Calculation of three-center overlap integrals over Cartesian Gaussian-type functions for the second term V(ppl) of the local part of the Goedecker pseudopotential (GTH): More...

Functions/Subroutines
subroutine, public	ppl_integral (la_max_set, la_min_set, npgfa, rpgfa, zeta, lb_max_set, lb_min_set, npgfb, rpgfb, zetb, nexp_ppl, alpha_ppl, nct_ppl, cexp_ppl, rpgfc, rab, dab, rac, dac, rbc, dbc, vab, s, pab, force_a, force_b, fs, hab2, hab2_work, deltar, iatom, jatom, katom)
	Calculation of three-center overlap integrals <a\|c\|b> over Cartesian Gaussian functions for the local part of the Goedecker pseudopotential (GTH). c is a primitive Gaussian-type function with a set of even angular momentum indices.

subroutine, public	ecploc_integral (la_max_set, la_min_set, npgfa, rpgfa, zeta, lb_max_set, lb_min_set, npgfb, rpgfb, zetb, nexp_ppl, alpha_ppl, nct_ppl, cexp_ppl, rpgfc, rab, dab, rac, dac, rbc, dbc, vab, s, pab, force_a, force_b, fs, hab2, hab2_work, deltar, iatom, jatom, katom)
	Calculation of three-center potential integrals <a\|V(r)\|b> over Cartesian Gaussian functions for the local part of ECP pseudopotential. Multiple terms C1-4 are possible.

subroutine, public	ppl_integral_ri (la_max_set, la_min_set, npgfa, rpgfa, zeta, nexp_ppl, alpha_ppl, nct_ppl, cexp_ppl, rpgfc, rac, dac, va, dva)
	Calculation of two-center overlap integrals <a\|c> over Cartesian Gaussian functions for the local part of the Goedecker pseudopotential (GTH). c is a primitive Gaussian-type function with a set of even angular momentum indices.

Detailed Description

Calculation of three-center overlap integrals over Cartesian Gaussian-type functions for the second term V(ppl) of the local part of the Goedecker pseudopotential (GTH):

<a|V(local)|b> = <a|V(erf) + V(ppl)|b> = <a|V(erf)|b> + <a|V(ppl)|b> = <a|-Z(eff)*erf(SQRT(2)*alpha*r)/r + (C1 + C2*(alpha*r)**2 + C3*(alpha*r)**4 + C4*(alpha*r)**6)*exp(-(alpha*r)**2/2))|b>

Literature: S. Obara and A. Saika, J. Chem. Phys. 84, 3963 (1986) S. Goedecker, M. Teter and J. Hutter, Phys. Rev. B 54, 1703 (1996) C. Hartwigsen, S. Goedecker and J. Hutter, Phys. Rev. B 58, 3641 (1998)

History

Derivatives added (17.05.2002,MK)
Complete refactoring (05.2011,jhu)

Author: Matthias Krack (04.10.2000)

Function/Subroutine Documentation

◆ ppl_integral()

subroutine, public ai_overlap_ppl::ppl_integral	(	integer, intent(in)	la_max_set,
		integer, intent(in)	la_min_set,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	rpgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		integer, intent(in)	lb_max_set,
		integer, intent(in)	lb_min_set,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	rpgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		integer, intent(in)	nexp_ppl,
		real(kind=dp), dimension(:), intent(in)	alpha_ppl,
		integer, dimension(:), intent(in)	nct_ppl,
		real(kind=dp), dimension(:, :), intent(in)	cexp_ppl,
		real(kind=dp), intent(in)	rpgfc,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), intent(in)	dab,
		real(kind=dp), dimension(3), intent(in)	rac,
		real(kind=dp), intent(in)	dac,
		real(kind=dp), dimension(3), intent(in)	rbc,
		real(kind=dp), intent(in)	dbc,
		real(kind=dp), dimension(:, :), intent(inout)	vab,
		real(kind=dp), dimension(:, :, :), intent(inout)	s,
		real(kind=dp), dimension(:, :), intent(in), optional	pab,
		real(kind=dp), dimension(3), intent(out), optional	force_a,
		real(kind=dp), dimension(3), intent(out), optional	force_b,
		real(kind=dp), dimension(:, :, :), intent(inout), optional	fs,
		real(kind=dp), dimension(:, :, :), intent(inout), optional	hab2,
		real(kind=dp), dimension(:, :, :), intent(inout), optional	hab2_work,
		real(kind=dp), dimension(:, :), intent(in), optional	deltar,
		integer, intent(in), optional	iatom,
		integer, intent(in), optional	jatom,
		integer, intent(in), optional	katom
	)

Calculation of three-center overlap integrals <a|c|b> over Cartesian Gaussian functions for the local part of the Goedecker pseudopotential (GTH). c is a primitive Gaussian-type function with a set of even angular momentum indices.

<a|V(ppl)|b> = <a| (C1 + C2*(alpha*r)**2 + C3*(alpha*r)**4 + C4*(alpha*r)**6)*exp(-(alpha*r)**2/2))|b> zetc = alpha**2/2

Parameters

la_max_set	...
la_min_set	...
npgfa	...
rpgfa	...
zeta	...
lb_max_set	...
lb_min_set	...
npgfb	...
rpgfb	...
zetb	...
nexp_ppl	...
alpha_ppl	...
nct_ppl	...
cexp_ppl	...
rpgfc	...
rab	...
dab	...
rac	...
dac	...
rbc	...
dbc	...
vab	...
s	...
pab	...
force_a	...
force_b	...
fs	...
hab2	The derivative of the ppl integrals according to the weighting factors deltaR
hab2_work	...
deltaR	Weighting factors for the derivatives wrt. nuclear positions
iatom	...
jatom	...
katom	...

