#include <LinearExpansion.hpp>

Collaboration diagram for GQCP::LinearExpansion< _Scalar, _ONVBasis >:

Public Types
using	Scalar = _Scalar

using	ONVBasis = _ONVBasis

Public Member Functions
	LinearExpansion (const ONVBasis &onv_basis, const VectorX< Scalar > &coefficients)

	LinearExpansion ()=default

Scalar	coefficient (const size_t i) const

const VectorX< Scalar > &	coefficients () const

const ONVBasis &	onvBasis () const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value >	basisTransform (const RTransformation< double > &T)

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinUnresolvedONVBasis >::value, G1DM< double > >	calculate1DM () const

template<typename Z = ONVBasis>
enable_if_t< std::is_same< Z, SpinUnresolvedONVBasis >::value, Scalar >	calculateNDMElement (const std::vector< size_t > &bra_indices, const std::vector< size_t > &ket_indices) const

template<typename Z = ONVBasis>
enable_if_t< std::is_same< Z, SpinUnresolvedSelectedONVBasis >::value, Scalar >	calculateNDMElement (const std::vector< size_t > &bra_indices, const std::vector< size_t > &ket_indices) const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value, SpinResolved1DM< double > >	calculateSpinResolved1DM () const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value, SpinResolved2DM< double > >	calculateSpinResolved2DM () const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value, Orbital1DM< double > >	calculate1DM () const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value, Orbital2DM< double > >	calculate2DM () const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SeniorityZeroONVBasis >::value, Orbital1DM< double > >	calculate1DM () const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SeniorityZeroONVBasis >::value, Orbital2DM< double > >	calculate2DM () const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SeniorityZeroONVBasis >::value, SpinResolved1DM< double > >	calculateSpinResolved1DM () const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SeniorityZeroONVBasis >::value, SpinResolved2DM< double > >	calculateSpinResolved2DM () const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedSelectedONVBasis >::value, SpinResolved1DM< double > >	calculateSpinResolved1DM () const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedSelectedONVBasis >::value, SpinResolved2DM< double > >	calculateSpinResolved2DM () const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedSelectedONVBasis >::value, Orbital1DM< double > >	calculate1DM () const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedSelectedONVBasis >::value, Orbital2DM< double > >	calculate2DM () const

template<typename Z = ONVBasis>
enable_if_t< std::is_same< Z, SpinUnresolvedSelectedONVBasis >::value, G1DM< Scalar > >	calculate1DM () const

template<typename Z = ONVBasis>
enable_if_t< std::is_same< Z, SpinUnresolvedSelectedONVBasis >::value, G2DM< Scalar > >	calculate2DM () const

template<typename Z = ONVBasis>
enable_if_t< std::is_same< Z, SpinUnresolvedONVBasis >::value\|std::is_same< Z, SpinResolvedONVBasis >::value, GQCP::Tensor< Scalar, 2 > >	tensorizeCoefficients (const std::vector< typename ONVBasis::ONV > &system_onvs, const std::vector< typename ONVBasis::ONV > &environment_onvs) const

template<typename Z = ONVBasis>
enable_if_t< std::is_same< Z, SpinResolvedONVBasis >::value, Tensor< Scalar, 2 > >	calculateSystemOrbitalRDM (const DiscreteDomainPartition &domain_partition) const

template<typename Z = ONVBasis>
enable_if_t< std::is_same< Z, SpinUnresolvedONVBasis >::value, Tensor< Scalar, 2 > >	calculateSystemOrbitalRDM (const DiscreteDomainPartition &domain_partition) const

template<typename Z = Scalar>
enable_if_t< std::is_same< Z, double >::value, double >	calculateShannonEntropy () const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value, double >	calculateSingleOrbitalEntropy (const size_t orbital_index) const

