Calculation of the integrals over solid harmonic Gaussian(SHG) functions. Routines for (a|O(r12)|b) and overlap integrals (ab), (aba) and (abb). More...

Functions/Subroutines
subroutine, public	get_real_scaled_solid_harmonic (rlm_c, rlm_s, l, r, r2)
	computes the real scaled solid harmonics Rlm up to a given l

subroutine, public	get_w_matrix (lamax, lbmax, lmax, rc, rs, waux_mat)
	calculates the angular dependent-part of the SHG integrals, transformation matrix W, see literature above

subroutine, public	get_dw_matrix (lamax, lbmax, waux_mat, dwaux_mat)
	calculates derivatives of transformation matrix W,

subroutine, public	construct_int_shg_ab (la, first_sgfa, nshella, lb, first_sgfb, nshellb, swork_cont, waux_mat, sab)
	calculates [ab] SHG overlap integrals using precomputed angular- dependent part

subroutine, public	construct_dev_shg_ab (la, first_sgfa, nshella, lb, first_sgfb, nshellb, rab, swork_cont, waux_mat, dwaux_mat, dsab)
	calculates derivatives of [ab] SHG overlap integrals using precomputed angular-dependent part

subroutine, public	construct_overlap_shg_aba (la, first_sgfa, nshella, lb, first_sgfb, nshellb, lca, first_sgfca, nshellca, cg_coeff, cg_none0_list, ncg_none0, swork_cont, waux_mat, saba)
	calculates [aba] SHG overlap integrals using precomputed angular- dependent part

subroutine, public	dev_overlap_shg_aba (la, first_sgfa, nshella, lb, first_sgfb, nshellb, lca, first_sgfca, nshellca, cg_coeff, cg_none0_list, ncg_none0, rab, swork_cont, waux_mat, dwaux_mat, dsaba)
	calculates derivatives of [aba] SHG overlap integrals using precomputed angular-dependent part

subroutine, public	construct_overlap_shg_abb (la, first_sgfa, nshella, lb, first_sgfb, nshellb, lcb, first_sgfcb, nshellcb, cg_coeff, cg_none0_list, ncg_none0, swork_cont, waux_mat, sabb)
	calculates [abb] SHG overlap integrals using precomputed angular- dependent part

subroutine, public	dev_overlap_shg_abb (la, first_sgfa, nshella, lb, first_sgfb, nshellb, lcb, first_sgfcb, nshellcb, cg_coeff, cg_none0_list, ncg_none0, rab, swork_cont, waux_mat, dwaux_mat, dsabb)
	calculates derivatives of [abb] SHG overlap integrals using precomputed angular-dependent part

Detailed Description

Calculation of the integrals over solid harmonic Gaussian(SHG) functions. Routines for (a|O(r12)|b) and overlap integrals (ab), (aba) and (abb).

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

History: created [04.2015]

Author: Dorothea Golze

Function/Subroutine Documentation

◆ get_real_scaled_solid_harmonic()

subroutine, public construct_shg::get_real_scaled_solid_harmonic	(	real(kind=dp), dimension(0:l, -2l:2l), intent(out)	rlm_c,
		real(kind=dp), dimension(0:l, -2l:2l), intent(out)	rlm_s,
		integer, intent(in)	l,
		real(kind=dp), dimension(3)	r,
		real(kind=dp)	r2
	)

computes the real scaled solid harmonics Rlm up to a given l

Parameters

Rlm_c	cosine part of real scaled soldi harmonics
Rlm_s	sine part of real scaled soldi harmonics
l	maximal l quantum up to where Rlm is calculated
r	distance vector between a and b
r2	square of distance vector

Definition at line 49 of file construct_shg.F.

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◆ get_w_matrix()

subroutine, public construct_shg::get_w_matrix	(	integer, dimension(:), pointer	lamax,
		integer, intent(in)	lbmax,
		integer, intent(in)	lmax,
		real(kind=dp), dimension(0:lmax, -2lmax:2lmax), intent(in)	rc,
		real(kind=dp), dimension(0:lmax, -2lmax:2lmax), intent(in)	rs,
		real(kind=dp), dimension(:, :, :), intent(inout)	waux_mat
	)

calculates the angular dependent-part of the SHG integrals, transformation matrix W, see literature above

Parameters

lamax	array of maximal l quantum number on a; lamax(lb) with lb= 0..lbmax
lbmax	maximal l quantum number on b
lmax	maximal l quantum number
Rc	cosine part of real scaled solid harmonics
Rs	sine part of real scaled solid harmonics
Waux_mat	stores the angular-dependent part of the SHG integrals

Definition at line 210 of file construct_shg.F.

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◆ get_dw_matrix()

subroutine, public construct_shg::get_dw_matrix	(	integer, dimension(:), pointer	lamax,
		integer, intent(in)	lbmax,
		real(kind=dp), dimension(:, :, :), intent(inout)	waux_mat,
		real(kind=dp), dimension(:, :, :, :), intent(inout)	dwaux_mat
	)

calculates derivatives of transformation matrix W,

Parameters

lamax	array of maximal l quantum number on a; lamax(lb) with lb= 0..lbmax
lbmax	maximal l quantum number on b
Waux_mat	stores the angular-dependent part of the SHG integrals
dWaux_mat	stores the derivatives of the angular-dependent part of the SHG integrals

Definition at line 313 of file construct_shg.F.

