s_contract_shg Module Reference

Routines for calculating the s-integrals and their scalar derivatives with respect to rab2 over solid harmonic Gaussian (SHG) functions + contraction routines for these integrals i) (s|O(r12)|s) where O(r12) is the overlap, coulomb operator etc. ii) (aba) and (abb) s-overlaps. More...

Functions/Subroutines
subroutine, public	s_overlap_ab (la_max, npgfa, zeta, lb_max, npgfb, zetb, rab, s, calculate_forces)
	calculates the uncontracted, not normalized [s|s] overlap
subroutine, public	s_overlap_abb (la_max, npgfa, zeta, lb_max, npgfb, zetb, lcb_max, npgfcb, zetcb, rab, s, calculate_forces)
	calculates [s|ra^n|s] integrals for [aba] and the [s|rb^n|s] integrals for [abb]
subroutine, public	s_ra2m_ab (la_max, npgfa, zeta, lb_max, npgfb, zetb, m, rab, s, calculate_forces)
	calculates the uncontracted, not normalized [0a|ra^(2m)|0b] two-center integral, where ra = r-Ra and Ra center of a
subroutine, public	s_coulomb_ab (la_max, npgfa, zeta, lb_max, npgfb, zetb, omega, rab, v, calculate_forces)
	calculates the uncontracted, not normalized [s|1/r12|s] two-center coulomb integral
subroutine, public	s_verf_ab (la_max, npgfa, zeta, lb_max, npgfb, zetb, omega, rab, v, calculate_forces)
	calculates the uncontracted, not normalized [s|1/erf(omega*r12)/r12|s] two-center integral
subroutine, public	s_verfc_ab (la_max, npgfa, zeta, lb_max, npgfb, zetb, omega, rab, v, calculate_forces)
	calculates the uncontracted, not normalized [s|1/erfc(omega*r12)/r12|s] two-center integral
subroutine, public	s_vgauss_ab (la_max, npgfa, zeta, lb_max, npgfb, zetb, omega, rab, v, calculate_forces)
	calculates the uncontracted, not normalized [s|exp(-omega*r12**2)/r12|s] two-center integral
subroutine, public	s_gauss_ab (la_max, npgfa, zeta, lb_max, npgfb, zetb, omega, rab, v, calculate_forces)
	calculates the uncontracted, not normalized [s|exp(-omega*r12**2)|s] two-center integral
subroutine, public	contract_sint_ab_clow (la, npgfa, nshella, scona_shg, lb, npgfb, nshellb, sconb_shg, swork, swork_cont, calculate_forces)
	Contraction and normalization of the [s|O(r12)|s] integrals and their scalar derivatives; this routine is more efficient for uncontracted basis sets (clow), e.g. for ri basis sets.
subroutine, public	contract_sint_ab_chigh (npgfa, nshella, scona, npgfb, nshellb, sconb, nds, swork, swork_cont)
	Contraction and normalization of the [s|O(r12)|s] integrals and their scalar derivatives; this routine is more efficient for highly contracted basis sets (chigh)
subroutine, public	contract_s_ra2m_ab (npgfa, nshella, scon_ra2m, npgfb, nshellb, sconb, swork, swork_cont, m, nds_max)
	Contraction, normalization and combinatiorial combination of the [0a|(r-Ra)^(2m)|0b] integrals and their scalar derivatives.
subroutine, public	contract_s_overlap_abb (la, npgfa, nshella, scona_shg, lb, npgfb, nshellb, lcb, npgfcb, nshellcb, orbb_index, rib_index, sconb_mix, nl_max, nds_max, swork, swork_cont, calculate_forces)
	Contraction and normalization of the (abb) overlap.
subroutine, public	contract_s_overlap_aba (la, npgfa, nshella, lb, npgfb, nshellb, sconb_shg, lca, npgfca, nshellca, orba_index, ria_index, scona_mix, nl_max, nds_max, swork, swork_cont, calculate_forces)
	Contraction and normalization of the (aba) overlap.

