Calculation of contracted, spherical Gaussian integrals using the solid harmonic Gaussian (SHG) integral scheme. Routines for the following two-center integrals: i) (a|O(r12)|b) where O(r12) is the overlap, coulomb operator etc. ii) (aba) and (abb) s-overlaps. More...

Functions/Subroutines
subroutine, public	int_operators_r12_ab_shg (r12_operator, vab, dvab, rab, fba, fbb, scona_shg, sconb_shg, omega, calculate_forces)
	Calcululates the two-center integrals of the type (a\|O(r12)\|b) using the SHG scheme.

subroutine, public	int_overlap_ab_shg (vab, dvab, rab, fba, fbb, scona_shg, sconb_shg, calculate_forces)
	calculate overlap integrals (a,b)

subroutine, public	int_ra2m_ab_shg (vab, dvab, rab, fba, fbb, scon_ra2m, sconb_shg, m, calculate_forces)
	Calcululates the two-center integrals of the type (a\|(r-Ra)^(2m)\|b) using the SHG scheme.

subroutine, public	int_overlap_aba_shg (saba, dsaba, rab, oba, obb, fba, scon_obb, scona_mix, oba_index, fba_index, cg_coeff, cg_none0_list, ncg_none0, calculate_forces)
	calculate integrals (a,b,fa)

subroutine, public	int_overlap_abb_shg (sabb, dsabb, rab, oba, obb, fbb, scon_oba, sconb_mix, obb_index, fbb_index, cg_coeff, cg_none0_list, ncg_none0, calculate_forces)
	calculate integrals (a,b,fb)

subroutine, public	int_overlap_ab_shg_low (sab, dsab, rab, fba, fbb, scona_shg, sconb_shg, waux_mat, dwaux_mat, calculate_ints, calculate_forces, contraction_high)
	calculate overlap integrals (a,b); requires angular-dependent part as input

subroutine, public	int_ra2m_ab_shg_low (vab, dvab, rab, fba, fbb, sconb_shg, scon_ra2m, m, waux_mat, dwaux_mat, calculate_forces)
	calculate integrals (a\|ra^2m)\|b); requires angular-dependent part as input

subroutine, public	int_overlap_abb_shg_low (abbint, dabbint, rab, oba, obb, fbb, scon_oba, sconb_mix, obb_index, fbb_index, cg_coeff, cg_none0_list, ncg_none0, waux_mat, dwaux_mat, calculate_ints, calculate_forces)
	calculate integrals (a,b,fb); requires angular-dependent part as input

subroutine, public	get_abb_same_kind (abbint, dabbint, abaint, dabdaint, rab, oba, fba, calculate_ints, calculate_forces)
	obtain integrals (a,b,fb) by symmetry relations from (a,b,fa) if basis sets at a and b are of the same kind, i.e. a and b are same atom type

subroutine, public	int_overlap_aba_shg_low (abaint, dabdaint, rab, oba, obb, fba, scon_obb, scona_mix, oba_index, fba_index, cg_coeff, cg_none0_list, ncg_none0, waux_mat, dwaux_mat, calculate_ints, calculate_forces)
	calculate integrals (a,b,fa); requires angular-dependent part as input

subroutine, public	lri_precalc_angular_shg_part (oba, obb, fba, fbb, rab, waux_mat, dwaux_mat, calculate_forces)
	precalculates the angular part of the SHG integrals for the matrices (fa,fb), (a,b), (a,b,fa) and (b,fb,a); the same Waux_mat can then be used for all for integrals; specific for LRIGPW

Detailed Description

Calculation of contracted, spherical Gaussian integrals using the solid harmonic Gaussian (SHG) integral scheme. Routines for the following two-center integrals: i) (a|O(r12)|b) where O(r12) is the overlap, coulomb operator etc. ii) (aba) and (abb) s-overlaps.