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◆ construct_int_shg_ab()

subroutine, public construct_shg::construct_int_shg_ab	(	integer, dimension(:), intent(in)	la,
		integer, dimension(:), intent(in)	first_sgfa,
		integer, intent(in)	nshella,
		integer, dimension(:), intent(in)	lb,
		integer, dimension(:), intent(in)	first_sgfb,
		integer, intent(in)	nshellb,
		real(kind=dp), dimension(:, :, :), intent(in)	swork_cont,
		real(kind=dp), dimension(:, :, :), intent(in)	waux_mat,
		real(kind=dp), dimension(:, :), intent(inout)	sab
	)

calculates [ab] SHG overlap integrals using precomputed angular- dependent part

Parameters

la	set of l quantum number on a
first_sgfa	indexing
nshella	number of shells for a
lb	set of l quantum number on b
first_sgfb	indexing
nshellb	number of shells for b
swork_cont	contracted and normalized [s\|s] integrals
Waux_mat	precomputed angular-dependent part
sab	contracted integral of spherical harmonic Gaussianslm

Definition at line 483 of file construct_shg.F.

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◆ construct_dev_shg_ab()

subroutine, public construct_shg::construct_dev_shg_ab	(	integer, dimension(:), intent(in)	la,
		integer, dimension(:), intent(in)	first_sgfa,
		integer, intent(in)	nshella,
		integer, dimension(:), intent(in)	lb,
		integer, dimension(:), intent(in)	first_sgfb,
		integer, intent(in)	nshellb,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), dimension(:, :, :), intent(in)	swork_cont,
		real(kind=dp), dimension(:, :, :), intent(in)	waux_mat,
		real(kind=dp), dimension(:, :, :, :), intent(in)	dwaux_mat,
		real(kind=dp), dimension(:, :, :), intent(inout)	dsab
	)

calculates derivatives of [ab] SHG overlap integrals using precomputed angular-dependent part

Parameters

la	set of l quantum number on a
first_sgfa	indexing
nshella	number of shells for a
lb	set of l quantum number on b
first_sgfb	indexing
nshellb	number of shells for b
rab	distance vector Ra-Rb
swork_cont	contracted and normalized [s\|s] integrals
Waux_mat	precomputed angular-dependent part
dWaux_mat	...
dsab	derivative of contracted integral of spherical harmonic Gaussians

Definition at line 540 of file construct_shg.F.

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◆ construct_overlap_shg_aba()

subroutine, public construct_shg::construct_overlap_shg_aba	(	integer, dimension(:), intent(in)	la,
		integer, dimension(:), intent(in)	first_sgfa,
		integer, intent(in)	nshella,
		integer, dimension(:), intent(in)	lb,
		integer, dimension(:), intent(in)	first_sgfb,
		integer, intent(in)	nshellb,
		integer, dimension(:), intent(in)	lca,
		integer, dimension(:), intent(in)	first_sgfca,
		integer, intent(in)	nshellca,
		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(:, 0:, :, :, :), intent(in)	swork_cont,
		real(kind=dp), dimension(:, :, :), intent(in)	waux_mat,
		real(kind=dp), dimension(:, :, :), intent(inout)	saba
	)

calculates [aba] SHG overlap integrals using precomputed angular- dependent part

Parameters

la	set of l quantum number on a, orbital basis
first_sgfa	indexing
nshella	number of shells for a, orbital basis
lb	set of l quantum number on b. orbital basis
first_sgfb	indexing
nshellb	number of shells for b, orbital basis
lca	of l quantum number on a, aux basis
first_sgfca	indexing
nshellca	number of shells for a, aux basis
cg_coeff	Clebsch-Gordon coefficients
cg_none0_list	list of none-zero Clebsch-Gordon coefficients
ncg_none0	number of non-zero Clebsch-Gordon coefficients
swork_cont	contracted and normalized [s\|ra^n\|s] integrals
Waux_mat	precomputed angular-dependent part
saba	contracted overlap [aba] of spherical harmonic Gaussians

Definition at line 604 of file construct_shg.F.

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◆ dev_overlap_shg_aba()

subroutine, public construct_shg::dev_overlap_shg_aba	(	integer, dimension(:), intent(in)	la,
		integer, dimension(:), intent(in)	first_sgfa,
		integer, intent(in)	nshella,
		integer, dimension(:), intent(in)	lb,
		integer, dimension(:), intent(in)	first_sgfb,
		integer, intent(in)	nshellb,
		integer, dimension(:), intent(in)	lca,
		integer, dimension(:), intent(in)	first_sgfca,
		integer, intent(in)	nshellca,
		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(3), intent(in)	rab,
		real(kind=dp), dimension(:, 0:, :, :, :), intent(in)	swork_cont,
		real(kind=dp), dimension(:, :, :), intent(in)	waux_mat,
		real(kind=dp), dimension(:, :, :, :), intent(in)	dwaux_mat,
		real(kind=dp), dimension(:, :, :, :), intent(inout)	dsaba
	)

calculates derivatives of [aba] SHG overlap integrals using precomputed angular-dependent part

