Calculation of the moment integrals over Cartesian Gaussian-type functions. More...

Functions/Subroutines
subroutine, public	contract_expikr (cos_block, sin_block, iatom, ncoa, nsgfa, sgfa, sphi_a, ldsa, jatom, ncob, nsgfb, sgfb, sphi_b, ldsb, expab, work, ldwork, ordered)
	Contract complex primitive integrals into real cosine and sine AO blocks.
subroutine, public	expikr (la_max_set, npgfa, zeta, rpgfa, la_min_set, lb_max, npgfb, zetb, rpgfb, lb_min, rac, rbc, kvec, expab, dexpab, dexpba, momentab)
	Evaluate primitive exp(i k.r) integrals through the complex overlap recurrence.
subroutine, public	moment (la_max, npgfa, zeta, rpgfa, la_min, lb_max, npgfb, zetb, rpgfb, lc_max, rac, rbc, mab, overlap)
	...
subroutine, public	diff_momop (la_max, npgfa, zeta, rpgfa, la_min, lb_max, npgfb, zetb, rpgfb, lb_min, order, rac, rbc, difmab, mab_ext, deltar, lambda, iatom, jatom)
	This returns the derivative of the moment integrals [a\|\mu\|b]. By default, it differentiates the primitive on the right: [a\|\mu\|d/dR_bi] = 2zetb[a\|\mu\|b+1i] - Ni(b)[a\|\mu\|b-1i] A weighted derivative combines the left and right primitive derivatives using deltaR for the corresponding atom centers. order indicates the max order of the moment operator to be calculated 1: dipole 2: quadrupole ...
subroutine, public	dipole_force (la_max, npgfa, zeta, rpgfa, la_min, lb_max, npgfb, zetb, rpgfb, lb_min, order, rac, rbc, pab, forcea, forceb)
	This returns the derivative of the dipole integrals [a\|x\|b], with respect to the position of the primitive on the left and right, i.e. [da/dR_ai\|\mu\|b] = 2zeta[a+1i\|\mu\|b] - Ni(a)[a-1i\|\mu\|b].

Detailed Description

Calculation of the moment integrals over Cartesian Gaussian-type functions.

Literature: S. Obara and A. Saika, J. Chem. Phys. 84, 3963 (1986)

History: none

Author: J. Hutter (16.02.2005)

Function/Subroutine Documentation

◆ contract_expikr()

subroutine, public ai_moments::contract_expikr	(	real(dp), dimension(:, :), pointer	cos_block,
		real(dp), dimension(:, :), pointer	sin_block,
		integer, intent(in)	iatom,
		integer, intent(in)	ncoa,
		integer, intent(in)	nsgfa,
		integer, intent(in)	sgfa,
		real(dp), dimension(:, :), intent(in)	sphi_a,
		integer, intent(in)	ldsa,
		integer, intent(in)	jatom,
		integer, intent(in)	ncob,
		integer, intent(in)	nsgfb,
		integer, intent(in)	sgfb,
		real(dp), dimension(:, :), intent(in)	sphi_b,
		integer, intent(in)	ldsb,
		complex(dp), dimension(:, :), intent(in)	expab,
		real(dp), dimension(:, :)	work,
		integer, intent(in)	ldwork,
		logical, intent(in), optional	ordered )

Contract complex primitive integrals into real cosine and sine AO blocks.

Parameters

cos_block	...
sin_block	...
iatom	...
ncoa	...
nsgfa	...
sgfa	...
sphi_a	...
ldsa	...
jatom	...
ncob	...
nsgfb	...
sgfb	...
sphi_b	...
ldsb	...
expab	complex primitive plane-wave integrals
work	...
ldwork	...
ordered	retain the ordered atom pair instead of mapping to an upper block

Definition at line 76 of file ai_moments.F.

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◆ expikr()

subroutine, public ai_moments::expikr	(	integer, intent(in)	la_max_set,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		real(kind=dp), dimension(:), intent(in)	rpgfa,
		integer, intent(in)	la_min_set,
		integer, intent(in)	lb_max,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		real(kind=dp), dimension(:), intent(in)	rpgfb,
		integer, intent(in)	lb_min,
		real(kind=dp), dimension(3), intent(in)	rac,
		real(kind=dp), dimension(3), intent(in)	rbc,
		real(kind=dp), dimension(3), intent(in)	kvec,
		complex(kind=dp), dimension(:, :), intent(inout)	expab,
		complex(kind=dp), dimension(:, :, :), intent(inout), optional, target	dexpab,
		complex(kind=dp), dimension(:, :, :), intent(inout), optional, target	dexpba,
		complex(kind=dp), dimension(:, :, :), intent(inout), optional, target	momentab )

Evaluate primitive exp(i k.r) integrals through the complex overlap recurrence.