Literature: T.J. Giese and D. M. York, J. Chem. Phys, 128, 064104 (2008) T. Helgaker, P Joergensen, J. Olsen, Molecular Electronic-Structure Theory, Wiley

History: created [05.2016]

Author: Dorothea Golze

Function/Subroutine Documentation

◆ int_operators_r12_ab_shg()

subroutine, public generic_shg_integrals::int_operators_r12_ab_shg	(	integer, intent(in)	r12_operator,
		real(kind=dp), dimension(:, :), intent(inout)	vab,
		real(kind=dp), dimension(:, :, :), intent(inout), optional	dvab,
		real(kind=dp), dimension(3), intent(in)	rab,
		type(gto_basis_set_type), pointer	fba,
		type(gto_basis_set_type), pointer	fbb,
		real(kind=dp), dimension(:, :, :), pointer	scona_shg,
		real(kind=dp), dimension(:, :, :), pointer	sconb_shg,
		real(kind=dp), intent(in), optional	omega,
		logical, intent(in)	calculate_forces
	)

Calcululates the two-center integrals of the type (a|O(r12)|b) using the SHG scheme.

Parameters

r12_operator	the integral operator, which depends on r12=\|r1-r2\|
vab	integral matrix of spherical contracted Gaussian functions
dvab	derivative of the integrals
rab	distance vector between center A and B
fba	basis at center A
fbb	basis at center B
scona_shg	SHG contraction matrix for A
sconb_shg	SHG contraction matrix for B
omega	parameter in the operator
calculate_forces	...

Definition at line 98 of file generic_shg_integrals.F.

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◆ int_overlap_ab_shg()

subroutine, public generic_shg_integrals::int_overlap_ab_shg	(	real(kind=dp), dimension(:, :), intent(inout), allocatable	vab,
		real(kind=dp), dimension(:, :, :), intent(inout), allocatable	dvab,
		real(kind=dp), dimension(3), intent(in)	rab,
		type(gto_basis_set_type), pointer	fba,
		type(gto_basis_set_type), pointer	fbb,
		real(kind=dp), dimension(:, :, :), intent(in)	scona_shg,
		real(kind=dp), dimension(:, :, :), intent(in)	sconb_shg,
		logical, intent(in)	calculate_forces
	)

calculate overlap integrals (a,b)

Parameters

vab	integral (a,b)
dvab	derivative of sab
rab	distance vector
fba	basis at center A
fbb	basis at center B
scona_shg	contraction matrix A
sconb_shg	contraxtion matrix B
calculate_forces	...

Definition at line 163 of file generic_shg_integrals.F.

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◆ int_ra2m_ab_shg()

subroutine, public generic_shg_integrals::int_ra2m_ab_shg	(	real(kind=dp), dimension(:, :), intent(inout)	vab,
		real(kind=dp), dimension(:, :, :), intent(inout)	dvab,
		real(kind=dp), dimension(3), intent(in)	rab,
		type(gto_basis_set_type), pointer	fba,
		type(gto_basis_set_type), pointer	fbb,
		real(kind=dp), dimension(:, :, :, :), intent(in)	scon_ra2m,
		real(kind=dp), dimension(:, :, :), intent(in)	sconb_shg,
		integer, intent(in)	m,
		logical, intent(in)	calculate_forces
	)

Calcululates the two-center integrals of the type (a|(r-Ra)^(2m)|b) using the SHG scheme.

Parameters

vab	integral matrix of spherical contracted Gaussian functions
dvab	derivative of the integrals
rab	distance vector between center A and B
fba	basis at center A
fbb	basis at center B
scon_ra2m	contraction matrix for A including the combinatorial factors
sconb_shg	SHG contraction matrix for B
m	exponent in (r-Ra)^(2m) operator
calculate_forces	...

Definition at line 203 of file generic_shg_integrals.F.

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◆ int_overlap_aba_shg()

subroutine, public generic_shg_integrals::int_overlap_aba_shg	(	real(kind=dp), dimension(:, :, :), intent(inout), allocatable	saba,
		real(kind=dp), dimension(:, :, :, :), intent(inout), allocatable	dsaba,
		real(kind=dp), dimension(3), intent(in)	rab,
		type(gto_basis_set_type), pointer	oba,
		type(gto_basis_set_type), pointer	obb,
		type(gto_basis_set_type), pointer	fba,
		real(kind=dp), dimension(:, :, :), intent(in)	scon_obb,
		real(kind=dp), dimension(:, :, :, :), intent(in)	scona_mix,
		integer, dimension(:, :, :), intent(in)	oba_index,
		integer, dimension(:, :, :), intent(in)	fba_index,
		real(kind=dp), dimension(:, :, :), intent(in)	cg_coeff,
		integer, dimension(:, :, :), intent(in)	cg_none0_list,
		integer, dimension(:, :), intent(in)	ncg_none0,
		logical, intent(in)	calculate_forces
	)

calculate integrals (a,b,fa)