Parameters

la	set of l quantum number on a, orbital basis
first_sgfa	indexing
nshella	number of shells for a, orbital basis
lb	set of l quantum number on b. orbital basis
first_sgfb	indexing
nshellb	number of shells for b, orbital basis
lca	of l quantum number on a, aux basis
first_sgfca	indexing
nshellca	number of shells for a, aux basis
cg_coeff	Clebsch-Gordon coefficients
cg_none0_list	list of none-zero Clebsch-Gordon coefficients
ncg_none0	number of non-zero Clebsch-Gordon coefficients
rab	distance vector Ra-Rb
swork_cont	contracted and normalized [s\|ra^n\|s] integrals
Waux_mat	precomputed angular-dependent part
dWaux_mat	derivatives of precomputed angular-dependent part
dsaba	derivative of contracted overlap [aba] of spherical harmonic Gaussians

Definition at line 689 of file construct_shg.F.

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◆ construct_overlap_shg_abb()

subroutine, public construct_shg::construct_overlap_shg_abb	(	integer, dimension(:), intent(in)	la,
		integer, dimension(:), intent(in)	first_sgfa,
		integer, intent(in)	nshella,
		integer, dimension(:), intent(in)	lb,
		integer, dimension(:), intent(in)	first_sgfb,
		integer, intent(in)	nshellb,
		integer, dimension(:), intent(in)	lcb,
		integer, dimension(:), intent(in)	first_sgfcb,
		integer, intent(in)	nshellcb,
		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(:, 0:, :, :, :), intent(in)	swork_cont,
		real(kind=dp), dimension(:, :, :), intent(in)	waux_mat,
		real(kind=dp), dimension(:, :, :), intent(inout)	sabb
	)

calculates [abb] SHG overlap integrals using precomputed angular- dependent part

Parameters

la	set of l quantum number on a, orbital basis
first_sgfa	indexing
nshella	number of shells for a, orbital basis
lb	set of l quantum number on b. orbital basis
first_sgfb	indexing
nshellb	number of shells for b, orbital basis
lcb	l quantum number on b, aux basis
first_sgfcb	indexing
nshellcb	number of shells for b, aux basis
cg_coeff	Clebsch-Gordon coefficients
cg_none0_list	list of none-zero Clebsch-Gordon coefficients
ncg_none0	number of non-zero Clebsch-Gordon coefficients
swork_cont	contracted and normalized [s\|rb^n\|s] integrals
Waux_mat	precomputed angular-dependent part
sabb	contracted overlap [abb] of spherical harmonic Gaussians

Definition at line 783 of file construct_shg.F.

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◆ dev_overlap_shg_abb()

subroutine, public construct_shg::dev_overlap_shg_abb	(	integer, dimension(:), intent(in)	la,
		integer, dimension(:), intent(in)	first_sgfa,
		integer, intent(in)	nshella,
		integer, dimension(:), intent(in)	lb,
		integer, dimension(:), intent(in)	first_sgfb,
		integer, intent(in)	nshellb,
		integer, dimension(:), intent(in)	lcb,
		integer, dimension(:), intent(in)	first_sgfcb,
		integer, intent(in)	nshellcb,
		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(3), intent(in)	rab,
		real(kind=dp), dimension(:, 0:, :, :, :), intent(in)	swork_cont,
		real(kind=dp), dimension(:, :, :), intent(in)	waux_mat,
		real(kind=dp), dimension(:, :, :, :), intent(in)	dwaux_mat,
		real(kind=dp), dimension(:, :, :, :), intent(inout)	dsabb
	)

calculates derivatives of [abb] SHG overlap integrals using precomputed angular-dependent part

Parameters

la	set of l quantum number on a, orbital basis
first_sgfa	indexing
nshella	number of shells for a, orbital basis
lb	set of l quantum number on b. orbital basis
first_sgfb	indexing
nshellb	number of shells for b, orbital basis
lcb	l quantum number on b, aux basis
first_sgfcb	indexing
nshellcb	number of shells for b, aux basis
cg_coeff	Clebsch-Gordon coefficients
cg_none0_list	list of none-zero Clebsch-Gordon coefficients
ncg_none0	number of non-zero Clebsch-Gordon coefficients
rab	distance vector Ra-Rb
swork_cont	contracted and normalized [s\|rb^n\|s] integrals
Waux_mat	precomputed angular-dependent part
dWaux_mat	derivatives of precomputed angular-dependent part
dsabb	derivative of contracted overlap [abb] of spherical harmonic Gaussians

Definition at line 871 of file construct_shg.F.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ get_real_scaled_solid_harmonic()

◆ get_w_matrix()

◆ get_dw_matrix()

◆ construct_int_shg_ab()

◆ construct_dev_shg_ab()

◆ construct_overlap_shg_aba()

◆ dev_overlap_shg_aba()

◆ construct_overlap_shg_abb()

◆ dev_overlap_shg_abb()