Parameters

la_max_set	highest bra shell
npgfa	number of bra primitives
zeta	bra Gaussian exponents
rpgfa	bra primitive radii
la_min_set	lowest bra shell
lb_max	highest ket shell
npgfb	number of ket primitives
zetb	ket Gaussian exponents
rpgfb	ket primitive radii
lb_min	lowest ket shell
rac	bra-center coordinates relative to the phase origin
rbc	ket-center coordinates relative to the phase origin
kvec	plane-wave vector
expab	primitive integrals in the full Cartesian layout, zero below the requested shells
dexpab	optional bra-center derivatives with the plane-wave operator held fixed
dexpba	optional ket-center derivatives in the same bra/ket layout
momentab	optional coordinate-weighted integrals relative to the phase origin Derivative and moment outputs cover the full Cartesian range.

Definition at line 161 of file ai_moments.F.

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◆ moment()

subroutine, public ai_moments::moment	(	integer, intent(in)	la_max,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		real(kind=dp), dimension(:), intent(in)	rpgfa,
		integer, intent(in)	la_min,
		integer, intent(in)	lb_max,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		real(kind=dp), dimension(:), intent(in)	rpgfb,
		integer, intent(in)	lc_max,
		real(kind=dp), dimension(3), intent(in)	rac,
		real(kind=dp), dimension(3), intent(in)	rbc,
		real(kind=dp), dimension(:, :, :), intent(inout)	mab,
		real(kind=dp), dimension(:, :), intent(inout), optional	overlap )

...

Parameters

la_max	...
npgfa	...
zeta	...
rpgfa	...
la_min	...
lb_max	...
npgfb	...
zetb	...
rpgfb	...
lc_max	...
rac	...
rbc	...
mab	...
overlap	optional zeroth moment in primitive-major cumulative Cartesian order; entries outside the requested row and column ranges are untouched

Definition at line 287 of file ai_moments.F.

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◆ diff_momop()

subroutine, public ai_moments::diff_momop	(	integer, intent(in)	la_max,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		real(kind=dp), dimension(:), intent(in)	rpgfa,
		integer, intent(in)	la_min,
		integer, intent(in)	lb_max,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		real(kind=dp), dimension(:), intent(in)	rpgfb,
		integer, intent(in)	lb_min,
		integer, intent(in)	order,
		real(kind=dp), dimension(3), intent(in)	rac,
		real(kind=dp), dimension(3), intent(in)	rbc,
		real(kind=dp), dimension(:, :, :, :), intent(out)	difmab,
		real(kind=dp), dimension(:, :, :), optional, pointer	mab_ext,
		real(kind=dp), dimension(:, :), optional, pointer	deltar,
		integer, intent(in), optional	lambda,
		integer, intent(in), optional	iatom,
		integer, intent(in), optional	jatom )

This returns the derivative of the moment integrals [a|\mu|b]. By default, it differentiates the primitive on the right: [a|\mu|d/dR_bi] = 2*zetb*[a|\mu|b+1i] - Ni(b)[a|\mu|b-1i] A weighted derivative combines the left and right primitive derivatives using deltaR for the corresponding atom centers. order indicates the max order of the moment operator to be calculated 1: dipole 2: quadrupole ...

Parameters

la_max	...
npgfa	...
zeta	...
rpgfa	...
la_min	...
lb_max	...
npgfb	...
zetb	...
rpgfb	...
lb_min	...
order	...
rac	...
rbc	...
difmab	...
mab_ext	optional precomputed moments with zero screened primitive blocks, including raised shells
deltaR	optional weights for the left and right primitive derivatives
lambda	optional atom selector for the factor (iatom == lambda) - (jatom == lambda)
iatom	atom associated with the left basis function
jatom	atom associated with the right basis function

Note

Definition at line 387 of file ai_moments.F.

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◆ dipole_force()

subroutine, public ai_moments::dipole_force	(	integer, intent(in)	la_max,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		real(kind=dp), dimension(:), intent(in)	rpgfa,
		integer, intent(in)	la_min,
		integer, intent(in)	lb_max,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		real(kind=dp), dimension(:), intent(in)	rpgfb,
		integer, intent(in)	lb_min,
		integer, intent(in)	order,
		real(kind=dp), dimension(3), intent(in)	rac,
		real(kind=dp), dimension(3), intent(in)	rbc,
		real(kind=dp), dimension(:, :), intent(in)	pab,
		real(kind=dp), dimension(:, :), intent(inout), target	forcea,
		real(kind=dp), dimension(:, :), intent(inout), target	forceb )

This returns the derivative of the dipole integrals [a|x|b], with respect to the position of the primitive on the left and right, i.e. [da/dR_ai|\mu|b] = 2*zeta*[a+1i|\mu|b] - Ni(a)[a-1i|\mu|b].

Parameters

la_max	...
npgfa	...
zeta	...
rpgfa	...
la_min	...
lb_max	...
npgfb	...
zetb	...
rpgfb	...
lb_min	...
order	...
rac	...
rbc	...
pab	...
forcea	...
forceb	...

Note

Definition at line 492 of file ai_moments.F.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ contract_expikr()

◆ expikr()

◆ moment()

◆ diff_momop()

◆ dipole_force()