * 2.0;
4443
4444 q_xx_e2or = dot(Qxx_am("a,m"), Dbn_E2("a,m"));
4445 q_yy_e2or = dot(Qyy_am("a,m"), Dbn_E2("a,m"));
4446 q_zz_e2or = dot(Qzz_am("a,m"), Dbn_E2("a,m"));
4447 }
4448
4449 // CABS singles contribution to
4450 // electric field gradient near the 1st nucleus
4451 if (compute_EFG) {
4452 TArray2 v_xx_mA = xy("<m|ddphi_xx|A'>");
4453 TArray2 v_yy_mA = xy("<m|ddphi_yy|A'>");
4454 TArray2 v_zz_mA = xy("<m|ddphi_zz|A'>");
4455 TArray2 v_xy_mA = xy("<m|ddphi_xy|A'>");
4456 TArray2 v_xz_mA = xy("<m|ddphi_xz|A'>");
4457 TArray2 v_yz_mA = xy("<m|ddphi_yz|A'>");
4458
4459 TArray2 v_xx_AB = xy("<A'|ddphi_xx|B'>");
4460 TArray2 v_yy_AB = xy("<A'|ddphi_yy|B'>");
4461 TArray2 v_zz_AB = xy("<A'|ddphi_zz|B'>");
4462 TArray2 v_xy_AB = xy("<A'|ddphi_xy|B'>");
4463 TArray2 v_xz_AB = xy("<A'|ddphi_xz|B'>");
4464 TArray2 v_yz_AB = xy("<A'|ddphi_yz|B'>");
4465
4466 const double v_xx_e2 = - dot(v_xx_mn("m,n"), D_e2_mn("m,n"))
4467 + dot(v_xx_AB("A',B'"), D_e2_AB("A',B'"))
4468 + dot(v_xx_mA("m,A'"), TmA("m,A'")) * 2.0;
4469 const double v_yy_e2 = - dot(v_yy_mn("m,n"), D_e2_mn("m,n"))
4470 + dot(v_yy_AB("A',B'"), D_e2_AB("A',B'"))
4471 + dot(v_yy_mA("m,A'"), TmA("m,A'")) * 2.0;
4472 const double v_zz_e2 = - dot(v_zz_mn("m,n"), D_e2_mn("m,n"))
4473 + dot(v_zz_AB("A',B'"), D_e2_AB("A',B'"))
4474 + dot(v_zz_mA("m,A'"), TmA("m,A'")) * 2.0;
4475 const double v_xy_e2 = - dot(v_xy_mn("m,n"), D_e2_mn("m,n"))
4476 + dot(v_xy_AB("A',B'"), D_e2_AB("A',B'"))
4477 + dot(v_xy_mA("m,A'"), TmA("m,A'")) * 2.0;
4478 const double v_xz_e2 = - dot(v_xz_mn("m,n"), D_e2_mn("m,n"))
4479 + dot(v_xz_AB("A',B'"), D_e2_AB("A',B'"))
4480 + dot(v_xz_mA("m,A'"), TmA("m,A'")) * 2.0;
4481 const double v_yz_e2 = - dot(v_yz_mn("m,n"), D_e2_mn("m,n"))
4482 + dot(v_yz_AB("A',B'"), D_e2_AB("A',B'"))
4483 + dot(v_yz_mA("m,A'"), TmA("m,A'")) * 2.0;
4484
4485 const double v_xx_e2or = dot(v_xx_am("a,m"), Dbn_E2("a,m"));
4486 const double v_yy_e2or = dot(v_yy_am("a,m"), Dbn_E2("a,m"));
4487 const double v_zz_e2or = dot(v_zz_am("a,m"), Dbn_E2("a,m"));
4488 const double v_xy_e2or = dot(v_xy_am("a,m"), Dbn_E2("a,m"));
4489 const double v_xz_e2or = dot(v_xz_am("a,m"), Dbn_E2("a,m"));
4490 const double v_yz_e2or = dot(v_yz_am("a,m"), Dbn_E2("a,m"));
4491
4492 std::cout << std::endl << indent
4493 << "electric gradient (E2)" << std::endl
4494 << indent << "v_xx (E2) = " << scprintf("%12.10f", v_xx_e2 * 2.0)
4495 << indent << " v_yy (E2) = " << scprintf("%12.10f", v_yy_e2 * 2.0)
4496 << indent << " v_zz (E2) = " << scprintf("%12.10f", v_zz_e2 * 2.0)
4497 << std::endl
4498 << indent << "v_xy (E2) = " << scprintf("%12.10f", v_xy_e2 * 2.0)
4499 << indent << " v_xz (E2) = " << scprintf("%12.10f", v_xz_e2 * 2.0)
4500 << indent << " v_yz (E2) = " << scprintf("%12.10f", v_yz_e2 * 2.0)
4501 << std::endl;
4502 std::cout << std::endl << indent
4503 << "electric gradient (E2 orbital response)" << std::endl
4504 << indent << "v_xx (E2 or) = " << scprintf("%12.10f", v_xx_e2or * 2.0)
4505 << indent << " v_yy (E2 or) = " << scprintf("%12.10f", v_yy_e2or * 2.0)
4506 << indent << " v_zz (E2 or) = " << scprintf("%12.10f", v_zz_e2or * 2.0)
4507 << std::endl
4508 << indent << "v_xy (E2 or) = " << scprintf("%12.10f", v_xy_e2or * 2.0)
4509 << indent << " v_xz (E2 or) = " << scprintf("%12.10f", v_xz_e2or * 2.0)
4510 << indent << " v_yz (E2 or) = " << scprintf("%12.10f", v_yz_e2or * 2.0)
4511 << std::endl << std::endl;
4512 }
4513
4514 }
4515 world_.gop.fence(); // clear memory
4516#endif
4517
4518 // determine if it is frozen-core
4519 TArray2 Fij = xy("<i|F|j>");
4520 const std::size_t nocc = mFmn.trange().elements_range().extent()[0];
4521 const std::size_t naocc = Fij.trange().elements_range().extent()[0];
4522
4523 // compute integrals needed for MP2 and following calculations of properties
4524 // dipole integrals
4525 TArray2 mu_z_ij, mu_z_ab, mu_z_ijp;
4526 if (compute_dipole) {
4527 mu_z_ij = xy("<i|mu_z|j>");
4528 mu_z_ab = xy("<a|mu_z|b>");
4529
4530 if (nocc != naocc) {
4531 mu_z_ijp = xy("<i|mu_z|j'>");
4532 }
4533 }
4534
4535 // quadrupole integrals
4536 TArray2 q_xx_ij, q_yy_ij, q_zz_ij, Qxx_ij, Qyy_ij, Qzz_ij;
4537 TArray2 q_xx_ab, q_yy_ab, q_zz_ab, Qxx_ab, Qyy_ab, Qzz_ab;
4538 // integrals for frozen-core
4539 TArray2 Qxx_ijp, Qyy_ijp, Qzz_ijp;
4540 if (compute_quadrupole){
4541 q_xx_ij = xy("<i|q_xx|j>");
4542 q_yy_ij = xy("<i|q_yy|j>");
4543 q_zz_ij = xy("<i|q_zz|j>");
4544 Qxx_ij("i,j") = q_xx_ij("i,j") - (q_zz_ij("i,j") + q_yy_ij("i,j")) * 0.5;
4545 Qyy_ij("i,j") = q_yy_ij("i,j") - (q_zz_ij("i,j") + q_xx_ij("i,j")) * 0.5;
4546 Qzz_ij("i,j") = q_zz_ij("i,j") - (q_xx_ij("i,j") + q_yy_ij("i,j")) * 0.5;
4547
4548 q_xx_ab = xy("<a|q_xx|b>");
4549 q_yy_ab = xy("<a|q_yy|b>");
4550 q_zz_ab = xy("<a|q_zz|b>");
4551 Qxx_ab("a,b") = q_xx_ab("a,b") - (q_zz_ab("a,b") + q_yy_ab("a,b")) * 0.5;
4552 Qyy_ab("a,b") = q_yy_ab("a,b") - (q_zz_ab("a,b") + q_xx_ab("a,b")) * 0.5;
4553 Qzz_ab("a,b") = q_zz_ab("a,b") - (q_xx_ab("a,b") + q_yy_ab("a,b")) * 0.5;
4554
4555 if (nocc != naocc) {
4556 TArray2 q_xx_ijp = xy("<i|q_xx|j'>");
4557 TArray2 q_yy_ijp = xy("<i|q_yy|j'>");
4558 TArray2 q_zz_ijp = xy("<i|q_zz|j'>");
4559 Qxx_ijp("i,j'") = q_xx_ijp("i,j'") - (q_zz_ijp("i,j'") + q_yy_ijp("i,j'")) * 0.5;
4560 Qyy_ijp("i,j'") = q_yy_ijp("i,j'") - (q_zz_ijp("i,j'") + q_xx_ijp("i,j'")) * 0.5;
4561 Qzz_ijp("i,j'") = q_zz_ijp("i,j'") - (q_xx_ijp("i,j'") + q_yy_ijp("i,j'")) * 0.5;
4562 }
4563 }
4564
4565 // electric field gradient integrals
4566 TArray2 v_xx_ij, v_yy_ij, v_zz_ij, v_xy_ij, v_xz_ij, v_yz_ij;
4567 TArray2 v_xx_ab, v_yy_ab, v_zz_ab, v_xy_ab, v_xz_ab, v_yz_ab;
4568 if (compute_EFG) {
4569 v_xx_ij = xy("<i|ddphi_xx|j>");
4570 v_yy_ij = xy("<i|ddphi_yy|j>");
4571 v_zz_ij = xy("<i|ddphi_zz|j>");
4572 v_xy_ij = xy("<i|ddphi_xy|j>");
4573 v_xz_ij = xy("<i|ddphi_xz|j>");
4574 v_yz_ij = xy("<i|ddphi_yz|j>");
4575
4576 v_xx_ab = xy("<a|ddphi_xx|b>");
4577 v_yy_ab = xy("<a|ddphi_yy|b>");
4578 v_zz_ab = xy("<a|ddphi_zz|b>");
4579 v_xy_ab = xy("<a|ddphi_xy|b>");
4580 v_xz_ab = xy("<a|ddphi_xz|b>");
4581 v_yz_ab = xy("<a|ddphi_yz|b>");
4582 }
4583
4584 // compute terms needed for frozen-core
4585 TArray2 Delta_ijp_F;
4586 TArray4 A_ijpam;
4587 if (nocc != naocc) {
4588 // compute 1 / (Fi'i' - Fjj)
4589 TArray2 Fipjp = xy("<i'|F|j'>");
4590 pceval_type Delta_ijp_gen(TA::array_to_eigen(Fij), TA::array_to_eigen(Fipjp));
4591
4592 TArray2 Fijp = xy("<i|F|j'>");
4593 TArray2d Delta_ijp(Fijp.world(), Fijp.trange());
4594 // construct local tiles
4595 for(auto t = Delta_ijp.trange().tiles_range().begin();
4596 t != Delta_ijp.trange().tiles_range().end(); ++t)
4597 if (Delta_ijp.is_local(*t)) {
4598 std::array<std::size_t, 2> index;
4599 std::copy(t->begin(), t->end(), index.begin());
4600 madness::Future < typename TArray2d::value_type >
4601 tile((LazyTensor<T, 2, pceval_type >(&Delta_ijp, index, &Delta_ijp_gen)
4602 ));
4603
4604 // Insert the tile into the array
4605 Delta_ijp.set(*t, tile);
4606 }
4607 Delta_ijp_F("i,j'") = Delta_ijp("i,j'");
4608
4609 A_ijpam("i,j',a,m") = 4.0 * _4("<i a|g|j' m>") - _4("<i a|g|m j'>") - _4("<i m|g|a j'>");
4610 }
4611
4612 // compute MP2 and its orbital response contribution
4613 // compute Delta_ijab = - 1 / (- <i|F|i> - <j|F|j> + <a|F|a> + <b|F|b>)
4614 // which is needed for MP2 amplitudes & MP2 F12 coupling
4615 TArray2 mFij;
4616 mFij("i,j") = - _2("<i|F|j>");
4617 TArray4d g_ijab = ijxy("<i j|g|a b>");
4618
4619 typedef detail::diag_precond4<double> pc4eval_type;
4620 typedef TA::Array<T, 4, LazyTensor<T, 4, pc4eval_type > > TArray4dLazy;
4621 TArray4dLazy Delta_ijab(g_ijab.world(), g_ijab.trange());
4622 pc4eval_type Delta_ijab_gen(TA::array_to_eigen(mFij), TA::array_to_eigen(mFij),
4623 TA::array_to_eigen(mFab),TA::array_to_eigen(mFab));
4624 // construct local tiles
4625 for(auto t = Delta_ijab.trange().tiles_range().begin();
4626 t != Delta_ijab.trange().tiles_range().end(); ++t)
4627 if (Delta_ijab.is_local(*t)) {
4628 std::array<std::size_t, 4> index;
4629 std::copy(t->begin(), t->end(), index.begin());
4630 madness::Future < typename TArray4dLazy::value_type >
4631 tile((LazyTensor<T, 4, pc4eval_type >(&Delta_ijab, index, &Delta_ijab_gen)
4632 ));
4633
4634 // Insert the tile into the array
4635 Delta_ijab.set(*t, tile);
4636 }
4637
4638 // MP2 amplitues which are needed for MP2 and coupling contibutions
4639 TArray4 T2_ijab;
4640 T2_ijab("i,j,a,b") = g_ijab("i,j,a,b") * Delta_ijab("i,j,a,b");
4641
4642 double mu_z_mp2 = 0.0, mu_z_mp2or = 0.0;
4643 double q_xx_mp2 = 0.0, q_yy_mp2 = 0.0, q_zz_mp2 = 0.0;
4644 double q_xx_mp2or = 0.0, q_yy_mp2or = 0.0, q_zz_mp2or = 0.0;
4645#if INCLUDE_MP2_CONTRI
4646 {
4647 ExEnv::out0() << std::endl << indent
4648 << "Compute MP2 contributions" << std::endl;
4649 // MP2 density
4650 TArray2 D_mp2_ij, D_mp2_ab;
4651 D_mp2_ij("i,j") = (2.0 * T2_ijab("i,k,a,b") - T2_ijab("k,i,a,b"))
4652 * T2_ijab("j,k,a,b");
4653 D_mp2_ab("a,b") = (2.0 * T2_ijab("i,j,a,c") - T2_ijab("i,j,c,a"))
4654 * T2_ijab("i,j,b,c");
4655
4656 // MP2 orbital response
4657 TArray2 X_mp2_nfzc = Xam_mp2(T2_ijab, D_mp2_ij, D_mp2_ab);
4658
4659 TArray2 X_mp2;
4660 // frozen-core contribution
4661 TArray2 Dijp_or_mp2;
4662 if (nocc != naocc) {
4663 ExEnv::out0() << std::endl << indent
4664 << "Include frozen-core MP2 contributions" << std::endl;
4665 Dijp_or_mp2("i,j'") = - ( _4("<j' l|g|c d>")
4666 * (2.0 * T2_ijab("i,l,c,d") - T2_ijab("l,i,c,d"))
4667 ) * Delta_ijp_F("i,j'") * 2.0;
4668 TArray2 Xam_Dijp_or;
4669 Xam_Dijp_or("a,m") = A_ijpam("i,j',a,m") * Dijp_or_mp2("i,j'");
4670 X_mp2("a,m") = X_mp2_nfzc("a,m") - Xam_Dijp_or("a,m");
4671
4672 // test code: print out Ima in frozen-core case
4673// TArray2 Iia, Ima;
4674// Iia("a,i") = _4("<a l|g|c d>")
4675// * (2.0 * T2_ijab("i,l,c,d") - T2_ijab("l,i,c,d"));
4676// Ima("a,m") = (2.0 * _4("<a c|g|m d>") - _4("<a c|g|d m>"))
4677// * D_mp2_ab("d,c")
4678// - (2.0 * _4("<a l|g|m k>") - _4("<a l|g|k m>"))
4679// * D_mp2_ij("k,l")
4680// ;
4681// TArray2 Iima = XaiAddToXam(Ima, Iia);
4682// TArray2 Iima_fzc;
4683// Iima_fzc("a,m") = Iima("a,m") + Xam_Dijp_or("a,m") * 0.5;
4684// ExEnv::out0() << std::endl << "FZC Ima : " << std::endl << Iima_fzc << std::endl;
4685 } else {
4686 X_mp2("a,m") = X_mp2_nfzc("a,m");
4687 }
4688 // *** end of frozen-core ***
4689
4690 TArray2 Dbn_mp2(X_mp2.world(), X_mp2.trange());
4691 auto resnorm_mp2 = cg_solver2(Orbital_relaxation_Abnam,
4692 X_mp2,
4693 Dbn_mp2,
4694 preconditioner,
4695 conv_target);
4696
4697 // MP2 dipole
4698 if (compute_dipole) {
4699 // MP2 density contribution to dipole
4700 mu_z_mp2 = - dot(mu_z_ij("i,j"), D_mp2_ij("i,j"))
4701 + dot(mu_z_ab("a,b"), D_mp2_ab("a,b"));
4702
4703 // MP2 orbital response contribution to dipole
4704 mu_z_mp2or = dot(mu_z_am("a,m"), Dbn_mp2("a,m"));
4705
4706 if (nocc != naocc) {
4707 mu_z_mp2or += dot(mu_z_ijp("i,j'"), Dijp_or_mp2("i,j'"));
4708 }
4709 }
4710
4711 // MP2 contribution to quadrupoles
4712 if (compute_quadrupole) {
4713 q_xx_mp2 = - dot(Qxx_ij("i,j"), D_mp2_ij("i,j"))
4714 + dot(Qxx_ab("a,b"), D_mp2_ab("a,b"));
4715 q_yy_mp2 = - dot(Qyy_ij("i,j"), D_mp2_ij("i,j"))
4716 + dot(Qyy_ab("a,b"), D_mp2_ab("a,b"));
4717 q_zz_mp2 = - dot(Qzz_ij("i,j"), D_mp2_ij("i,j"))
4718 + dot(Qzz_ab("a,b"), D_mp2_ab("a,b"));
4719// // x2, y2, z2 components to quadrupole moment
4720// q_xx_mp2 = - dot(q_xx_ij("i,j"), D_mp2_ij("i,j"))
4721// + dot(q_xx_ab("a,b"), D_mp2_ab("a,b"));
4722// q_yy_mp2 = - dot(q_yy_ij("i,j"), D_mp2_ij("i,j"))
4723// + dot(q_yy_ab("a,b"), D_mp2_ab("a,b"));
4724// q_zz_mp2 = - dot(q_zz_ij("i,j"), D_mp2_ij("i,j"))
4725// + dot(q_zz_ab("a,b"), D_mp2_ab("a,b"));
4726
4727 q_xx_mp2or = dot(Qxx_am("a,m"), Dbn_mp2("a,m"));
4728 q_yy_mp2or = dot(Qyy_am("a,m"), Dbn_mp2("a,m"));
4729 q_zz_mp2or = dot(Qzz_am("a,m"), Dbn_mp2("a,m"));
4730// // x2, y2, z2 components to quadrupole moment
4731// q_xx_mp2or = dot(q_xx_am("a,m"), Dbn_mp2("a,m"));
4732// q_yy_mp2or = dot(q_yy_am("a,m"), Dbn_mp2("a,m"));
4733// q_zz_mp2or = dot(q_zz_am("a,m"), Dbn_mp2("a,m"));
4734
4735 if (nocc != naocc) {
4736 q_xx_mp2or += dot(Qxx_ijp("i,j'"), Dijp_or_mp2("i,j'"));
4737 q_yy_mp2or += dot(Qyy_ijp("i,j'"), Dijp_or_mp2("i,j'"));
4738 q_zz_mp2or += dot(Qzz_ijp("i,j'"), Dijp_or_mp2("i,j'"));
4739 }
4740 }
4741
4742 // Electric field gradient near the 1st nucleus
4743 if (compute_EFG) {
4744 const double v_xx_mp2 = - dot(v_xx_ij("i,j"), D_mp2_ij("i,j"))
4745 + dot(v_xx_ab("a,b"), D_mp2_ab("a,b"));
4746 const double v_yy_mp2 = - dot(v_yy_ij("i,j"), D_mp2_ij("i,j"))
4747 + dot(v_yy_ab("a,b"), D_mp2_ab("a,b"));
4748 const double v_zz_mp2 = - dot(v_zz_ij("i,j"), D_mp2_ij("i,j"))
4749 + dot(v_zz_ab("a,b"), D_mp2_ab("a,b"));
4750 const double v_xy_mp2 = - dot(v_xy_ij("i,j"), D_mp2_ij("i,j"))
4751 + dot(v_xy_ab("a,b"), D_mp2_ab("a,b"));
4752 const double v_xz_mp2 = - dot(v_xz_ij("i,j"), D_mp2_ij("i,j"))
4753 + dot(v_xz_ab("a,b"), D_mp2_ab("a,b"));
4754 const double v_yz_mp2 = - dot(v_yz_ij("i,j"), D_mp2_ij("i,j"))
4755 + dot(v_yz_ab("a,b"), D_mp2_ab("a,b"));
4756
4757 const double v_xx_mp2or = dot(v_xx_am("a,m"), Dbn_mp2("a,m"));
4758 const double v_yy_mp2or = dot(v_yy_am("a,m"), Dbn_mp2("a,m"));
4759 const double v_zz_mp2or = dot(v_zz_am("a,m"), Dbn_mp2("a,m"));
4760 const double v_xy_mp2or = dot(v_xy_am("a,m"), Dbn_mp2("a,m"));
4761 const double v_xz_mp2or = dot(v_xz_am("a,m"), Dbn_mp2("a,m"));
4762 const double v_yz_mp2or = dot(v_yz_am("a,m"), Dbn_mp2("a,m"));
4763
4764 std::cout << std::endl << indent
4765 << "electric gradient (MP2)" << std::endl
4766 << indent << "v_xx (MP2) = " << scprintf("%12.10f", - v_xx_mp2 * 2.0)
4767 << indent << " v_yy (MP2) = " << scprintf("%12.10f", - v_yy_mp2 * 2.0)
4768 << indent << " v_zz (MP2) = " << scprintf("%12.10f", - v_zz_mp2 * 2.0)
4769 << std::endl
4770 << indent << "v_xy (MP2) = " << scprintf("%12.10f", - v_xy_mp2 * 2.0)
4771 << indent << " v_xz (MP2) = " << scprintf("%12.10f", - v_xz_mp2 * 2.0)
4772 << indent << " v_yz (MP2) = " << scprintf("%12.10f", - v_yz_mp2 * 2.0)
4773 << std::endl;
4774 std::cout << std::endl << indent
4775 << "electric gradient (MP2 orbital response)" << std::endl
4776 << indent << "v_xx (MP2 or) = " << scprintf("%12.10f", - v_xx_mp2or * 2.0)
4777 << indent << " v_yy (MP2 or) = " << scprintf("%12.10f", - v_yy_mp2or * 2.0)
4778 << indent << " v_zz (MP2 or) = " << scprintf("%12.10f", - v_zz_mp2or * 2.0)
4779 << std::endl
4780 << indent << "v_xy (MP2 or) = " << scprintf("%12.10f", - v_xy_mp2or * 2.0)
4781 << indent << " v_xz (MP2 or) = " << scprintf("%12.10f", - v_xz_mp2or * 2.0)
4782 << indent << " v_yz (MP2 or) = " << scprintf("%12.10f", - v_yz_mp2or * 2.0)