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
enable_if_t< std::is_same< Z1, Scalar >::value &&std::is_same< Z2, SeniorityZeroONVBasis >::value, double >	calculateSingleOrbitalEntropy (const size_t orbital_index) const

template<typename ElectronPartition , typename Z = ONVBasis, std::enable_if_t< std::is_same< Z, SpinResolvedONVBasis >::value, bool > = true>
double	calculateProbabilityOfFindingElectronPartition (const DiscreteDomainPartition &domain_partition, const ElectronPartition &electron_partition) const

template<typename ElectronPartition , typename Z = ONVBasis, std::enable_if_t< std::is_same< Z, SpinUnresolvedONVBasis >::value, bool > = true>
double	calculateProbabilityOfFindingElectronPartition (const DiscreteDomainPartition &domain_partition, const ElectronPartition &electron_partition) const

template<typename Z = ONVBasis>
enable_if_t< std::is_same< Z, SpinResolvedONVBasis >::value, void >	forEach (const std::function< void(const Scalar, const SpinResolvedONV)> &callback) const

template<typename Z = ONVBasis>
enable_if_t< std::is_same< Z, SpinUnresolvedONVBasis >::value, void >	forEach (const std::function< void(const Scalar, const SpinUnresolvedONV)> &callback) const

bool	isApprox (const LinearExpansion< Scalar, ONVBasis > &other, double tolerance=1.0e-12) const

Static Public Member Functions
static LinearExpansion< Scalar, ONVBasis >	Constant (const ONVBasis &onv_basis)

static LinearExpansion< Scalar, ONVBasis >	HartreeFock (const ONVBasis &onv_basis)

static LinearExpansion< Scalar, ONVBasis >	Normalized (const ONVBasis &onv_basis, const VectorX< Scalar > &coefficients)

static LinearExpansion< Scalar, ONVBasis >	Random (const ONVBasis &onv_basis)

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
static enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedSelectedONVBasis >::value, LinearExpansion< double, SpinResolvedSelectedONVBasis > >	FromGAMESSUS (const std::string &GAMESSUS_filename)

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
static enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value, LinearExpansion< double, SpinResolvedONVBasis > >	FromONVProjection (const SpinResolvedONV &onv, const RSpinOrbitalBasis< double, GTOShell > &r_spinor_basis, const USpinOrbitalBasis< double, GTOShell > &u_spinor_basis)

template<typename Z1 = Scalar, typename Z2 = ONVBasis>
static enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinUnresolvedONVBasis >::value, LinearExpansion< double, SpinUnresolvedONVBasis > >	FromONVProjection (const SpinUnresolvedONV &onv_of, const GSpinorBasis< double, GTOShell > &spinor_basis_on, const GSpinorBasis< double, GTOShell > &spinor_basis_of)

Detailed Description

template<typename _Scalar, typename _ONVBasis>
class GQCP::LinearExpansion< _Scalar, _ONVBasis >

A class that represents a linear expansion inside an ONV basis.

Template Parameters

_Scalar	The scalar type of the expansion coefficients: real or complex.
_ONVBasis	The type of ONV basis.

Member Typedef Documentation

◆ ONVBasis

template<typename _Scalar , typename _ONVBasis >

using GQCP::LinearExpansion< _Scalar, _ONVBasis >::ONVBasis = _ONVBasis

◆ Scalar

template<typename _Scalar , typename _ONVBasis >

using GQCP::LinearExpansion< _Scalar, _ONVBasis >::Scalar = _Scalar

Constructor & Destructor Documentation

◆ LinearExpansion() [1/2]

template<typename _Scalar , typename _ONVBasis >

GQCP::LinearExpansion< _Scalar, _ONVBasis >::LinearExpansion	(	const ONVBasis &	onv_basis,
		const VectorX< Scalar > &	coefficients
	)

inline

Construct a linear expansion inside the given ONV basis, with corresponding expansion coefficients.

Parameters

onv_basis	The ONV basis with respect to which the coefficients are defined.
coefficients	The expansion coefficients.

◆ LinearExpansion() [2/2]

template<typename _Scalar , typename _ONVBasis >

GQCP::LinearExpansion< _Scalar, _ONVBasis >::LinearExpansion ( )

default

Member Function Documentation

◆ basisTransform()

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value > GQCP::LinearExpansion< _Scalar, _ONVBasis >::basisTransform ( const RTransformation< double > & T )

inline

Update the expansion coefficients of this linear expansion so that they correspond to the situation after a transformation of the underlying spinor basis with the given basis transformation.

Parameters

T	The transformation between the old and the new restricted spin-orbital basis.

Note: This method is only available for the full spin-resolved ONV basis.; This algorithm was implemented from a description in Helgaker2000.

