upf_local_integrals Module Reference

Local UPF matrix elements from the original radial potential. The Gaussian core electrostatics supplies -Z erf(sqrt(alpha)*r)/r. Its complement is integrated with analytic angles and radial quadrature. Gaussian products, center derivatives and RI integrals share this operator. More...

Data Types
type	upf_local_type

Functions/Subroutines
subroutine, public	upf_local_init (pot, alpha, degree, local, eps)
	Prepare the short-range local potential outside parallel regions.
subroutine, public	upf_local_matrix (local, la, alpha, lb, beta, rab, rac, v, da, db)
	Evaluate primitive three-center local integrals by the Gaussian product theorem.
subroutine, public	upf_local_ri (local, la, zeta, rac, v, dv)
	Local potential against a single Cartesian Gaussian for RI.

Detailed Description

Local UPF matrix elements from the original radial potential. The Gaussian core electrostatics supplies -Z erf(sqrt(alpha)*r)/r. Its complement is integrated with analytic angles and radial quadrature. Gaussian products, center derivatives and RI integrals share this operator.

Function/Subroutine Documentation

upf_local_init()

subroutine, public upf_local_integrals::upf_local_init	(	type(atom_upfpot_type), intent(in)	pot,
		real(kind=dp), intent(in)	alpha,
		integer, intent(in)	degree,
		type(upf_local_type), intent(inout)	local,
		real(kind=dp), intent(in), optional	eps )

Prepare the short-range local potential outside parallel regions.

Parameters

pot	Original UPF data, with PP_LOCAL already converted to Hartree.
alpha	Gaussian core-charge exponent, not its screening radius.
degree	Largest Gaussian product degree, including derivatives or moments.
local	Immutable integration data. Reinitialization retains its threshold.
eps	Optional threshold for estimating the potential's neighbor-list radius. This is NOT an integration tolerance: EPS_PPL is normally 1e-2. All original radial samples, including the tail, enter the quadrature.

Definition at line 51 of file upf_local_integrals.F.

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upf_local_matrix()

subroutine, public upf_local_integrals::upf_local_matrix	(	type(upf_local_type), intent(in)	local,
		integer, intent(in)	la,
		real(kind=dp), dimension(:), intent(in)	alpha,
		integer, intent(in)	lb,
		real(kind=dp), dimension(:), intent(in)	beta,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), dimension(3), intent(in)	rac,
		real(kind=dp), dimension(:, :), intent(out)	v,
		real(kind=dp), dimension(:, :, :), intent(out), optional	da,
		real(kind=dp), dimension(:, :, :), intent(out), optional	db )

Evaluate primitive three-center local integrals by the Gaussian product theorem.

Parameters

local	Prepared radial potential.
la	Largest Cartesian degree at A; all degrees 0..la are returned.
alpha	Primitive exponents at A.
lb	Largest Cartesian degree at B; all degrees 0..lb are returned.
beta	Primitive exponents at B.
rab	B minus A.
rac	Potential center C minus A.
v	Matrix elements in primitive-major Cartesian order.
da	Optional derivatives with respect to A, at fixed B and C.
db	Optional derivatives with respect to B, at fixed A and C. The derivative with respect to C is -(da+db).

Definition at line 114 of file upf_local_integrals.F.

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upf_local_ri()

subroutine, public upf_local_integrals::upf_local_ri	(	type(upf_local_type), intent(in)	local,
		integer, intent(in)	la,
		real(kind=dp), dimension(:), intent(in)	zeta,
		real(kind=dp), dimension(3), intent(in)	rac,
		real(kind=dp), dimension(:), intent(out)	v,
		real(kind=dp), dimension(:, :), intent(out), optional	dv )

Local potential against a single Cartesian Gaussian for RI.

Parameters

local	Prepared radial potential.
la	Largest Cartesian degree.
zeta	Primitive exponents.
rac	Potential center minus Gaussian center.
v	Primitive-major Cartesian integrals.
dv	Optional Gaussian-center derivatives, in x,y,z order.

Definition at line 238 of file upf_local_integrals.F.

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