4783 << std::endl << std::endl;
4784 }
4785
4786 }
4787 world_.gop.fence();
4788#endif
4789
4790 // compute integrals needed for F12 related calculations of properties
4791 TArray2 mu_z_apb;
4792 if (compute_dipole) {
4793 mu_z_apb = xy("<a'|mu_z|b>");
4794 }
4795
4796 TArray2 q_xx_apb, q_yy_apb, q_zz_apb;
4797 TArray2 Qxx_apb, Qyy_apb, Qzz_apb, Qxy_apb, Qxz_apb, Qyz_apb;
4798 if (compute_quadrupole) {
4799 q_xx_apb = xy("<a'|q_xx|b>");
4800 q_yy_apb = xy("<a'|q_yy|b>");
4801 q_zz_apb = xy("<a'|q_zz|b>");
4802
4803 Qxx_apb("a',b") = q_xx_apb("a',b") - (q_zz_apb("a',b") + q_yy_apb("a',b")) * 0.5;
4804 Qyy_apb("a',b") = q_yy_apb("a',b") - (q_zz_apb("a',b") + q_xx_apb("a',b")) * 0.5 ;
4805 Qzz_apb("a',b") = q_zz_apb("a',b") - (q_xx_apb("a',b") + q_yy_apb("a',b")) * 0.5;
4806 Qxy_apb("a',b") = _2("<a'|q_xy|b>") * 1.5;
4807 Qxz_apb("a',b") = _2("<a'|q_xz|b>") * 1.5;
4808 Qyz_apb("a',b") = _2("<a'|q_yz|b>") * 1.5;
4809 }
4810
4811 TArray2 v_xx_apb, v_yy_apb, v_zz_apb, v_xy_apb, v_xz_apb, v_yz_apb;
4812 if (compute_EFG) {
4813 v_xx_apb = xy("<a'|ddphi_xx|b>");
4814 v_yy_apb = xy("<a'|ddphi_yy|b>");
4815 v_zz_apb = xy("<a'|ddphi_zz|b>");
4816 v_xy_apb = xy("<a'|ddphi_xy|b>");
4817 v_xz_apb = xy("<a'|ddphi_xz|b>");
4818 v_yz_apb = xy("<a'|ddphi_yz|b>");
4819 }
4820
4821 // singlet and triplet coefficients for F12 and coupling terms
4822 const double C_0 = 1.0 / 2.0;
4823 const double C_1 = 1.0 / 4.0;
4824 // compute coefficients needed in the F12 and coupling calculations
4825 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
4826 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
4827 const double RR_C1 = 0.5 * C_0 * C_0 + 1.5 * C_1 * C_1;
4828 const double RR_C2 = 0.5 * C_0 * C_0 - 1.5 * C_1 * C_1;
4829
4830 // MP2 F12 coupling part
4831 double mu_z_mp2f12C = 0.0, mu_z_mp2f12Cor = 0.0;
4832 double q_xx_mp2f12C = 0.0, q_yy_mp2f12C = 0.0, q_zz_mp2f12C = 0.0;
4833 double q_xx_mp2f12Cor = 0.0, q_yy_mp2f12Cor = 0.0, q_zz_mp2f12Cor = 0.0;
4834#if INCLUDE_MP2F12C_CONTRI
4835 {
4836 ExEnv::out0() << std::endl << indent
4837 << "Compute MP2 F12 coupling contributions" << std::endl;
4838 TArray4 C_ijab, A_ijab;
4839 C_ijab("i,j,a,b") = _4("<i j|r|a_F(a') b>") + _4("<i j|r|a b_F(a')>");
4840 A_ijab("i,j,a,b") = C_ijab("i,j,a,b") * Delta_ijab("i,j,a,b");
4841
4842 // Coupling and F12 part of MP2F12 density
4843 ExEnv::out0() << indent
4844 << "Compute density from coupling contribution" << std::endl;
4845 TArray2 D_mp2f12_ij, D_mp2f12_ab;
4846 D_mp2f12_ij("i,j") = (R_C1 * A_ijab("i,k,a,b") + R_C2 * A_ijab("k,i,a,b"))
4847 * T2_ijab("j,k,a,b")
4848 // A_jk^ab T_ab^ik
4849 + (R_C1 * A_ijab("j,k,a,b") + R_C2 * A_ijab("k,j,a,b"))
4850 * T2_ijab("i,k,a,b")
4851 // A^ik_ab A^ab_jk
4852 + (RR_C1 * A_ijab("i,k,a,b") + RR_C2 * A_ijab("k,i,a,b"))
4853 * A_ijab("j,k,a,b");
4854 D_mp2f12_ab("a,b") = (R_C1 * T2_ijab("i,j,a,c") + R_C2 * T2_ijab("i,j,c,a"))
4855 * A_ijab("i,j,b,c")
4856 // A^ac_ij T^ij_bc
4857 + (R_C1 * T2_ijab("i,j,b,c") + R_C2 * T2_ijab("i,j,c,b"))
4858 * A_ijab("i,j,a,c")
4859 // A_ac^ij A_ij^bc
4860 + (RR_C1 * A_ijab("i,j,a,c") + RR_C2 * A_ijab("i,j,c,a"))
4861 * A_ijab("i,j,b,c");
4862
4863 // 1/2 R^kl_a'c \tilde{T}^bc_kl
4864 TArray2 RT_apb;
4865 RT_apb("a',b") = _4("<a' c|r|k l>")
4866 * ( R_C1 * T2_ijab("k,l,b,c") + R_C2 * T2_ijab("k,l,c,b")
4867 + RR_C1 * A_ijab("k,l,b,c") + RR_C2 * A_ijab("k,l,c,b")
4868 );
4869
4870 // MP2 F12 coupling contribution to orbital response
4871 ExEnv::out0() << indent
4872 << "Compute orbital response from coupling contribution" << std::endl;
4873 TArray2 Xmp2f12_contri_nfzc = Xam_Cmp2f12(C_0, C_1,T2_ijab, A_ijab,
4874 D_mp2f12_ij, D_mp2f12_ab, RT_apb);
4875
4876 TArray2 Xmp2f12_contri;
4877 // frozen-core contribution
4878 TArray2 Diip_Cmp2;
4879 if (nocc != naocc) {
4880 ExEnv::out0() << std::endl << indent
4881 << "Include frozen-core contributions for MP2 F12 coupling" << std::endl;
4882 TArray2 Xiip_CT2_mp2;
4883 Xiip_CT2_mp2("i,i'") = // F^a'_b R^i'l_a'c \tilde{T}^bc_il
4884 _4("<i' l|r|b_F(a') c>")
4885 * ( R_C1 * T2_ijab("i,l,b,c") + R_C2 * T2_ijab("l,i,b,c")
4886 + RR_C1 * A_ijab("i,l,b,c") + RR_C2 * A_ijab("l,i,b,c")
4887 )
4888 + _4("<i' l|r|c b_F(a')>")
4889 * ( R_C1 * T2_ijab("i,l,c,b") + R_C2 * T2_ijab("l,i,c,b")
4890 + RR_C1 * A_ijab("i,l,c,b") + RR_C2 * A_ijab("l,i,c,b")
4891 )
4892 // g^i'l_cd A^cd_il
4893 + _4("<i' l|g|c d>")
4894 * (R_C1 * A_ijab("i,l,c,d") + R_C2 * A_ijab("l,i,c,d"))
4895 ; // 2.0 is not multiplied as 4.0 is multiplied in the end
4896
4897 Diip_Cmp2("i,i'") = - Xiip_CT2_mp2("i,i'") * Delta_ijp_F("i,i'");
4898
4899 Xmp2f12_contri("a,m") = Xmp2f12_contri_nfzc("a,m") - A_ijpam("i,j',a,m") * Diip_Cmp2("i,j'");
4900
4901 } else {
4902 Xmp2f12_contri("a,m") = Xmp2f12_contri_nfzc("a,m");
4903 }
4904
4905 TArray2 Dbn_mp2f12(Xmp2f12_contri.world(), Xmp2f12_contri.trange());
4906 auto resnorm_mp2f12 = cg_solver2(Orbital_relaxation_Abnam,
4907 Xmp2f12_contri,
4908 Dbn_mp2f12,
4909 preconditioner,
4910 conv_target);
4911
4912 // MP2-F12 coupling contribution to dipole
4913 if (compute_dipole) {
4914 // MP2 F12 coupling density contribution to dipole
4915 mu_z_mp2f12C = - dot(mu_z_ij("i,j"), D_mp2f12_ij("i,j"))
4916 + dot(mu_z_ab("a,b"), D_mp2f12_ab("a,b"))
4917 + dot(mu_z_apb("a',b"), RT_apb("a',b")) * 2.0;
4918
4919 // MP2-F12 coupling orbital response contribution to dipole
4920 mu_z_mp2f12Cor = dot(mu_z_am("a,m"), Dbn_mp2f12("a,m"));
4921
4922 if (nocc != naocc) {
4923 mu_z_mp2f12Cor += dot(mu_z_ijp("i,j'"), Diip_Cmp2("i,j'"));
4924 }
4925 }
4926
4927 // MP2-F12 coupling contribution to quadrupoles
4928 if (compute_quadrupole) {
4929 q_xx_mp2f12C = - dot(Qxx_ij("i,j"), D_mp2f12_ij("i,j"))
4930 + dot(Qxx_ab("a,b"), D_mp2f12_ab("a,b"))
4931 + dot(Qxx_apb("a',b"), RT_apb("a',b")) * 2.0;
4932 q_yy_mp2f12C = - dot(Qyy_ij("i,j"), D_mp2f12_ij("i,j"))
4933 + dot(Qyy_ab("a,b"), D_mp2f12_ab("a,b"))
4934 + dot(Qyy_apb("a',b"), RT_apb("a',b")) * 2.0;
4935 q_zz_mp2f12C = - dot(Qzz_ij("i,j"), D_mp2f12_ij("i,j"))
4936 + dot(Qzz_ab("a,b"), D_mp2f12_ab("a,b"))
4937 + dot(Qzz_apb("a',b"), RT_apb("a',b")) * 2.0;
4938// // x2, y2, z2 components to quadrupole moment
4939// q_xx_mp2f12C = - dot(q_xx_ij("i,j"), D_mp2f12_ij("i,j"))
4940// + dot(q_xx_ab("a,b"), D_mp2f12_ab("a,b"))
4941// + dot(q_xx_apb("a',b"), RT_apb("a',b")) * 2.0;
4942// q_yy_mp2f12C = - dot(q_yy_ij("i,j"), D_mp2f12_ij("i,j"))
4943// + dot(q_yy_ab("a,b"), D_mp2f12_ab("a,b"))
4944// + dot(q_yy_apb("a',b"), RT_apb("a',b")) * 2.0;
4945// q_zz_mp2f12C = - dot(q_zz_ij("i,j"), D_mp2f12_ij("i,j"))
4946// + dot(q_zz_ab("a,b"), D_mp2f12_ab("a,b"))
4947// + dot(q_zz_apb("a',b"), RT_apb("a',b")) * 2.0;
4948
4949 q_xx_mp2f12Cor = dot(Qxx_am("a,m"), Dbn_mp2f12("a,m"));
4950 q_yy_mp2f12Cor = dot(Qyy_am("a,m"), Dbn_mp2f12("a,m"));
4951 q_zz_mp2f12Cor = dot(Qzz_am("a,m"), Dbn_mp2f12("a,m"));
4952// // x2, y2, z2 components to quadrupole moment
4953// q_xx_mp2f12Cor = dot(q_xx_am("a,m"), Dbn_mp2f12("a,m"));
4954// q_yy_mp2f12Cor = dot(q_yy_am("a,m"), Dbn_mp2f12("a,m"));
4955// q_zz_mp2f12Cor = dot(q_zz_am("a,m"), Dbn_mp2f12("a,m"));
4956
4957 if (nocc != naocc) {
4958 q_xx_mp2f12Cor += dot(Qxx_ijp("i,j'"), Diip_Cmp2("i,j'"));
4959 q_yy_mp2f12Cor += dot(Qyy_ijp("i,j'"), Diip_Cmp2("i,j'"));
4960 q_zz_mp2f12Cor += dot(Qzz_ijp("i,j'"), Diip_Cmp2("i,j'"));
4961 }
4962 }
4963
4964 // MP2-F12 coupling contribution to electric field gradient on 1st nucleus
4965 if (compute_EFG) {
4966 const double v_xx_mp2f12C = - dot(v_xx_ij("i,j"), D_mp2f12_ij("i,j"))
4967 + dot(v_xx_ab("a,b"), D_mp2f12_ab("a,b"))
4968 + dot(v_xx_apb("a',b"), RT_apb("a',b")) * 2.0;
4969 const double v_yy_mp2f12C = - dot(v_yy_ij("i,j"), D_mp2f12_ij("i,j"))
4970 + dot(v_yy_ab("a,b"), D_mp2f12_ab("a,b"))
4971 + dot(v_yy_apb("a',b"), RT_apb("a',b")) * 2.0;
4972 const double v_zz_mp2f12C = - dot(v_zz_ij("i,j"), D_mp2f12_ij("i,j"))
4973 + dot(v_zz_ab("a,b"), D_mp2f12_ab("a,b"))
4974 + dot(v_zz_apb("a',b"), RT_apb("a',b")) * 2.0;
4975 const double v_xy_mp2f12C = - dot(v_xy_ij("i,j"), D_mp2f12_ij("i,j"))
4976 + dot(v_xy_ab("a,b"), D_mp2f12_ab("a,b"))
4977 + dot(v_xy_apb("a',b"), RT_apb("a',b")) * 2.0;
4978 const double v_xz_mp2f12C = - dot(v_xz_ij("i,j"), D_mp2f12_ij("i,j"))
4979 + dot(v_xz_ab("a,b"), D_mp2f12_ab("a,b"))
4980 + dot(v_xz_apb("a',b"), RT_apb("a',b")) * 2.0;
4981 const double v_yz_mp2f12C = - dot(v_yz_ij("i,j"), D_mp2f12_ij("i,j"))
4982 + dot(v_yz_ab("a,b"), D_mp2f12_ab("a,b"))
4983 + dot(v_yz_apb("a',b"), RT_apb("a',b")) * 2.0;
4984
4985 const double v_xx_mp2f12Cor = dot(v_xx_am("a,m"), Dbn_mp2f12("a,m"));
4986 const double v_yy_mp2f12Cor = dot(v_yy_am("a,m"), Dbn_mp2f12("a,m"));
4987 const double v_zz_mp2f12Cor = dot(v_zz_am("a,m"), Dbn_mp2f12("a,m"));
4988 const double v_xy_mp2f12Cor = dot(v_xy_am("a,m"), Dbn_mp2f12("a,m"));
4989 const double v_xz_mp2f12Cor = dot(v_xz_am("a,m"), Dbn_mp2f12("a,m"));
4990 const double v_yz_mp2f12Cor = dot(v_yz_am("a,m"), Dbn_mp2f12("a,m"));
4991
4992 std::cout << std::endl << indent
4993 << "electric gradient (MP2F12 coupling)" << std::endl
4994 << indent << "v_xx (MP2F12 C) = " << scprintf("%12.10f", v_xx_mp2f12C * 2.0)
4995 << indent << " v_yy (MP2F12 C) = " << scprintf("%12.10f", v_yy_mp2f12C * 2.0)
4996 << indent << " v_zz (MP2F12 C) = " << scprintf("%12.10f", v_zz_mp2f12C * 2.0)
4997 << std::endl
4998 << indent << "v_xy (MP2F12 C) = " << scprintf("%12.10f", v_xy_mp2f12C * 2.0)
4999 << indent << " v_xz (MP2F12 C) = " << scprintf("%12.10f", v_xz_mp2f12C * 2.0)
5000 << indent << " v_yz (MP2F12 C) = " << scprintf("%12.10f", v_yz_mp2f12C * 2.0)
5001 << std::endl;
5002 std::cout << std::endl << indent
5003 << "electric gradient (MP2F12 coupling orbital response)" << std::endl
5004 << indent << "v_xx (MP2F12 C or) = " << scprintf("%12.10f", v_xx_mp2f12Cor * 2.0)
5005 << indent << " v_yy (MP2F12 C or) = " << scprintf("%12.10f", v_yy_mp2f12Cor * 2.0)
5006 << indent << " v_zz (MP2F12 C or) = " << scprintf("%12.10f", v_zz_mp2f12Cor * 2.0)
5007 << std::endl
5008 << indent << "v_xy (MP2F12 C or) = " << scprintf("%12.10f", v_xy_mp2f12Cor * 2.0)
5009 << indent << " v_xz (MP2F12 C or) = " << scprintf("%12.10f", v_xz_mp2f12Cor * 2.0)
5010 << indent << " v_yz (MP2F12 C or) = " << scprintf("%12.10f", v_yz_mp2f12Cor * 2.0)
5011 << std::endl << std::endl;
5012 }
5013
5014 }
5015 world_.gop.fence();
5016#endif
5017
5018 // F12 contribution
5019 double mu_z_f12 = 0.0, mu_z_f12or = 0.0;
5020 double q_xx_f12 = 0.0, q_yy_f12 = 0.0, q_zz_f12 = 0.0;
5021 double q_xx_f12or = 0.0, q_yy_f12or = 0.0, q_zz_f12or = 0.0;
5022#if INCLUDE_F12_CONTRI
5023 {
5024 ExEnv::out0() << std::endl << indent
5025 << "Compute F12 contributions" << std::endl;
5026
5027 ExEnv::out0() << std::endl << indent << "Compute D_f12" << std::endl;
5028 // F12 density from X and B terms
5029 TArray2 D_f12_ij, D_f12_ab, D_f12_apbp, D_f12_apb;
5030 compute_Df12_XB(C_0, C_1, D_f12_ij, D_f12_ab, D_f12_apbp, D_f12_apb);
5031
5032
5033 // F12 orbital response contribution
5034
5035 ExEnv::out0() << std::endl << indent << "Compute X and B density contribution to Xam" << std::endl;
5036 // X and B density contribution to Xam
5037 TArray2 gdf12_am = Xam_Df12_XB(C_0, C_1, D_f12_ij,D_f12_ab,
5038 D_f12_apbp, D_f12_apb);
5039
5040 // Xam from F12 (V, X, and B) contributions
5041 ExEnv::out0() << std::endl << indent << "Compute V Xam" << std::endl;
5042 TArray2 Xam_Vcontri = Xam_V(C_0, C_1);
5043 ExEnv::out0() << std::endl << indent << "Compute X Xam" << std::endl;
5044 TArray2 Xam_Xcontri = Xam_X(C_0, C_1);
5045 ExEnv::out0() << std::endl << indent << "Compute B Xam" << std::endl;
5046 TArray2 Xam_Bcontri = Xam_B(C_0, C_1);
5047
5048 // F12 contribution to orbital response
5049 TArray2 Xam_f12_nfzc;
5050 Xam_f12_nfzc("a,m") = 2.0 * ( Xam_Vcontri("a,m")
5051 - Xam_Xcontri("a,m")
5052 + Xam_Bcontri("a,m")
5053 + gdf12_am("a,m") // F12 density terms
5054 );
5055 TArray2 Xam_f12;
5056 // frozen-core contribution of F12 part: Xii'
5057 TArray2 Diip_f12;
5058 if (nocc != naocc) {
5059 ExEnv::out0() << std::endl << indent
5060 << "Include frozen-core F12 contributions" << std::endl;
5061 TArray2 Xiip_f12 = Xiip_VBX(C_0, C_1);
5062 Diip_f12("i,i'") = - Xiip_f12("i,i'") * Delta_ijp_F("i,i'");
5063
5064 Xam_f12("a,m") = Xam_f12_nfzc("a,m") - A_ijpam("i,j',a,m") * Diip_f12("i,j'");
5065 } else {
5066 Xam_f12("a,m") = Xam_f12_nfzc("a,m");
5067 }
5068
5069 TArray2 Dbn_f12(Xam_f12.world(), Xam_f12.trange());
5070 auto resnorm_f12 = cg_solver2(Orbital_relaxation_Abnam,
5071 Xam_f12,
5072 Dbn_f12,
5073 preconditioner,
5074 conv_target);
5075
5076 // print out each contribution in F12 contribution
5077#if 0
5078 TArray2 gdf12_X_am;
5079 gdf12_X_am("a,m") = // X related contribution
5080 (2.0 * _4("<a k|g|m l>") - _4("<a k|g|l m>"))
5081 * D_f12_ij("k,l");
5082 TArray2 gdf12_B_am;
5083 gdf12_B_am("a,m") = // B related contribution
5084 - (2.0 * g_abmc("a,b,m,c") - g_abmc("b,a,m,c"))
5085 * D_f12_ab("b,c")
5086 - (2.0 * _4("<a b'|g|m c'>") - _4("<a b'|g|c' m>"))
5087 * D_f12_apbp("b',c'")
5088 - (2.0 * _4("<a b'|g|m c>") - _4("<a b'|g|c m>"))
5089 * D_f12_apb("b',c")
5090 - (2.0 * _4("<a b|g|m c'>") - _4("<a b|g|c' m>"))
5091 * D_f12_apb("c',b");
5092
5093 TArray2 Xam_V_nfzc;
5094 Xam_V_nfzc("a,m") = 2.0 * Xam_Vcontri("a,m");
5095 TArray2 Xam_X_nfzc;
5096 Xam_X_nfzc("a,m") = 2.0 * (- Xam_Xcontri("a,m") + gdf12_X_am("a,m"));
5097 TArray2 Xam_B_nfzc;
5098 Xam_B_nfzc("a,m") = 2.0 * (Xam_Bcontri("a,m")+ gdf12_B_am("a,m"));
5099
5100 TArray2 Xam_V, Xam_X, Xam_B;
5101 // frozen-core contribution of F12 part: Xii'
5102 TArray2 D_iip_V, D_iip_X, D_iip_B;
5103 if (nocc != naocc) {
5104 ExEnv::out0() << std::endl << indent
5105 << "Include frozen-core V, X, and B contributions" << std::endl;
5106 TArray2 Xiip_V;
5107 const char* ip = "i'";
5108 const char* i = "i";
5109 TArray2 V_ipi = VRk_Sk(ip,i,C_0, C_1);
5110 TArray2 V_iip = VRk_Sk(i,ip,C_0, C_1);
5111 Xiip_V("i,i'") = // 2 * (1/2 R^i'k_A'C' g^A'C'_ik + 1/2 R^ik_A'C' g^A'C'_i'k)
5112 2.0 * (V_ipi("i',i") + V_iip("i,i'"));
5113 D_iip_V("i,i'") = - Xiip_V("i,i'") * Delta_ijp_F("i,i'");
5114 Xam_V("a,m") = Xam_V_nfzc("a,m") - A_ijpam("i,j',a,m") * D_iip_V("i,j'");
5115
5116 TArray2 Xiip_X;
5117 TArray2 F_ij = xy("<i|F|j>");
5118 TArray4d r2_ipk_jl = ijxy("<i' k|r2|j l>");
5119 TArray4d r_ipk_pq = ijxy("<i' k|r|p q>");
5120 TArray4d r_pqkl = ijxy("<p q|r|k l>");
5121 TArray4d r_ipk_apn = ijxy("<i' k|r|a' n>");
5122 TArray4d r_apn_kl = ijxy("<a' n|r|k l>");
5123 TArray4d r_kip_apn = ijxy("<k i'|r|a' n>");
5124 Xiip_X("i,i'") = // 2 * (F^i_i + F^k_k) 1/2 R^i'k_A'B' R_ik^A'B'
