cgto_pw_expansions_gbl Module Reference

Functions/Subroutines
subroutine, public	init_CGTO_pw_expansions_mod (inp_max_l_pw, max_l_cgto)
subroutine, public	init_dbg (bspline_grid)
	USED ONLY FOR DEBUGGING. More...
subroutine	construct_radial_grid (this, inp_bspline_grid, first_bspline_index, nuclei, delta_r1, x, w, n, n_rng_knot)
subroutine	final (this)
subroutine	construct_GK_angular_grid (this, n_div, r, w1, n_points)
subroutine	eval_Xlm_on_lebedev_grid (this, n)
subroutine	eval_Y_l_BTO_BTO (this)
subroutine	eval_regular_grid (this, A, B, delta_r)
subroutine	eval_exponential_grid (this, alp, n)
	Exponential grid on [0,1] with points accumulating towards 1. More...
subroutine	assign_grid (this, r_points, weights)
subroutine	write_CGTO_shell_pw_expansion_obj (this)
subroutine	eval_BTO_CGTO_Y_lm (this, grid_r1_r2)
subroutine	write_Y_lm_to_file (this, scratch_directory)
subroutine	expand_pw_in_bsplines (this, grid_r1_r2, cgto_m, lm)
subroutine	eval_coulomb_integrals (this, grid_r1_r2)
subroutine	eval_radial_GG_BB (this, grid_r1_r2)
	Calculates the radial integral 2-electron integrals between all pairs of BTOs and all partial waves of the GG pair. More...
subroutine	eval_CGTO_pair_radial_grid (this, a, x, w, n)
subroutine	eval_CGTO_radial_grid (this, only_on_bto_grid, grid_r1_r2, delta_r1, x, w, n, n_rng_knot, nuclei)
subroutine	radial_grid_mo (centers, R_min, R_max, bspline_grid, delta_cgto_grid, x, w, n, r_points, weights, n_total_points)
	Radial grid used when integrating over the molecular orbitals purely numerically. More...
subroutine	radial_grid (centers, only_on_bto_grid, R_min, R_max, bspline_grid, delta_cgto_grid, x, w, n, n_rng_knot, r_points, weights, n_total_points)
	Determines the radial grid needed to describe, integrals involving the CGTO and the B-splines on the given grid. We assume that if the CGTO spanned the whole B-spline grid it would be sufficient to use the given quadrature rule (x,w,n) within each knot interval. For CGTOs whose radial extent is smaller than the range of the B-spline grid the number of quadrature points within each knot interval is expanded by the factor ceiling(n_int/R), where R is the extent of the CGTO (determined to coincide with the nearest larger knot) and n_int is the number of distinct intervals of knots in the B-spline basis. More...
subroutine	radial_grid_CGTO_pair (cgto_A, cgto_B, R_min, R_max, x, w, n, delta_cgto_grid, r_points, weights, n_total_points)
subroutine	omp_calculate_CGTO_pw_coefficients_analytic (threshold, max_l_inp, max_lp, cgto_shell, r_points, angular_integrals, non_neg_indices_l, gaunt_angular_integrals, non_neg_indices_l_lp)
	Calculates the partial wave expansion of CGTO up to partial wave L=max_l_inp and on the grid of radial points r_points. From this it generates the double angular projections for X_lm up to l=max_lp. It uses auxiliary arrays declared on top of this routine. More...
subroutine	omp_calculate_CGTO_pair_pw_coefficients_analytic (max_l, cgto_A, cgto_B, r_points, angular_integrals)
	Calculates the partial wave expansion of a product of two CGTOs up to partial wave L=max_l and on the grid of radial points r_points. More...
real(kind=cfp) function	eval_Xlm_x_pair_cgto_surface (this, x, y)
	Evaluates the product of CGTO and a real spherical harmonic at a given point in space. x,y are the spherical polar coordinates on the sphere. More...
real(kind=cfp) function	gto_pair_eval_R (cgto_A, m_A, cgto_B, m_B, x, R)
	Evaluates the product of a pair of CGTOs for the given m values at radial distance x and for angular direction given by vector R. More...
subroutine	precalculate_pair_solh_translation_coeffs (CGTO_A_L, RA_A, Xlm_CGTO_A_center, CGTO_B_L, RA_B, Xlm_CGTO_B_center, transl_cfs_AB)
subroutine	calculate_pair_lambda_couplings (l, m, CGTO_A_L, CGTO_B_L, n_contr_pairs, Xlm_product_CGTO_center, transl_cfs_AB, c_pair_lambda)
real(kind=cfp) function	CGTO_pw_coefficient_stable (asym, r, l, lm, Lg, Lg_Mg, c_lambda, contraction_besi, prim_fac, n_prim, besi_args)
subroutine	precalculate_solh_translation_coeffs (CGTO_L, RA, Xlm_CGTO_center, transl_cfs)
subroutine	calculate_lambda_couplings (CGTO_L, l, m, Xlm_CGTO_center, transl_cfs, c_lambda)
real(kind=cfp) function	besi_half_asym (z, l)
subroutine, public	precalculate_Xlm_for_nuclei (nuclei, max_l, Xlm_nuclei, n_Xlm_nuclei)
	Calculates the real spherical harmonics for all l,m up to l=max_l for directions corresponding to the nuclear positions. More...
subroutine	precalculate_Xlm_for_CGTO_center (RA, max_l, Xlm_CGTO_center)
	Calculates the real spherical harmonics for all l,m up to l=max_l for directions corresponding to the nuclear positions. More...
subroutine	precalculate_Xlm_for_CGTO_product_center (n_contr_pairs, RA, max_l, Xlm_product_CGTO_center)
subroutine	calc_resh_coefficients (L)
subroutine	calc_solh_coefficients (L)

