MPQC 3.0.0-alpha
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sc::IntegralV3 Class Reference

IntegralV3 computes integrals between Gaussian basis functions. More...

#include <chemistry/qc/intv3/intv3.h>

Inheritance diagram for sc::IntegralV3:
sc::Integral sc::SavableState sc::DescribedClass sc::RefCount

Public Member Functions

 IntegralV3 (const Ref< GaussianBasisSet > &b1=0, const Ref< GaussianBasisSet > &b2=0, const Ref< GaussianBasisSet > &b3=0, const Ref< GaussianBasisSet > &b4=0)
 
 IntegralV3 (StateIn &)
 
 IntegralV3 (const Ref< KeyVal > &)
 
void save_data_state (StateOut &)
 Save the base classes (with save_data_state) and the members in the same order that the StateIn CTOR initializes them.
 
Integralclone ()
 Clones the given Integral factory. The new factory may need to have set_basis and set_storage to be called on it.
 
CartesianOrdering cartesian_ordering () const
 implements Integral::cartesian_ordering()
 
CartesianIternew_cartesian_iter (int)
 Return a CartesianIter object.
 
RedundantCartesianIternew_redundant_cartesian_iter (int)
 Return a RedundantCartesianIter object.
 
RedundantCartesianSubIternew_redundant_cartesian_sub_iter (int)
 Return a RedundantCartesianSubIter object.
 
SphericalTransformIternew_spherical_transform_iter (int l, int inv=0, int subl=-1)
 Return a SphericalTransformIter object.
 
const SphericalTransformspherical_transform (int l, int inv=0, int subl=-1)
 Return a SphericalTransform object.
 
Ref< OneBodyIntoverlap ()
 Return a OneBodyInt that computes the overlap.
 
Ref< OneBodyIntkinetic ()
 Return a OneBodyInt that computes the kinetic energy.
 
Ref< OneBodyIntpoint_charge (const Ref< PointChargeData > &=0)
 Return a OneBodyInt that computes the integrals for interactions with point charges.
 
Ref< OneBodyOneCenterIntpoint_charge1 (const Ref< PointChargeData > &)
 Return a OneBodyInt that computes the integrals for interactions with point charges.
 
Ref< OneBodyIntnuclear ()
 Return a OneBodyInt that computes the nuclear repulsion integrals.
 
Ref< OneBodyIntp_dot_nuclear_p ()
 Return a OneBodyInt that computes $\bar{p}\cdot V\bar{p}$, where $V$ is the nuclear potential.
 
Ref< OneBodyIntp4 ()
 Return a OneBodyInt that computes $p^4 = (\bar{p} \cdot \bar{p})^2$.
 
Ref< OneBodyInthcore ()
 Return a OneBodyInt that computes the core Hamiltonian integrals.
 
Ref< OneBodyIntefield (const Ref< IntParamsOrigin > &)
 Return a OneBodyInt that computes the electric field integrals at specified point.
 
Ref< OneBodyIntefield_dot_vector (const Ref< EfieldDotVectorData > &=0)
 Return a OneBodyInt that computes the electric field integrals at a given position dotted with a given vector.
 
Ref< OneBodyIntdipole (const Ref< IntParamsOrigin > &=0)
 Return a OneBodyInt that computes electric dipole moment integrals, i.e.
 
Ref< OneBodyIntquadrupole (const Ref< IntParamsOrigin > &=0)
 Return a OneBodyInt that computes electric quadrupole moment integrals, i.e.
 
Ref< OneBodyDerivIntoverlap_deriv ()
 Return a OneBodyDerivInt that computes overlap derivatives.
 
Ref< OneBodyDerivIntkinetic_deriv ()
 Return a OneBodyDerivInt that computes kinetic energy derivatives.
 
Ref< OneBodyDerivIntnuclear_deriv ()
 Return a OneBodyDerivInt that computes nuclear repulsion derivatives.
 
Ref< OneBodyDerivInthcore_deriv ()
 Return a OneBodyDerivInt that computes core Hamiltonian derivatives.
 
Ref< TwoBodyIntelectron_repulsion ()
 Return a TwoBodyInt that computes electron repulsion integrals.
 
Ref< TwoBodyTwoCenterIntelectron_repulsion2 ()
 Return a TwoBodyTwoCenterInt that computes electron repulsion integrals.
 