5125 - 2.0 * ( (RR_C1 * r2_ipk_jl("i',k,j,l") + RR_C2 * r2_ipk_jl("i',k,l,j"))
5126 * _2("<l|I|k>") * F_ij("j,i")
5127 + (RR_C1 * r2_ipk_jl("i',k,i,l") + RR_C2 * r2_ipk_jl("i',k,l,i"))
5128 * F_ij("l,k")
5129
5130 - (RR_C1 * r_ipk_pq("i',k,p,q") + RR_C2 * r_ipk_pq("i',k,q,p"))
5131 * ( r_pqkl("p,q,j,k") * F_ij("j,i")
5132 + r_pqkl("p,q,i,l") * F_ij("l,k"))
5133
5134 - (RR_C1 * r_ipk_apn("i',k,a',n") + RR_C2 * r_kip_apn("k,i',a',n"))
5135 * ( r_apn_kl("a',n,j,k") * F_ij("j,i")
5136 + r_apn_kl("a',n,i,l") * F_ij("l,k"))
5137
5138 - (RR_C1 * r_kip_apn("k,i',a',n") + RR_C2 * r_ipk_apn("i',k,a',n"))
5139 * ( r_apn_kl("a',n,k,j") * F_ij("j,i")
5140 + r_apn_kl("a',n,l,i") * F_ij("l,k"))
5141 );
5142 D_iip_X("i,i'") = - Xiip_X("i,i'") * Delta_ijp_F("i,i'");
5143 Xam_X("a,m") = Xam_X_nfzc("a,m") - A_ijpam("i,j',a,m") * D_iip_X("i,j'");
5144
5145 TArray2 Xiip_B;
5146 TArray2 B_ipi = BPk_Qk(ip,i,C_0,C_1);
5147 Xiip_B("i,i'") = // 2 R^i'k_A'B' F^A'_C' R^ik_C'B'
5148 2.0 * B_ipi("i',i");
5149 D_iip_B("i,i'") = - Xiip_B("i,i'") * Delta_ijp_F("i,i'");
5150 Xam_B("a,m") = Xam_B_nfzc("a,m") - A_ijpam("i,j',a,m") * D_iip_B("i,j'");
5151 } else {
5152 Xam_V("a,m") = Xam_V_nfzc("a,m");
5153 Xam_X("a,m") = Xam_X_nfzc("a,m");
5154 Xam_B("a,m") = Xam_B_nfzc("a,m");
5155 }
5156
5157 TArray2 Dbn_V(Xam_V.world(), Xam_V.trange());
5158 auto resnorm_V = cg_solver2(Orbital_relaxation_Abnam,
5159 Xam_V,
5160 Dbn_V,
5161 preconditioner,
5162 conv_target);
5163 TArray2 Dbn_X(Xam_X.world(), Xam_X.trange());
5164 auto resnorm_X = cg_solver2(Orbital_relaxation_Abnam,
5165 Xam_X,
5166 Dbn_X,
5167 preconditioner,
5168 conv_target);
5169 TArray2 Dbn_B(Xam_B.world(), Xam_B.trange());
5170 auto resnorm_B = cg_solver2(Orbital_relaxation_Abnam,
5171 Xam_B,
5172 Dbn_B,
5173 preconditioner,
5174 conv_target);
5175
5176 if (compute_dipole) {
5177 double mu_z_X, mu_z_B, mu_z_Vor, mu_z_Xor, mu_z_Bor;
5178 // F12 density contribution to dipole
5179 mu_z_X = // X related contribution
5180 - dot(mu_z_ij("i,j"), D_f12_ij("i,j"));
5181 TArray2 mu_z_apbp = xy("<a'|mu_z|b'>");
5182 mu_z_B = // B related contribution
5183 dot(mu_z_ab("a,b"), D_f12_ab("a,b"))
5184 + dot(mu_z_apbp("a',b'"), D_f12_apbp("a',b'"))
5185 + dot(mu_z_apb("a',b"), D_f12_apb("a',b")) * 2.0;
5186
5187 mu_z_Vor = dot(mu_z_am("a,m"), Dbn_V("a,m"));
5188 mu_z_Xor = dot(mu_z_am("a,m"), Dbn_X("a,m"));
5189 mu_z_Bor = dot(mu_z_am("a,m"), Dbn_B("a,m"));
5190 if (nocc != naocc) {
5191 mu_z_Vor += dot(mu_z_ijp("i,j'"), D_iip_V("i,j'"));
5192 mu_z_Xor += dot(mu_z_ijp("i,j'"), D_iip_X("i,j'"));
5193 mu_z_Bor += dot(mu_z_ijp("i,j'"), D_iip_B("i,j'"));
5194 }
5195
5196 std::cout << std::endl << indent
5197 << "mu_z (V orbital response) = " << scprintf("%15.12f", - mu_z_Vor * 2.0)
5198 << std::endl << indent
5199 << "mu_z (X) = " << scprintf("%15.12f",- mu_z_X * 2.0)
5200 << std::endl << indent
5201 << "mu_z (X orbital response) = " << scprintf("%15.12f", - mu_z_Xor * 2.0)
5202 << std::endl << indent
5203 << "mu_z (B) = " << scprintf("%15.12f",- mu_z_B * 2.0)
5204 << std::endl << indent
5205 << "mu_z (B orbital response) = " << scprintf("%15.12f", - mu_z_Bor * 2.0)
5206 << std::endl;
5207 }
5208#endif
5209
5210 if (compute_dipole) {
5211 TArray2 mu_z_apbp = xy("<a'|mu_z|b'>");
5212 // F12 density contribution to dipole
5213 mu_z_f12 = // X related contribution
5214 - dot(mu_z_ij("i,j"), D_f12_ij("i,j"))
5215 // B related contribution
5216 + dot(mu_z_ab("a,b"), D_f12_ab("a,b"))
5217 + dot(mu_z_apbp("a',b'"), D_f12_apbp("a',b'"))
5218 + dot(mu_z_apb("a',b"), D_f12_apb("a',b")) * 2.0
5219 ;
5220 mu_z_f12or = dot(mu_z_am("a,m"), Dbn_f12("a,m"));
5221 if (nocc != naocc) {
5222 mu_z_f12or += dot(mu_z_ijp("i,j'"), Diip_f12("i,j'"));
5223 }
5224 }
5225
5226 // F12 contribution to quadrupoles
5227 if (compute_quadrupole) {
5228 TArray2 q_xx_apbp = xy("<a'|q_xx|b'>");
5229 TArray2 q_yy_apbp = xy("<a'|q_yy|b'>");
5230 TArray2 q_zz_apbp = xy("<a'|q_zz|b'>");
5231
5232 TArray2 Qxx_apbp, Qyy_apbp, Qzz_apbp;
5233 Qxx_apbp("a',b'") = q_xx_apbp("a',b'") - (q_zz_apbp("a',b'") + q_yy_apbp("a',b'")) * 0.5;
5234 Qyy_apbp("a',b'") = q_yy_apbp("a',b'") - (q_zz_apbp("a',b'") + q_xx_apbp("a',b'")) * 0.5;
5235 Qzz_apbp("a',b'") = q_zz_apbp("a',b'") - (q_xx_apbp("a',b'") + q_yy_apbp("a',b'")) * 0.5;
5236
5237 q_xx_f12 = - dot(Qxx_ij("i,j"), D_f12_ij("i,j"))
5238 + dot(Qxx_ab("a,b"), D_f12_ab("a,b"))
5239 + dot(Qxx_apbp("a',b'"), D_f12_apbp("a',b'"))
5240 + dot(Qxx_apb("a',b"), D_f12_apb("a',b")) * 2.0
5241 ;
5242 q_yy_f12 = - dot(Qyy_ij("i,j"), D_f12_ij("i,j"))
5243 + dot(Qyy_ab("a,b"), D_f12_ab("a,b"))
5244 + dot(Qyy_apbp("a',b'"), D_f12_apbp("a',b'"))
5245 + dot(Qyy_apb("a',b"), D_f12_apb("a',b")) * 2.0
5246 ;
5247 q_zz_f12 = - dot(Qzz_ij("i,j"), D_f12_ij("i,j"))
5248 + dot(Qzz_ab("a,b"), D_f12_ab("a,b"))
5249 + dot(Qzz_apbp("a',b'"), D_f12_apbp("a',b'"))
5250 + dot(Qzz_apb("a',b"), D_f12_apb("a',b")) * 2.0
5251 ;
5252// // x2, y2, z2 components to quadrupole moment
5253// q_xx_f12 = - dot(q_xx_ij("i,j"), D_f12_ij("i,j"))
5254// + dot(q_xx_ab("a,b"), D_f12_ab("a,b"))
5255// + dot(q_xx_apbp("a',b'"), D_f12_apbp("a',b'"))
5256// + dot(q_xx_apb("a',b"), D_f12_apb("a',b")) * 2.0;
5257// q_yy_f12 = - dot(q_yy_ij("i,j"), D_f12_ij("i,j"))
5258// + dot(q_yy_ab("a,b"), D_f12_ab("a,b"))
5259// + dot(q_yy_apbp("a',b'"), D_f12_apbp("a',b'"))
5260// + dot(q_yy_apb("a',b"), D_f12_apb("a',b")) * 2.0;
5261// q_zz_f12 = - dot(q_zz_ij("i,j"), D_f12_ij("i,j"))
5262// + dot(q_zz_ab("a,b"), D_f12_ab("a,b"))
5263// + dot(q_zz_apbp("a',b'"), D_f12_apbp("a',b'"))
5264// + dot(q_zz_apb("a',b"), D_f12_apb("a',b")) * 2.0;
5265
5266 q_xx_f12or = dot(Qxx_am("a,m"), Dbn_f12("a,m"));
5267 q_yy_f12or = dot(Qyy_am("a,m"), Dbn_f12("a,m"));
5268 q_zz_f12or = dot(Qzz_am("a,m"), Dbn_f12("a,m"));
5269// // x2, y2, z2 components to quadrupole moment
5270// q_xx_f12or = dot(q_xx_am("a,m"), Dbn_f12("a,m"));
5271// q_yy_f12or = dot(q_yy_am("a,m"), Dbn_f12("a,m"));
5272// q_zz_f12or = dot(q_zz_am("a,m"), Dbn_f12("a,m"));
5273
5274 if (nocc != naocc) {
5275 q_xx_f12or += dot(Qxx_ijp("i,j'"), Diip_f12("i,j'"));
5276 q_yy_f12or += dot(Qyy_ijp("i,j'"), Diip_f12("i,j'"));
5277 q_zz_f12or += dot(Qzz_ijp("i,j'"), Diip_f12("i,j'"));
5278 }
5279 }
5280
5281 if (compute_EFG) {
5282 TArray2 v_xx_apbp = xy("<a'|ddphi_xx|b'>");
5283 TArray2 v_yy_apbp = xy("<a'|ddphi_yy|b'>");
5284 TArray2 v_zz_apbp = xy("<a'|ddphi_zz|b'>");
5285 TArray2 v_xy_apbp = xy("<a'|ddphi_xy|b'>");
5286 TArray2 v_xz_apbp = xy("<a'|ddphi_xz|b'>");
5287 TArray2 v_yz_apbp = xy("<a'|ddphi_yz|b'>");
5288
5289 // F12 contribution to electric gradient
5290 const double v_xx_f12 = - dot(v_xx_ij("i,j"), D_f12_ij("i,j"))
5291 + dot(v_xx_ab("a,b"), D_f12_ab("a,b"))
5292 + dot(v_xx_apbp("a',b'"), D_f12_apbp("a',b'"))
5293 + dot(v_xx_apb("a',b"), D_f12_apb("a',b")) * 2.0;
5294 const double v_yy_f12 = - dot(v_yy_ij("i,j"), D_f12_ij("i,j"))
5295 + dot(v_yy_ab("a,b"), D_f12_ab("a,b"))
5296 + dot(v_yy_apbp("a',b'"), D_f12_apbp("a',b'"))
5297 + dot(v_yy_apb("a',b"), D_f12_apb("a',b")) * 2.0;
5298 const double v_zz_f12 = - dot(v_zz_ij("i,j"), D_f12_ij("i,j"))
5299 + dot(v_zz_ab("a,b"), D_f12_ab("a,b"))
5300 + dot(v_zz_apbp("a',b'"), D_f12_apbp("a',b'"))
5301 + dot(v_zz_apb("a',b"), D_f12_apb("a',b")) * 2.0;
5302 const double v_xy_f12 = - dot(v_xy_ij("i,j"), D_f12_ij("i,j"))
5303 + dot(v_xy_ab("a,b"), D_f12_ab("a,b"))
5304 + dot(v_xy_apbp("a',b'"), D_f12_apbp("a',b'"))
5305 + dot(v_xy_apb("a',b"), D_f12_apb("a',b")) * 2.0;
5306 const double v_xz_f12 = - dot(v_xz_ij("i,j"), D_f12_ij("i,j"))
5307 + dot(v_xz_ab("a,b"), D_f12_ab("a,b"))
5308 + dot(v_xz_apbp("a',b'"), D_f12_apbp("a',b'"))
5309 + dot(v_xz_apb("a',b"), D_f12_apb("a',b")) * 2.0;
5310 const double v_yz_f12 = - dot(v_yz_ij("i,j"), D_f12_ij("i,j"))
5311 + dot(v_yz_ab("a,b"), D_f12_ab("a,b"))
5312 + dot(v_yz_apbp("a',b'"), D_f12_apbp("a',b'"))
5313 + dot(v_yz_apb("a',b"), D_f12_apb("a',b")) * 2.0;
5314
5315 const double v_xx_f12or = dot(v_xx_am("a,m"), Dbn_f12("a,m"));
5316 const double v_yy_f12or = dot(v_yy_am("a,m"), Dbn_f12("a,m"));
5317 const double v_zz_f12or = dot(v_zz_am("a,m"), Dbn_f12("a,m"));
5318 const double v_xy_f12or = dot(v_xy_am("a,m"), Dbn_f12("a,m"));
5319 const double v_xz_f12or = dot(v_xz_am("a,m"), Dbn_f12("a,m"));
5320 const double v_yz_f12or = dot(v_yz_am("a,m"), Dbn_f12("a,m"));
5321
5322 std::cout << indent << "electric gradient (F12)" << std::endl
5323 << indent << "v_xx (F12) = " << scprintf("%12.10f", v_xx_f12 * 2.0)
5324 << indent << " v_yy (F12) = " << scprintf("%12.10f", v_yy_f12 * 2.0)
5325 << indent << " v_zz (F12) = " << scprintf("%12.10f", v_zz_f12 * 2.0)
5326 << std::endl
5327 << indent << "v_xy (F12) = " << scprintf("%12.10f", v_xy_f12 * 2.0)
5328 << indent << " v_xz (F12) = " << scprintf("%12.10f", v_xz_f12 * 2.0)
5329 << indent << " v_yz (F12) = " << scprintf("%12.10f", v_yz_f12 * 2.0)
5330 << std::endl;
5331 std::cout << indent << "electric gradient (F12 orbital response)" << std::endl
5332 << indent << "v_xx (F12 or) = " << scprintf("%12.10f", v_xx_f12or * 2.0)
5333 << indent << " v_yy (F12 or) = " << scprintf("%12.10f", v_yy_f12or * 2.0)
5334 << indent << " v_zz (F12 or) = " << scprintf("%12.10f", v_zz_f12or * 2.0)
5335 << std::endl
5336 << indent << "v_xy (F12 or) = " << scprintf("%12.10f", v_xy_f12or * 2.0)
5337 << indent << " v_xz (F12 or) = " << scprintf("%12.10f", v_xz_f12or * 2.0)
5338 << indent << " v_yz (F12 or) = " << scprintf("%12.10f", v_yz_f12or * 2.0)
5339 << std::endl << std::endl;
5340 }
5341 }
5342#endif
5343
5344 ExEnv::out0() << std::endl << indent << "Start CCSD computation" << std::endl;
5345 double mu_z_ccsd = 0.0, mu_z_ccsdor = 0.0;
5346 double q_xx_ccsd = 0.0, q_yy_ccsd = 0.0, q_zz_ccsd = 0.0;
5347 double q_xx_ccsdor = 0.0, q_yy_ccsdor = 0.0, q_zz_ccsdor = 0.0;
5348
5349 TArray2 mu_z_ai;
5350 TArray2 Qxx_ai, Qyy_ai, Qzz_ai, Qxy_ai, Qxz_ai, Qyz_ai;
5351#if 0
5352 // compute CC2 amplitudes using Schaefer's formula
5353 TArray2 T1_cc2, L1_cc2;
5354 TArray4 T2_cc2, L2_cc2;
5355
5356 ExEnv::out0() << std::endl << indent << "Compute CC2 T amplitudes " << std::endl;
5357 compute_T_cc2(T1_cc2,T2_cc2);
5358
5359 ExEnv::out0() << std::endl << indent << "Compute CC2 lambda amplitudes " << std::endl;
5360 compute_lambda_cc2(T1_cc2, T2_cc2, L1_cc2, L2_cc2);
5361
5362 // compute CC2 density from amplitudes
5363 TArray2 Dij_cc2, Dab_cc2, Dia_cc2, Dai_cc2;
5364 ExEnv::out0() << indent << "Compute CC2 density from amplitudes" << std::endl;
5365 compute_cc2_1rdm_amp(T1_cc2, T2_cc2, L1_cc2, L2_cc2,
5366 Dij_cc2, Dab_cc2, Dia_cc2, Dai_cc2);
5367#endif
5368
5369#if 0
5370 // compute CC2 lambda amplitudes using Gauss's formula
5371 TArray2 L1_cc2_2;
5372 TArray4 L2_cc2_2;
5373 ExEnv::out0() << indent << "Using Gauss's formula" << std::endl;
5374 compute_lambda_cc2_2(T1_cc2, T2_cc2, L1_cc2_2, L2_cc2_2);
5375#endif
5376
5377 ExEnv::out0() << indent << "Compute CCSD T amplitudes " << std::endl;
5378 TArray2 T1;
5379 TArray4 T2;
5380 compute_T_ccsd(T1, T2, "CCSD");
5381
5382 ExEnv::out0() << std::endl << indent << "Compute CCSD L amplitudes " << std::endl;
5383 TArray2 L1;
5384 TArray4 L2;
5385 compute_lambda_ccsd(T1, T2, L1, L2, "CCSD"); // do not include F12 contributions
5386
5387#if INCLUDE_CCSD_CONTRI
5388 {
5389 // compute CCSD density from amplitudes
5390 TArray2 Dij_ccsd, Dab_ccsd, Dia_ccsd, Dai_ccsd;
5391 ExEnv::out0() << std::endl << indent
5392 << "Compute CCSD density from amplitudes" << std::endl;
5393 compute_ccsd_1rdm_amp(T1, T2, L1, L2,
5394 Dij_ccsd, Dab_ccsd, Dia_ccsd, Dai_ccsd);
5395
5396 ExEnv::out0() << std::endl << indent << "Compute CCSD Xam and Xai" << std::endl;
5397 TArray2 Xam_ccsd_nfzc, Xiip_ccsd;
5398 compute_Xam_ccsd(T1, T2, L1, L2, Xam_ccsd_nfzc, Xiip_ccsd);
5399
5400 TArray2 Diip_or_ccsd, Xam_ccsd;
5401 if (nocc != naocc) {
5402 ExEnv::out0() << std::endl << indent
5403 << "Include frozen-core CCSD contributions" << std::endl;
5404 Diip_or_ccsd("i,i'") = Xiip_ccsd("i,i'") * Delta_ijp_F("i,i'");
5405
5406 TArray2 Xam_Diip_ccsd;
5407 Xam_Diip_ccsd("a,m") = A_ijpam("i,i',a,m") * Diip_or_ccsd("i,i'");
5408 Xam_ccsd("a,m") = Xam_ccsd_nfzc("a,m") - Xam_Diip_ccsd("a,m");
5409
5410 // test code: print out frozen-core contribution to Ima
5411// TArray2 I_ma_fzc;
5412// I_ma_fzc("a,m") = - Xam_Diip_ccsd("a,m") * 0.5;
5413// std::cout << "Ima frozen-core part: " << std::endl << I_ma_fzc << std::endl;
5414 } else {
5415 Xam_ccsd("a,m") = Xam_ccsd_nfzc("a,m");
5416 }
5417
5418 // solve the Z-vector equation for CCSD
5419 TArray2 Dbn_ccsd(Xam_ccsd.world(), Xam_ccsd.trange());
5420 auto resnorm_ccsd = cg_solver2(Orbital_relaxation_Abnam,
5421 Xam_ccsd,
5422 Dbn_ccsd,
5423 preconditioner,
5424 conv_target);
5425
5426 if (compute_dipole) {
5427 mu_z_ai = xy("<a|mu_z|i>");
5428 mu_z_ccsd = dot(mu_z_ij("i,j"), Dij_ccsd("i,j"))
5429 + dot(mu_z_ab("a,b"), Dab_ccsd("a,b"))
5430 + dot(mu_z_ai("a,i"), Dai_ccsd("a,i"))
5431 + dot(mu_z_ai("a,i"), Dia_ccsd("i,a"))
5432 ;
5433
5434 mu_z_ccsdor = dot(mu_z_am("a,m"), Dbn_ccsd("a,m"));
5435 if (nocc != naocc) {
5436 mu_z_ccsdor += dot(mu_z_ijp("i,i'"), Diip_or_ccsd("i,i'"));
5437 }
5438
5439// std::cout << std::endl << indent
5440// << "mu_z (CCSD) = " << scprintf("%15.12f", - mu_z_ccsd * 2.0)
5441// << std::endl << indent
5442// << "mu_z (CCSD orbital response) = " << scprintf("%15.12f", - mu_z_ccsdor * 2.0)
5443// << std::endl;
5444 }
5445
5446 if (compute_quadrupole) {
5447 TArray2 q_xx_ai = xy("<a|q_xx|i>");
5448 TArray2 q_yy_ai = xy("<a|q_yy|i>");
5449 TArray2 q_zz_ai = xy("<a|q_zz|i>");
5450 Qxx_ai("a,i") = q_xx_ai("a,i") - (q_zz_ai("a,i") + q_yy_ai("a,i")) * 0.5;
5451 Qyy_ai("a,i") = q_yy_ai("a,i") - (q_zz_ai("a,i") + q_xx_ai("a,i")) * 0.5;
5452 Qzz_ai("a,i") = q_zz_ai("a,i") - (q_xx_ai("a,i") + q_yy_ai("a,i")) * 0.5;
5453
5454 q_xx_ccsd = dot(Qxx_ij("i,j"), Dij_ccsd("i,j"))
5455 + dot(Qxx_ab("a,b"), Dab_ccsd("a,b"))
5456 + dot(Qxx_ai("a,i"), Dai_ccsd("a,i"))
5457 + dot(Qxx_ai("a,i"), Dia_ccsd("i,a"))
5458 ;
5459 q_yy_ccsd = dot(Qyy_ij("i,j"), Dij_ccsd("i,j"))
5460 + dot(Qyy_ab("a,b"), Dab_ccsd("a,b"))
5461 + dot(Qyy_ai("a,i"), Dai_ccsd("a,i"))
5462 + dot(Qyy_ai("a,i"), Dia_ccsd("i,a"))
5463 ;
5464 q_zz_ccsd = dot(Qzz_ij("i,j"), Dij_ccsd("i,j"))
5465 + dot(Qzz_ab("a,b"), Dab_ccsd("a,b"))
5466 + dot(Qzz_ai("a,i"), Dai_ccsd("a,i"))
5467 + dot(Qzz_ai("a,i"), Dia_ccsd("i,a"))
5468 ;
5469
5470 q_xx_ccsdor = dot(Qxx_am("a,m"), Dbn_ccsd("a,m"));
5471 q_yy_ccsdor = dot(Qyy_am("a,m"), Dbn_ccsd("a,m"));
5472 q_zz_ccsdor = dot(Qzz_am("a,m"), Dbn_ccsd("a,m"));
5473
5474 if (nocc != naocc) {