Detailed Description

Routines for calculating the s-integrals and their scalar derivatives with respect to rab2 over solid harmonic Gaussian (SHG) functions + contraction routines for these integrals i) (s|O(r12)|s) where O(r12) is the overlap, coulomb operator etc. ii) (aba) and (abb) s-overlaps.

Literature (partly)

T.J. Giese and D. M. York, J. Chem. Phys, 128, 064104 (2008) T. Helgaker, P Joergensen, J. Olsen, Molecular Electronic-Structure Theory, Wiley R. Ahlrichs, PCCP, 8, 3072 (2006)

History

created [05.2016]

Author

Dorothea Golze

Function/Subroutine Documentation

s_overlap_ab()

subroutine, public s_contract_shg::s_overlap_ab	(	integer, intent(in)	la_max,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		integer, intent(in)	lb_max,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), dimension(:, :, :), intent(inout)	s,
		logical, intent(in)	calculate_forces
	)

calculates the uncontracted, not normalized [s|s] overlap

Parameters

la_max	maximal l quantum number on a
npgfa	number of primitive Gaussian on a
zeta	set of exponents on a
lb_max	maximal l quantum number on b
npgfb	number of primitive Gaussian on a
zetb	set of exponents on a
rab	distance vector between a and b
s	uncontracted overlap of s functions
calculate_forces	...

Definition at line 57 of file s_contract_shg.F.

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s_overlap_abb()

subroutine, public s_contract_shg::s_overlap_abb	(	integer, intent(in)	la_max,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		integer, intent(in)	lb_max,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		integer, intent(in)	lcb_max,
		integer, intent(in)	npgfcb,
		real(kind=dp), dimension(:), intent(in)	zetcb,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), dimension(:, :, :, :, :), intent(inout)	s,
		logical, intent(in)	calculate_forces
	)

calculates [s|ra^n|s] integrals for [aba] and the [s|rb^n|s] integrals for [abb]

Parameters

la_max	maximal l quantum number on a, orbital basis
npgfa	number of primitive Gaussian on a, orbital basis
zeta	set of exponents on a, orbital basis
lb_max	maximal l quantum number on b, orbital basis
npgfb	number of primitive Gaussian on a, orbital basis
zetb	set of exponents on b, orbital basis
lcb_max	maximal l quantum number of aux basis on b
npgfcb	number of primitive Gaussian on b. aux basis
zetcb	set of exponents on b, aux basis
rab	distance vector between a and b
s	uncontracted [s|r^n|s] integrals
calculate_forces	...

Definition at line 114 of file s_contract_shg.F.

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s_ra2m_ab()

subroutine, public s_contract_shg::s_ra2m_ab	(	integer, intent(in)	la_max,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		integer, intent(in)	lb_max,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		integer, intent(in)	m,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), dimension(:, :, :, :), intent(inout)	s,
		logical, intent(in)	calculate_forces
	)

calculates the uncontracted, not normalized [0a|ra^(2m)|0b] two-center integral, where ra = r-Ra and Ra center of a

Parameters

la_max	maximal l quantum number on a
npgfa	number of primitive Gaussian on a
zeta	set of exponents on a
lb_max	maximal l quantum number on b
npgfb	number of primitive Gaussian on a
zetb	set of exponents on a
m	exponent of the ra operator
rab	distance vector between a and b
s	...
calculate_forces	...

Definition at line 346 of file s_contract_shg.F.

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s_coulomb_ab()

subroutine, public s_contract_shg::s_coulomb_ab	(	integer, intent(in)	la_max,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		integer, intent(in)	lb_max,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		real(kind=dp), intent(in)	omega,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), dimension(:, :, :), intent(inout)	v,
		logical, intent(in)	calculate_forces
	)

calculates the uncontracted, not normalized [s|1/r12|s] two-center coulomb integral

Parameters

la_max	maximal l quantum number on a
npgfa	number of primitive Gaussian on a
zeta	set of exponents on a
lb_max	maximal l quantum number on b
npgfb	number of primitive Gaussian on a
zetb	set of exponents on a
omega	parameter not needed, but given for the sake of the abstract interface
rab	distance vector between a and b
v	uncontracted coulomb integral of s functions
calculate_forces	...