Ref< TwoBodyThreeCenterIntelectron_repulsion3 ()
 Return a TwoBodyThreeCenterInt that computes electron repulsion integrals.
 
Ref< TwoBodyDerivIntelectron_repulsion_deriv ()
 Return a TwoBodyDerivInt that computes electron repulsion derivatives.
 
void set_basis (const Ref< GaussianBasisSet > &b1, const Ref< GaussianBasisSet > &b2=0, const Ref< GaussianBasisSet > &b3=0, const Ref< GaussianBasisSet > &b4=0)
 Set the basis set for each center.
 
- Public Member Functions inherited from sc::Integral
 Integral (StateIn &)
 Restore the Integral object from the given StateIn object.
 
 Integral (const Ref< KeyVal > &)
 Construct the Integral object from the given KeyVal object.
 
virtual int equiv (const Ref< Integral > &)
 Returns nonzero if this and the given Integral object have the same integral ordering, normalization conventions, etc.
 
virtual void set_storage (size_t i)
 Sets the total amount of storage, in bytes, that is available.
 
size_t storage_used () const
 Returns how much storage has been used.
 
size_t storage_unused () const
 Returns how much storage was not needed.
 
virtual size_t storage_required (TwoBodyOper::type opertype, TwoBodyIntShape::value tbinttype, size_t deriv_level=0, const Ref< GaussianBasisSet > &b1=0, const Ref< GaussianBasisSet > &b2=0, const Ref< GaussianBasisSet > &b3=0, const Ref< GaussianBasisSet > &b4=0)
 Reports the approximate amount of memory required, in bytes, to create an evaluator for opertype.
 
virtual size_t storage_required_eri (const Ref< GaussianBasisSet > &b1, const Ref< GaussianBasisSet > &b2=0, const Ref< GaussianBasisSet > &b3=0, const Ref< GaussianBasisSet > &b4=0)
 Returns how much storage will be needed to initialize a two-body integrals evaluator for electron repulsion integrals.
 
virtual size_t storage_required_grt (const Ref< GaussianBasisSet > &b1, const Ref< GaussianBasisSet > &b2=0, const Ref< GaussianBasisSet > &b3=0, const Ref< GaussianBasisSet > &b4=0)
 Returns how much storage will be needed to initialize a two-body integrals evaluator for linear R12 integrals.
 
virtual size_t storage_required_g12 (const Ref< GaussianBasisSet > &b1, const Ref< GaussianBasisSet > &b2=0, const Ref< GaussianBasisSet > &b3=0, const Ref< GaussianBasisSet > &b4=0)
 Returns how much storage will be needed to initialize a two-body integrals evaluator for G12 integrals.
 
virtual size_t storage_required_g12nc (const Ref< GaussianBasisSet > &b1, const Ref< GaussianBasisSet > &b2=0, const Ref< GaussianBasisSet > &b3=0, const Ref< GaussianBasisSet > &b4=0)
 Returns how much storage will be needed to initialize a two-body integrals evaluator for G12NC integrals.
 
virtual size_t storage_required_g12dkh (const Ref< GaussianBasisSet > &b1, const Ref< GaussianBasisSet > &b2=0, const Ref< GaussianBasisSet > &b3=0, const Ref< GaussianBasisSet > &b4=0)
 Returns how much storage will be needed to initialize a two-body integrals evaluator for G12DKH integrals.
 
virtual size_t storage_required_eri_deriv (const Ref< GaussianBasisSet > &b1, const Ref< GaussianBasisSet > &b2=0, const Ref< GaussianBasisSet > &b3=0, const Ref< GaussianBasisSet > &b4=0)
 Returns how much storage will be needed to initialize a two-body integrals evaluator for derivative electron repulsion integrals.
 
void adjust_storage (ptrdiff_t s)
 The specific integral classes use this to tell Integral how much memory they are using/freeing.
 
Ref< PetiteListpetite_list ()
 Return the PetiteList object.
 
Ref< PetiteListpetite_list (const Ref< GaussianBasisSet > &)
 Return the PetiteList object for the given basis set.
 