Parameters

saba	integral [aba]
dsaba	derivative of [aba]
rab	distance vector between A and B
oba	orbital basis at center A
obb	orbital basis at center B
fba	auxiliary basis set at center A
scon_obb	contraction matrix for orb bas on B
scona_mix	mixed contraction matrix orb + ri basis on A
oba_index	orbital basis index for scona_mix
fba_index	ri basis index for scona_mix
cg_coeff	Clebsch-Gordon coefficients
cg_none0_list	list of none-zero Clebsch-Gordon coefficients
ncg_none0	number of non-zero Clebsch-Gordon coefficients
calculate_forces	...

Definition at line 247 of file generic_shg_integrals.F.

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◆ int_overlap_abb_shg()

subroutine, public generic_shg_integrals::int_overlap_abb_shg	(	real(kind=dp), dimension(:, :, :), intent(inout), allocatable	sabb,
		real(kind=dp), dimension(:, :, :, :), intent(inout), allocatable	dsabb,
		real(kind=dp), dimension(3), intent(in)	rab,
		type(gto_basis_set_type), pointer	oba,
		type(gto_basis_set_type), pointer	obb,
		type(gto_basis_set_type), pointer	fbb,
		real(kind=dp), dimension(:, :, :), intent(in)	scon_oba,
		real(kind=dp), dimension(:, :, :, :), intent(in)	sconb_mix,
		integer, dimension(:, :, :), intent(in)	obb_index,
		integer, dimension(:, :, :), intent(in)	fbb_index,
		real(kind=dp), dimension(:, :, :), intent(in)	cg_coeff,
		integer, dimension(:, :, :), intent(in)	cg_none0_list,
		integer, dimension(:, :), intent(in)	ncg_none0,
		logical, intent(in)	calculate_forces
	)

calculate integrals (a,b,fb)

Parameters

sabb	integral [abb]
dsabb	derivative of [abb]
rab	distance vector between A and B
oba	orbital basis at center A
obb	orbital basis at center B
fbb	auxiliary basis set at center B
scon_oba	contraction matrix for orb bas on A
sconb_mix	mixed contraction matrix orb + ri basis on B
obb_index	orbital basis index for sconb_mix
fbb_index	ri basis index for sconb_mix
cg_coeff	Clebsch-Gordon coefficients
cg_none0_list	list of none-zero Clebsch-Gordon coefficients
ncg_none0	number of non-zero Clebsch-Gordon coefficients
calculate_forces	...

Definition at line 303 of file generic_shg_integrals.F.

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◆ int_overlap_ab_shg_low()

subroutine, public generic_shg_integrals::int_overlap_ab_shg_low	(	real(kind=dp), dimension(:, :), intent(inout), allocatable	sab,
		real(kind=dp), dimension(:, :, :), intent(inout), allocatable	dsab,
		real(kind=dp), dimension(3), intent(in)	rab,
		type(gto_basis_set_type), pointer	fba,
		type(gto_basis_set_type), pointer	fbb,
		real(kind=dp), dimension(:, :, :), intent(in)	scona_shg,
		real(kind=dp), dimension(:, :, :), intent(in)	sconb_shg,
		real(kind=dp), dimension(:, :, :), intent(in)	waux_mat,
		real(kind=dp), dimension(:, :, :, :), intent(in)	dwaux_mat,
		logical, intent(in)	calculate_ints,
		logical, intent(in)	calculate_forces,
		logical, intent(in), optional	contraction_high
	)

calculate overlap integrals (a,b); requires angular-dependent part as input

Parameters

sab	integral (a,b)
dsab	derivative of sab
rab	distance vector
fba	basis at center A
fbb	basis at center B
scona_shg	contraction matrix A
sconb_shg	contraxtion matrix B
Waux_mat	W matrix that contains the angular-dependent part
dWaux_mat	derivative of the W matrix
calculate_ints	...
calculate_forces	...
contraction_high	...

Definition at line 524 of file generic_shg_integrals.F.

