Documentation

template<typename Factory>
class mpqc::pbc::ma::MA_CFFLatticeSum< Factory >

This class computes the contribution to the Coulomb lattice sum from unit cells in Crystal Far Field (CFF) using multipole approximation.

Template Parameters

Factory a periodic AO factory object; only pbc::AOFactory is supported

Classes
struct	LMPair

struct	MSet
	container of values for each m for a given L More...

Public Types
using	TArray = typename Factory::TArray

using	Tile = typename TArray::value_type

using	Policy = typename TArray::policy_type

using	Shell = ::mpqc::lcao::gaussian::Shell

using	Basis = ::mpqc::lcao::gaussian::Basis

using	Ord2lmMap = std::vector< LMPair >

using	UnitCellList = std::vector< std::pair< Vector3i, Vector3d > >

using	MMType = ma::MultipoleMomentsType

template<typename T , unsigned int lmax = LMAX>
using	MultipoleMoments = ma::MultipoleMoments< T, MMType::o, lmax >

template<typename T , unsigned int lmax = LMAX>
using	MultipoleMomentsP = ma::MultipoleMoments< T, MMType::o_plus, lmax >

template<typename T , unsigned int lmax = LMAX>
using	MultipoleMomentsM = ma::MultipoleMoments< T, MMType::o_minus, lmax >

template<typename T , unsigned int lmax = LMAX>
using	MultipoleMomentsPM = ma::MultipoleMoments< T, MMType::o_plusminus, lmax >

template<typename T >
using	eQMoment = std::array< T, 10 >

template<typename T , unsigned int lmax = LMAX>
using	Shell2KernelMap = std::vector< MultipoleMoments< double, 2 *LMAX > >

using	shellpair_list_t = std::vector< std::vector< size_t > >

using	result_type = std::tuple< TArray, std::optional< double > >

Public Member Functions
	MA_CFFLatticeSum (Factory &ao_factory, bool df=false)
	This constructs PeriodicMA using a `Factory` object. More...

decltype(sphemm_) const &	sphemm () const

decltype(sphemm_df_) const &	sphemm_df () const

decltype(eQ_) const &	eQ () const

decltype(eQ_df_) const &	eQ_df () const

const Vector3i &	CFF_boundary ()
	This returns the boundary of Crystal Far Field. More...

template<typename T >
std::tuple< MultipoleMoments< T >, std::vector< AtomBasedClusterable >, std::vector< T > >	compute_L (const MultipoleMoments< T > &O_ref, const eQMoment< T > &eQ_ref, double target_precision)
	This methods compute Coulomb interaction for the reference cell contributed from all cells in CFF using multipole approximation. Note that multipole moments will be separated into dipoles and higher-order moments for systems with large dipole moments. More...

result_type	compute_J (const MultipoleMoments< double > &L, const std::vector< AtomBasedClusterable > &Q_cnf, const MultipoleMoments< TArray > &O_elec)
	This methods compute (obs\|obs) Coulomb matrix contribution from CFF. More...

result_type	compute_J_df (const MultipoleMoments< double > &L, const std::vector< AtomBasedClusterable > &Q_cnf, const MultipoleMoments< TArray > &O_elec)
	This methods compute (dfbs\|1) Coulomb matrix contribution from CFF + surface CNF charges. More...

auto	compute_elec_multipole_moments (const TArray &D) const
	compute electronic multipole moments for the reference unit cell More...

auto	compute_elec_multipole_moments_df (const TArray &rho) const
	compute electronic multipole moments for the reference unit cell More...

bool	CFF_reached () const
	This determines whether Crystal Far Field has been reached for user-specified `rjmax`. More...

bool	CFF_reached (int dim) const
	This determines whether Crystal Far Field has been reached for user-specified `rjmax` for a given direction. More...

template<unsigned int lmax>
std::pair< double, MultipoleMoments< double, lmax > >	solve_multipole_approx (const MultipoleMoments< double, lmax > &Oref, const MultipoleMoments< double, lmax > &Osrc)
	This computes Coulomb interaction for the reference cell contributed from all cells in CFF. Energy contribution is computed per spherical shell from the CFF boundary to the user-given `rjmax` unless it is converged. More...