The transformation of the expansion coefficients is adapted from Helgaker2000, chapter 11.9. For every orbital, a set of correction coefficients will be calculated (Delta C in Helgaker), to update the current coefficients.

◆ calculate1DM() [1/5]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinUnresolvedONVBasis >::value, G1DM< double > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculate1DM ( ) const

inline

◆ calculate1DM() [2/5]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value, Orbital1DM< double > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculate1DM ( ) const

inline

Calculate the one-electron density matrix for a full spin-resolved wave function expansion.

Returns: The orbital (total, spin-summed) 1-DM

◆ calculate1DM() [3/5]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SeniorityZeroONVBasis >::value, Orbital1DM< double > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculate1DM ( ) const

inline

Calculate the orbital one-electron density matrix for a seniority-zero wave function expansion.

Returns: The orbital (total, spin-summed) 1-DM.

◆ calculate1DM() [4/5]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedSelectedONVBasis >::value, Orbital1DM< double > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculate1DM ( ) const

inline

Calculate the one-electron density matrix for a spin-resolved selected wave function expansion.

Returns: The orbital (total, spin-summed) 1-DM.

◆ calculate1DM() [5/5]

template<typename _Scalar , typename _ONVBasis >

template<typename Z = ONVBasis>

enable_if_t< std::is_same< Z, SpinUnresolvedSelectedONVBasis >::value, G1DM< Scalar > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculate1DM ( ) const

inline

Calculate the generalized (G) one-electron density matrix for a spin-unresolved selected wave function expansion.

Returns: The generalized (G) 1-DM.

◆ calculate2DM() [1/4]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value, Orbital2DM< double > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculate2DM ( ) const

inline

Calculate the two-electron density matrix for a full spin-resolved wave function expansion.

Returns: The orbital (total, spin-summed) 2-DM.

◆ calculate2DM() [2/4]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SeniorityZeroONVBasis >::value, Orbital2DM< double > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculate2DM ( ) const

inline

Calculate the two-electron density matrix for a seniority-zero wave function expansion.

Returns: The orbital (total, spin-summed) 2-DM.

◆ calculate2DM() [3/4]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedSelectedONVBasis >::value, Orbital2DM< double > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculate2DM ( ) const

inline

Calculate the two-electron density matrix for a spin-resolved selected wave function expansion.

Returns: The orbital (total, spin-summed) 2-DM.

◆ calculate2DM() [4/4]

template<typename _Scalar , typename _ONVBasis >

template<typename Z = ONVBasis>

enable_if_t< std::is_same< Z, SpinUnresolvedSelectedONVBasis >::value, G2DM< Scalar > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculate2DM ( ) const

inline

Calculate the generalized (G) two-electron density matrix (1-DM) for a spin-unresolved selected wave function expansion.

Returns: The generalized (G) 2-DM.

◆ calculateNDMElement() [1/2]

template<typename _Scalar , typename _ONVBasis >

template<typename Z = ONVBasis>

enable_if_t< std::is_same< Z, SpinUnresolvedONVBasis >::value, Scalar > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateNDMElement	(	const std::vector< size_t > &	bra_indices,
		const std::vector< size_t > &	ket_indices
	)		const

inline

Calculate an element of the N-electron density matrix.

Parameters

bra_indices	The indices of the orbitals that should be annihilated on the left (on the bra).
ket_indices	The indices of the orbitals that should be annihilated on the right (on the ket).

Returns: An element of the N-DM, as specified by the given bra and ket indices. calculateNDMElement({0, 1}, {2, 1}) would calculate an element of the 2-NDM d^{(2)} (0, 1, 1, 2) corresponding the operator string: a^\dagger_0 a^\dagger_1 a_2 a_1.

Note: This method is only enabled for linear expansions related to spin-unresolved ONV bases.

◆ calculateNDMElement() [2/2]

template<typename _Scalar , typename _ONVBasis >

template<typename Z = ONVBasis>

enable_if_t< std::is_same< Z, SpinUnresolvedSelectedONVBasis >::value, Scalar > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateNDMElement	(	const std::vector< size_t > &	bra_indices,
		const std::vector< size_t > &	ket_indices
	)		const

inline

Calculate an element of the N-electron density matrix.