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◆ int_ra2m_ab_shg_low()

subroutine, public generic_shg_integrals::int_ra2m_ab_shg_low	(	real(kind=dp), dimension(:, :), intent(inout)	vab,
		real(kind=dp), dimension(:, :, :), intent(inout)	dvab,
		real(kind=dp), dimension(3), intent(in)	rab,
		type(gto_basis_set_type), pointer	fba,
		type(gto_basis_set_type), pointer	fbb,
		real(kind=dp), dimension(:, :, :), intent(in)	sconb_shg,
		real(kind=dp), dimension(:, :, :, :), intent(in)	scon_ra2m,
		integer, intent(in)	m,
		real(kind=dp), dimension(:, :, :), intent(in)	waux_mat,
		real(kind=dp), dimension(:, :, :, :), intent(in)	dwaux_mat,
		logical, intent(in)	calculate_forces
	)

calculate integrals (a|ra^2m)|b); requires angular-dependent part as input

Parameters

vab	integral matrix of spherical contracted Gaussian functions
dvab	derivative of the integrals
rab	distance vector between center A and B
fba	basis at center A
fbb	basis at center B
sconb_shg	SHG contraction matrix for B
scon_ra2m	contraction matrix for A including the combinatorial factors
m	exponent in (r-Ra)^(2m) operator
Waux_mat	W matrix that contains the angular-dependent part
dWaux_mat	derivative of the W matrix
calculate_forces	...

Definition at line 652 of file generic_shg_integrals.F.

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◆ int_overlap_abb_shg_low()

subroutine, public generic_shg_integrals::int_overlap_abb_shg_low	(	real(kind=dp), dimension(:, :, :), intent(inout), allocatable	abbint,
		real(kind=dp), dimension(:, :, :, :), intent(inout), allocatable	dabbint,
		real(kind=dp), dimension(3), intent(in)	rab,
		type(gto_basis_set_type), pointer	oba,
		type(gto_basis_set_type), pointer	obb,
		type(gto_basis_set_type), pointer	fbb,
		real(kind=dp), dimension(:, :, :), intent(in)	scon_oba,
		real(kind=dp), dimension(:, :, :, :), intent(in)	sconb_mix,
		integer, dimension(:, :, :), intent(in)	obb_index,
		integer, dimension(:, :, :), intent(in)	fbb_index,
		real(kind=dp), dimension(:, :, :), intent(in)	cg_coeff,
		integer, dimension(:, :, :), intent(in)	cg_none0_list,
		integer, dimension(:, :), intent(in)	ncg_none0,
		real(kind=dp), dimension(:, :, :), intent(in)	waux_mat,
		real(kind=dp), dimension(:, :, :, :), intent(in)	dwaux_mat,
		logical, intent(in)	calculate_ints,
		logical, intent(in)	calculate_forces
	)

calculate integrals (a,b,fb); requires angular-dependent part as input

Parameters

abbint	integral (a,b,fb)
dabbint	derivative of abbint
rab	distance vector between A and B
oba	orbital basis at center A
obb	orbital basis at center B
fbb	auxiliary basis set at center B
scon_oba	contraction matrix for orb bas on A
sconb_mix	mixed contraction matrix orb + ri basis on B
obb_index	orbital basis index for sconb_mix
fbb_index	ri basis index for sconb_mix
cg_coeff	Clebsch-Gordon coefficients
cg_none0_list	list of none-zero Clebsch-Gordon coefficients
ncg_none0	number of non-zero Clebsch-Gordon coefficients
Waux_mat	W matrix that contains the angular-dependent part
dWaux_mat	derivative of the W matrix
calculate_ints	...
calculate_forces	...

Definition at line 769 of file generic_shg_integrals.F.

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◆ get_abb_same_kind()

subroutine, public generic_shg_integrals::get_abb_same_kind	(	real(kind=dp), dimension(:, :, :), intent(inout), allocatable	abbint,
		real(kind=dp), dimension(:, :, :, :), intent(inout), allocatable	dabbint,
		real(kind=dp), dimension(:, :, :), intent(inout), allocatable	abaint,
		real(kind=dp), dimension(:, :, :, :), intent(inout), allocatable	dabdaint,
		real(kind=dp), dimension(3), intent(in)	rab,
		type(gto_basis_set_type), pointer	oba,
		type(gto_basis_set_type), pointer	fba,
		logical, intent(in)	calculate_ints,
		logical, intent(in)	calculate_forces
	)

obtain integrals (a,b,fb) by symmetry relations from (a,b,fa) if basis sets at a and b are of the same kind, i.e. a and b are same atom type

Parameters

abbint	integral (a,b,fb)
dabbint	derivative of abbint
abaint	integral (a,b,fa)
dabdaint	derivative of abaint
rab	distance vector between A and B
oba	orbital basis at center A
fba	auxiliary basis set at center A
calculate_ints	...
calculate_forces	...