CFF lattice sums evaluators
These compute contribution to the Coulomb potential generated by the CFF cells (including compensating charges on CNF surfaces) in the reference cell + the energy of its interaction with the nuclei. Up to (cartesian) quadrupole moments are compensated.
result_type	compute_multipole_approx (const TArray &D, double target_precision)
	Computes CFF lattice sum for the given density matrix `D` (and nuclear charges). More...

result_type	compute_multipole_approx_df (const TArray &rho, double target_precision)
	Computes CFF lattice sum for the given (fitted) density `rho` (and nuclear charges) More...

result_type	compute_multipole_approx_dfrev (const TArray &D, double target_precision)
	Computes CFF lattice sum for the given (exact) density `D` (and nuclear charges) More...

Static Public Member Functions
static constexpr unsigned int	number_of_multipoles (unsigned int lmax)

template<typename T >
static eQMoment< T >	plus (const eQMoment< T > &eQ1, const eQMoment< T > &eQ2)

Static Public Attributes
static constexpr const libint2::Operator	Oper

static constexpr const unsigned int	LMAX = MULTIPOLE_MAX_ORDER

static constexpr const unsigned int	NUMBER_OF_MULTIPOLES

Member Typedef Documentation

◆ Basis

template<typename Factory >

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::Basis = ::mpqc::lcao::gaussian::Basis

◆ eQMoment

template<typename Factory >

template<typename T >

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::eQMoment = std::array<T, 10>

◆ MMType

template<typename Factory >

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::MMType = ma::MultipoleMomentsType

◆ MultipoleMoments

template<typename Factory >

template<typename T , unsigned int lmax = LMAX>

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::MultipoleMoments = ma::MultipoleMoments<T, MMType::o, lmax>

◆ MultipoleMomentsM

template<typename Factory >

template<typename T , unsigned int lmax = LMAX>

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::MultipoleMomentsM = ma::MultipoleMoments<T, MMType::o_minus, lmax>

◆ MultipoleMomentsP

template<typename Factory >

template<typename T , unsigned int lmax = LMAX>

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::MultipoleMomentsP = ma::MultipoleMoments<T, MMType::o_plus, lmax>

◆ MultipoleMomentsPM

template<typename Factory >

template<typename T , unsigned int lmax = LMAX>

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::MultipoleMomentsPM = ma::MultipoleMoments<T, MMType::o_plusminus, lmax>

◆ Ord2lmMap

template<typename Factory >

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::Ord2lmMap = std::vector<LMPair>

◆ Policy

template<typename Factory >

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::Policy = typename TArray::policy_type

◆ result_type

template<typename Factory >

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::result_type = std::tuple<TArray, std::optional<double> >

◆ Shell

template<typename Factory >

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::Shell = ::mpqc::lcao::gaussian::Shell

◆ Shell2KernelMap

template<typename Factory >

template<typename T , unsigned int lmax = LMAX>

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::Shell2KernelMap = std::vector<MultipoleMoments<double, 2 * LMAX> >

◆ shellpair_list_t

template<typename Factory >

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::shellpair_list_t = std::vector<std::vector<size_t> >

◆ TArray

template<typename Factory >

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::TArray = typename Factory::TArray

◆ Tile

template<typename Factory >

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::Tile = typename TArray::value_type

◆ UnitCellList

template<typename Factory >

using mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::UnitCellList = std::vector<std::pair<Vector3i, Vector3d> >

Constructor & Destructor Documentation

◆ MA_CFFLatticeSum()

template<typename Factory >

mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::MA_CFFLatticeSum	(	Factory &	ao_factory,
		bool	df = `false`
	)

inline

This constructs PeriodicMA using a Factory object.