Definition at line 588 of file s_contract_shg.F.

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s_verf_ab()

subroutine, public s_contract_shg::s_verf_ab	(	integer, intent(in)	la_max,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		integer, intent(in)	lb_max,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		real(kind=dp), intent(in)	omega,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), dimension(:, :, :), intent(inout)	v,
		logical, intent(in)	calculate_forces
	)

calculates the uncontracted, not normalized [s|1/erf(omega*r12)/r12|s] two-center integral

Parameters

la_max	maximal l quantum number on a
npgfa	number of primitive Gaussian on a
zeta	set of exponents on a
lb_max	maximal l quantum number on b
npgfb	number of primitive Gaussian on a
zetb	set of exponents on a
omega	parameter in the operator
rab	distance vector between a and b
v	uncontracted erf(r)/r integral of s functions
calculate_forces	...

Definition at line 648 of file s_contract_shg.F.

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s_verfc_ab()

subroutine, public s_contract_shg::s_verfc_ab	(	integer, intent(in)	la_max,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		integer, intent(in)	lb_max,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		real(kind=dp), intent(in)	omega,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), dimension(:, :, :), intent(inout)	v,
		logical, intent(in)	calculate_forces
	)

calculates the uncontracted, not normalized [s|1/erfc(omega*r12)/r12|s] two-center integral

Parameters

la_max	maximal l quantum number on a
npgfa	number of primitive Gaussian on a
zeta	set of exponents on a
lb_max	maximal l quantum number on b
npgfb	number of primitive Gaussian on a
zetb	set of exponents on a
omega	parameter in the operator
rab	distance vector between a and b
v	uncontracted erf(r)/r integral of s functions
calculate_forces	...

Definition at line 710 of file s_contract_shg.F.

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s_vgauss_ab()

subroutine, public s_contract_shg::s_vgauss_ab	(	integer, intent(in)	la_max,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		integer, intent(in)	lb_max,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		real(kind=dp), intent(in)	omega,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), dimension(:, :, :), intent(inout)	v,
		logical, intent(in)	calculate_forces
	)

calculates the uncontracted, not normalized [s|exp(-omega*r12**2)/r12|s] two-center integral

Parameters

la_max	maximal l quantum number on a
npgfa	number of primitive Gaussian on a
zeta	set of exponents on a
lb_max	maximal l quantum number on b
npgfb	number of primitive Gaussian on a
zetb	set of exponents on a
omega	parameter in the operator
rab	distance vector between a and b
v	uncontracted exp(-omega*r**2)/r integral of s functions
calculate_forces	...

Definition at line 773 of file s_contract_shg.F.

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s_gauss_ab()

subroutine, public s_contract_shg::s_gauss_ab	(	integer, intent(in)	la_max,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		integer, intent(in)	lb_max,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		real(kind=dp), intent(in)	omega,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), dimension(:, :, :), intent(inout)	v,
		logical, intent(in)	calculate_forces
	)

calculates the uncontracted, not normalized [s|exp(-omega*r12**2)|s] two-center integral

Parameters

la_max	maximal l quantum number on a
npgfa	number of primitive Gaussian on a
zeta	set of exponents on a
lb_max	maximal l quantum number on b
npgfb	number of primitive Gaussian on a
zetb	set of exponents on a
omega	parameter in the operator
rab	distance vector between a and b
v	uncontracted exp(-omega*r**2) integral of s functions
calculate_forces	...

Definition at line 842 of file s_contract_shg.F.

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contract_sint_ab_clow()

subroutine, public s_contract_shg::contract_sint_ab_clow	(	integer, dimension(:), intent(in)	la,
		integer, intent(in)	npgfa,
		integer, intent(in)	nshella,
		real(kind=dp), dimension(:, :), intent(in)	scona_shg,
		integer, dimension(:), intent(in)	lb,
		integer, intent(in)	npgfb,
		integer, intent(in)	nshellb,
		real(kind=dp), dimension(:, :), intent(in)	sconb_shg,
		real(kind=dp), dimension(:, :, :), intent(in)	swork,
		real(kind=dp), dimension(:, :, :), intent(inout)	swork_cont,
		logical, intent(in)	calculate_forces
	)

Contraction and normalization of the [s|O(r12)|s] integrals and their scalar derivatives; this routine is more efficient for uncontracted basis sets (clow), e.g. for ri basis sets.