Parameters

bra_indices	The indices of the orbitals that should be annihilated on the left (on the bra).
ket_indices	The indices of the orbitals that should be annihilated on the right (on the ket).

Returns: An element of the N-DM, as specified by the given bra and ket indices. calculateNDMElement({0, 1}, {2, 1}) would calculate an element of the 2-NDM d^{(2)} (0, 1, 1, 2) corresponding the operator string: a^\dagger_0 a^\dagger_1 a_2 a_1.

Note: This method is only enabled for linear expansions related to spin-unresolved selected ONV bases.

◆ calculateProbabilityOfFindingElectronPartition() [1/2]

template<typename _Scalar , typename _ONVBasis >

template<typename ElectronPartition , typename Z = ONVBasis, std::enable_if_t< std::is_same< Z, SpinResolvedONVBasis >::value, bool > = true>

double GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateProbabilityOfFindingElectronPartition	(	const DiscreteDomainPartition &	domain_partition,
		const ElectronPartition &	electron_partition
	)		const

inline

MARK: Probability Calculate the probability of finding a given electron distribution over the discrete domains according to equation (11) in VanHende2022 (https://doi.org/10.1002/jcc.26806).

Parameters

domain_partition	The partition of the orbitals in discrete domains.
electron_partition	Electron occupation number in each discrete domain.

Returns: the probability of finding a given electron distribution over the discrete domains.

◆ calculateProbabilityOfFindingElectronPartition() [2/2]

template<typename _Scalar , typename _ONVBasis >

template<typename ElectronPartition , typename Z = ONVBasis, std::enable_if_t< std::is_same< Z, SpinUnresolvedONVBasis >::value, bool > = true>

double GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateProbabilityOfFindingElectronPartition	(	const DiscreteDomainPartition &	domain_partition,
		const ElectronPartition &	electron_partition
	)		const

inline

Calculate the probability of finding a given electron distribution over the discrete domains according to equation (11) in VanHende2022 (https://doi.org/10.1002/jcc.26806).

Parameters

domain_partition	The partition of the orbitals in discrete domains.
electron_partition	Electron occupation number in each discrete domain.

Returns: The probability of finding a given electron distribution over the discrete domains.

◆ calculateShannonEntropy()

template<typename _Scalar , typename _ONVBasis >

template<typename Z = Scalar>

enable_if_t< std::is_same< Z, double >::value, double > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateShannonEntropy ( ) const

inline

Returns: The Shannon entropy (information content) of the wave function.

◆ calculateSingleOrbitalEntropy() [1/2]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value, double > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateSingleOrbitalEntropy ( const size_t orbital_index ) const

inline

Calculate the single orbital entropy of the orbital at the selected index, from the spin-resolved 1- and two-particle density matrix. The implementation is based on https://doi.org/10.1002/qua.24832.

Parameters

orbital_index The index of the orbital for which the single orbital entropy needs to be calculated.

Returns: The single orbital entropy of the orbital at the specified index.

Note: This version of this method is used when the linear expansion is based on a spin-resolved ONV basis.

◆ calculateSingleOrbitalEntropy() [2/2]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, Scalar >::value &&std::is_same< Z2, SeniorityZeroONVBasis >::value, double > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateSingleOrbitalEntropy ( const size_t orbital_index ) const

inline

Calculate the single orbital entropy of the orbital at the selected index, from the spin-resolved 1- and two-particle density matrix. The implementation is based on https://doi.org/10.1002/qua.24832.

Parameters

orbital_index The index of the orbital for which the single orbital entropy needs to be calculated.

Returns: The single orbital entropy of the orbital at the specified index.

Note: This version of this method is used when the linear expansion is based on a seniority-zero ONV basis.

◆ calculateSpinResolved1DM() [1/3]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value, SpinResolved1DM< double > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateSpinResolved1DM ( ) const

inline

Calculate the spin-resolved one-electron density matrix for a full spin-resolved wave function expansion.

Returns: The spin-resolved 1-DM.

◆ calculateSpinResolved1DM() [2/3]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SeniorityZeroONVBasis >::value, SpinResolved1DM< double > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateSpinResolved1DM ( ) const

inline

Calculate the spin-resolved one-electron density matrix for a seniority-zero wave function expansion.