ShellRotation shell_rotation (int am, SymmetryOperation &, int pure=0)
 Return the ShellRotation object for a shell of the given angular momentum.
 
const Ref< GaussianBasisSet > & basis1 () const
 retrieves basis for center 1
 
const Ref< GaussianBasisSet > & basis2 () const
 retrieves basis for center 2
 
const Ref< GaussianBasisSet > & basis3 () const
 retrieves basis for center 3
 
const Ref< GaussianBasisSet > & basis4 () const
 retrieves basis for center 4
 
Ref< MessageGrpmessagegrp ()
 Return the MessageGrp used by the integrals objects.
 
virtual Ref< OneBodyIntp_cross_nuclear_p ()
 Return a OneBodyInt that computes $\bar{p}\times V\bar{p}$, where $V$ is the nuclear potential.
 
virtual Ref< OneBodyIntefield_gradient (const Ref< IntParamsOrigin > &O)
 Return a OneBodyInt that computes the electric field gradient integrals at specified point.
 
virtual Ref< TwoBodyThreeCenterDerivIntelectron_repulsion3_deriv ()
 Return a TwoBodyThreeCenterInt that computes electron repulsion integrals.
 
virtual Ref< TwoBodyTwoCenterDerivIntelectron_repulsion2_deriv ()
 Return a TwoBodyTwoCenterInt that computes electron repulsion integrals.
 
virtual Ref< TwoBodyIntEvalmake_eval (TwoBodyOper::type opertype, TwoBodyIntShape::value tbinttype, size_t deriv_level=0, const Ref< GaussianBasisSet > &b1=0, const Ref< GaussianBasisSet > &b2=0, const Ref< GaussianBasisSet > &b3=0, const Ref< GaussianBasisSet > &b4=0)
 Creates an evaluator for opertype.
 
template<int NumCenters>
Ref< typename TwoBodyIntEvalType< NumCenters >::value > coulomb ()
 Return the evaluator of two-body integrals with Coulomb kernel: $
  r_{12}^{-1},
$ The evaluator will produce a set of integrals described by TwoBodyNCenterIntDescr<NumCenters,TwoBodyOperSet::ERI>.
 
template<int NumCenters>
DEPRECATED Ref< typename TwoBodyIntEvalType< NumCenters >::value > grt ()
 Return a 2-body evaluator that computes two-electron integrals specific to linear R12 methods.
 
template<int NumCenters>
DEPRECATED Ref< typename TwoBodyIntEvalType< NumCenters >::value > g12 (const Ref< IntParamsG12 > &p)
 Return a TwoBodyInt that computes two-electron integrals specific to explicitly correlated methods which use Gaussian geminals.
 
template<int NumCenters>
DEPRECATED Ref< typename TwoBodyIntEvalType< NumCenters >::value > g12nc (const Ref< IntParamsG12 > &p)
 Return a TwoBodyInt that computes two-electron integrals specific to explicitly correlated methods which use Gaussian geminals.
 
template<int NumCenters>
Ref< typename TwoBodyIntEvalType< NumCenters >::value > g12dkh (const Ref< IntParamsG12 > &p)
 Return a TwoBodyInt that computes two-electron integrals specific to relativistic explicitly correlated methods which use Gaussian geminals.
 
template<int NumCenters>
Ref< typename TwoBodyIntEvalType< NumCenters >::value > r12_k_g12 (const Ref< IntParamsG12 > &p, int k)
 Return the evaluator of two-body integrals with kernel $
  r_{12}^k g_{12}, \, k=-1,0,
$ where $ g_{12} $ is a geminal described by the IntParamsG12 object.
 
template<int NumCenters>
Ref< typename TwoBodyIntEvalType< NumCenters >::value > g12t1g12 (const Ref< IntParamsG12 > &p)
 Return the evaluator of two-body integrals with kernel $
  [g_{12},[\hat{T}_1,g_{12}]]
$ where $ g_{12} $ is a geminal described by the IntParamsG12 object.
 
template<int NumCenters>
Ref< typename TwoBodyIntEvalType< NumCenters >::value > delta_function ()
 Return the evaluator of two-body integrals with kernel $
  \delta_3({\bf r}_1 - {\bf r}_2),
$ i.e.
 
- Public Member Functions inherited from sc::SavableState
SavableStateoperator= (const SavableState &)
 
void save_state (StateOut &)
 Save the state of the object as specified by the StateOut object.
 
void save_object_state (StateOut &)
 This can be used for saving state when the exact type of the object is known for both the save and the restore.
 
virtual void save_vbase_state (StateOut &)
 Save the virtual bases for the object.
 