Parameters

ao_factory	a Factory object
e_thresh	threshold of multipole expansion error
ws	well-separateness criterion

Member Function Documentation

◆ CFF_boundary()

template<typename Factory >

const Vector3i& mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::CFF_boundary ( )

inline

This returns the boundary of Crystal Far Field.

◆ CFF_reached() [1/2]

template<typename Factory >

bool mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::CFF_reached ( ) const

inline

This determines whether Crystal Far Field has been reached for user-specified rjmax.

Returns: true if CFF has been reached in any direction, false otherwise

◆ CFF_reached() [2/2]

template<typename Factory >

bool mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::CFF_reached ( int dim ) const

inline

This determines whether Crystal Far Field has been reached for user-specified rjmax for a given direction.

Parameters

dim	0 for x direction, 1 for y direction, 2 for z direction

Returns: true if CFF has been reached in direction dim, false otherwise

◆ compute_elec_multipole_moments()

template<typename Factory >

auto mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::compute_elec_multipole_moments ( const TArray & D ) const

inline

compute electronic multipole moments for the reference unit cell

◆ compute_elec_multipole_moments_df()

template<typename Factory >

auto mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::compute_elec_multipole_moments_df ( const TArray & rho ) const

inline

compute electronic multipole moments for the reference unit cell

◆ compute_J()

template<typename Factory >

result_type mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::compute_J	(	const MultipoleMoments< double > &	L,
		const std::vector< AtomBasedClusterable > &	Q_cnf,
		const MultipoleMoments< TArray > &	O_elec
	)

inline

This methods compute (obs|obs) Coulomb matrix contribution from CFF.

surface CNF charges.
Returns

◆ compute_J_df()

template<typename Factory >

result_type mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::compute_J_df	(	const MultipoleMoments< double > &	L,
		const std::vector< AtomBasedClusterable > &	Q_cnf,
		const MultipoleMoments< TArray > &	O_elec
	)

inline

This methods compute (dfbs|1) Coulomb matrix contribution from CFF + surface CNF charges.

Returns

◆ compute_L()

template<typename Factory >

template<typename T >

std::tuple<MultipoleMoments<T>, std::vector<AtomBasedClusterable>, std::vector<T> > mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::compute_L	(	const MultipoleMoments< T > &	O_ref,
		const eQMoment< T > &	eQ_ref,
		double	target_precision
	)

inline

This methods compute Coulomb interaction for the reference cell contributed from all cells in CFF using multipole approximation. Note that multipole moments will be separated into dipoles and higher-order moments for systems with large dipole moments.

Returns: {L, R_cnf, Q_cnf}, with L the CFF contribution to the multipole expansion of the coulomb potential in the reference cell, R_cnf and Q_cnf the Cartesian coordinates and charges of the CNF surface compensating charges

◆ compute_multipole_approx()

template<typename Factory >

result_type mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::compute_multipole_approx	(	const TArray &	D,
		double	target_precision
	)

inline

Computes CFF lattice sum for the given density matrix D (and nuclear charges).

Parameters

D	the 1-RDM
target_precision	the target precision

Returns: {Coulomb potential matrix, energy of its interaction with the nuclei}

◆ compute_multipole_approx_df()

template<typename Factory >

result_type mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::compute_multipole_approx_df	(	const TArray &	rho,
		double	target_precision
	)

inline

Computes CFF lattice sum for the given (fitted) density rho (and nuclear charges)

Parameters

rho	the (fitted) charge density
target_precision	the target precision

Returns: {Coulomb potential matrix, energy of its interaction with the nuclei}

◆ compute_multipole_approx_dfrev()

template<typename Factory >

result_type mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::compute_multipole_approx_dfrev	(	const TArray &	D,
		double	target_precision
	)

inline

Computes CFF lattice sum for the given (exact) density D (and nuclear charges)

Parameters

D	the (exact) charge density
target_precision	the target precision

Returns: {Coulomb potential matrix in DF basis, energy of its interaction with the nuclei}