Returns: The spin-resolved 1-DM.

◆ calculateSpinResolved1DM() [3/3]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedSelectedONVBasis >::value, SpinResolved1DM< double > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateSpinResolved1DM ( ) const

inline

Calculate the spin-resolved one-electron density matrix for a spin-resolved selected wave function expansion.

Returns: The spin-resolved 1-DM.

◆ calculateSpinResolved2DM() [1/3]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value, SpinResolved2DM< double > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateSpinResolved2DM ( ) const

inline

Calculate the spin-resolved two-electron density matrix for a full spin-resolved wave function expansion.

Returns: The spin-resolved 2-DM.

◆ calculateSpinResolved2DM() [2/3]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SeniorityZeroONVBasis >::value, SpinResolved2DM< double > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateSpinResolved2DM ( ) const

inline

Calculate the spin-resolved two-electron density matrix for a seniority-zero wave function expansion.

Returns: The spin-resolved 2-DM.

◆ calculateSpinResolved2DM() [3/3]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedSelectedONVBasis >::value, SpinResolved2DM< double > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateSpinResolved2DM ( ) const

inline

Calculate the spin-resolved two-electron density matrix for a spin-resolved selected wave function expansion.

Returns: The spin-resolved 2-DM.

◆ calculateSystemOrbitalRDM() [1/2]

template<typename _Scalar , typename _ONVBasis >

template<typename Z = ONVBasis>

enable_if_t< std::is_same< Z, SpinResolvedONVBasis >::value, Tensor< Scalar, 2 > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateSystemOrbitalRDM ( const DiscreteDomainPartition & domain_partition ) const

inline

Calculate the system orbital reduced density matrix as defined in equation (2) of Rissler2005 (https://doi.org/10.1016/j.chemphys.2005.10.018).

Parameters

domain_partition The (discrete) domain partition used to partition the spin-resolved ONVs in this LinearExpansion.

Returns: The system orbital reduced density matrix.

◆ calculateSystemOrbitalRDM() [2/2]

template<typename _Scalar , typename _ONVBasis >

template<typename Z = ONVBasis>

enable_if_t< std::is_same< Z, SpinUnresolvedONVBasis >::value, Tensor< Scalar, 2 > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::calculateSystemOrbitalRDM ( const DiscreteDomainPartition & domain_partition ) const

inline

Calculate the system orbital reduced density matrix as defined in equation (2) of Rissler2005 (https://doi.org/10.1016/j.chemphys.2005.10.018).

Parameters

domain_partition The (discrete) domain partition used to partition the spin-unresolved ONVs in this LinearExpansion.

Returns: The system orbital reduced density matrix.

◆ coefficient()

template<typename _Scalar , typename _ONVBasis >

Scalar GQCP::LinearExpansion< _Scalar, _ONVBasis >::coefficient ( const size_t i ) const

inline

Access a coefficient of the linear expansion.

Parameters

i	The index (address) of the coefficient that should be obtained.

Returns: The i-th expansion coefficient.

◆ coefficients()

template<typename _Scalar , typename _ONVBasis >

const VectorX< Scalar > & GQCP::LinearExpansion< _Scalar, _ONVBasis >::coefficients ( ) const

inline

Returns: The expansion coefficients of this linear expansion wave function model.

◆ Constant()

template<typename _Scalar , typename _ONVBasis >

static LinearExpansion< Scalar, ONVBasis > GQCP::LinearExpansion< _Scalar, _ONVBasis >::Constant ( const ONVBasis & onv_basis )

inlinestatic

Create a linear expansion with a normalized coefficient vector (i.e. all the coefficients are equal).

Parameters

onv_basis The ONV basis with respect to which the coefficients are defined.

Returns: A constant LinearExpansion.

◆ forEach() [1/2]

template<typename _Scalar , typename _ONVBasis >

template<typename Z = ONVBasis>

enable_if_t< std::is_same< Z, SpinResolvedONVBasis >::value, void > GQCP::LinearExpansion< _Scalar, _ONVBasis >::forEach ( const std::function< void(const Scalar, const SpinResolvedONV)> & callback ) const

inline

Iterate over all expansion coefficients and corresponding ONVs, and apply the given callback function.