5475 q_xx_ccsdor += dot(Qxx_ijp("i,j'"), Diip_or_ccsd("i,j'"));
5476 q_yy_ccsdor += dot(Qyy_ijp("i,j'"), Diip_or_ccsd("i,j'"));
5477 q_zz_ccsdor += dot(Qzz_ijp("i,j'"), Diip_or_ccsd("i,j'"));
5478 }
5479 }
5480 }
5481#endif
5482
5483 // CC F12 coupling contribution to Xam
5484 double mu_z_Cccsdf12 = 0.0, mu_z_Cccsdf12or = 0.0;
5485 double q_xx_Cccsdf12 = 0.0, q_yy_Cccsdf12 = 0.0, q_zz_Cccsdf12 = 0.0;
5486 double q_xx_Cccsdf12or = 0.0, q_yy_Cccsdf12or = 0.0, q_zz_Cccsdf12or = 0.0;
5487#if INCLUDE_CCSDF12C_CONTRI
5488 {
5489 // resolve CCSD lambda amplitudes, density, and Xam in the framework of CCSD(2)_F12
5490 ExEnv::out0() << std::endl << indent << "Compute CCSD(2)_F12 L amplitudes " << std::endl;
5491 TArray2 L1_f12;
5492 TArray4 L2_f12;
5493 compute_lambda_ccsd(T1, T2, L1_f12, L2_f12, "F12");
5494
5495 // compute CCSD density from amplitudes
5496 TArray2 Dij_ccsd_f12, Dab_ccsd_f12, Dia_ccsd_f12, Dai_ccsd_f12;
5497 ExEnv::out0() << std::endl << indent
5498 << "Compute CCSD density from amplitudes in CCSD(2)_F12" << std::endl;
5499 compute_ccsd_1rdm_amp(T1, T2, L1_f12, L2_f12,
5500 Dij_ccsd_f12, Dab_ccsd_f12, Dia_ccsd_f12, Dai_ccsd_f12);
5501
5502 ExEnv::out0() << std::endl << indent
5503 << "Compute CCSD Xam and Xai in CCSD(2)_F12" << std::endl;
5504 TArray2 Xam_ccsd_f12_nfzc, Xiip_ccsd_f12;
5505 compute_Xam_ccsd(T1, T2, L1_f12, L2_f12, Xam_ccsd_f12_nfzc, Xiip_ccsd_f12);
5506 //compute_Xam_ccsd(T1, T2, L1, L2_f12, Xam_ccsd_f12_nfzc, Xiip_ccsd_f12);
5507
5508 TArray2 Diip_ccsd_f12, Xam_ccsd_f12;
5509 if (nocc != naocc) {
5510 Diip_ccsd_f12("i,i'") = Xiip_ccsd_f12("i,i'") * Delta_ijp_F("i,i'");
5511 Xam_ccsd_f12("a,m") = Xam_ccsd_f12_nfzc("a,m") - A_ijpam("i,i',a,m") * Diip_ccsd_f12("i,i'");
5512 } else {
5513 Xam_ccsd_f12("a,m") = Xam_ccsd_f12_nfzc("a,m");
5514 }
5515
5516 TArray2 Dbn_ccsd_f12(Xam_ccsd_f12.world(), Xam_ccsd_f12.trange());
5517 auto resnorm_ccsd_f12 = cg_solver2(Orbital_relaxation_Abnam,
5518 Xam_ccsd_f12,
5519 Dbn_ccsd_f12,
5520 preconditioner,
5521 1e-12);
5522
5523 ExEnv::out0() << std::endl << indent
5524 << "Compute CCSD F12 coupling contributions" << std::endl;
5525 // CC CT2
5526 // 1/2 R^kl_a'c T2^bc_kl
5527 TArray2 RT2_aPb;
5528 RT2_aPb("a',b") = _4("<a' c|r|k l>")
5529 * (R_C1 * T2("b,c,k,l") + R_C2 * T2("c,b,k,l"));
5530
5531 TArray2 Xam_CT2_cc = Xam_CT2_ccsd(C_0, C_1, T2, RT2_aPb);
5532 // VT1 & VT2 coupling contribution to F12 Xam
5533 TArray2 Xam_VT_cc = Xam_VT_ccsd(C_0, C_1, T1, T2);
5534 TArray2 Xam_CVT_cc_nfzc;
5535 Xam_CVT_cc_nfzc("a,m") = Xam_CT2_cc("a,m") + Xam_VT_cc("a,m");
5536
5537 // frozen-core contribution
5538 TArray2 Diip_CVT_cc, Xam_CVT_cc;
5539 if (nocc != naocc) {
5540 ExEnv::out0() << std::endl << indent
5541 << "Include frozen-core contributions for CCSD F12 coupling" << std::endl;
5542 TArray2 Xiip_couling = Xiip_CVT(C_0, C_1, T1, T2);
5543 Diip_CVT_cc("i,i'") = - Xiip_couling("i,i'") * Delta_ijp_F("i,i'");
5544
5545 TArray2 Xam_Diip_CVT;
5546 Xam_Diip_CVT("a,m") = - A_ijpam("i,j',a,m") * Diip_CVT_cc("i,j'");
5547
5548 Xam_CVT_cc("a,m") = Xam_CVT_cc_nfzc("a,m") + Xam_Diip_CVT("a,m");
5549 } else {
5550 Xam_CVT_cc("a,m") = Xam_CVT_cc_nfzc("a,m");
5551 }
5552
5553 TArray2 Dbn_CVT_cc(Xam_CVT_cc.world(), Xam_CVT_cc.trange());
5554 auto resnorm_CVT_cc = cg_solver2(Orbital_relaxation_Abnam,
5555 Xam_CVT_cc,
5556 Dbn_CVT_cc,
5557 preconditioner,
5558 conv_target);
5559
5560 if (compute_dipole) {
5561 double mu_z_ccsd_f12 = dot(mu_z_ij("i,j"), Dij_ccsd_f12("i,j"))
5562 + dot(mu_z_ab("a,b"), Dab_ccsd_f12("a,b"))
5563 + dot(mu_z_ai("a,i"), Dai_ccsd_f12("a,i"))
5564 + dot(mu_z_ai("a,i"), Dia_ccsd_f12("i,a"))
5565 // F12 coupling density contribution
5566 + dot(mu_z_apb("a',b"), RT2_aPb("a',b")) * 2.0
5567 ;
5568
5569 double mu_z_ccsdor_f12 = dot(mu_z_am("a,m"), Dbn_ccsd_f12("a,m"))
5570 + dot(mu_z_am("a,m"), Dbn_CVT_cc("a,m"));
5571
5572 if (nocc != naocc) {
5573 mu_z_ccsdor_f12 += dot(mu_z_ijp("i,j'"), Diip_ccsd_f12("i,j'"))
5574 + dot(mu_z_ijp("i,j'"), Diip_CVT_cc("i,j'"));
5575 }
5576
5577 mu_z_Cccsdf12 = mu_z_ccsd_f12 - mu_z_ccsd;
5578 mu_z_Cccsdf12or = mu_z_ccsdor_f12 - mu_z_ccsdor;
5579 }
5580
5581 if (compute_quadrupole) {
5582 double q_xx_ccsd_f12 = dot(Qxx_ij("i,j"), Dij_ccsd_f12("i,j"))
5583 + dot(Qxx_ab("a,b"), Dab_ccsd_f12("a,b"))
5584 + dot(Qxx_ai("a,i"), Dai_ccsd_f12("a,i"))
5585 + dot(Qxx_ai("a,i"), Dia_ccsd_f12("i,a"))
5586 + dot(Qxx_apb("a',b"), RT2_aPb("a',b")) * 2.0
5587 ;
5588 double q_yy_ccsd_f12 = dot(Qyy_ij("i,j"), Dij_ccsd_f12("i,j"))
5589 + dot(Qyy_ab("a,b"), Dab_ccsd_f12("a,b"))
5590 + dot(Qyy_ai("a,i"), Dai_ccsd_f12("a,i"))
5591 + dot(Qyy_ai("a,i"), Dia_ccsd_f12("i,a"))
5592 + dot(Qyy_apb("a',b"), RT2_aPb("a',b")) * 2.0
5593 ;
5594 double q_zz_ccsd_f12 = dot(Qzz_ij("i,j"), Dij_ccsd_f12("i,j"))
5595 + dot(Qzz_ab("a,b"), Dab_ccsd_f12("a,b"))
5596 + dot(Qzz_ai("a,i"), Dai_ccsd_f12("a,i"))
5597 + dot(Qzz_ai("a,i"), Dia_ccsd_f12("i,a"))
5598 + dot(Qzz_apb("a',b"), RT2_aPb("a',b")) * 2.0
5599 ;
5600
5601 double q_xx_ccsdor_f12 = dot(Qxx_am("a,m"), Dbn_ccsd_f12("a,m"))
5602 + dot(Qxx_am("a,m"), Dbn_CVT_cc("a,m"));
5603 double q_yy_ccsdor_f12 = dot(Qyy_am("a,m"), Dbn_ccsd_f12("a,m"))
5604 + dot(Qyy_am("a,m"), Dbn_CVT_cc("a,m"));
5605 double q_zz_ccsdor_f12 = dot(Qzz_am("a,m"), Dbn_ccsd_f12("a,m"))
5606 + dot(Qzz_am("a,m"), Dbn_CVT_cc("a,m"));
5607
5608 if (nocc != naocc) {
5609 q_xx_ccsdor_f12 += dot(Qxx_ijp("i,j'"), Diip_ccsd_f12("i,j'"))
5610 + dot(Qxx_ijp("i,j'"), Diip_CVT_cc("i,j'"));
5611 q_yy_ccsdor_f12 += dot(Qyy_ijp("i,j'"), Diip_ccsd_f12("i,j'"))
5612 + dot(Qyy_ijp("i,j'"), Diip_CVT_cc("i,j'"));
5613 q_zz_ccsdor_f12 += dot(Qzz_ijp("i,j'"), Diip_ccsd_f12("i,j'"))
5614 + dot(Qzz_ijp("i,j'"), Diip_CVT_cc("i,j'"));
5615 }
5616
5617 q_xx_Cccsdf12 = q_xx_ccsd_f12 - q_xx_ccsd;
5618 q_yy_Cccsdf12 = q_yy_ccsd_f12 - q_yy_ccsd;
5619 q_zz_Cccsdf12 = q_zz_ccsd_f12 - q_zz_ccsd;
5620 q_xx_Cccsdf12or = q_xx_ccsdor_f12 - q_xx_ccsdor;
5621 q_yy_Cccsdf12or = q_yy_ccsdor_f12 - q_yy_ccsdor;
5622 q_zz_Cccsdf12or = q_zz_ccsdor_f12 - q_zz_ccsdor;
5623 }
5624
5625 }
5626#endif
5627
5628 // print results
5629 if (compute_dipole) {
5630 std::cout << std::endl << indent << "Dipole moment "
5631 << std::endl << indent
5632 << "mu_z (HF=SCF+N) = " << scprintf("%15.12f", mu_z_n - mu_z_scf * 2.0)
5633 //electron charge = -1, hence the minus
5634 << std::endl << std::endl << indent
5635 << "mu_z (E2) = " << scprintf("%15.12f", - mu_z_e2 * 2.0)
5636 << std::endl << indent
5637 << "mu_z (E2 orbital response) = " << scprintf("%15.12f", - mu_z_e2or * 2.0)
5638 << std::endl << std::endl << indent
5639 << "mu_z (MP2) = " << scprintf("%15.12f", - mu_z_mp2 * 2.0)
5640 << std::endl << indent
5641 << "mu_z (MP2 orbital response) = "<< scprintf("%15.12f", - mu_z_mp2or * 2.0)
5642 << std::endl << std::endl << indent
5643 << "mu_z (MP2F12 coupling) = " << scprintf("%15.12f", - mu_z_mp2f12C * 2.0)
5644 << std::endl << indent
5645 << "mu_z (MP2-F12 coupling orbital response) = " << scprintf("%15.12f", - mu_z_mp2f12Cor * 4.0)
5646 << std::endl << std::endl << indent
5647 << "mu_z (F12) = " << scprintf("%15.12f",- mu_z_f12 * 2.0)
5648 << std::endl << indent
5649 << "mu_z (F12 orbital response) = " << scprintf("%15.12f", - mu_z_f12or * 2.0)
5650 << std::endl << std::endl << indent
5651 << "mu_z (CCSD) = " << scprintf("%15.12f", - mu_z_ccsd * 2.0)
5652 << std::endl << indent
5653 << "mu_z (CCSD orbital response) = " << scprintf("%15.12f", - mu_z_ccsdor * 2.0)
5654 << std::endl << std::endl << indent
5655 << "mu_z (CCSDF12 coupling) = " << scprintf("%15.12f", - mu_z_Cccsdf12 * 2.0)
5656 << std::endl << indent
5657 << "mu_z (CCSDF12 coupling orbital response) = " << scprintf("%15.12f", - mu_z_Cccsdf12or * 2.0)
5658 << std::endl;
5659 }
5660
5661 if (compute_quadrupole) {
5662 std::cout << std::endl << indent
5663 << "Traceless quadrupole moment"
5664 << std::endl << indent
5665 << "q_xx (HF) = " << scprintf("%12.10f", q_xx_n - q_xx_scf * 2.0)
5666 << " q_yy (HF) = " << scprintf("%12.10f", q_yy_n - q_yy_scf * 2.0)
5667 << " q_zz (HF) = " << scprintf("%12.10f", q_zz_n - q_zz_scf * 2.0)
5668 << std::endl << indent
5669 << "q_xy (HF) = " << scprintf("%12.10f", q_xy_n - q_xy_scf * 2.0)
5670 << " q_xz (HF) = " << scprintf("%12.10f", q_xz_n - q_xz_scf * 2.0)
5671 << " q_yz (HF) = " << scprintf("%12.10f", q_yz_n - q_yz_scf * 2.0)
5672 << std::endl;
5673
5674 std::cout << std::endl << indent
5675 << "q_xx (E2) = " << scprintf("%12.10f", - q_xx_e2 * 2.0)
5676 << " q_yy (E2) = " << scprintf("%12.10f", - q_yy_e2 * 2.0)
5677 << " q_zz (E2) = " << scprintf("%12.10f", - q_zz_e2 * 2.0)
5678 << std::endl << indent
5679 << "q_xx (E2 or) = " << scprintf("%12.10f", - q_xx_e2or * 2.0)
5680 << " q_yy (E2 or) = " << scprintf("%12.10f", - q_yy_e2or * 2.0)
5681 << " q_zz (E2 or) = " << scprintf("%12.10f", - q_zz_e2or * 2.0)
5682 << std::endl;
5683
5684 std::cout << std::endl << indent
5685 << "q_xx (MP2) = " << scprintf("%12.10f", - q_xx_mp2 * 2.0)
5686 << " q_yy (MP2) = " << scprintf("%12.10f", - q_yy_mp2 * 2.0)
5687 << " q_zz (MP2) = " << scprintf("%12.10f", - q_zz_mp2 * 2.0)
5688 << std::endl << indent
5689 << "q_xx (MP2 or) = " << scprintf("%12.10f", - q_xx_mp2or * 2.0)
5690 << " q_yy (MP2 or) = " << scprintf("%12.10f", - q_yy_mp2or * 2.0)
5691 << " q_zz (MP2 or) = " << scprintf("%12.10f", - q_zz_mp2or * 2.0)
5692 << std::endl;
5693
5694 std::cout << std::endl << indent
5695 << "q_xx (MP2F12 C) = " << scprintf("%12.10f", - q_xx_mp2f12C * 2.0)
5696 << " q_yy (MP2F12 C) = " << scprintf("%12.10f", - q_yy_mp2f12C * 2.0)
5697 << " q_zz (MP2F12 C) = " << scprintf("%12.10f", - q_zz_mp2f12C * 2.0)
5698 << std::endl << indent
5699 << "q_xx (MP2F12 C or) = " << scprintf("%12.10f", - q_xx_mp2f12Cor * 2.0)
5700 << " q_yy (MP2F12 C or) = " << scprintf("%12.10f", - q_yy_mp2f12Cor * 2.0)
5701 << " q_zz (MP2F12 C or) = " << scprintf("%12.10f", - q_zz_mp2f12Cor * 2.0)
5702 << std::endl;
5703
5704 std::cout << std::endl << indent
5705 << "q_xx (F12) = " << scprintf("%12.10f", - q_xx_f12 * 2.0)
5706 << " q_yy (F12) = " << scprintf("%12.10f", - q_yy_f12 * 2.0)
5707 << " q_zz (F12) = " << scprintf("%12.10f", - q_zz_f12 * 2.0)
5708 << std::endl << indent
5709 << "q_xx (F12 or) = " << scprintf("%12.10f", - q_xx_f12or * 2.0)
5710 << " q_yy (F12 or) = " << scprintf("%12.10f", - q_yy_f12or * 2.0)
5711 << " q_zz (F12 or) = " << scprintf("%12.10f", - q_zz_f12or * 2.0)
5712 << std::endl;
5713
5714 std::cout << std::endl << indent
5715 << "q_xx (CCSD) = " << scprintf("%12.10f", - q_xx_ccsd * 2.0)
5716 << " q_yy (CCSD) = " << scprintf("%12.10f", - q_yy_ccsd * 2.0)
5717 << " q_zz (CCSD) = " << scprintf("%12.10f", - q_zz_ccsd * 2.0)
5718 << std::endl << indent
5719 << "q_xx (CCSD or) = " << scprintf("%12.10f", - q_xx_ccsdor * 2.0)
5720 << " q_yy (CCSD or) = " << scprintf("%12.10f", - q_yy_ccsdor * 2.0)
5721 << " q_zz (CCSD or) = " << scprintf("%12.10f", - q_zz_ccsdor * 2.0)
5722 << std::endl;
5723
5724 std::cout << std::endl << indent
5725 << "q_xx (CCSDF12 C) = " << scprintf("%12.10f", - q_xx_Cccsdf12 * 2.0)
5726 << " q_yy (CCSDF12 C) = " << scprintf("%12.10f", - q_yy_Cccsdf12 * 2.0)
5727 << " q_zz (CCSDF12 C) = " << scprintf("%12.10f", - q_zz_Cccsdf12 * 2.0)
5728 << std::endl << indent
5729 << "q_xx (CCSDF12 C or) = " << scprintf("%12.10f", - q_xx_Cccsdf12or * 2.0)
5730 << " q_yy (CCSDF12 C or) = " << scprintf("%12.10f", - q_yy_Cccsdf12or * 2.0)
5731 << " q_zz (CCSDF12 C or) = " << scprintf("%12.10f", - q_zz_Cccsdf12or * 2.0)
5732 << std::endl << std::endl;
5733 }
5734 }
5735
5736 // F12b method
5737 // Xam contribution of CT2 part resulted from CCSD F12 coupling
5738 template <typename T>
5739 typename SingleReference_R12Intermediates<T>::TArray2
5740 SingleReference_R12Intermediates<T>::Xam_CT2L2_f12b(const double C_0, const double C_1,
5741 const TArray4& T2, const TArray2& RT2_aPb,
5742 const TArray4& L2, const TArray2& RL2_aPb) {
5743 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
5744 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
5745
5746 TArray4d g_abmaP = ijxy("<a b|g|m a'>");
5747 TArray2 Xam_CT2, Xai_CT2;
5748 Xam_CT2("a,m") = // + 1/2 F^a'_m R^kl_a'b (T2^ab_kl + L2^ab_kl)
5749 // + 1/2 F^a'_b R^kl_ma' (T2^ab_kl + L2^ab_kl)
5750 ( R_C1 * T2("a,b,k,l") + R_C2 * T2("b,a,k,l")
5751 + R_C1 * L2("a,b,k,l") + R_C2 * L2("b,a,k,l")
5752 ) * (_4("<k l|r|m_F(a') b>") + _4("<k l|r|m b_F(a')>"))
5753
5754 // - g^aa'_mb 1/2 R^kl_a'c (T2^bc_kl + L2^bc_kl)
5755 // - g^ab_ma' 1/2 R^kl_a'c (T2^bc_kl + L2^bc_kl)
5756 - ( 2.0 * _4("<a a'|g|m b>") - _4("<a a'|g|b m>")
5757 + 2.0 * g_abmaP("a,b,m,a'") - g_abmaP("b,a,m,a'")
5758 ) * (RT2_aPb("a',b") + RL2_aPb("a',b")
5759 )
5760 ;
5761 Xai_CT2("a,i") = // - F^a'_b R^al_a'c (T2^bc_il + L2^bc_il)
5762 - _4("<a l|r|b_F(a') c>")
5763 * ( R_C1 * T2("b,c,i,l") + R_C2 * T2("b,c,l,i")
5764 + R_C1 * L2("b,c,i,l") + R_C2 * L2("b,c,l,i")
5765 )
5766 - _4("<a l|r|c b_F(a')>")
5767 * ( R_C1 * T2("c,b,i,l") + R_C2 * T2("c,b,l,i")
5768 + R_C1 * L2("c,b,i,l") + R_C2 * L2("c,b,l,i")
5769 )
5770 ;
5771
5772 return XaiAddToXam(Xam_CT2, Xai_CT2);
5773 }
5774
5775 // F12b method
5776 // Xam contribution of VT(T1&T2) part resulted from CCSD F12 coupling
5777 template <typename T>
5778 typename SingleReference_R12Intermediates<T>::TArray2
5779 SingleReference_R12Intermediates<T>::Xam_VTL_f12b(const double C_0, const double C_1,
5780 const TArray2& T1, const TArray4& T2,
5781 const TArray2& L1, const TArray4& L2) {
5782
5783 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
5784 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
5785
5786 const char* i = "i";
5787 const char* j = "j";
5788 const char* k = "k";
5789 const char* l = "l";
5790 const char* m = "m";
5791
5792 const char* a = "a";
5793 const char* c = "c";
5794 const char* d = "d";
5795
5796 TArray4 V_alic = VPq_Rs(a,l,i,c, C_0, C_1);
5797 TArray4 V_ilac = VPq_Rs(i,l,a,c,C_0, C_1);
5798 TArray2 V_ac = VRk_Sk(a,c,C_0, C_1);
5799 TArray2 V_jm = VRk_Sk(j,m,C_0, C_1);
5800 TArray4d r_klmaP = ijxy("<k l|r|m a'>");
5801 TArray4d r_abPkl = ijxy("<a b'|r|k l>");
5802 TArray2 Xam_VT1L1, Xai_VT1L1;
5803 Xam_VT1L1("a,m") = // + 1/2 R^jk_A'B' g^A'B'_mk (t1^a_j + l1^a_j)
5804 (T1("a,j") + L1("a,j")) * V_jm("j,m")
5805
5806 + ( // + R^kl_mb' g^ab'_kc (t1^c_l + l1^c_l)
5807 _4("<a b'|g|k c>")
5808 * (R_C1 * r_klmaP("k,l,m,b'") + R_C2 * r_klmaP("l,k,m,b'"))
5809 + _4("<a b'|g|c k>")
5810 * (R_C1 * r_klmaP("l,k,m,b'") + R_C2 * r_klmaP("k,l,m,b'"))
5811 // + R^kl_ab' g^mb'_kc (t1^c_l + l1^c_l)
5812 + (R_C1 * r_abPkl("a,b',k,l") + R_C2 * r_abPkl("a,b',l,k"))
5813 * _4("<k c|g|m b'>")
5814 + (R_C1 * r_abPkl("a,b',l,k") + R_C2 * r_abPkl("a,b',k,l"))