Date: May 2011

Author: Juerg Hutter

Version: 1.0

Note: Extended by the derivatives for DFPT [Sandra Luber, Edward Ditler, 2021]

Definition at line 101 of file ai_overlap_ppl.F.

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◆ ecploc_integral()

subroutine, public ai_overlap_ppl::ecploc_integral	(	integer, intent(in)	la_max_set,
		integer, intent(in)	la_min_set,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	rpgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		integer, intent(in)	lb_max_set,
		integer, intent(in)	lb_min_set,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:), intent(in)	rpgfb,
		real(kind=dp), dimension(:), intent(in)	zetb,
		integer, intent(in)	nexp_ppl,
		real(kind=dp), dimension(:), intent(in)	alpha_ppl,
		integer, dimension(:), intent(in)	nct_ppl,
		real(kind=dp), dimension(:, :), intent(in)	cexp_ppl,
		real(kind=dp), intent(in)	rpgfc,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), intent(in)	dab,
		real(kind=dp), dimension(3), intent(in)	rac,
		real(kind=dp), intent(in)	dac,
		real(kind=dp), dimension(3), intent(in)	rbc,
		real(kind=dp), intent(in)	dbc,
		real(kind=dp), dimension(:, :), intent(inout)	vab,
		real(kind=dp), dimension(:, :, :), intent(inout)	s,
		real(kind=dp), dimension(:, :), intent(in), optional	pab,
		real(kind=dp), dimension(3), intent(out), optional	force_a,
		real(kind=dp), dimension(3), intent(out), optional	force_b,
		real(kind=dp), dimension(:, :, :), intent(inout), optional	fs,
		real(kind=dp), dimension(:, :, :), intent(inout), optional	hab2,
		real(kind=dp), dimension(:, :, :), intent(inout), optional	hab2_work,
		real(kind=dp), dimension(:, :), intent(in), optional	deltar,
		integer, intent(in), optional	iatom,
		integer, intent(in), optional	jatom,
		integer, intent(in), optional	katom
	)

Calculation of three-center potential integrals <a|V(r)|b> over Cartesian Gaussian functions for the local part of ECP pseudopotential. Multiple terms C1-4 are possible.

<a|V(ecploc)|b> = <a| C1/r*exp(-a1*r**2) + C2*exp(-a2*r**2) + C3*r*exp(-a3*r**2) + C4*r**2*exp(-a4*r**2)|b>

Parameters

la_max_set	...
la_min_set	...
npgfa	...
rpgfa	...
zeta	...
lb_max_set	...
lb_min_set	...
npgfb	...
rpgfb	...
zetb	...
nexp_ppl	...
alpha_ppl	...
nct_ppl	...
cexp_ppl	...
rpgfc	...
rab	...
dab	...
rac	...
dac	...
rbc	...
dbc	...
vab	...
s	...
pab	...
force_a	...
force_b	...
fs	...
hab2	The derivative of the ppl integrals according to the weighting factors deltaR
hab2_work	...
deltaR	Weighting factors for the derivatives wrt. nuclear positions
iatom	...
jatom	...
katom	...

Date: 2025

Author: Juerg Hutter

Version: 1.0

Definition at line 233 of file ai_overlap_ppl.F.

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◆ ppl_integral_ri()

subroutine, public ai_overlap_ppl::ppl_integral_ri	(	integer, intent(in)	la_max_set,
		integer, intent(in)	la_min_set,
		integer, intent(in)	npgfa,
		real(kind=dp), dimension(:), intent(in)	rpgfa,
		real(kind=dp), dimension(:), intent(in)	zeta,
		integer, intent(in)	nexp_ppl,
		real(kind=dp), dimension(:), intent(in)	alpha_ppl,
		integer, dimension(:), intent(in)	nct_ppl,
		real(kind=dp), dimension(:, :), intent(in)	cexp_ppl,
		real(kind=dp), intent(in)	rpgfc,
		real(kind=dp), dimension(3), intent(in)	rac,
		real(kind=dp), intent(in)	dac,
		real(kind=dp), dimension(:), intent(inout)	va,
		real(kind=dp), dimension(:, :), intent(inout), optional	dva
	)

Calculation of two-center overlap integrals <a|c> over Cartesian Gaussian functions for the local part of the Goedecker pseudopotential (GTH). c is a primitive Gaussian-type function with a set of even angular momentum indices.

<a|V(ppl)|b> = <a| (C1 + C2*(alpha*r)**2 + C3*(alpha*r)**4 + C4*(alpha*r)**6)*exp(-(alpha*r)**2/2))|b> zetc = alpha**2/2

Parameters

la_max_set	...
la_min_set	...
npgfa	...
rpgfa	...
zeta	...
nexp_ppl	...
alpha_ppl	...
nct_ppl	...
cexp_ppl	...
rpgfc	...
rac	...
dac	...
va	...
dva	...

Date: December 2017

Author: Juerg Hutter

Version: 1.0

Definition at line 349 of file ai_overlap_ppl.F.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ ppl_integral()

◆ ecploc_integral()

◆ ppl_integral_ri()