occ::qm::SplitRIJ Class Reference

Split-RI-J: Coulomb matrix via Hermite Gaussian basis (Neese 2003). More...

#include <split_ri_j.h>

Public Member Functions
	SplitRIJ (const gto::AOBasis &ao_basis, const gto::AOBasis &aux_basis, const ShellPairList &shellpairs, const Mat &schwarz=Mat())
	Construct Split-RI-J engine.
	SplitRIJ (const gto::AOBasis &ao_basis, const gto::AOBasis &aux_basis, const ShellPairList &shellpairs, const Mat &schwarz, const CoulombMetric &metric, const Vec &V_diag_sqrt)
	As above, reusing a factorization of the Coulomb metric V = (P|Q) the caller already has, and sqrt(V_PP) (for screening).
	~SplitRIJ ()
	SplitRIJ (const SplitRIJ &)=delete
SplitRIJ &	operator= (const SplitRIJ &)=delete
	SplitRIJ (SplitRIJ &&) noexcept
SplitRIJ &	operator= (SplitRIJ &&) noexcept
Mat	coulomb (const MolecularOrbitals &mo) const
	Compute Coulomb matrix from molecular orbitals.
Mat	coulomb_from_density (const Mat &D) const
	Compute Coulomb matrix from density matrix directly.
Mat3N	three_center_gradient (const Mat &D, Vec *fitted=nullptr) const
	Nuclear gradient (3 x natom) of d^T g, g_P = sum_mn (mn|P) D_mn, at fixed fitted coefficients d = V^-1 g (the 3-centre part of the RI-J energy gradient; the metric part is d^T dV d).
const gto::AOBasis &	aux_basis () const
	Get the auxiliary basis.
const gto::AOBasis &	ao_basis () const
	Get the AO basis.
size_t	naux () const
	Get number of auxiliary basis functions.
size_t	nbf () const
	Get number of AO basis functions.

Static Public Member Functions
static bool	supports (const gto::AOBasis &ao_basis, const gto::AOBasis &aux_basis)
	Whether the compiled kernels cover these bases (AO l <= 4, auxiliary l <= 6); the constructor throws otherwise.

Detailed Description

Split-RI-J: Coulomb matrix via Hermite Gaussian basis (Neese 2003).

This implementation uses the McMurchie-Davidson (MMD) scheme to work in Hermite Gaussian basis, computing Coulomb matrices without explicitly forming the 3-center integrals (μν|P).

Algorithm (Scheme 4 from Neese 2003): Forward pass:

1. Transform density to Hermite basis: X = E_ab^T × D
2. Contract with R-integrals: Y = R^T × X
3. Transform to aux basis: g = E_c × Y Solve: d = V^{-1} × g Backward pass (reusing same R-integrals):

1. Transform d to Hermite basis: T = E_c^T × d
2. Contract with R-integrals: U = R × T
3. Transform to orbital basis: J = E_ab × U

Reference: Neese, F. (2003). An improvement of the resolution of the identity approximation for the formation of the Coulomb matrix. J. Comput. Chem. 24, 1740-1747.

Constructor & Destructor Documentation

SplitRIJ() [1/4]

occ::qm::SplitRIJ::SplitRIJ	(	const gto::AOBasis &	ao_basis,
		const gto::AOBasis &	aux_basis,
		const ShellPairList &	shellpairs,
		const Mat &	schwarz = Mat() )

Construct Split-RI-J engine.

Parameters

ao_basis	Atomic orbital basis
aux_basis	Auxiliary (density fitting) basis
shellpairs	Significant shell pair list from IntegralEngine
schwarz	Optional Schwarz screening matrix (shell-pair indexed)

SplitRIJ() [2/4]

occ::qm::SplitRIJ::SplitRIJ	(	const gto::AOBasis &	ao_basis,
		const gto::AOBasis &	aux_basis,
		const ShellPairList &	shellpairs,
		const Mat &	schwarz,
		const CoulombMetric &	metric,
		const Vec &	V_diag_sqrt )

As above, reusing a factorization of the Coulomb metric V = (P|Q) the caller already has, and sqrt(V_PP) (for screening).

~SplitRIJ()

occ::qm::SplitRIJ::~SplitRIJ

(

)

SplitRIJ() [3/4]

occ::qm::SplitRIJ::SplitRIJ ( const SplitRIJ & )

delete

SplitRIJ() [4/4]

occ::qm::SplitRIJ::SplitRIJ ( SplitRIJ && )

noexcept

Member Function Documentation

ao_basis()

const gto::AOBasis & occ::qm::SplitRIJ::ao_basis

(

)

const

Get the AO basis.

aux_basis()

const gto::AOBasis & occ::qm::SplitRIJ::aux_basis

(

)

const

Get the auxiliary basis.

coulomb()

Mat occ::qm::SplitRIJ::coulomb

(

const MolecularOrbitals &

mo

)

const

Compute Coulomb matrix from molecular orbitals.

Parameters

mo	Molecular orbitals containing density matrix

Returns

J matrix (nbf × nbf)

coulomb_from_density()

Mat occ::qm::SplitRIJ::coulomb_from_density

(

const Mat &

D

)

const

Compute Coulomb matrix from density matrix directly.

Parameters

D	Density matrix (nbf × nbf)

Returns

J matrix (nbf × nbf)

naux()

size_t occ::qm::SplitRIJ::naux

(

)

const

Get number of auxiliary basis functions.

nbf()

size_t occ::qm::SplitRIJ::nbf

(

)

const

Get number of AO basis functions.

operator=() [1/2]

SplitRIJ & occ::qm::SplitRIJ::operator= ( const SplitRIJ & )

delete

operator=() [2/2]

SplitRIJ & occ::qm::SplitRIJ::operator= ( SplitRIJ && )

noexcept

supports()

bool occ::qm::SplitRIJ::supports ( const gto::AOBasis & ao_basis, const gto::AOBasis & aux_basis )

static

Whether the compiled kernels cover these bases (AO l <= 4, auxiliary l <= 6); the constructor throws otherwise.

three_center_gradient()

Mat3N occ::qm::SplitRIJ::three_center_gradient	(	const Mat &	D,
		Vec *	fitted = nullptr ) const

Nuclear gradient (3 x natom) of d^T g, g_P = sum_mn (mn|P) D_mn, at fixed fitted coefficients d = V^-1 g (the 3-centre part of the RI-J energy gradient; the metric part is d^T dV d).

D is the density whose g is fitted (off-diagonal elements counted once each way, as in J).

Parameters

fitted

if given, receives d

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

• /home/runner/work/occ/occ/include/occ/qm/split_ri_j.h