5815 * _4("<c k|g|m b'>")
5816 ) * (T1("c,l") + L1("c,l"))
5817 ;
5818 Xai_VT1L1("a,i") = // - 1/2 R^al_A'B' g^A'B'_ic (t1^c_l + l1^c_l)
5819 // - 1/2 R^il_A'B' g^A'B'_ac (t1^c_l + l1^c_l)
5820 - (V_alic("a,l,i,c") + V_ilac("i,l,a,c"))
5821 * (T1("c,l") + L1("c,l"))
5822
5823 // - 1/2 R^ak_A'B' g^A'B'_ck (t1^c_i + l1^c_i)
5824 - V_ac("a,c") * (T1("c,i") + L1("c,i"))
5825 ;
5826 TArray2 Xam_VT1L1_tot = XaiAddToXam(Xam_VT1L1, Xai_VT1L1);
5827
5828 TArray4 V_alcd = VPq_Rs(a,l,c,d,C_0, C_1);
5829 TArray4 V_klmd = VPq_Rs(k,l,m,d,C_0, C_1);
5830 TArray2 Xam_VT2L2, Xai_VT2L2;
5831 Xam_VT2L2("a,m") = // 1/4 R^kl_A'B' g^A'B'_md (T^ad_kl + L^ad_kl)
5832 (T2("a,d,k,l") + L2("a,d,k,l")) * V_klmd("k,l,m,d")
5833
5834 + ( // + 1/4 R^kl_ab' g^mb'_cd (T^cd_kl + L^cd_kl)
5835 (R_C1 * r_abPkl("a,b',k,l") + R_C2 * r_abPkl("a,b',l,k"))
5836 * _4("<c d|g|m b'>")
5837 // + 1/4 R^kl_mb' g^ab'_cd (T^cd_kl + L^cd_kl)
5838 + _4("<a b'|g|c d>")
5839 * (R_C1 * r_klmaP("k,l,m,b'") + R_C2 * r_klmaP("l,k,m,b'"))
5840 ) * (T2("c,d,k,l") + L2("c,d,k,l"))
5841 ;
5842 Xai_VT2L2("a,i") = // - 1/4 R^al_A'B' g^A'B'_cd (T^cd_il + L^cd_il)
5843 - V_alcd("a,l,c,d") * (T2("c,d,i,l") + L2("c,d,i,l"))
5844 ;
5845 TArray2 Xam_VT2L2_tot = XaiAddToXam(Xam_VT2L2, Xai_VT2L2);
5846
5847 TArray2 Xam_VTL_tot;
5848 Xam_VTL_tot("a,m") = Xam_VT1L1_tot("a,m") + Xam_VT2L2_tot("a,m");
5849 return Xam_VTL_tot;
5850 }
5851
5852 // F12b method
5853 // Xam contribution of VT1T1 part resulted from CCSD F12 coupling
5854 // VT1T1: 1/2 [V^dagger]^cd_kl t^k_c t^l_d
5855 // (1/4 R^AB_kl g^cd_AB t^k_c t^l_d)
5856 template <typename T>
5857 typename SingleReference_R12Intermediates<T>::TArray2
5858 SingleReference_R12Intermediates<T>::Xam_VT1T1_f12b(const double C_0, const double C_1,
5859 const TArray2& T1) {
5860 const char* k = "k";
5861 const char* l = "l";
5862 const char* m = "m";
5863
5864 const char* a = "a";
5865 const char* c = "c";
5866 const char* d = "d";
5867
5868 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
5869 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
5870
5871 TArray4 Vklmd = VPq_Rs(k, l, m, d, C_0, C_1); // V^Rk_Sk = 1/2 bar{R}^Rk_A'B' bar{g}^A'B'_Sk
5872 TArray4 Valcd = VPq_Rs(a, l, c, d, C_0, C_1);
5873
5874 // test for VPQ_RS
5875 //TArray4 V_KLMD = VPQ_RS(k, l, m, d);
5876
5877 TArray4d rmbp_kl = ijxy("<m b'|r|k l>");
5878 TArray4d rabp_kl = ijxy("<a b'|r|k l>");
5879
5880 TArray2 Xam_VT1T1;
5881 Xam_VT1T1("a,m") = // 1/2 R^AB_kl g^md_AB t^k_a t^l_d
5882 Vklmd("k,l,m,d")
5883 //(R_C1 * V_KLMD("k,l,m,d") + R_C2 * V_KLMD("l,k,m,d"))
5884 * T1("a,k") * T1("d,l")
5885
5886 // 1/2 R^mb'_kl g^cd_ab' t^k_c t^l_d
5887 // 1/2 R^ab'_kl g^cd_mb' t^k_c t^l_d
5888 + ( (R_C1 * rmbp_kl("m,b',k,l") + R_C2 * rmbp_kl("m,b',l,k"))
5889 * _4("<a b'|g|c d>")
5890 + (R_C1 * rabp_kl("a,b',k,l") + R_C2 * rabp_kl("a,b',l,k"))
5891 * _4("<m b'|g|c d>")
5892 ) * T1("c,k") * T1("d,l")
5893 ;
5894 TArray2 Xai_VT1T1;
5895 Xai_VT1T1("a,i") = // - 1/2 R^AB_al g^cd_AB t^i_c t^l_d
5896 - Valcd("a,l,c,d") * T1("c,i") * T1("d,l")
5897 ;
5898
5899 return XaiAddToXam(Xam_VT1T1, Xai_VT1T1);
5900 }
5901
5902 template <typename T>
5903 typename SingleReference_R12Intermediates<T>::TArray2
5904 SingleReference_R12Intermediates<T>::Xam_VT1T1_f12b_test(const double C_0, const double C_1,
5905 const TArray4& tauT1_ab) {
5906
5907 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
5908 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
5909
5910 const char* k = "k";
5911 const char* l = "l";
5912 const char* m = "m";
5913
5914 const char* a = "a";
5915 const char* c = "c";
5916 const char* d = "d";
5917
5918 TArray4d r_klmaP = ijxy("<k l|r|m a'>");
5919 TArray4d r_abPkl = ijxy("<a b'|r|k l>");
5920
5921
5922 TArray4 V_alcd = VPq_Rs(a,l,c,d,C_0, C_1);
5923 TArray4 V_klmd = VPq_Rs(k,l,m,d,C_0, C_1);
5924 TArray2 Xam, Xai;
5925 Xam("a,m") = //
5926 tauT1_ab("a,d,k,l") * V_klmd("k,l,m,d")
5927
5928 + ( //
5929 (R_C1 * r_abPkl("a,b',k,l") + R_C2 * r_abPkl("a,b',l,k"))
5930 * _4("<c d|g|m b'>")
5931 //
5932 + _4("<a b'|g|c d>")
5933 * (R_C1 * r_klmaP("k,l,m,b'") + R_C2 * r_klmaP("l,k,m,b'"))
5934 ) * tauT1_ab("c,d,k,l")
5935 ;
5936 Xai("a,i") = //
5937 - V_alcd("a,l,c,d") * tauT1_ab("c,d,i,l")
5938 ;
5939
5940 return XaiAddToXam(Xam, Xai);
5941 }
5942
5943 // F12b method
5944 // Xam contribution of VL2T1 part resulted from CCSD F12 coupling
5945 // VL2T1: 1/2 L^cd_kl V^cd_jc t^j_d
5946 // (- 1/4 L^cd_kl R^kl_AB g^AB_cj t^j_d)
5947 template <typename T>
5948 typename SingleReference_R12Intermediates<T>::TArray2
5949 SingleReference_R12Intermediates<T>::Xam_VL2T1_f12b(const double C_0, const double C_1,
5950 const TArray2& T1, const TArray4& L2) {
5951
5952 const char* k = "k";
5953 const char* l = "l";
5954 const char* j = "j";
5955 const char* m = "m";
5956 const char* a = "a";
5957 const char* c = "c";
5958
5959 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
5960 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
5961
5962 TArray4d rmbp_kl = ijxy("<m b'|r|k l>");
5963 TArray4d rabp_kl = ijxy("<a b'|r|k l>");
5964
5965 TArray4 V_ALCJ = VPQ_RS(a, l, c, j);
5966 TArray4 V_LACJ = VPQ_RS(l, a, c, j);
5967 TArray4 V_KLCA = VPQ_RS(k, l, c, a);
5968 TArray4 V_KLMJ = VPQ_RS(k, l, m, j);
5969
5970 TArray2 Xam_VL2T1;
5971 Xam_VL2T1("a,m") = // - 1/2 l^ad_kl R^kl_AB g^AB_mj t^j_d
5972 - (R_C1 * V_KLMJ("k,l,m,j") + R_C2 * V_KLMJ("l,k,m,j"))
5973 * L2("a,d,k,l") * T1("d,j")
5974
5975 // - 1/2 l^cd_kl R^kl_mb' g^ab'_cj t^j_d
5976 // - 1/2 l^cd_kl R^kl_ab' g^mb'_cj t^j_d
5977 - ( (R_C1 * rmbp_kl("m,b',k,l") + R_C2 * rmbp_kl("m,b',l,k"))
5978 * _4("<a b'|g|c j>")
5979 + (R_C1 * rmbp_kl("m,b',l,k") + R_C2 * rmbp_kl("m,b',k,l"))
5980 * _4("<a b'|g|j c>")
5981 //
5982 + (R_C1 * rabp_kl("a,b',k,l") + R_C2 * rabp_kl("a,b',l,k"))
5983 * _4("<m b'|g|c j>")
5984 + (R_C1 * rabp_kl("a,b',l,k") + R_C2 * rabp_kl("a,b',k,l"))
5985 * _4("<m b'|g|j c>")
5986 ) * L2("c,d,k,l") * T1("d,j")
5987 ;
5988 TArray2 Xai_VL2T1;
5989 Xai_VL2T1("a,i") = // + 1/2 l^cd_il R^al_AB g^AB_cj t^j_d
5990 ( R_C1 * ( V_ALCJ("a,l,c,j") * L2("c,d,i,l")
5991 + V_LACJ("l,a,c,j") * L2("c,d,l,i"))
5992 + R_C2 * ( V_ALCJ("a,l,c,j") * L2("c,d,l,i")
5993 + V_LACJ("l,a,c,j") * L2("c,d,i,l"))
5994 ) * T1("d,j")
5995
5996 // + 1/2 l^cd_kl R^kl_AB g^AB_ca t^i_d
5997 + (R_C1 * V_KLCA("k,l,c,a") + R_C2 * V_KLCA("l,k,c,a"))
5998 * L2("c,d,k,l") * T1("d,i")
5999 ;
6000
6001 return XaiAddToXam(Xam_VL2T1, Xai_VL2T1);
6002
6003 }
6004
6005 template <typename T>
6006 typename SingleReference_R12Intermediates<T>::TArray2
6007 SingleReference_R12Intermediates<T>::Xam_VL2T1_f12b_test(const double C_0, const double C_1,
6008 const TArray2& T1, const TArray4& L2) {
6009
6010 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
6011 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
6012
6013 const char* j = "j";
6014 const char* k = "k";
6015 const char* l = "l";
6016 const char* m = "m";
6017
6018 const char* a = "a";
6019 const char* c = "c";
6020
6021 TArray4d r_klmaP = ijxy("<k l|r|m a'>");
6022 TArray4d r_abPkl = ijxy("<a b'|r|k l>");
6023
6024 TArray4 V_alcj = VPq_Rs(a,l,c,j,C_0, C_1);
6025 TArray4 V_lacj = VPq_Rs(l,a,c,j,C_0, C_1);
6026 TArray4 V_klca = VPq_Rs(k,l,c,a,C_0, C_1);
6027 TArray4 V_klmj = VPq_Rs(k,l,m,j,C_0, C_1);
6028 TArray2 Xam, Xai;
6029 Xam("a,m") = //
6030 - L2("a,d,k,l") * V_klmj("k,l,m,j") * T1("d,j")
6031
6032 - ( //
6033 (R_C1 * r_abPkl("a,b',k,l") + R_C2 * r_abPkl("a,b',l,k"))
6034 * _4("<c j|g|m b'>")
6035 + (R_C1 * r_abPkl("a,b',l,k") + R_C2 * r_abPkl("a,b',k,l"))
6036 * _4("<j c|g|m b'>")
6037 //
6038 + _4("<a b'|g|c j>")
6039 * (R_C1 * r_klmaP("k,l,m,b'") + R_C2 * r_klmaP("l,k,m,b'"))
6040 + _4("<a b'|g|j c>")
6041 * (R_C1 * r_klmaP("l,k,m,b'") + R_C2 * r_klmaP("k,l,m,b'"))
6042 ) * L2("c,d,k,l") * T1("d,j")
6043 ;
6044 Xai("a,i") = //
6045 (V_alcj("a,l,c,j") * L2("c,d,i,l") + V_lacj("l,a,c,j") * L2("c,d,l,i"))
6046 * T1("d,j")
6047 //
6048 + L2("c,d,k,l") * V_klca("k,l,c,a") * T1("d,i")
6049 ;
6050
6051 return XaiAddToXam(Xam, Xai);
6052 }
6053
6054 // F12b method
6055 // Xam contribution of VL2T1T1 part resulted from CCSD F12 coupling
6056 template <typename T>
6057 typename SingleReference_R12Intermediates<T>::TArray2
6058 SingleReference_R12Intermediates<T>::Xam_VL2T1T1_f12b(const double C_0, const double C_1,
6059 const TArray2& T1, const TArray4& L2) {
6060
6061 const char* k = "k";
6062 const char* l = "l";
6063 const char* j = "j";
6064 const char* a = "a";
6065
6066 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
6067 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
6068
6069 TArray4d rmbp_kl = ijxy("<m b'|r|k l>");
6070 TArray4d rabp_kl = ijxy("<a b'|r|k l>");
6071
6072 TArray4 V_AJKL = VPQ_RS(a, j, k, l);
6073 TArray4 V_KLAJ = VPQ_RS(k, l, a, j);
6074
6075 // compute Xam from 1/4 L^cd_kl V^cd_k1l1 t^k1_c t^l1_d
6076 // (1/8 L^cd_kl R^kl_AB g^AB_k1l1 t^k1_c t^l1_d)
6077 TArray2 Xam_VL2T1T1;
6078 Xam_VL2T1T1("a,m") = // 1/4 l^cd_kl R^kl_mb' g^ab'_k1l1 t^k1_c t^l1_d
6079 // 1/4 l^cd_kl R^kl_ab' g^mb'_k1l1 t^k1_c t^l1_d
6080 ( (R_C1 * rmbp_kl("m,b',k,l") + R_C2 * rmbp_kl("m,b',l,k"))
6081 * _4("<a b'|g|i j>")
6082 //
6083 + (R_C1 * rabp_kl("a,b',k,l") + R_C2 * rabp_kl("a,b',l,k"))
6084 * _4("<m b'|g|i j>")
6085 ) * L2("c,d,k,l") * T1("c,i") * T1("d,j")
6086 ;
6087 TArray2 Xai_VL2T1T1;
6088 Xai_VL2T1T1("a,i") = // - 1/4 l^cd_il R^al_AB g^AB_k1l1 t^k1_c t^l1_d
6089 - (R_C1 * V_AJKL("a,j,k,l") + R_C2 * V_AJKL("a,j,l,k"))
6090 * L2("c,d,i,j") * T1("c,k") * T1("d,l")
6091
6092 // - 1/4 l^cd_kl R^kl_AB g^AB_al1 t^i_c t^l1_d
6093 - (R_C1 * V_KLAJ("k,l,a,j") + R_C2 * V_KLAJ("l,k,a,j"))
6094 * L2("c,d,k,l") * T1("c,i") * T1("d,j")
6095 ;
6096
6097 return XaiAddToXam(Xam_VL2T1T1, Xai_VL2T1T1);
6098 }
6099
6100 template <typename T>
6101 typename SingleReference_R12Intermediates<T>::TArray2
6102 SingleReference_R12Intermediates<T>::Xam_VL2T1T1_f12b_test(const double C_0, const double C_1,
6103 const TArray2& T1, const TArray4& L2) {
6104
6105 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
6106 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
6107
6108 const char* j = "j";
6109 const char* k = "k";
6110 const char* l = "l";
6111 const char* a = "a";
6112
6113 TArray4d r_klmaP = ijxy("<k l|r|m a'>");
6114 TArray4d r_abPkl = ijxy("<a b'|r|k l>");
6115
6116 TArray4 V_ajkl = VPq_Rs(a,j,k,l,C_0, C_1);
6117 TArray4 V_klaj = VPq_Rs(k,l,a,j,C_0, C_1);
6118 TArray2 Xam, Xai;
6119 Xam("a,m") = ( //
6120 (R_C1 * r_abPkl("a,b',k,l") + R_C2 * r_abPkl("a,b',l,k"))
6121 * _4("<i j|g|m b'>")
6122 //
6123 + _4("<a b'|g|i j>")
6124 * (R_C1 * r_klmaP("k,l,m,b'") + R_C2 * r_klmaP("l,k,m,b'"))
6125 ) * L2("c,d,k,l") * T1("c,i") * T1("d,j")
6126 ;
6127 Xai("a,i") = //
6128 - L2("c,d,k,l") * V_klaj("k,l,a,j") * T1("c,i") * T1("d,j")
6129 //
6130 - V_ajkl("a,j,k,l") * T1("c,k") * T1("d,l") * L2("c,d,i,j")
6131 ;
6132
6133 return XaiAddToXam(Xam, Xai);
6134 }
6135
6136 // frozen-core Xii' contribution resulting from CT2, VT2, and VT1 in F12b
6137 template <typename T>
6138 typename SingleReference_R12Intermediates<T>::TArray2
6139 SingleReference_R12Intermediates<T>::Xiip_CVT_f12b(const double C_0, const double C_1,
6140 const TArray2& T1, const TArray4& T2,
6141 const TArray2& L1, const TArray4& L2){
6142
6143 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
6144 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
6145
6146 const char* ip = "i'";
6147 const char* i = "i";
6148 const char* l = "l";
6149 const char* c = "c";
6150 const char* d = "d";
6151
6152 TArray2 Xiip_CTL;
6153 Xiip_CTL("i,i'") = // F^a'_b R^i'l_a'c (T2^bc_il + L2^bc_il)
6154 _4("<i' l|r|b_F(a') c>")
6155 * ( R_C1 * T2("b,c,i,l") + R_C2 * T2("b,c,l,i")
6156 + R_C1 * L2("b,c,i,l") + R_C2 * L2("b,c,l,i"))
6157 + _4("<i' l|r|c b_F(a')>")
6158 * ( R_C1 * T2("c,b,i,l") + R_C2 * T2("c,b,l,i")
6159 + R_C1 * L2("c,b,i,l") + R_C2 * L2("c,b,l,i"))
6160 ;
6161
6162 TArray2 Xiip_VT2L2;
6163 TArray4 V_ipl_cd = VPq_Rs(ip,l,c,d,C_0, C_1);
6164 Xiip_VT2L2("i,i'") = // 1/4 R^i'l_A'B' g^A'B'_cd (T^cd_il +L^cd_il)
6165 V_ipl_cd("i',l,c,d") * (T2("c,d,i,l") + L2("c,d,i,l"));
6166
6167 TArray2 Xiip_VT1L1;
6168 TArray4 V_ipl_ic = VPq_Rs(ip,l,i,c, C_0, C_1);
6169 TArray4 V_il_ipc = VPq_Rs(i,l,ip,c,C_0, C_1);
6170 TArray2 V_ipc = VRk_Sk(ip,c,C_0, C_1);
6171 Xiip_VT1L1("i,i'") = // 1/2 R^i'l_A'B' g^A'B'_ic (T^c_l + L^c_l)
6172 // 1/2 R^il_A'B' g^A'B'_i'c (T^c_l + L^c_l)
6173 (V_ipl_ic("i',l,i,c") + V_il_ipc("i,l,i',c"))
6174 * (T1("c,l") + L1("c,l"))
6175
6176 // 1/2 R^i'k_A'B' g^A'B'_ck (T^c_i + L^c_i)
6177 + V_ipc("i',c") * (T1("c,i") + L1("c,i"))
6178 ;
6179
6180 TArray2 Xiip_C1;
6181 Xiip_C1("i,i'") = Xiip_CTL("i,i'") + Xiip_VT2L2("i,i'") + Xiip_VT1L1("i,i'");
6182 return Xiip_C1;
6183 }
6184
6185 // frozen-core Xii' contribution resulting from VT1T1 in F12b
6186 template <typename T>
6187 typename SingleReference_R12Intermediates<T>::TArray2
6188 SingleReference_R12Intermediates<T>::Xiip_VT1T1_f12b(const double C_0, const double C_1,
6189 const TArray2& T1, const TArray4& T2,
6190 const TArray4& L2) {
6191 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
6192 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
6193
6194 const char* ip = "i'";
6195 const char* i = "i";
6196 const char* j = "j";
6197 const char* k = "k";
6198 const char* l = "l";
6199 const char* c = "c";
6200 const char* d = "d";
6201
6202 TArray4 V_ipl_cd = VPq_Rs(ip,l,c,d,C_0, C_1);
6203 TArray2 Xiip_VT1T1;
6204 Xiip_VT1T1("i,i'") = // 1/2 R^i'l_A'B' g^A'B'_cd T^i_c t^l_d
6205 V_ipl_cd("i',l,c,d") * T1("c,i") * T1("d,l");
6206
6207
6208 TArray4 V_IPL_CJ = VPQ_RS(ip, l, c, j);
6209 TArray4 V_LIP_CJ = VPQ_RS(l, ip, c, j);
6210 TArray4 V_KL_CIP = VPQ_RS(k, l, c, ip);
6211 TArray2 Xai_VL2T1;
6212 Xai_VL2T1("i,i'") = // - 1/2 l^cd_il R^i'l_AB g^AB_cj t^j_d
6213 ( R_C1 * ( V_IPL_CJ("i',l,c,j") * L2("c,d,i,l")
6214 + V_LIP_CJ("l,i',c,j") * L2("c,d,l,i"))
6215 + R_C2 * ( V_IPL_CJ("i',l,c,j") * L2("c,d,l,i")
6216 + V_LIP_CJ("l,i',c,j") * L2("c,d,i,l"))
6217 ) * T1("d,j")
6218
6219 // - 1/2 l^cd_kl R^kl_AB g^AB_ci' t^i_d
6220 + (R_C1 * V_KL_CIP("k,l,c,i'") + R_C2 * V_KL_CIP("l,k,c,i'"))
6221 * L2("c,d,k,l") * T1("d,i")
6222 ;
6223
6224 TArray4 V_IPJ_KL = VPQ_RS(ip, j, k, l);
6225 TArray4 V_KL_IPJ = VPQ_RS(k, l, ip, j);
6226 TArray2 Xai_VL2T1T1;
6227 Xai_VL2T1T1("i,i'") = // 1/4 l^cd_il R^i'l_AB g^AB_k1l1 t^k1_c t^l1_d
6228 (R_C1 * V_IPJ_KL("i',j,k,l") + R_C2 * V_IPJ_KL("i',j,l,k"))
6229 * L2("c,d,i,j") * T1("c,k") * T1("d,l")
6230
6231 // + 1/4 l^cd_kl R^kl_AB g^AB_i'l1 t^i_c t^l1_d