- Public Member Functions inherited from sc::DescribedClass
 DescribedClass (const DescribedClass &)
 
DescribedClassoperator= (const DescribedClass &)
 
ClassDescclass_desc () const MPQC__NOEXCEPT
 This returns the unique pointer to the ClassDesc corresponding to the given type_info object.
 
const char * class_name () const
 Return the name of the object's exact type.
 
int class_version () const
 Return the version of the class.
 
virtual void print (std::ostream &=ExEnv::out0()) const
 Print the object.
 
Ref< DescribedClassref ()
 Return this object wrapped up in a Ref smart pointer.
 
- Public Member Functions inherited from sc::RefCount
size_t identifier () const
 Return the unique identifier for this object that can be compared for different objects of different types.
 
int lock_ptr () const
 Lock this object.
 
int unlock_ptr () const
 Unlock this object.
 
void use_locks (bool inVal)
 start and stop using locks on this object
 
refcount_t nreference () const
 Return the reference count.
 
refcount_t reference ()
 Increment the reference count and return the new count.
 
refcount_t dereference ()
 Decrement the reference count and return the new count.
 
int managed () const
 Return 1 if the object is managed. Otherwise return 0.
 

Additional Inherited Members

- Public Types inherited from sc::Integral
enum  CartesianOrdering { IntV3CartesianOrdering , CCACartesianOrdering , GAMESSCartesianOrdering }
 Describes the ordering of the cartesian functions in a shell.
 
- Static Public Member Functions inherited from sc::Integral
static Integralinitial_integral (int &argc, char **argv)
 Create an integral factory.
 
static void set_default_integral (const Ref< Integral > &)
 Specifies a new default Integral factory.
 
static Integralget_default_integral ()
 Returns the default Integral factory.
 
- Static Public Member Functions inherited from sc::SavableState
static void save_state (SavableState *s, StateOut &)
 
static SavableStaterestore_state (StateIn &si)
 Restores objects saved with save_state.
 
static SavableStatekey_restore_state (StateIn &si, const char *keyword)
 Like restore_state, but keyword is used to override values while restoring.
 
static SavableStatedir_restore_state (StateIn &si, const char *objectname, const char *keyword=0)
 
- Protected Types inherited from sc::Integral
enum  SolidHarmonicsOrdering { MPQCSolidHarmonicsOrdering , CCASolidHarmonicsOrdering }
 
- Protected Member Functions inherited from sc::Integral
 Integral (const Ref< GaussianBasisSet > &b1, const Ref< GaussianBasisSet > &b2, const Ref< GaussianBasisSet > &b3, const Ref< GaussianBasisSet > &b4)
 Initialize the Integral object given a GaussianBasisSet for each center.
 
- Protected Member Functions inherited from sc::SavableState
 SavableState (const SavableState &)
 
 SavableState (StateIn &)
 Each derived class StateIn CTOR handles the restore corresponding to calling save_object_state, save_vbase_state, and save_data_state listed above.
 
- Protected Member Functions inherited from sc::RefCount
 RefCount (const RefCount &)
 
RefCountoperator= (const RefCount &)
 
- Protected Attributes inherited from sc::Integral
Ref< GaussianBasisSetbs1_
 
Ref< GaussianBasisSetbs2_
 
Ref< GaussianBasisSetbs3_
 
Ref< GaussianBasisSetbs4_
 
SolidHarmonicsOrdering sharmorder_
 
size_t storage_
 
size_t storage_used_
 
Ref< ThreadLocktlock_
 
Ref< MessageGrpgrp_
 

Detailed Description

IntegralV3 computes integrals between Gaussian basis functions.

Member Function Documentation

◆ cartesian_ordering()

CartesianOrdering sc::IntegralV3::cartesian_ordering ( ) const
inlinevirtual

◆ clone()

Integral * sc::IntegralV3::clone ( )
virtual

Clones the given Integral factory. The new factory may need to have set_basis and set_storage to be called on it.

Implements sc::Integral.

◆ dipole()

Ref< OneBodyInt > sc::IntegralV3::dipole ( const Ref< IntParamsOrigin > & O = 0)
virtual

Return a OneBodyInt that computes electric dipole moment integrals, i.e.

integrals of the $e (\mathbf{r}-\mathbf{O})$ operator. The canonical order of integrals in a set is x, y, z.