Parameters

la	set of l quantum numbers for a
npgfa	number of primitive Gaussian on a
nshella	number of shells for a
scona_shg	SHG contraction/normalization matrix for a
lb	set of l quantum numbers for b
npgfb	number of primitive Gaussian on b
nshellb	number of shells for b
sconb_shg	SHG contraction/normalization matrix for b
swork	matrix storing the uncontracted and unnormalized s-integrals and derivatives
swork_cont	matrix storing the contracted and normalized s-integrals and derivatives
calculate_forces	...

Definition at line 905 of file s_contract_shg.F.

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contract_sint_ab_chigh()

subroutine, public s_contract_shg::contract_sint_ab_chigh	(	integer, intent(in)	npgfa,
		integer, intent(in)	nshella,
		real(kind=dp), dimension(:, :), intent(in)	scona,
		integer, intent(in)	npgfb,
		integer, intent(in)	nshellb,
		real(kind=dp), dimension(:, :), intent(in)	sconb,
		integer, intent(in)	nds,
		real(kind=dp), dimension(:, :, :), intent(in)	swork,
		real(kind=dp), dimension(:, :, :), intent(inout)	swork_cont
	)

Contraction and normalization of the [s|O(r12)|s] integrals and their scalar derivatives; this routine is more efficient for highly contracted basis sets (chigh)

Parameters

npgfa	number of primitive Gaussian on a
nshella	number of shells for a
scona	SHG contraction/normalization matrix for a
npgfb	number of primitive Gaussian on b
nshellb	number of shells for b
sconb	SHG contraction/normalization matrix for b
nds	maximal derivative of [s|O(r12)|s] with respect to rab2
swork	matrix storing the uncontracted and unnormalized s-integrals and derivatives
swork_cont	matrix storing the contracted and normalized s-integrals and derivatives

Definition at line 959 of file s_contract_shg.F.

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contract_s_ra2m_ab()

subroutine, public s_contract_shg::contract_s_ra2m_ab	(	integer, intent(in)	npgfa,
		integer, intent(in)	nshella,
		real(kind=dp), dimension(:, :, :), intent(in)	scon_ra2m,
		integer, intent(in)	npgfb,
		integer, intent(in)	nshellb,
		real(kind=dp), dimension(:, :), intent(in)	sconb,
		real(kind=dp), dimension(:, :, :, :), intent(inout)	swork,
		real(kind=dp), dimension(:, :, :), intent(inout)	swork_cont,
		integer, intent(in)	m,
		integer, intent(in)	nds_max
	)

Contraction, normalization and combinatiorial combination of the [0a|(r-Ra)^(2m)|0b] integrals and their scalar derivatives.

Parameters

npgfa	number of primitive Gaussian on a
nshella	number of shells for a
scon_ra2m	contraction matrix on a containg the combinatorial factors
npgfb	number of primitive Gaussian on b
nshellb	number of shells for b
sconb	SHG contraction/normalization matrix for b
swork	matrix storing the uncontracted and unnormalized s-integrals and derivatives
swork_cont	matrix storing the contracted and normalized s-integrals and derivatives
m	exponent in operator (r-Ra)^(2m)
nds_max	maximal derivative with respect to rab2

Definition at line 999 of file s_contract_shg.F.