6232 + (R_C1 * V_KL_IPJ("k,l,i',j") + R_C2 * V_KL_IPJ("l,k,i',j"))
6233 * L2("c,d,k,l") * T1("c,i") * T1("d,j")
6234 ;
6235
6236 TArray2 Xiip_C2;
6237 Xiip_C2("i,i'") = Xiip_VT1T1("i,i'") + Xai_VL2T1("i,i'") + Xai_VL2T1T1("i,i'");
6238 return Xiip_C2;
6239 }
6240
6241 template <typename T>
6242 void SingleReference_R12Intermediates<T>::compute_multipole_F12b_coupling() {
6243
6244 ExEnv::out0() << std::endl << indent
6245 << "Compute CCSD-F12b coupling contri. to dipole and quadrupole moments" << std::endl;
6246
6247 bool compute_dipole = true;
6248 bool compute_quadrupole = true;
6249
6250 double conv_target = 1e-10;
6251
6252 // singlet and triplet coefficients for F12 and coupling terms
6253 const double C_0 = 1.0 / 2.0;
6254 const double C_1 = 1.0 / 4.0;
6255 const double RC1 = 0.5 * (C_0 + C_1);
6256 const double RC2 = 0.5 * (C_0 - C_1);
6257 // compute coefficients needed in the F12 and coupling calculations
6258 const double R_C1 = (0.5 * C_0 + 1.5 * C_1);
6259 const double R_C2 = (0.5 * C_0 - 1.5 * C_1);
6260
6261 const char* i = "i";
6262 const char* j = "j";
6263 const char* k = "k";
6264 const char* l = "l";
6265 const char* m = "m";
6266
6267 const char* a = "a";
6268 const char* b = "b";
6269 const char* c = "c";
6270 const char* d = "d";
6271
6272 // compute integrals needed for orbital relaxation
6273 // i.e. solve Abnam Dbn = Xam (close-shell formula)
6274 TArray4d g_mnab = ijxy("<m n|g|a b>");
6275 TArray4 A_bnam;
6276 A_bnam("b,n,a,m") = - _4("<b n|g|a m>") - g_mnab("m,n,b,a") + 4.0 * g_mnab("n,m,b,a")
6277 + _2("<b|F|a>") * _2("<m|I|n>") - _2("<a|I|b>") * _2("<m|F|n>");
6278
6279 // Make preconditioner: Delta_am = 1 / (<a|F|a> - <m|F|m>) for
6280 // solving k_bn A_bnam = X_am
6281 TArray2 mFmn, mFab;
6282 mFmn("m,n") = - _2("<m|F|n>");
6283 mFab("a,b") = - _2("<a|F|b>");
6284 typedef detail::diag_precond2<double> pceval_type;
6285 pceval_type Delta_am_gen(TA::array_to_eigen(mFab), TA::array_to_eigen(mFmn));
6286
6287 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2d;
6288 TArray2 Iam = xy("<a|I|m>");
6289 TArray2d Delta_am(Iam.world(), Iam.trange());
6290
6291 // construct local tiles
6292 for(auto t = Delta_am.trange().tiles_range().begin();
6293 t != Delta_am.trange().tiles_range().end(); ++t)
6294 if (Delta_am.is_local(*t)) {
6295 std::array<std::size_t, 2> index;
6296 std::copy(t->begin(), t->end(), index.begin());
6297 madness::Future < typename TArray2d::value_type >
6298 tile((LazyTensor<T, 2, pceval_type >(&Delta_am, index, &Delta_am_gen)
6299 ));
6300
6301 // Insert the tile into the array
6302 Delta_am.set(*t, tile);
6303 }
6304 TArray2 preconditioner;
6305 preconditioner("a,m") = Delta_am("a,m");
6306
6307 detail::Orbital_relaxation_Abjai<double> Orbital_relaxation_Abnam(A_bnam);
6308 TA::ConjugateGradientSolver<TiledArray::Array<T,2>,
6309 detail::Orbital_relaxation_Abjai<double> > cg_solver2;
6310
6311
6312 // determine if it is frozen-core
6313 TArray2 Fij = xy("<i|F|j>");
6314 const std::size_t nocc = mFmn.trange().elements_range().extent()[0];
6315 const std::size_t naocc = Fij.trange().elements_range().extent()[0];
6316
6317 // compute terms needed for frozen-core
6318 TArray2 Delta_ijp_F;
6319 TArray4 A_ijpam;
6320 if (nocc != naocc) {
6321 // compute 1 / (Fi'i' - Fjj)
6322 TArray2 Fipjp = xy("<i'|F|j'>");
6323 pceval_type Delta_ijp_gen(TA::array_to_eigen(Fij), TA::array_to_eigen(Fipjp));
6324
6325 TArray2 Fijp = xy("<i|F|j'>");
6326 TArray2d Delta_ijp(Fijp.world(), Fijp.trange());
6327 // construct local tiles
6328 for(auto t = Delta_ijp.trange().tiles_range().begin();
6329 t != Delta_ijp.trange().tiles_range().end(); ++t)
6330 if (Delta_ijp.is_local(*t)) {
6331 std::array<std::size_t, 2> index;
6332 std::copy(t->begin(), t->end(), index.begin());
6333 madness::Future < typename TArray2d::value_type >
6334 tile((LazyTensor<T, 2, pceval_type >(&Delta_ijp, index, &Delta_ijp_gen)
6335 ));
6336
6337 // Insert the tile into the array
6338 Delta_ijp.set(*t, tile);
6339 }
6340 Delta_ijp_F("i,j'") = Delta_ijp("i,j'");
6341
6342 A_ijpam("i,j',a,m") = 4.0 * _4("<i a|g|j' m>") - _4("<i a|g|m j'>") - _4("<i m|g|a j'>");
6343 }
6344
6345 TArray2 mu_z_ij, mu_z_ijp, mu_z_ab, mu_z_ai, mu_z_am;
6346 if (compute_dipole) {
6347 mu_z_ij = xy("<i|mu_z|j>");
6348 mu_z_ab = xy("<a|mu_z|b>");
6349 mu_z_ai = xy("<a|mu_z|i>");
6350 mu_z_am = xy("<a|mu_z|m>");
6351
6352 if (nocc != naocc)
6353 mu_z_ijp = xy("<i|mu_z|j'>");
6354 }
6355
6356 // quadrupole integrals
6357 TArray2 Qxx_ij, Qyy_ij, Qzz_ij, Qxx_ab, Qyy_ab, Qzz_ab,
6358 Qxx_ai, Qyy_ai, Qzz_ai, Qxx_am, Qyy_am, Qzz_am,
6359 Qxx_apb, Qyy_apb, Qzz_apb,
6360 // integrals for frozen-core
6361 Qxx_ijp, Qyy_ijp, Qzz_ijp;
6362
6363 if (compute_quadrupole){
6364
6365 TArray2 q_xx_ij = xy("<i|q_xx|j>");
6366 TArray2 q_yy_ij = xy("<i|q_yy|j>");
6367 TArray2 q_zz_ij = xy("<i|q_zz|j>");
6368 Qxx_ij("i,j") = q_xx_ij("i,j") - (q_zz_ij("i,j") + q_yy_ij("i,j")) * 0.5;
6369 Qyy_ij("i,j") = q_yy_ij("i,j") - (q_zz_ij("i,j") + q_xx_ij("i,j")) * 0.5;
6370 Qzz_ij("i,j") = q_zz_ij("i,j") - (q_xx_ij("i,j") + q_yy_ij("i,j")) * 0.5;
6371
6372 TArray2 q_xx_ab = xy("<a|q_xx|b>");
6373 TArray2 q_yy_ab = xy("<a|q_yy|b>");
6374 TArray2 q_zz_ab = xy("<a|q_zz|b>");
6375 Qxx_ab("a,b") = q_xx_ab("a,b") - (q_zz_ab("a,b") + q_yy_ab("a,b")) * 0.5;
6376 Qyy_ab("a,b") = q_yy_ab("a,b") - (q_zz_ab("a,b") + q_xx_ab("a,b")) * 0.5;
6377 Qzz_ab("a,b") = q_zz_ab("a,b") - (q_xx_ab("a,b") + q_yy_ab("a,b")) * 0.5;
6378
6379 TArray2 q_xx_ai = xy("<a|q_xx|i>");
6380 TArray2 q_yy_ai = xy("<a|q_yy|i>");
6381 TArray2 q_zz_ai = xy("<a|q_zz|i>");
6382 Qxx_ai("a,i") = q_xx_ai("a,i") - (q_zz_ai("a,i") + q_yy_ai("a,i")) * 0.5;
6383 Qyy_ai("a,i") = q_yy_ai("a,i") - (q_zz_ai("a,i") + q_xx_ai("a,i")) * 0.5;
6384 Qzz_ai("a,i") = q_zz_ai("a,i") - (q_xx_ai("a,i") + q_yy_ai("a,i")) * 0.5;
6385
6386 TArray2 q_xx_am = xy("<a|q_xx|m>");
6387 TArray2 q_yy_am = xy("<a|q_yy|m>");
6388 TArray2 q_zz_am = xy("<a|q_zz|m>");
6389 Qxx_am("a,m") = q_xx_am("a,m") - (q_zz_am("a,m") + q_yy_am("a,m")) * 0.5;
6390 Qyy_am("a,m") = q_yy_am("a,m") - (q_zz_am("a,m") + q_xx_am("a,m")) * 0.5;
6391 Qzz_am("a,m") = q_zz_am("a,m") - (q_xx_am("a,m") + q_yy_am("a,m")) * 0.5;
6392
6393 TArray2 q_xx_apb = xy("<a'|q_xx|b>");
6394 TArray2 q_yy_apb = xy("<a'|q_yy|b>");
6395 TArray2 q_zz_apb = xy("<a'|q_zz|b>");
6396 Qxx_apb("a',b") = q_xx_apb("a',b") - (q_zz_apb("a',b") + q_yy_apb("a',b")) * 0.5;
6397 Qyy_apb("a',b") = q_yy_apb("a',b") - (q_zz_apb("a',b") + q_xx_apb("a',b")) * 0.5 ;
6398 Qzz_apb("a',b") = q_zz_apb("a',b") - (q_xx_apb("a',b") + q_yy_apb("a',b")) * 0.5;
6399
6400 if (nocc != naocc) {
6401 TArray2 q_xx_ijp = xy("<i|q_xx|j'>");
6402 TArray2 q_yy_ijp = xy("<i|q_yy|j'>");
6403 TArray2 q_zz_ijp = xy("<i|q_zz|j'>");
6404 Qxx_ijp("i,j'") = q_xx_ijp("i,j'") - (q_zz_ijp("i,j'") + q_yy_ijp("i,j'")) * 0.5;
6405 Qyy_ijp("i,j'") = q_yy_ijp("i,j'") - (q_zz_ijp("i,j'") + q_xx_ijp("i,j'")) * 0.5;
6406 Qzz_ijp("i,j'") = q_zz_ijp("i,j'") - (q_xx_ijp("i,j'") + q_yy_ijp("i,j'")) * 0.5;
6407 }
6408 }
6409
6410 double muz_ccsd = 0.0, muz_ccsdor = 0.0;
6411 double q_xx_ccsd = 0.0, q_yy_ccsd = 0.0, q_zz_ccsd = 0.0;
6412 double q_xx_ccsdor = 0.0, q_yy_ccsdor = 0.0, q_zz_ccsdor = 0.0;
6413#if 1 // CCSD
6414 ExEnv::out0() << indent << "Compute CCSD T amplitudes " << std::endl;
6415 TArray2 T1_ccsd;
6416 TArray4 T2_ccsd;
6417 compute_T_ccsd(T1_ccsd, T2_ccsd, "CCSD");
6418
6419 ExEnv::out0() << indent << "Compute CCSD L amplitudes " << std::endl;
6420 TArray2 L1_ccsd;
6421 TArray4 L2_ccsd;
6422 compute_lambda_ccsd(T1_ccsd, T2_ccsd, L1_ccsd, L2_ccsd, "CCSD");
6423
6424 // compute CCSD density from amplitudes
6425 TArray2 Dij_ccsd, Dab_ccsd, Dia_ccsd, Dai_ccsd;
6426 ExEnv::out0() << std::endl << indent
6427 << "Compute CCSD density from amplitudes" << std::endl;
6428 compute_ccsd_1rdm_amp(T1_ccsd, T2_ccsd, L1_ccsd, L2_ccsd,
6429 Dij_ccsd, Dab_ccsd, Dia_ccsd, Dai_ccsd);
6430
6431 ExEnv::out0() << std::endl << indent << "Compute CCSD Xam and Xai" << std::endl;
6432 TArray2 Xam_ccsd_nfzc, Xiip_ccsd;
6433 compute_Xam_ccsd(T1_ccsd, T2_ccsd, L1_ccsd, L2_ccsd,
6434 Xam_ccsd_nfzc, Xiip_ccsd);
6435
6436 TArray2 Diip_or_ccsd, Xam_ccsd;
6437 if (nocc != naocc) {
6438 ExEnv::out0() << std::endl << indent
6439 << "Include frozen-core CCSD contributions" << std::endl;
6440 Diip_or_ccsd("i,i'") = Xiip_ccsd("i,i'") * Delta_ijp_F("i,i'");
6441
6442 TArray2 Xam_Diip_ccsd;
6443 Xam_Diip_ccsd("a,m") = A_ijpam("i,i',a,m") * Diip_or_ccsd("i,i'");
6444 Xam_ccsd("a,m") = Xam_ccsd_nfzc("a,m") - Xam_Diip_ccsd("a,m");
6445 } else {
6446 Xam_ccsd("a,m") = Xam_ccsd_nfzc("a,m");
6447 }
6448
6449 // solve the Z-vector equation for CCSD
6450 TArray2 Dbn_ccsd(Xam_ccsd.world(), Xam_ccsd.trange());
6451 auto resnorm_ccsd = cg_solver2(Orbital_relaxation_Abnam,
6452 Xam_ccsd,
6453 Dbn_ccsd,
6454 preconditioner,
6455 conv_target);
6456
6457 if (compute_dipole) {
6458 muz_ccsd = dot(mu_z_ij("i,j"), Dij_ccsd("i,j"))
6459 + dot(mu_z_ab("a,b"), Dab_ccsd("a,b"))
6460 + dot(mu_z_ai("a,i"), Dai_ccsd("a,i"))
6461 + dot(mu_z_ai("a,i"), Dia_ccsd("i,a"))
6462 ;
6463
6464 muz_ccsdor = dot(mu_z_am("a,m"), Dbn_ccsd("a,m"));
6465 if (nocc != naocc) {
6466 muz_ccsdor += dot(mu_z_ijp("i,i'"), Diip_or_ccsd("i,i'"));
6467 }
6468
6469// std::cout << std::endl << indent
6470// << "muz_CCSD = " << scprintf("%15.12f", - muz_ccsd * 2.0)
6471// << std::endl << indent
6472// << "muz_CCSDor = " << scprintf("%15.12f", - muz_ccsdor * 2.0)
6473// << std::endl;
6474 }
6475
6476 if (compute_quadrupole) {
6477 q_xx_ccsd = dot(Qxx_ij("i,j"), Dij_ccsd("i,j"))
6478 + dot(Qxx_ab("a,b"), Dab_ccsd("a,b"))
6479 + dot(Qxx_ai("a,i"), Dai_ccsd("a,i"))
6480 + dot(Qxx_ai("a,i"), Dia_ccsd("i,a"))
6481 ;
6482 q_yy_ccsd = dot(Qyy_ij("i,j"), Dij_ccsd("i,j"))
6483 + dot(Qyy_ab("a,b"), Dab_ccsd("a,b"))
6484 + dot(Qyy_ai("a,i"), Dai_ccsd("a,i"))
6485 + dot(Qyy_ai("a,i"), Dia_ccsd("i,a"))
6486 ;
6487 q_zz_ccsd = dot(Qzz_ij("i,j"), Dij_ccsd("i,j"))
6488 + dot(Qzz_ab("a,b"), Dab_ccsd("a,b"))
6489 + dot(Qzz_ai("a,i"), Dai_ccsd("a,i"))
6490 + dot(Qzz_ai("a,i"), Dia_ccsd("i,a"))
6491 ;
6492
6493 q_xx_ccsdor = dot(Qxx_am("a,m"), Dbn_ccsd("a,m"));
6494 q_yy_ccsdor = dot(Qyy_am("a,m"), Dbn_ccsd("a,m"));
6495 q_zz_ccsdor = dot(Qzz_am("a,m"), Dbn_ccsd("a,m"));
6496
6497 if (nocc != naocc) {
6498 q_xx_ccsdor += dot(Qxx_ijp("i,j'"), Diip_or_ccsd("i,j'"));
6499 q_yy_ccsdor += dot(Qyy_ijp("i,j'"), Diip_or_ccsd("i,j'"));
6500 q_zz_ccsdor += dot(Qzz_ijp("i,j'"), Diip_or_ccsd("i,j'"));
6501 }
6502
6503// std::cout << std::endl << indent
6504// << "qxx_ccsd = " << scprintf("%12.10f", - q_xx_ccsd * 2.0)
6505// << " qyy_ccsd = " << scprintf("%12.10f", - q_yy_ccsd * 2.0)
6506// << " qzz_ccsd = " << scprintf("%12.10f", - q_zz_ccsd * 2.0)
6507// << std::endl << indent
6508// << "qxx_ccsdor = " << scprintf("%12.10f", - q_xx_ccsdor * 2.0)
6509// << " qyy_ccsdor = " << scprintf("%12.10f", - q_yy_ccsdor * 2.0)
6510// << " qzz_ccsdor = " << scprintf("%12.10f", - q_zz_ccsdor * 2.0)
6511// << std::endl;
6512 }
6513#endif
6514
6515 // resolve CCSD T amplitudes in the framework of CCSD-F12b
6516 ExEnv::out0() << indent << "Compute CCSD-F12b T amplitudes " << std::endl;
6517 TArray2 T1_f12b;
6518 TArray4 T2_f12b;
6519 compute_T_ccsd(T1_f12b, T2_f12b, "F12b");
6520
6521 // resolve CCSD lambda amplitudes in the framework of CCSD-F12b
6522 ExEnv::out0() << std::endl << indent << "Compute CCSD-F12b L amplitudes " << std::endl;
6523 TArray2 L1_f12b;
6524 TArray4 L2_f12b;
6525 compute_lambda_ccsd(T1_f12b, T2_f12b, L1_f12b, L2_f12b, "F12b");
6526
6527 // compute energy from coupling in F12b
6528#if 0
6529 // CT2 energy
6530 // F^a'_a R^ij_a'b + F^a'_b R^ij_aa'
6531 TArray4 Cijab;
6532 TArray4d r_ijaFb = ijxy("<i j|r|a_F(c') b>");
6533 Cijab("i,j,a,b") = R_C1 * r_ijaFb("i,j,a,b") + R_C2 * r_ijaFb("j,i,a,b")
6534 + R_C1 * r_ijaFb("j,i,b,a") + R_C2 * r_ijaFb("i,j,b,a");
6535 TArray2 CT2;
6536 CT2("i,j") = Cijab("i,k,a,b") * T2_f12b("a,b,j,k");
6537 double E_CT2 = dot(CT2("i,j"), _2("<j|I|i>"));
6538 std::cout << std::endl
6539 << indent << "E_CT2 = " << scprintf("%15.12f", E_CT2)
6540 << std::endl;
6541
6542 // VT1 + VT2 energy
6543 TArray2 V_ia;
6544 V_ia = VRk_Sk(i,a, C_0, C_1);
6545
6546 TArray4 Vijab = VPq_Rs(i, j, a, b, C_0, C_1);
6547 TArray2 VT2;
6548 VT2("i,j") = Vijab("i,k,a,b") * T2_f12b("a,b,j,k");
6549
6550 double E_VT = dot(V_ia("i,a"), T1_f12b("a,i")) * 2.0
6551 + dot(VT2("i,j"), _2("<j|I|i>"));
6552 std::cout << indent << "E_VT = " << scprintf("%15.12f", E_VT)
6553 << std::endl;
6554
6555 // VT1T1 energy
6556 double E_VT1T1 = dot(Vijab("i,j,a,b"), T1_f12b("a,i") * T1_f12b("b,j"));
6557 std::cout << indent << "E_VT1T1 = " << scprintf("%15.12f", E_VT1T1)
6558 << std::endl;
6559
6560 std::cout << indent << "E (Coupling in F12b) = "
6561 << scprintf("%15.12f", (E_CT2+E_VT+E_VT1T1))
6562 << std::endl;
6563#endif
6564
6565 // CC F12b coupling contribution to Xam
6566 TArray2 mu_z_apb;
6567#if 1
6568 // compute CCSD-F12b density from amplitudes
6569 TArray2 Dij_f12b, Dab_f12b, Dia_f12b, Dai_f12b;
6570 ExEnv::out0() << std::endl << indent
6571 << "Compute CCSD density from amplitudes in CCSD-F12b" << std::endl;
6572 compute_ccsd_1rdm_amp(T1_f12b, T2_f12b, L1_f12b, L2_f12b,
6573 Dij_f12b, Dab_f12b, Dia_f12b, Dai_f12b);
6574
6575 ExEnv::out0() << std::endl << indent
6576 << "Compute CCSD Xam and Xai in CCSD-F12b" << std::endl;
6577 TArray2 Xam_f12b_nfzc, Xiip_f12b;
6578 compute_Xam_ccsd(T1_f12b, T2_f12b, L1_f12b, L2_f12b, Xam_f12b_nfzc, Xiip_f12b);
6579
6580 TArray2 Diip_f12b, Xam_f12b;
6581 if (nocc != naocc) {
6582 Diip_f12b("i,i'") = Xiip_f12b("i,i'") * Delta_ijp_F("i,i'");
6583 Xam_f12b("a,m") = Xam_f12b_nfzc("a,m") - A_ijpam("i,i',a,m") * Diip_f12b("i,i'");
6584 } else {
6585 Xam_f12b("a,m") = Xam_f12b_nfzc("a,m");
6586 }
6587
6588 TArray2 Dbn_f12b(Xam_f12b.world(), Xam_f12b.trange());
6589 auto resnorm_f12b = cg_solver2(Orbital_relaxation_Abnam,
6590 Xam_f12b,
6591 Dbn_f12b,
6592 preconditioner,
6593 conv_target);
6594
6595
6596 ExEnv::out0() << std::endl << indent
6597 << "Compute CCSD F12b coupling contributions" << std::endl;
6598 // CC CT2
6599 TArray2 RT2_aPb, RL2_aPb;
6600 // 1/2 R^kl_a'c T2^bc_kl
6601 RT2_aPb("a',b") = _4("<a' c|r|k l>")
6602 * (R_C1 * T2_f12b("b,c,k,l") + R_C2 * T2_f12b("c,b,k,l"));
6603 // 1/2 R^kl_a'c L2^bc_kl
6604 RL2_aPb("a',b") = _4("<a' c|r|k l>")
6605 * (R_C1 * L2_f12b("b,c,k,l") + R_C2 * L2_f12b("c,b,k,l"));
6606
6607 TArray2 Xam_CT2L2 = Xam_CT2L2_f12b(C_0, C_1, T2_f12b, RT2_aPb, L2_f12b, RL2_aPb);
6608
6609 // VT1 & VT2 coupling contribution to F12 Xam
6610 TArray2 Xam_VTL = Xam_VTL_f12b(C_0, C_1, T1_f12b, T2_f12b, L1_f12b, L2_f12b);