Parameters
OIntParamsOrigin object that specifies the origin of the multipole expansion; the default is to use the origin of the coordinate system.
Note
Multiply by -1 to obtain electronic electric quadrupole integrals.

Implements sc::Integral.

◆ efield()

Ref< OneBodyInt > sc::IntegralV3::efield ( const Ref< IntParamsOrigin > & O)
virtual

Return a OneBodyInt that computes the electric field integrals at specified point.

The canonical order of integrals in a set is x, y, z (i.e. Ex, Ey, Ey).

Parameters
OIntParamsOrigin object that specifies the point where the electric field is computed; there is no default.
See also
efield_dot_vector()

Implements sc::Integral.

◆ efield_dot_vector()

Ref< OneBodyInt > sc::IntegralV3::efield_dot_vector ( const Ref< EfieldDotVectorData > & = 0)
virtual

Return a OneBodyInt that computes the electric field integrals at a given position dotted with a given vector.

See also
efield()

Implements sc::Integral.

◆ electron_repulsion()

Ref< TwoBodyInt > sc::IntegralV3::electron_repulsion ( )
virtual

Return a TwoBodyInt that computes electron repulsion integrals.

This TwoBodyInt will produce a set of integrals described by TwoBodyIntDescrERI.

Deprecated
Use sc::Integral::coulomb<4>() instead.

Reimplemented from sc::Integral.

◆ electron_repulsion2()

Ref< TwoBodyTwoCenterInt > sc::IntegralV3::electron_repulsion2 ( )
virtual

Return a TwoBodyTwoCenterInt that computes electron repulsion integrals.

If this is not re-implemented it will throw.

Deprecated
Use sc::Integral::coulomb<2>() instead.

Reimplemented from sc::Integral.

◆ electron_repulsion3()

Ref< TwoBodyThreeCenterInt > sc::IntegralV3::electron_repulsion3 ( )
virtual

Return a TwoBodyThreeCenterInt that computes electron repulsion integrals.

Electron 1 corresponds to centers 1 and 2, electron 2 corresponds to center 3. If this is not re-implemented it will throw.

Deprecated
Use sc::Integral::coulomb<3>() instead.

Reimplemented from sc::Integral.

◆ electron_repulsion_deriv()

Ref< TwoBodyDerivInt > sc::IntegralV3::electron_repulsion_deriv ( )
virtual

Return a TwoBodyDerivInt that computes electron repulsion derivatives.

Reimplemented from sc::Integral.

◆ hcore()

Ref< OneBodyInt > sc::IntegralV3::hcore ( )
virtual

Return a OneBodyInt that computes the core Hamiltonian integrals.

See also
nuclear()

Implements sc::Integral.

◆ hcore_deriv()

Ref< OneBodyDerivInt > sc::IntegralV3::hcore_deriv ( )
virtual

Return a OneBodyDerivInt that computes core Hamiltonian derivatives.

Implements sc::Integral.

◆ kinetic()

Ref< OneBodyInt > sc::IntegralV3::kinetic ( )
virtual

Return a OneBodyInt that computes the kinetic energy.

Implements sc::Integral.

◆ kinetic_deriv()

Ref< OneBodyDerivInt > sc::IntegralV3::kinetic_deriv ( )
virtual

Return a OneBodyDerivInt that computes kinetic energy derivatives.

Implements sc::Integral.

◆ new_cartesian_iter()

CartesianIter * sc::IntegralV3::new_cartesian_iter ( int )
virtual

Return a CartesianIter object.

The caller is responsible for freeing the object.

Implements sc::Integral.

◆ new_redundant_cartesian_iter()

RedundantCartesianIter * sc::IntegralV3::new_redundant_cartesian_iter ( int )
virtual

Return a RedundantCartesianIter object.

The caller is responsible for freeing the object.

Implements sc::Integral.

◆ new_redundant_cartesian_sub_iter()

RedundantCartesianSubIter * sc::IntegralV3::new_redundant_cartesian_sub_iter ( int )
virtual

Return a RedundantCartesianSubIter object.

The caller is responsible for freeing the object.

Implements sc::Integral.

◆ new_spherical_transform_iter()

SphericalTransformIter * sc::IntegralV3::new_spherical_transform_iter ( int l,
int inv = 0,
int subl = -1 )
virtual

Return a SphericalTransformIter object.