Definition at line 933 of file generic_shg_integrals.F.

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◆ int_overlap_aba_shg_low()

subroutine, public generic_shg_integrals::int_overlap_aba_shg_low	(	real(kind=dp), dimension(:, :, :), intent(inout), allocatable	abaint,
		real(kind=dp), dimension(:, :, :, :), intent(inout), allocatable	dabdaint,
		real(kind=dp), dimension(3), intent(in)	rab,
		type(gto_basis_set_type), pointer	oba,
		type(gto_basis_set_type), pointer	obb,
		type(gto_basis_set_type), pointer	fba,
		real(kind=dp), dimension(:, :, :), intent(in)	scon_obb,
		real(kind=dp), dimension(:, :, :, :), intent(in)	scona_mix,
		integer, dimension(:, :, :), intent(in)	oba_index,
		integer, dimension(:, :, :), intent(in)	fba_index,
		real(kind=dp), dimension(:, :, :), intent(in)	cg_coeff,
		integer, dimension(:, :, :), intent(in)	cg_none0_list,
		integer, dimension(:, :), intent(in)	ncg_none0,
		real(kind=dp), dimension(:, :, :), intent(in)	waux_mat,
		real(kind=dp), dimension(:, :, :, :), intent(in)	dwaux_mat,
		logical, intent(in)	calculate_ints,
		logical, intent(in)	calculate_forces
	)

calculate integrals (a,b,fa); requires angular-dependent part as input

Parameters

abaint	integral (a,b,fa)
dabdaint	...
rab	distance vector between A and B
oba	orbital basis at center A
obb	orbital basis at center B
fba	auxiliary basis set at center A
scon_obb	contraction matrix for orb bas on B
scona_mix	mixed contraction matrix orb + ri basis on A
oba_index	orbital basis index for scona_mix
fba_index	ri basis index for scona_mix
cg_coeff	Clebsch-Gordon coefficients
cg_none0_list	list of none-zero Clebsch-Gordon coefficients
ncg_none0	number of non-zero Clebsch-Gordon coefficients
Waux_mat	W matrix that contains the angular-dependent part
dWaux_mat	derivative of the W matrix
calculate_ints	...
calculate_forces	...

Definition at line 1075 of file generic_shg_integrals.F.

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◆ lri_precalc_angular_shg_part()

subroutine, public generic_shg_integrals::lri_precalc_angular_shg_part	(	type(gto_basis_set_type), pointer	oba,
		type(gto_basis_set_type), pointer	obb,
		type(gto_basis_set_type), pointer	fba,
		type(gto_basis_set_type), pointer	fbb,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), dimension(:, :, :), intent(out), allocatable	waux_mat,
		real(kind=dp), dimension(:, :, :, :), intent(out), allocatable	dwaux_mat,
		logical, intent(in)	calculate_forces
	)

precalculates the angular part of the SHG integrals for the matrices (fa,fb), (a,b), (a,b,fa) and (b,fb,a); the same Waux_mat can then be used for all for integrals; specific for LRIGPW

Parameters

oba	orbital basis on a
obb	orbital basis on b
fba	aux basis on a
fbb	aux basis on b
rab	distance vector between a and b
Waux_mat	W matrix that contains the angular-dependent part
dWaux_mat	derivative of the W matrix
calculate_forces	...

Definition at line 1241 of file generic_shg_integrals.F.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ int_operators_r12_ab_shg()

◆ int_overlap_ab_shg()

◆ int_ra2m_ab_shg()

◆ int_overlap_aba_shg()

◆ int_overlap_abb_shg()

◆ int_overlap_ab_shg_low()

◆ int_ra2m_ab_shg_low()

◆ int_overlap_abb_shg_low()

◆ get_abb_same_kind()

◆ int_overlap_aba_shg_low()

◆ lri_precalc_angular_shg_part()