6611
6612 // VT1T1
6613 TArray2 X_VT1T1 = Xam_VT1T1_f12b(C_0, C_1, T1_f12b);
6614// // *** test
6615// TArray4 tauT1_ab;
6616// tauT1_ab("a,b,i,j") = T1_f12b("a,i") * T1_f12b("b,j");
6617// TArray2 X_VT1T1 = Xam_VT1T1_f12b_test(C_0, C_1, tauT1_ab);
6618
6619 // VL2T1
6620 TArray2 X_VL2T1 = Xam_VL2T1_f12b(C_0, C_1, T1_f12b, L2_f12b);
6621// // *** test
6622// TArray2 X_VL2T1 = Xam_VL2T1_f12b_test(C_0, C_1, T1_f12b, L2_f12b);
6623
6624 // VL2T1T1
6625 TArray2 X_VL2T1T1 = Xam_VL2T1T1_f12b(C_0, C_1, T1_f12b, L2_f12b);
6626// // *** test
6627// TArray2 X_VL2T1T1 = Xam_VL2T1T1_f12b_test(C_0, C_1, T1_f12b, L2_f12b);
6628
6629 TArray2 Xam_C_nfzc;
6630 Xam_C_nfzc("a,m") = Xam_CT2L2("a,m")
6631 + Xam_VTL("a,m")
6632 + X_VT1T1("a,m")
6633 + X_VL2T1("a,m")
6634 + X_VL2T1T1("a,m")
6635 ;
6636
6637 // frozen-core contribution
6638 TArray2 Diip_C, Xam_C;
6639 if (nocc != naocc) {
6640 ExEnv::out0() << std::endl << indent
6641 << "Include frozen-core contributions for CCSD F12 coupling" << std::endl;
6642 TArray2 Xiip_couling1 = Xiip_CVT_f12b(C_0, C_1, T1_f12b, T2_f12b, L1_f12b, L2_f12b);
6643 TArray2 Xiip_couling2 = Xiip_VT1T1_f12b(C_0, C_1, T1_f12b, T2_f12b, L2_f12b);
6644 Diip_C("i,i'") = - (Xiip_couling1("i,i'") + Xiip_couling2("i,i'"))
6645 * Delta_ijp_F("i,i'");
6646
6647 TArray2 Xam_Diip_C;
6648 Xam_Diip_C("a,m") = - A_ijpam("i,j',a,m") * Diip_C("i,j'");
6649
6650 Xam_C("a,m") = Xam_C_nfzc("a,m") + Xam_Diip_C("a,m");
6651 } else {
6652 Xam_C("a,m") = Xam_C_nfzc("a,m");
6653 }
6654
6655 TArray2 Dbn_C(Xam_C.world(), Xam_C.trange());
6656 auto resnorm_C = cg_solver2(Orbital_relaxation_Abnam,
6657 Xam_C,
6658 Dbn_C,
6659 preconditioner,
6660 conv_target);
6661
6662// TArray2 Dbn_CT2L2(Xam_CT2L2.world(), Xam_CT2L2.trange());
6663// auto resnorm_CT2L2 = cg_solver2(Orbital_relaxation_Abnam,
6664// Xam_CT2L2,
6665// Dbn_CT2L2,
6666// preconditioner,
6667// conv_target);
6668//
6669// TArray2 Dbn_VTL(Xam_VTL.world(), Xam_VTL.trange());
6670// auto resnorm_VTL = cg_solver2(Orbital_relaxation_Abnam,
6671// Xam_VTL,
6672// Dbn_VTL,
6673// preconditioner,
6674// conv_target);
6675
6676 if (compute_dipole) {
6677 mu_z_apb = xy("<a'|mu_z|b>");
6678 double muz_f12b = dot(mu_z_ij("i,j"), Dij_f12b("i,j"))
6679 + dot(mu_z_ab("a,b"), Dab_f12b("a,b"))
6680 + dot(mu_z_ai("a,i"), Dai_f12b("a,i"))
6681 + dot(mu_z_ai("a,i"), Dia_f12b("i,a"))
6682 // F12 coupling density contribution
6683 + dot(mu_z_apb("a',b"), RT2_aPb("a',b"))
6684 + dot(mu_z_apb("a',b"), RL2_aPb("a',b"))
6685 ;
6686
6687 double muz_f12bor = dot(mu_z_am("a,m"), Dbn_f12b("a,m"))
6688 + dot(mu_z_am("a,m"), Dbn_C("a,m"))
6689 ;
6690
6691 if (nocc != naocc) {
6692 muz_f12b += dot(mu_z_ijp("i,j'"), Diip_f12b("i,j'"))
6693 + dot(mu_z_ijp("i,j'"), Diip_C("i,j'"));
6694 }
6695
6696// std::cout << std::endl << indent
6697// << "muz_ccsd (F12b) = " << scprintf("%15.12f", - muz_f12b * 2.0)
6698// << std::endl << indent
6699// << "muz_ccsdor (F12b) = " << scprintf("%15.12f", - muz_f12bor * 2.0)
6700// << std::endl;
6701
6702 double muz_Cf12b = muz_f12b - muz_ccsd;
6703 double muz_Cf12bor = muz_f12bor - muz_ccsdor;
6704
6705 std::cout << std::endl << indent
6706 << "mu_z (F12b C) = " << scprintf("%15.12f", - muz_Cf12b * 2.0)
6707 << std::endl << indent
6708 << "mu_z (F12b C or) = " << scprintf("%15.12f", - muz_Cf12bor * 2.0)
6709 << std::endl << std::endl;
6710 }
6711
6712 if (compute_quadrupole) {
6713 double q_xx_f12b = dot(Qxx_ij("i,j"), Dij_f12b("i,j"))
6714 + dot(Qxx_ab("a,b"), Dab_f12b("a,b"))
6715 + dot(Qxx_ai("a,i"), Dai_f12b("a,i"))
6716 + dot(Qxx_ai("a,i"), Dia_f12b("i,a"))
6717 + dot(Qxx_apb("a',b"), RT2_aPb("a',b"))
6718 + dot(Qxx_apb("a',b"), RL2_aPb("a',b"))
6719 ;
6720 double q_yy_f12b = dot(Qyy_ij("i,j"), Dij_f12b("i,j"))
6721 + dot(Qyy_ab("a,b"), Dab_f12b("a,b"))
6722 + dot(Qyy_ai("a,i"), Dai_f12b("a,i"))
6723 + dot(Qyy_ai("a,i"), Dia_f12b("i,a"))
6724 + dot(Qyy_apb("a',b"), RT2_aPb("a',b"))
6725 + dot(Qyy_apb("a',b"), RL2_aPb("a',b"))
6726 ;
6727 double q_zz_f12b = dot(Qzz_ij("i,j"), Dij_f12b("i,j"))
6728 + dot(Qzz_ab("a,b"), Dab_f12b("a,b"))
6729 + dot(Qzz_ai("a,i"), Dai_f12b("a,i"))
6730 + dot(Qzz_ai("a,i"), Dia_f12b("i,a"))
6731 + dot(Qzz_apb("a',b"), RT2_aPb("a',b"))
6732 + dot(Qzz_apb("a',b"), RL2_aPb("a',b"))
6733 ;
6734
6735 double q_xx_f12bor = dot(Qxx_am("a,m"), Dbn_f12b("a,m"))
6736 + dot(Qxx_am("a,m"), Dbn_C("a,m"));
6737 double q_yy_f12bor = dot(Qyy_am("a,m"), Dbn_f12b("a,m"))
6738 + dot(Qyy_am("a,m"), Dbn_C("a,m"));
6739 double q_zz_f12bor = dot(Qzz_am("a,m"), Dbn_f12b("a,m"))
6740 + dot(Qzz_am("a,m"), Dbn_C("a,m"));
6741
6742 if (nocc != naocc) {
6743 q_xx_f12bor += dot(Qxx_ijp("i,j'"), Diip_f12b("i,j'"))
6744 + dot(Qxx_ijp("i,j'"), Diip_C("i,j'"));
6745 q_yy_f12bor += dot(Qyy_ijp("i,j'"), Diip_f12b("i,j'"))
6746 + dot(Qyy_ijp("i,j'"), Diip_C("i,j'"));
6747 q_zz_f12bor += dot(Qzz_ijp("i,j'"), Diip_f12b("i,j'"))
6748 + dot(Qzz_ijp("i,j'"), Diip_C("i,j'"));
6749 }
6750
6751// std::cout << std::endl << indent
6752// << "q_xx (F12b) = " << scprintf("%12.10f", - q_xx_f12b * 2.0)
6753// << " q_yy (F12b) = " << scprintf("%12.10f", - q_yy_f12b * 2.0)
6754// << " q_zz (F12b) = " << scprintf("%12.10f", - q_zz_f12b * 2.0)
6755// << std::endl << indent
6756// << "q_xx (F12b or) = " << scprintf("%12.10f", - q_xx_f12bor * 2.0)
6757// << " q_yy (F12b or) = " << scprintf("%12.10f", - q_yy_f12bor * 2.0)
6758// << " q_zz (F12b or) = " << scprintf("%12.10f", - q_zz_f12bor * 2.0)
6759// << std::endl << std::endl;
6760
6761 double q_xx_f12b_C = q_xx_f12b - q_xx_ccsd;
6762 double q_yy_f12b_C = q_yy_f12b - q_yy_ccsd;
6763 double q_zz_f12b_C = q_zz_f12b - q_zz_ccsd;
6764 double q_xx_f12bor_C = q_xx_f12bor - q_xx_ccsdor;
6765 double q_yy_f12bor_C = q_yy_f12bor - q_yy_ccsdor;
6766 double q_zz_f12bor_C = q_zz_f12bor - q_zz_ccsdor;
6767 std::cout << std::endl << indent
6768 << "q_xx (F12b C) = " << scprintf("%12.10f", - q_xx_f12b_C * 2.0)
6769 << " q_yy (F12b C) = " << scprintf("%12.10f", - q_yy_f12b_C * 2.0)
6770 << " q_zz (F12b C) = " << scprintf("%12.10f", - q_zz_f12b_C * 2.0)
6771 << std::endl << indent
6772 << "q_xx (F12b C or) = " << scprintf("%12.10f", - q_xx_f12bor_C * 2.0)
6773 << " q_yy (F12b C or) = " << scprintf("%12.10f", - q_yy_f12bor_C * 2.0)
6774 << " q_zz (F12b C or) = " << scprintf("%12.10f", - q_zz_f12bor_C * 2.0)
6775 << std::endl << std::endl;
6776 }
6777#endif
6778
6779 }
6780
6781 template <typename T>
6782 typename SingleReference_R12Intermediates<T>::TArray2
6783 SingleReference_R12Intermediates<T>::rdm1() {
6784
6785#define ENABLE_SRR12_RDM1 1
6786
6787#if ENABLE_SRR12_RDM1
6788// if (0) {
6789// {
6790// typedef TiledArray::Array<T,2> Array;
6791// Array FiA = _2("<i|F|A'>");
6792// Array FAi = _2("<A'|F|i>");
6793// std::cout << "<i|F|A'>:" << std::endl << FiA << std::endl;
6794// std::cout << "<A'|F|i>:" << std::endl << FAi << std::endl;
6795// Array FiA_2(FiA.world(), FiA.trange());
6796// FiA_2("i,A'") = FAi("A',i");
6797// std::cout << "<i|F|A'>=Perm(<A'|F|i>):" << std::endl << FiA_2 << std::endl;
6798// }
6799// {
6800// typedef TiledArray::Array<T,4> Array;
6801// Array g_ij_ab = _4("<i j|g|a b>");
6802// Array g_ab_ij = _4("<a b|g|i j>");
6803// std::cout << "<i j|g|a b>:" << std::endl << g_ij_ab << std::endl;
6804// std::cout << "<a b|g|i j>:" << std::endl << g_ab_ij << std::endl;
6805// Array g_ij_ab_2(g_ij_ab.world(), g_ij_ab.trange());
6806// g_ij_ab_2("i,j,a,b") = g_ab_ij("a,b,i,j");
6807// std::cout << "<i j|g|a b>=Perm(<a b|g|i j>):" << std::endl << g_ij_ab_2 << std::endl;
6808// Array should_be_zero = g_ij_ab("i,j,a,b") - g_ab_ij("a,b,i,j");
6809// std::cout << "<i j|g|a b> - Perm(<a b|g|i j>):" << std::endl << should_be_zero << std::endl;
6810// const double max_nonzero = norminf(should_be_zero("i,j,a,b"));
6811// std::cout << "|| <i j|g|a b> - Perm(<a b|g|i j>) ||_\infty = " << max_nonzero << std::endl;
6812// }
6813// {
6814// typedef TiledArray::Array<T,2> Array;
6815// Array mu_z_ij = _2("<i|mu_z|j>");
6816// Array gamma_ij = _2("<i|gamma|j>");
6817// const double mu_z_e = dot(mu_z_ij("i,j"), gamma_ij("i,j"));
6818// double mu_z_n = 0.0;
6819// Ref<Molecule> mol = r12world_->basis()->molecule();
6820// for(int a=0; a<mol->natom(); ++a) {
6821// mu_z_n += mol->Z(a) * mol->r(a, 2);
6822// }
6823// std::cout << "mu_z = " << -mu_z_e+mu_z_n << std::endl;
6824// }
6825// }
6826
6827 // can only ask for T1 with i in bra!
6828 // since we computed T1 CABS, they are expressed in terms of all virtuals = A'
6829 // if you turn off vir-CABS coupling, use a' (i.e. CABS only)
6830// TArray2 T1iA = _2("<i|T1|A'>");
6831// //t1_cabs_.print("T1(RefSCMatrix)");
6832// //std::cout << "T1(cabs)\n" << T1iA << std::endl;
6833// TArray2 T1ia = _2("<i|T1|a>");
6834// //std::cout << "T1(cabs) => i by a block\n" << T1ia << std::endl;
6835//
6836// // recompute E2(CABS) = T1_cabs . H1
6837// const double E2_cabs = 2.0 * dot(T1iA("i,A'"), _2("<i|F|A'>"));
6838// std::cout << "E2_cabs (recomputed) = " << E2_cabs << std::endl;
6839
6840#if 0
6841 // recompute T1_cabs and re-recompute E2_cabs
6842 {
6843 typedef TiledArray::Array<T,2> Array;
6844 Array Fii = _2("<i|F|j>");
6845 Array FAA = _2("<A'|F|B'>");
6846 // this computes Z_i^A' = T_i^B' F_B'^A' - F_i^j T_j^A'
6847 detail::_CABS_singles_h0t1<double> cabs_singles_rhs_eval(FAA, Fii);
6848
6849 TA::ConjugateGradientSolver<Array, detail::_CABS_singles_h0t1<double> > cg_solver;
6850 Array FiA = _2("<i|F|A'>");
6851 Array minus_FiA = -1.0 * FiA("i,A'");
6852 Array T1_recomp = FiA;
6853
6854 // make preconditioner: Delta_iA = <i|F|i> - <A'|F|A'>
6855 typedef detail::diag_precond2<double> pceval_type;
6856 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2d;
6857 TArray2d Delta_iA(FiA.world(), FiA.trange());
6858 pceval_type Delta_iA_gen(TA::array_to_eigen(Fii),
6859 TA::array_to_eigen(FAA));
6860
6861 // construct local tiles
6862 for(auto t=Delta_iA.trange().tiles_range().begin();
6863 t!=Delta_iA.trange().tiles_range().end();
6864 ++t)
6865 if (Delta_iA.is_local(*t)) {
6866 std::array<std::size_t, 2> index; std::copy(t->begin(), t->end(), index.begin());
6867 madness::Future < typename TArray2d::value_type >
6868 tile((LazyTensor<T, 2, pceval_type >(&Delta_iA, index, &Delta_iA_gen)
6869 ));
6870
6871 // Insert the tile into the array
6872 Delta_iA.set(*t, tile);
6873 }
6874 Array preconditioner = Delta_iA("i,A'");
6875
6876#if 0
6877 std::cout << "FiA:\n" << FiA << std::endl;
6878 std::cout << "Fii:\n" << Fii << std::endl;
6879 std::cout << "FAA:\n" << FAA << std::endl;
6880 std::cout << "preconditioner:\n" << preconditioner << std::endl;
6881#endif
6882
6883 // solves CABS singles equations T_i^B' F_B'^A' - F_i^j T_j^A' = -F_i^A' using CG
6884 auto resnorm = cg_solver(cabs_singles_rhs_eval,
6885 minus_FiA,
6886 T1_recomp,
6887 preconditioner,
6888 1e-10);
6889 std::cout << "Converged CG to " << resnorm << std::endl;
6890 const double E2_cabs = 2.0 * dot(T1_recomp("i,A'"), _2("<i|F|A'>")); // 2 accounts for spin
6891 std::cout << "E2_cabs (re-recomputed) = " << E2_cabs << std::endl;
6892
6893 // compute the (2)_S dipole moment
6894 {
6895 const double mu_z_e = 2*dot(_2("<i|mu_z|A'>"), T1_recomp("i,A'"))
6896 - dot(_2("<i|mu_z|j>"), T1_recomp("i,A'") * T1_recomp("j,A'") )
6897 + dot(_2("<A'|mu_z|B'>"), T1_recomp("i,A'") * T1_recomp("i,B'") );
6898 std::cout << "Mu_z (2)_S = " << 2*mu_z_e << std::endl; // 2 accounts for spin degeneracy
6899 std::cout << "Mu_z ref = " << (dot(_2("<i|mu_z|j>"),_2("<i|gamma|j>")))
6900 << std::endl; // 2 is included in gamma!
6901 }
6902
6903 // compute the (2)_S quadrupole moment
6904 {
6905 const double q_zz_e = 2*dot(_2("<i|q_zz|A'>"), T1_recomp("i,A'"))
6906 - dot(_2("<i|q_zz|j>"), T1_recomp("i,A'") * T1_recomp("j,A'") )
6907 + dot(_2("<A'|q_zz|B'>"), T1_recomp("i,A'") * T1_recomp("i,B'") );
6908 std::cout << "Q_zz (2)_S = " << 2*q_zz_e << std::endl; // 2 accounts for spin degeneracy
6909 std::cout << "Q_zz ref = " << (dot(_2("<i|q_zz|j>"),_2("<i|gamma|j>")))
6910 << std::endl; // 2 is included in gamma!
6911 }
6912
6913 // compute orbital rotation multipliers in the (2)_S Lagrangian
6914 if (1) {
6915 TArray2 Tia = T1_recomp("j,A'") * _2("<A'|I|a>");
6916 TArray2 Xia_1 = 2* (_2("<i|F|j>") * Tia("j,a") - T1_recomp("i,B'") * _2("<B'|F|a>"))
6917 + 2 * _2("<i|F|C'>") * T1_recomp("j,C'") * Tia("j,a")
6918 - 2 * (2 * _4("<j i|g|B' a>") - _4("<j i|g|a B'>") + 2 * _4("<j a|g|B' i>") - _4("<j a|g|i B'>")) * T1_recomp("j,B'")
6919 - 2 * (2 * _4("<B' i|g|C' a>") - _4("<B' i|g|a C'>")) * T1_recomp("j,B'") * T1_recomp("j,C'")
6920 + 2 * (2 * _4("<j i|g|k a>") - _4("<j i|g|a k>")) * T1_recomp("j,B'") * T1_recomp("k,B'");
6921 std::cout << "Xia_1, should not be 0:\n" << Xia_1 << std::endl;
6922
6923 TArray2 Faa = _2("<a|F|b>");
6924 TArray4 G_ij_ab = _4("<i j|g|a b>");
6925 TArray4 G_ia_jb = _4("<i a|g|j b>");
6926 detail::_OrbResponse<double> response_lhs_eval(Faa, Fii, G_ij_ab, G_ia_jb);
6927
6928 TA::ConjugateGradientSolver<Array, detail::_OrbResponse<double> > cg_solver;
6929 Array kappa = Xia_1;
6930
6931 // make preconditioner: Delta_ia = <i|F|i> - <a|F|a>
6932 typedef detail::diag_precond2<double> pceval_type;
6933 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2d;
6934 TArray2d Delta_ia(Xia_1.world(), Xia_1.trange());
6935 pceval_type Delta_ia_gen(TA::array_to_eigen(Fii),
6936 TA::array_to_eigen(Faa));
6937
6938 // construct local tiles
6939 for(auto t=Delta_ia.trange().tiles_range().begin();
6940 t!=Delta_ia.trange().tiles_range().end();
6941 ++t)
6942 if (Delta_ia.is_local(*t)) {
6943 std::array<std::size_t, 2> index; std::copy(t->begin(), t->end(), index.begin());
6944 madness::Future < typename TArray2d::value_type >
6945 tile((LazyTensor<T, 2, pceval_type >(&Delta_ia, index, &Delta_ia_gen)
6946 ));
6947
6948 // Insert the tile into the array
6949 Delta_ia.set(*t, tile);
6950 }
6951 Array preconditioner = Delta_ia("i,a");
6952
6953 // solves orbital response using CG
6954 auto resnorm = cg_solver(response_lhs_eval,
6955 Xia_1,
6956 kappa,
6957 preconditioner,
6958 1e-10);
6959 std::cout << "Converged CG to " << resnorm << std::endl;
6960
6961 // verify the solution:
6962 {
6963 TArray2 res = Xia_1;
6964 response_lhs_eval(kappa, res);
6965 std::cout << "should be zero = " << TA::expressions::norm2(res("i,a") - Xia_1("i,a"));
6966 }
6967
6968 const double mu_z_e = dot(kappa("i,a"), _2("<i|mu_z|a>"));
6969 std::cout << "mu_z_e (orb response) = " << 2*mu_z_e << std::endl;
6970
6971 }
6972 }
6973
6974 // now recompute T1_cabs and E2_cabs using only CABS for perturbation!