Parameters

callback The function to be applied in every iteration. Its arguments are an expansion coefficient and the corresponding ONV.

◆ forEach() [2/2]

template<typename _Scalar , typename _ONVBasis >

template<typename Z = ONVBasis>

enable_if_t< std::is_same< Z, SpinUnresolvedONVBasis >::value, void > GQCP::LinearExpansion< _Scalar, _ONVBasis >::forEach ( const std::function< void(const Scalar, const SpinUnresolvedONV)> & callback ) const

inline

Iterate over all expansion coefficients and corresponding ONVs, and apply the given callback function.

Parameters

callback The function to be applied in every iteration. Its arguments are an expansion coefficient and the corresponding ONV.

◆ FromGAMESSUS()

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

static enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedSelectedONVBasis >::value, LinearExpansion< double, SpinResolvedSelectedONVBasis > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::FromGAMESSUS ( const std::string & GAMESSUS_filename )

inlinestatic

Create a linear expansion by reading in a GAMESS-US file.

Parameters

GAMESSUS_filename The name of the GAMESS-US file that contains the spin-resolved selected wave function expansion.

Returns: The corresponding spin-resolved selected linear expansion from a given GAMESS-US file.

◆ FromONVProjection() [1/2]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

static enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinResolvedONVBasis >::value, LinearExpansion< double, SpinResolvedONVBasis > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::FromONVProjection	(	const SpinResolvedONV &	onv,
		const RSpinOrbitalBasis< double, GTOShell > &	r_spinor_basis,
		const USpinOrbitalBasis< double, GTOShell > &	u_spinor_basis
	)

inlinestatic

Create the linear expansion of the given spin-resolved ONV that is expressed in the given USpinOrbitalBasis, by projection onto the spin-resolved ONVs expressed with respect to the given RSpinOrbitalBasis.

Parameters

onv	A spin-resolved ONV expressed with respect to an unrestricted spin-orbital basis.
r_spinor_basis	The restricted spin-orbital basis that is used to define the resulting linear expansion of ONVs against.
u_spinor_basis	The unrestricted spin-orbital basis against which the given ONV is expressed.

Returns: A linear expansion inside a spin-resolved ONV basis.

◆ FromONVProjection() [2/2]

template<typename _Scalar , typename _ONVBasis >

template<typename Z1 = Scalar, typename Z2 = ONVBasis>

static enable_if_t< std::is_same< Z1, double >::value &&std::is_same< Z2, SpinUnresolvedONVBasis >::value, LinearExpansion< double, SpinUnresolvedONVBasis > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::FromONVProjection	(	const SpinUnresolvedONV &	onv_of,
		const GSpinorBasis< double, GTOShell > &	spinor_basis_on,
		const GSpinorBasis< double, GTOShell > &	spinor_basis_of
	)

inlinestatic

Create the linear expansion of the given spin-unresolved ONV that is expressed in the given GSpinorBasis, by projection onto the spin-resolved ONVs expressed with respect to another given GSpinorBasis.

Parameters

onv_of	A spin-unresolved ONV expressed with respect to a general spinor basis.
spinor_basis_on	The general spinor basis that is used to define the resulting linear expansion of ONVs against.
spinor_basis_of	The general spinor basis against which the given ONV is expressed.

Returns: A linear expansion inside a spin-unresolved ONV basis.

◆ HartreeFock()

template<typename _Scalar , typename _ONVBasis >

static LinearExpansion< Scalar, ONVBasis > GQCP::LinearExpansion< _Scalar, _ONVBasis >::HartreeFock ( const ONVBasis & onv_basis )

inlinestatic

Create a linear expansion that represents the Hartree-Fock wave function.

Parameters

onv_basis The ONV basis with respect to which the coefficients are defined.

Returns: a LinearExpansion

◆ isApprox()

template<typename _Scalar , typename _ONVBasis >

bool GQCP::LinearExpansion< _Scalar, _ONVBasis >::isApprox	(	const LinearExpansion< Scalar, ONVBasis > &	other,
		double	tolerance = `1.0e-12`
	)		const

inline

Parameters

other	The other linear expansion for the comparison.
tolerance	The tolerance for the comparison of coefficients.

Returns: If the two linear expansions are equal within a given tolerance.