◆ eQ()

template<typename Factory >

decltype(eQ_) const& mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::eQ ( ) const

inline

◆ eQ_df()

template<typename Factory >

decltype(eQ_df_) const& mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::eQ_df ( ) const

inline

◆ number_of_multipoles()

template<typename Factory >

static constexpr unsigned int mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::number_of_multipoles ( unsigned int lmax )

inlinestaticconstexpr

◆ plus()

template<typename Factory >

template<typename T >

static eQMoment<T> mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::plus	(	const eQMoment< T > &	eQ1,
		const eQMoment< T > &	eQ2
	)

inlinestatic

◆ solve_multipole_approx()

template<typename Factory >

template<unsigned int lmax>

std::pair<double, MultipoleMoments<double, lmax> > mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::solve_multipole_approx	(	const MultipoleMoments< double, lmax > &	Oref,
		const MultipoleMoments< double, lmax > &	Osrc
	)

inline

This computes Coulomb interaction for the reference cell contributed from all cells in CFF. Energy contribution is computed per spherical shell from the CFF boundary to the user-given rjmax unless it is converged.

Template Parameters

lmax
nopers
nopers_doubled_lmax

Parameters

Oref	multipole moments of the reference cell
Osrc	multipole moments of the cells generating the Coulomb potential

Returns: std::tuple containing the interaction energy of CFF with Oref and the inner multipoles of the potential in the reference cell

Note: this is not collective, should be executed on 1 rank and broadcast

Warning: this is not bitwise reproducibile (due to task decomposition),

◆ sphemm()

template<typename Factory >

decltype(sphemm_) const& mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::sphemm ( ) const

inline

◆ sphemm_df()

template<typename Factory >

decltype(sphemm_df_) const& mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::sphemm_df ( ) const

inline

Member Data Documentation

◆ LMAX

template<typename Factory >

constexpr const unsigned int mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::LMAX = MULTIPOLE_MAX_ORDER

staticconstexpr

◆ NUMBER_OF_MULTIPOLES

template<typename Factory >

constexpr const unsigned int mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::NUMBER_OF_MULTIPOLES

staticconstexpr

Initial value:

=

number_of_multipoles(LMAX)

◆ Oper

template<typename Factory >

constexpr const libint2::Operator mpqc::pbc::ma::MA_CFFLatticeSum< Factory >::Oper

staticconstexpr

Initial value:

=

libint2::Operator::sphemultipole

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

mpqc/chemistry/qc/lcao/scf/fwd.h
mpqc/chemistry/qc/lcao/scf/pbc/ma.h

Documentation

template<typename Factory> class mpqc::pbc::ma::MA_CFFLatticeSum< Factory >

Classes

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Member Typedef Documentation

◆ Basis

◆ eQMoment

◆ MMType

◆ MultipoleMoments

◆ MultipoleMomentsM

◆ MultipoleMomentsP

◆ MultipoleMomentsPM

◆ Ord2lmMap

◆ Policy

◆ result_type

◆ Shell

◆ Shell2KernelMap

◆ shellpair_list_t

◆ TArray

◆ Tile

◆ UnitCellList

Constructor & Destructor Documentation

◆ MA_CFFLatticeSum()

Member Function Documentation

◆ CFF_boundary()

◆ CFF_reached() [1/2]

◆ CFF_reached() [2/2]

◆ compute_elec_multipole_moments()

◆ compute_elec_multipole_moments_df()

◆ compute_J()

◆ compute_J_df()

◆ compute_L()

◆ compute_multipole_approx()

◆ compute_multipole_approx_df()

◆ compute_multipole_approx_dfrev()

◆ eQ()

◆ eQ_df()

◆ number_of_multipoles()

◆ plus()

◆ solve_multipole_approx()

◆ sphemm()

◆ sphemm_df()

Member Data Documentation

◆ LMAX

◆ NUMBER_OF_MULTIPOLES

◆ Oper

template<typename Factory>
class mpqc::pbc::ma::MA_CFFLatticeSum< Factory >