This factory must have been initialized with a basis set whose maximum angular momentum is greater than or equal to l. The caller is responsible for freeing the object.

Implements sc::Integral.

◆ nuclear()

Ref< OneBodyInt > sc::IntegralV3::nuclear ( )
virtual

Return a OneBodyInt that computes the nuclear repulsion integrals.

Note
Charges from the Molecule of basis1 are used. If basis2->molecule() is not not identical to basis1->molecule() (even if not same object), then the charges of both molecules are used.

Implements sc::Integral.

◆ nuclear_deriv()

Ref< OneBodyDerivInt > sc::IntegralV3::nuclear_deriv ( )
virtual

Return a OneBodyDerivInt that computes nuclear repulsion derivatives.

Implements sc::Integral.

◆ overlap()

Ref< OneBodyInt > sc::IntegralV3::overlap ( )
virtual

Return a OneBodyInt that computes the overlap.

Implements sc::Integral.

◆ overlap_deriv()

Ref< OneBodyDerivInt > sc::IntegralV3::overlap_deriv ( )
virtual

Return a OneBodyDerivInt that computes overlap derivatives.

Implements sc::Integral.

◆ p4()

Ref< OneBodyInt > sc::IntegralV3::p4 ( )
virtual

Return a OneBodyInt that computes $p^4 = (\bar{p} \cdot \bar{p})^2$.

Implements sc::Integral.

◆ p_dot_nuclear_p()

Ref< OneBodyInt > sc::IntegralV3::p_dot_nuclear_p ( )
virtual

Return a OneBodyInt that computes $\bar{p}\cdot V\bar{p}$, where $V$ is the nuclear potential.

See also
nuclear()

Reimplemented from sc::Integral.

◆ point_charge()

Ref< OneBodyInt > sc::IntegralV3::point_charge ( const Ref< PointChargeData > & = 0)
virtual

Return a OneBodyInt that computes the integrals for interactions with point charges.

Implements sc::Integral.

◆ point_charge1()

Ref< OneBodyOneCenterInt > sc::IntegralV3::point_charge1 ( const Ref< PointChargeData > & )
virtual

Return a OneBodyInt that computes the integrals for interactions with point charges.

Reimplemented from sc::Integral.

◆ quadrupole()

Ref< OneBodyInt > sc::IntegralV3::quadrupole ( const Ref< IntParamsOrigin > & O = 0)
virtual

Return a OneBodyInt that computes electric quadrupole moment integrals, i.e.

integrals of the $e (\mathbf{r}-\mathbf{O}) \otimes (\mathbf{r}-\mathbf{O})$ operator. The canonical order of integrals in a set is x^2, xy, xz, y^2, yz, z^2.

Parameters
OIntParamsOrigin object that specifies the origin of the multipole expansion; the default is to use the origin of the coordinate system
Note
These are not traceless quadrupole integrals!!
Multiply by -1 to obtain electronic electric quadrupole integrals.

Implements sc::Integral.

◆ save_data_state()

void sc::IntegralV3::save_data_state ( StateOut & )
virtual

Save the base classes (with save_data_state) and the members in the same order that the StateIn CTOR initializes them.

This must be implemented by the derived class if the class has data.

Reimplemented from sc::Integral.

◆ set_basis()

void sc::IntegralV3::set_basis ( const Ref< GaussianBasisSet > & b1,
const Ref< GaussianBasisSet > & b2 = 0,
const Ref< GaussianBasisSet > & b3 = 0,
const Ref< GaussianBasisSet > & b4 = 0 )
virtual

Set the basis set for each center.

Parameters
[in]b1basis set on center 1; there is no default
[in]b2basis set on center 2; if null, will use b1
[in]b3basis set on center 3; if null, will use b2
[in]b4basis set on center 4; if null, will use b3

Reimplemented from sc::Integral.

◆ spherical_transform()

const SphericalTransform * sc::IntegralV3::spherical_transform ( int l,
int inv = 0,
int subl = -1 )
virtual

Return a SphericalTransform object.

This factory must have been initialized with a basis set whose maximum angular momentum is greater than or equal to l. The pointer is only valid while this Integral object is valid.

Implements sc::Integral.


The documentation for this class was generated from the following file:

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