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contract_s_overlap_abb()

subroutine, public s_contract_shg::contract_s_overlap_abb	(	integer, dimension(:), intent(in)	la,
		integer, intent(in)	npgfa,
		integer, intent(in)	nshella,
		real(kind=dp), dimension(:, :), intent(in)	scona_shg,
		integer, dimension(:), intent(in)	lb,
		integer, intent(in)	npgfb,
		integer, intent(in)	nshellb,
		integer, dimension(:), intent(in)	lcb,
		integer, intent(in)	npgfcb,
		integer, intent(in)	nshellcb,
		integer, dimension(:, :), intent(in)	orbb_index,
		integer, dimension(:, :), intent(in)	rib_index,
		real(kind=dp), dimension(:, :, :, :), intent(in)	sconb_mix,
		integer, intent(in)	nl_max,
		integer, intent(in)	nds_max,
		real(kind=dp), dimension(:, :, :, :, :), intent(in)	swork,
		real(kind=dp), dimension(:, 0:, :, :, :), intent(inout)	swork_cont,
		logical, intent(in)	calculate_forces
	)

Contraction and normalization of the (abb) overlap.

Parameters

la	set of l quantum numbers on a
npgfa	number of primitive Gaussians functions on a; orbital basis
nshella	number of shells for a; orbital basis
scona_shg	SHG contraction/normalization matrix for a; orbital basis
lb	set of l quantum numbers on b; orbital basis
npgfb	number of primitive Gaussians functions on b; orbital basis
nshellb	number of shells for b; orbital basis
lcb	set of l quantum numbers on b; ri basis
npgfcb	number of primitive Gaussians functions on b; ri basis
nshellcb	number of shells for b; ri basis
orbb_index	index for orbital basis at B for sconb_mix
rib_index	index for ri basis at B for sconb_mix
sconb_mix	mixed contraction matrix for orbital and ri basis at B
nl_max	related to the parameter m in (a|rb^(2m)|b)
nds_max	derivative with respect to rab**2
swork	matrix of storing the uncontracted and unnormalized s-integrals and derivatives
swork_cont	matrix storing the contracted and normalized s-integrals and derivatives
calculate_forces	...

Definition at line 1050 of file s_contract_shg.F.

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contract_s_overlap_aba()

subroutine, public s_contract_shg::contract_s_overlap_aba	(	integer, dimension(:), intent(in)	la,
		integer, intent(in)	npgfa,
		integer, intent(in)	nshella,
		integer, dimension(:), intent(in)	lb,
		integer, intent(in)	npgfb,
		integer, intent(in)	nshellb,
		real(kind=dp), dimension(:, :), intent(in)	sconb_shg,
		integer, dimension(:), intent(in)	lca,
		integer, intent(in)	npgfca,
		integer, intent(in)	nshellca,
		integer, dimension(:, :), intent(in)	orba_index,
		integer, dimension(:, :), intent(in)	ria_index,
		real(kind=dp), dimension(:, :, :, :), intent(in)	scona_mix,
		integer, intent(in)	nl_max,
		integer, intent(in)	nds_max,
		real(kind=dp), dimension(:, :, :, :, :), intent(in)	swork,
		real(kind=dp), dimension(:, 0:, :, :, :), intent(inout)	swork_cont,
		logical, intent(in)	calculate_forces
	)

Contraction and normalization of the (aba) overlap.

Parameters

la	set of l quantum numbers on a; orbital basis
npgfa	number of primitive Gaussians functions on a; orbital basis
nshella	number of shells for a; orbital basis
lb	set of l quantum numbers on b; orbital basis
npgfb	number of primitive Gaussians functions on b; orbital basis
nshellb	number of shells for b; orbital basis
sconb_shg	SHG contraction/normalization matrix for b; orbital basis
lca	set of l quantum numbers on a; ri basis
npgfca	number of primitive Gaussians functions on a; ri basis
nshellca	number of shells for a; ri basis
orba_index	index for orbital basis at A for scona_mix
ria_index	index for ri basis at A for scona_mix
scona_mix	mixed contraction matrix for orbital and ri basis at A
nl_max	related to the parameter m in (a|ra^(2m)|b)
nds_max	maximal derivative with respect to rab**2
swork	matrix of storing the uncontracted and unnormalized s-integrals and derivatives
swork_cont	matrix storing the contracted and normalized s-integrals and derivatives
calculate_forces	...

Definition at line 1139 of file s_contract_shg.F.

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