6975 {
6976 std::cout << "computing E2_cabs due to CABS only as the first-order space\n";
6977 typedef TiledArray::Array<T,2> Array;
6978 Array Fii = _2("<i|F|j>");
6979 Array FAA = _2("<a'|F|b'>");
6980 // this computes Z_i^a' = T_i^b' F_b'^a' - F_i^j T_j^a'
6981 detail::_CABS_singles_h0t1<double> cabs_singles_rhs_eval(FAA, Fii);
6982
6983 TA::ConjugateGradientSolver<Array, detail::_CABS_singles_h0t1<double> > cg_solver;
6984 Array FiA = _2("<i|F|a'>");
6985 Array minus_FiA = -1.0 * FiA("i,a'");
6986 Array T1_recomp = FiA;
6987
6988 // make preconditioner: Delta_iA = <i|F|i> - <a'|F|a'>
6989 typedef detail::diag_precond2<double> pceval_type;
6990 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2d;
6991 TArray2d Delta_iA(FiA.world(), FiA.trange());
6992 pceval_type Delta_iA_gen(TA::array_to_eigen(Fii),
6993 TA::array_to_eigen(FAA));
6994
6995 // construct local tiles
6996 for(auto t=Delta_iA.trange().tiles_range().begin();
6997 t!=Delta_iA.trange().tiles_range().end();
6998 ++t)
6999 if (Delta_iA.is_local(*t)) {
7000 std::array<std::size_t, 2> index; std::copy(t->begin(), t->end(), index.begin());
7001 madness::Future < typename TArray2d::value_type >
7002 tile((LazyTensor<T, 2, pceval_type >(&Delta_iA, index, &Delta_iA_gen)
7003 ));
7004
7005 // Insert the tile into the array
7006 Delta_iA.set(*t, tile);
7007 }
7008 Array preconditioner = Delta_iA("i,a'");
7009
7010#if 0
7011 std::cout << "FiA:\n" << FiA << std::endl;
7012 std::cout << "Fii:\n" << Fii << std::endl;
7013 std::cout << "FAA:\n" << FAA << std::endl;
7014 std::cout << "preconditioner:\n" << preconditioner << std::endl;
7015#endif
7016
7017 // solves CABS singles equations T_i^B' F_B'^A' - F_i^j T_j^A' = -F_i^A' using CG
7018 auto resnorm = cg_solver(cabs_singles_rhs_eval,
7019 minus_FiA,
7020 T1_recomp,
7021 preconditioner,
7022 1e-10);
7023 std::cout << "Converged CG to " << resnorm << std::endl;
7024 const double E2_cabs = 2.0 * dot(T1_recomp("i,a'"), _2("<i|F|a'>")); // 2 accounts for spin
7025 std::cout << "E2_cabs (re-recomputed) = " << E2_cabs << std::endl;
7026
7027 // compute the (2)_S dipole moment
7028 {
7029 const double mu_z_e = 2*dot(_2("<i|mu_z|a'>"), T1_recomp("i,a'"))
7030 - dot(_2("<i|mu_z|j>"), T1_recomp("i,a'") * T1_recomp("j,a'") )
7031 + dot(_2("<a'|mu_z|b'>"), T1_recomp("i,a'") * T1_recomp("i,b'") );
7032 std::cout << "Mu_z (2)_S = " << 2*mu_z_e << std::endl; // 2 accounts for spin degeneracy
7033 }
7034
7035 // compute orbital rotation multipliers in the (2)_S Lagrangian
7036 if (1) {
7037 // only include the first-order terms in the Lagrangian derivative
7038 TArray2 Xia_1 = - 2 * T1_recomp("i,b'") * _2("<b'|F|a>")
7039 - 2 * (2 * _4("<j i|g|b' a>") - _4("<j i|g|a b'>") + 2 * _4("<j a|g|b' i>") - _4("<j a|g|i b'>")) * T1_recomp("j,b'")
7040 - 2 * (2 * _4("<b' i|g|c' a>") - _4("<b' i|g|a c'>")) * T1_recomp("j,b'") * T1_recomp("j,c'")
7041 + 2 * (2 * _4("<j i|g|k a>") - _4("<j i|g|a k>")) * T1_recomp("j,b'") * T1_recomp("k,b'");
7042 std::cout << "Xia_1, should not be 0:\n" << Xia_1 << std::endl;
7043
7044 TArray2 Faa = _2("<a|F|b>");
7045 TArray4 G_ij_ab = _4("<i j|g|a b>");
7046 TArray4 G_ia_jb = _4("<i a|g|j b>");
7047 detail::_OrbResponse<double> response_lhs_eval(Faa, Fii, G_ij_ab, G_ia_jb);
7048
7049 TA::ConjugateGradientSolver<Array, detail::_OrbResponse<double> > cg_solver;
7050 Array kappa = Xia_1;
7051
7052 // make preconditioner: Delta_ia = <i|F|i> - <a|F|a>
7053 typedef detail::diag_precond2<double> pceval_type;
7054 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2d;
7055 TArray2d Delta_ia(Xia_1.world(), Xia_1.trange());
7056 pceval_type Delta_ia_gen(TA::array_to_eigen(Fii),
7057 TA::array_to_eigen(Faa));
7058
7059 // construct local tiles
7060 for(auto t=Delta_ia.trange().tiles_range().begin();
7061 t!=Delta_ia.trange().tiles_range().end();
7062 ++t)
7063 if (Delta_ia.is_local(*t)) {
7064 std::array<std::size_t, 2> index; std::copy(t->begin(), t->end(), index.begin());
7065 madness::Future < typename TArray2d::value_type >
7066 tile((LazyTensor<T, 2, pceval_type >(&Delta_ia, index, &Delta_ia_gen)
7067 ));
7068
7069 // Insert the tile into the array
7070 Delta_ia.set(*t, tile);
7071 }
7072 Array preconditioner = Delta_ia("i,a");
7073
7074 // solves orbital response using CG
7075 auto resnorm = cg_solver(response_lhs_eval,
7076 Xia_1,
7077 kappa,
7078 preconditioner,
7079 1e-10);
7080 std::cout << "Converged CG to " << resnorm << std::endl;
7081 const double mu_z_e = dot(kappa("i,a"), _2("<i|mu_z|a>"));
7082 std::cout << "mu_z_e (orb reponse) = " << 2*mu_z_e << std::endl;
7083
7084 }
7085 }
7086
7087 // compute T1_obs and E2_obs
7088 {
7089 std::cout << "computing E2_obs (virtuals is the first-order space)\n";
7090 typedef TiledArray::Array<T,2> Array;
7091 Array Fii = _2("<i|F|j>");
7092 Array FAA = _2("<a|F|b>");
7093 // this computes Z_i^a = T_i^b F_b^a - F_i^j T_j^a
7094 detail::_CABS_singles_h0t1<double> cabs_singles_rhs_eval(FAA, Fii);
7095
7096 TA::ConjugateGradientSolver<Array, detail::_CABS_singles_h0t1<double> > cg_solver;
7097 Array FiA = _2("<i|F|a>");
7098 Array minus_FiA = -1.0 * FiA("i,a");
7099 Array T1_obs = FiA;
7100
7101 // make preconditioner: Delta_iA = <i|F|i> - <a|F|a>
7102 typedef detail::diag_precond2<double> pceval_type;
7103 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2d;
7104 TArray2d Delta_iA(FiA.world(), FiA.trange());
7105 pceval_type Delta_iA_gen(TA::array_to_eigen(Fii),
7106 TA::array_to_eigen(FAA));
7107
7108 // construct local tiles
7109 for(auto t=Delta_iA.trange().tiles_range().begin();
7110 t!=Delta_iA.trange().tiles_range().end();
7111 ++t)
7112 if (Delta_iA.is_local(*t)) {
7113 std::array<std::size_t, 2> index; std::copy(t->begin(), t->end(), index.begin());
7114 madness::Future < typename TArray2d::value_type >
7115 tile((LazyTensor<T, 2, pceval_type >(&Delta_iA, index, &Delta_iA_gen)
7116 ));
7117
7118 // Insert the tile into the array
7119 Delta_iA.set(*t, tile);
7120 }
7121 Array preconditioner = Delta_iA("i,a");
7122
7123#if 0
7124 std::cout << "FiA:\n" << FiA << std::endl;
7125 std::cout << "Fii:\n" << Fii << std::endl;
7126 std::cout << "FAA:\n" << FAA << std::endl;
7127 std::cout << "preconditioner:\n" << preconditioner << std::endl;
7128#endif
7129
7130 // solves CABS singles equations T_i^B' F_B'^A' - F_i^j T_j^A' = -F_i^A' using CG
7131 auto resnorm = cg_solver(cabs_singles_rhs_eval,
7132 minus_FiA,
7133 T1_obs,
7134 preconditioner,
7135 1e-10);
7136 std::cout << "Converged CG to " << resnorm << std::endl;
7137 // same as the lagrangian since solved for T1 exactly
7138 const double E2_obs = 2.0 * dot(T1_obs("i,a"), _2("<i|F|a>")); // 2 accounts for spin
7139 std::cout << "E2_obs = " << E2_obs << std::endl;
7140 const double E0_obs = dot(_2("<i|F|j>"), _2("<i|gamma|j>")); // 2 included in gamma
7141 std::cout << "E0_obs = " << scprintf("%15.10lf",E0_obs) << std::endl;
7142
7143 // compute the (2)_S dipole moment
7144 {
7145 const double mu_z_e = 2*dot(_2("<i|mu_z|a>"), T1_obs("i,a"))
7146 - dot(_2("<i|mu_z|j>"), T1_obs("i,a") * T1_obs("j,a") )
7147 + dot(_2("<a|mu_z|b>"), T1_obs("i,a") * T1_obs("i,b") );
7148 std::cout << scprintf("Mu_z (2)_S OBS = %25.15lf", 2*mu_z_e) << std::endl; // 2 accounts for spin degeneracy
7149 std::cout << scprintf("Mu_z ref = %25.15lf", (dot(_2("<i|mu_z|j>"),_2("<i|gamma|j>")))) << std::endl;
7150 }
7151
7152 // compute orbital rotation multipliers in the (2)_S OBS Lagrangian
7153 if (1) {
7154 // only include the first-order terms in the Lagrangian derivative
7155 TArray2 Xia_1 = _2("<i|F|j>") * T1_obs("j,a") - T1_obs("i,b") * _2("<b|F|a>")
7156 + 2 * _2("<i|F|c>") * T1_obs("j,c") * T1_obs("j,a")
7157 + 2 * T1_obs("i,c") * T1_obs("j,c") * _2("<j|F|a>")
7158 ;
7159 std::cout << "Xia_1, should not be 0:\n" << Xia_1 << std::endl;
7160 TArray2 Fia = _2("<i|F|a>");
7161 std::cout << "Fia, should be close to Xia_1:\n" << Fia << std::endl;
7162
7163 TArray2 Faa = _2("<a|F|b>");
7164 TArray4 G_ij_ab = _4("<i j|g|a b>");
7165 TArray4 G_ia_jb = _4("<i a|g|j b>");
7166 detail::_OrbResponse<double> response_lhs_eval(Faa, Fii, G_ij_ab, G_ia_jb);
7167
7168 TA::ConjugateGradientSolver<Array, detail::_OrbResponse<double> > cg_solver;
7169 Array kappa = Xia_1;
7170
7171 // make preconditioner: Delta_ia = <i|F|i> - <a|F|a>
7172 typedef detail::diag_precond2<double> pceval_type;
7173 typedef TA::Array<T, 2, LazyTensor<T, 2, pceval_type > > TArray2d;
7174 TArray2d Delta_ia(Xia_1.world(), Xia_1.trange());
7175 pceval_type Delta_ia_gen(TA::array_to_eigen(Fii),
7176 TA::array_to_eigen(Faa));
7177
7178 // construct local tiles
7179 for(auto t=Delta_ia.trange().tiles_range().begin();
7180 t!=Delta_ia.trange().tiles_range().end();
7181 ++t)
7182 if (Delta_ia.is_local(*t)) {
7183 std::array<std::size_t, 2> index; std::copy(t->begin(), t->end(), index.begin());
7184 madness::Future < typename TArray2d::value_type >
7185 tile((LazyTensor<T, 2, pceval_type >(&Delta_ia, index, &Delta_ia_gen)
7186 ));
7187
7188 // Insert the tile into the array
7189 Delta_ia.set(*t, tile);
7190 }
7191 Array preconditioner = Delta_ia("i,a");
7192
7193 // solves orbital response using CG
7194 auto resnorm = cg_solver(response_lhs_eval,
7195 Xia_1,
7196 kappa,
7197 preconditioner,
7198 1e-10);
7199 std::cout << "Converged CG to " << resnorm << std::endl;
7200 std::cout << scprintf("E_2 (orb reponse) = %25.15lf", 2*dot(kappa("i,a"), _2("<i|F|a>"))) << std::endl;
7201 const double mu_z_e = dot(kappa("i,a"), _2("<i|mu_z|a>"));
7202 std::cout << scprintf("mu_z_e (orb reponse) = %25.15lf", 2*mu_z_e) << std::endl;
7203
7204 }
7205 }
7206
7207 if (1) {
7208 for(int i=0; i<10; ++i) {
7209 TArray4 should_be_zero = _4("<b j|g|a i>") - _4("<b i|g|a j>");
7210 std::cout << "should be 0: " << TA::expressions::norminf(should_be_zero("b,j,a,i")) << std::endl;
7211 }
7212 }
7213#endif
7214
7216 TArray2 r2_i_j;
7217 //r2_i_j("i,j") = _4("<i j|r|p q>") * _4("<k_F(p) j|r|p q>");
7218
7219 return r2_i_j;
7220#else // ENABLE_SRR12_RDM1
7221 MPQC_ASSERT(false); // not converted yet to the TiledArray expressions branch
7222 return TArray2();
7223#endif
7224 }
7225
7226 template <typename T>
7227 typename SingleReference_R12Intermediates<T>::TArray4
7228 SingleReference_R12Intermediates<T>::V_spinfree(bool symmetrize_p1_p2) {
7229
7230 TArray4 V_ij_mn;
7231 V_ij_mn("i1,i2,m1,m2") = _4("<i1 i2|gr|m1 m2>") - _4("<i1 i2|r|p1 p2>") * _4("<m1 m2|g|p1 p2>")
7232 - _4("<i1 i2|r|m3_gamma(m) a'>") * _4("<m1 m2|g|m3 a'>");
7233
7234 if (symmetrize_p1_p2)
7235 V_ij_mn("i1,i2,m1,m2") = 0.5 * (V_ij_mn("i1,i2,m1,m2") + V_ij_mn("i2,i1,m2,m1"));
7236
7237 return V_ij_mn;
7238 }
7239
7240 template <typename T>
7241 typename SingleReference_R12Intermediates<T>::TArray4
7242 SingleReference_R12Intermediates<T>::X_spinfree(bool symmetrize_p1_p2) {
7243
7244 TArray4 X_ij_kl;
7245 X_ij_kl("i1,i2,j1,j2") = _4("<i1 i2|r2|j1 j2>") - _4("<i1 i2|r|p1 p2>") * _4("<j1 j2|r|p1 p2>")
7246 - _4("<i1 i2|r|m3_gamma(m) a'>") * _4("<j1 j2|r|m3 a'>");
7247
7248 if (symmetrize_p1_p2)
7249 X_ij_kl("i1,i2,j1,j2") = 0.5 * (X_ij_kl("i1,i2,j1,j2") + X_ij_kl("i2,i1,j2,j1"));
7250
7251 return X_ij_kl;
7252 }
7253
7254 template <typename T>
7255 typename SingleReference_R12Intermediates<T>::TArray4
7256 SingleReference_R12Intermediates<T>::B_spinfree(bool symmetrize_p1_p2) {
7257
7258 TArray4 B_ij_kl;
7259 B_ij_kl("i1,i2,j1,j2") =
7260
7261 // everything seems scaled up by factor of 2 relative to Eq.(12) in J. Chem. Phys. 135, 214105 (2011),
7262 // due to including particle 1 and particle 2 contributions?
7263
7264 // diag Q
7265 _4("<i1 i2|rTr|j1 j2>") + 2.0 * _4("<i1 i2|r2|j1 j2_hJ(p')>")
7266
7267 // rKr
7268 - 2.0 * _4("<i1 i2|r|r' s'>") * _4("<j1 j2|r|r' s'_K(p')>")
7269
7270 // rFr
7271 - 2.0 * _4("<i1 i2|r|r s>") * _4("<j1 j2|r|r s_F(p)>")
7272
7273 // rFr_2, extra 2 due to bra-ket symmetrization
7274 - 4.0 * _4("<i1 i2|r|r s>") * _4("<j1 j2|r|r s_F(a')>")
7275
7276 // rFGr
7277 - _4("<i1 i2|r|n_gamma(m) b'>") * _4("<j1 j2|r|n b'_F(a')>")
7278
7279 // rFGr_2
7280 - _4("<i1 i2|r|n_gamma(m) a'>") * _4("<j1 j2|r|n_F(p') a'>");
7281
7282 B_ij_kl("i1,i2,j1,j2") = 0.5
7283 * (B_ij_kl("i1,i2,j1,j2") + B_ij_kl("i2,i1,j2,j1"));
7284 B_ij_kl("i1,i2,j1,j2") = 0.5
7285 * (B_ij_kl("i1,i2,j1,j2") + B_ij_kl("j1,j2,i1,i2"));
7286
7287 if (symmetrize_p1_p2)
7288 B_ij_kl("i1,i2,j1,j2") = 0.5
7289 * (B_ij_kl("i1,i2,j1,j2") + B_ij_kl("i2,i1,j2,j1"));
7290
7291 return B_ij_kl;
7292 }
7293
7294
7295}; // end of namespace sc
7296
7297#endif // end of header guard
7298
7299
7300// Local Variables:
7301// mode: c++
7302// c-file-style: "CLJ-CONDENSED"
7303// End:
sc::ExEnv::out0
static std::ostream & out0()
Return an ostream that writes from node 0.
sc::LazyTensor
Tile of a DIM-order tensor that's "evaluated" when needed by calling ElementGenerator({i0,...
Definition sr_r12intermediates.h:125
sc::Ref
A template class that maintains references counts.
Definition ref.h:361
sc::SingleReference_R12Intermediates
SingleReference_R12Intermediates computes R12/F12 intermediates using MPQC3 runtime.
Definition sr_r12intermediates.h:218
sc::SingleReference_R12Intermediates::V_diag
std::pair< TArray2, TArray2 > V_diag()
computes diagonal (spin-restricted, for now) V intermediate
Definition sr_r12intermediates_VXB_diag.h:433
sc::SingleReference_R12Intermediates::rdm1
TArray2 rdm1()
returns the 1-particle reduced density matrix
Definition sr_r12intermediates_VXB_diag.h:6783
sc::SingleReference_R12Intermediates::TArray2
TA::Array< T, 2 > TArray2
standard 2-index tensor
Definition sr_r12intermediates.h:226
sc::SingleReference_R12Intermediates::gf2_r12
void gf2_r12(int orbital)
Computes second-order Green's function IPs and EAs \parame orbital the index of the orbital,...
Definition sr_r12intermediates_VXB_diag.h:513
sc::SingleReference_R12Intermediates::TArray4
TA::Array< T, 4 > TArray4
standard 4-index tensor
Definition sr_r12intermediates.h:222
sc::SingleReference_R12Intermediates::TArray4d
TA::Array< T, 4, DA4_Tile< T > > TArray4d
4-index tensor with lazy tiles
Definition sr_r12intermediates.h:224
sc::SingleReference_R12Intermediates::B_spinfree
TArray4 B_spinfree(bool symmetrize_p1_p2=false)
computes spin-free B intermediate
Definition sr_r12intermediates_VXB_diag.h:7256
sc::SingleReference_R12Intermediates::compute_multipole
void compute_multipole()
Definition sr_r12intermediates_VXB_diag.h:4163
sc::SingleReference_R12Intermediates::X_spinfree
TArray4 X_spinfree(bool symmetrize_p1_p2=false)
computes spin-free X intermediate
Definition sr_r12intermediates_VXB_diag.h:7242
sc::SingleReference_R12Intermediates::V_spinfree
TArray4 V_spinfree(bool symmetrize_p1_p2=false)
computes spin-free V intermediate
Definition sr_r12intermediates_VXB_diag.h:7228
sc::SingleReference_R12Intermediates::TArray2d
TA::Array< T, 2, DA4_Tile< T > > TArray2d
2-index tensor with lazy tiles
Definition sr_r12intermediates.h:228
sc::SingleReference_R12Intermediates::compute_multipole_F12b_coupling
void compute_multipole_F12b_coupling()
Definition sr_r12intermediates_VXB_diag.h:6242
sc::SingleReference_R12Intermediates::X_diag
std::pair< TArray2, TArray2 > X_diag()
computes diagonal (spin-restricted, for now) X intermediate
Definition sr_r12intermediates_VXB_diag.h:453
sc::SingleReference_R12Intermediates::B_diag
std::pair< TArray2, TArray2 > B_diag()
computes diagonal (spin-restricted, for now) B intermediate
Definition sr_r12intermediates_VXB_diag.h:473
sc::scprintf
This class allows printf-like output to be sent to an ostream.
Definition formio.h:97
sc
Contains all MPQC code up to version 3.
Definition mpqcin.h:14
sc::detail::Orbital_relaxation_Abjai
Definition sr_r12intermediates_VXB_diag.h:700
sc::detail::Orbital_relaxation_Abjai::operator()
void operator()(const Array2 &K_bj, Array2 &R1)
Definition sr_r12intermediates_VXB_diag.h:718
sc::detail::Orbital_relaxation_Abjai::Orbital_relaxation_Abjai
Orbital_relaxation_Abjai(const Array4 &a_bjai)
Definition sr_r12intermediates_VXB_diag.h:708
sc::detail::_CABS_singles_h0t1
this functor helps to implement conjugate gradient CABS singles solver
Definition sr_r12intermediates_VXB_diag.h:600
sc::detail::_CABS_singles_h0t1::_CABS_singles_h0t1
_CABS_singles_h0t1(const Array &h0_AB, const Array &h0_ij)
Definition sr_r12intermediates_VXB_diag.h:608
sc::detail::_CABS_singles_h0t1::operator()
void operator()(const Array &T1, Array &R1)
Definition sr_r12intermediates_VXB_diag.h:619
sc::detail::_OrbResponse
this functor helps to implement orbital response
Definition sr_r12intermediates_VXB_diag.h:627
sc::detail::_OrbResponse::_OrbResponse
_OrbResponse(const Array2 &f_AB, const Array2 &f_ij, const Array4 &g_ij_ab, const Array4 &g_ia_jb)
Definition sr_r12intermediates_VXB_diag.h:638
sc::detail::_OrbResponse::operator()
void operator()(const Array2 &kappa, Array2 &residual)
Definition sr_r12intermediates_VXB_diag.h:652
sc::detail::diag_precond2
makes a diagonal 2-index preconditioner: pc_x^y = -1/ ( <x|O1|x> - <y|O2|y> )
Definition sr_r12intermediates_VXB_diag.h:662
sc::detail::diag_precond4
makes a diagonal 4-index preconditioner: pc_xy^zw = -1/ ( <x|O1|x> + <y|O2|y> - <z|O3|z> - <w|O4|w> )
Definition sr_r12intermediates_VXB_diag.h:679
sc::detail::e_ij
Definition sr_r12intermediates_VXB_diag.h:725
sc::detail::selfenergy_denom
makes a pseudo-3-index (4-index, but first index is dummy) self-energy denominator: (se_den)_{xyz}...
Definition sr_r12intermediates_VXB_diag.h:491
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