◆ Normalized()

template<typename _Scalar , typename _ONVBasis >

static LinearExpansion< Scalar, ONVBasis > GQCP::LinearExpansion< _Scalar, _ONVBasis >::Normalized	(	const ONVBasis &	onv_basis,
		const VectorX< Scalar > &	coefficients
	)

inlinestatic

Create a normalized linear expansion inside a given ONV basis with possibly non-normalized coefficients.

Parameters

onv_basis	The ONV basis with respect to which the coefficients are defined.
coefficients	the expansion coefficients

Returns: A normalized LinearExpansion.

◆ onvBasis()

template<typename _Scalar , typename _ONVBasis >

const ONVBasis & GQCP::LinearExpansion< _Scalar, _ONVBasis >::onvBasis ( ) const

inline

Returns: The ONV basis that is related to this linear expansion wave function model.

◆ Random()

template<typename _Scalar , typename _ONVBasis >

static LinearExpansion< Scalar, ONVBasis > GQCP::LinearExpansion< _Scalar, _ONVBasis >::Random ( const ONVBasis & onv_basis )

inlinestatic

Create a linear expansion with a random, normalized coefficient vector, with coefficients uniformly distributed in [-1, +1] before any normalization.

Parameters

onv_basis the ONV basis with respect to which the coefficients are defined

Returns: A random LinearExpansion.

◆ tensorizeCoefficients()

template<typename _Scalar , typename _ONVBasis >

template<typename Z = ONVBasis>

enable_if_t< std::is_same< Z, SpinUnresolvedONVBasis >::value\|std::is_same< Z, SpinResolvedONVBasis >::value, GQCP::Tensor< Scalar, 2 > > GQCP::LinearExpansion< _Scalar, _ONVBasis >::tensorizeCoefficients	(	const std::vector< typename ONVBasis::ONV > &	system_onvs,
		const std::vector< typename ONVBasis::ONV > &	environment_onvs
	)		const

inline

MARK: Entropy Construct the linear expansion in tensor form.

Parameters

system_onvs	A vector of all ONVs of the system that is obtained after splitting an ONV basis into two subsystems.
environment_onvs	A vector of all ONVs of the environment that is obtained after splitting an ONV basis into two subsystems.

Returns: The expansion coefficients in tensor form.

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

/__w/GQCP/GQCP/gqcp/include/QCModel/CI/LinearExpansion.hpp

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Typedef Documentation

◆ ONVBasis

◆ Scalar

Constructor & Destructor Documentation

◆ LinearExpansion() [1/2]

◆ LinearExpansion() [2/2]

Member Function Documentation

◆ basisTransform()

◆ calculate1DM() [1/5]

◆ calculate1DM() [2/5]

◆ calculate1DM() [3/5]

◆ calculate1DM() [4/5]

◆ calculate1DM() [5/5]

◆ calculate2DM() [1/4]

◆ calculate2DM() [2/4]

◆ calculate2DM() [3/4]

◆ calculate2DM() [4/4]

◆ calculateNDMElement() [1/2]

◆ calculateNDMElement() [2/2]

◆ calculateProbabilityOfFindingElectronPartition() [1/2]

◆ calculateProbabilityOfFindingElectronPartition() [2/2]

◆ calculateShannonEntropy()

◆ calculateSingleOrbitalEntropy() [1/2]

◆ calculateSingleOrbitalEntropy() [2/2]

◆ calculateSpinResolved1DM() [1/3]

◆ calculateSpinResolved1DM() [2/3]

◆ calculateSpinResolved1DM() [3/3]

◆ calculateSpinResolved2DM() [1/3]

◆ calculateSpinResolved2DM() [2/3]

◆ calculateSpinResolved2DM() [3/3]

◆ calculateSystemOrbitalRDM() [1/2]

◆ calculateSystemOrbitalRDM() [2/2]

◆ coefficient()

◆ coefficients()

◆ Constant()

◆ forEach() [1/2]

◆ forEach() [2/2]

◆ FromGAMESSUS()

◆ FromONVProjection() [1/2]

◆ FromONVProjection() [2/2]

◆ HartreeFock()

◆ isApprox()

◆ Normalized()

◆ onvBasis()

◆ Random()

◆ tensorizeCoefficients()