Variables
type(cgto_shell_data_obj), dimension(n_alp), public	dbg_cgto
type(couplings_type), public	cpl
	Used to evaluate various coupling coefficients. More...

Function/Subroutine Documentation

assign_grid()

subroutine cgto_pw_expansions_gbl::assign_grid	(	class(pw_expansion_obj)	this,
		real(kind=cfp), dimension(:), intent(in)	r_points,
		real(kind=cfp), dimension(:), intent(in)	weights
	)

besi_half_asym()

real(kind=cfp) function cgto_pw_expansions_gbl::besi_half_asym	(	real(kind=cfp), intent(in)	z,
		integer, intent(in)	l
	)

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calc_resh_coefficients()

subroutine cgto_pw_expansions_gbl::calc_resh_coefficients

(

integer, intent(in)

L

)

calc_solh_coefficients()

subroutine cgto_pw_expansions_gbl::calc_solh_coefficients

(

integer, intent(in)

L

)

calculate_lambda_couplings()

subroutine cgto_pw_expansions_gbl::calculate_lambda_couplings	(	integer, intent(in)	CGTO_L,
		integer, intent(in)	l,
		integer, intent(in)	m,
		real(kind=cfp), dimension(:), allocatable	Xlm_CGTO_center,
		real(kind=cfp), dimension(:,:,:), allocatable	transl_cfs,
		real(kind=cfp), dimension(:,:,:), allocatable	c_lambda
	)

Warning

Requires precalculated values of the real spherical harmonics at the position of the CGTO nucleus. The coupling coefficients should also be precalculated for performance reasons.

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calculate_pair_lambda_couplings()

subroutine cgto_pw_expansions_gbl::calculate_pair_lambda_couplings	(	integer, intent(in)	l,
		integer, intent(in)	m,
		integer, intent(in)	CGTO_A_L,
		integer, intent(in)	CGTO_B_L,
		integer, intent(in)	n_contr_pairs,
		real(kind=cfp), dimension(:), allocatable	Xlm_product_CGTO_center,
		real(kind=cfp), dimension(:,:,:,:,:), allocatable	transl_cfs_AB,
		real(kind=cfp), dimension(:,:,:,:,:), allocatable	c_pair_lambda
	)

CGTO_pw_coefficient_stable()

real(kind=cfp) function cgto_pw_expansions_gbl::CGTO_pw_coefficient_stable	(	real(kind=cfp), intent(in)	asym,
		real(kind=cfp), intent(in)	r,
		integer, intent(in)	l,
		integer, intent(in)	lm,
		integer, intent(in)	Lg,
		integer, intent(in)	Lg_Mg,
		real(kind=cfp), dimension(0:,0:,:,:), intent(in)	c_lambda,
		real(kind=cfp), dimension(0:), intent(in)	contraction_besi,
		real(kind=cfp), dimension(n_prim), intent(in)	prim_fac,
		integer, intent(in)	n_prim,
		real(kind=cfp), dimension(n_prim), intent(in)	besi_args
	)

construct_GK_angular_grid()

subroutine cgto_pw_expansions_gbl::construct_GK_angular_grid	(	class(legendre_grid_r1_r2_obj)	this,
		integer, intent(in)	n_div,
		real(kind=cfp), dimension(:,:), allocatable	r,
		real(kind=cfp), dimension(:), allocatable	w1,
		integer, intent(out)	n_points
	)

construct_radial_grid()

subroutine cgto_pw_expansions_gbl::construct_radial_grid	(	class(legendre_grid_r1_r2_obj)	this,
		type(bspline_grid_obj)	inp_bspline_grid,
		integer, intent(in)	first_bspline_index,
		type(nucleus_type), dimension(:)	nuclei,
		real(kind=cfp), intent(in)	delta_r1,
		real(kind=cfp), dimension(2*n+1), intent(in)	x,
		real(kind=cfp), dimension(2*n+1), intent(in)	w,
		integer, intent(in)	n,
		integer, intent(in)	n_rng_knot
	)

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eval_BTO_CGTO_Y_lm()

subroutine cgto_pw_expansions_gbl::eval_BTO_CGTO_Y_lm	(	class(cgto_shell_pw_expansion_obj)	this,
		class(legendre_grid_r1_r2_obj)	grid_r1_r2
	)

eval_CGTO_pair_radial_grid()

subroutine cgto_pw_expansions_gbl::eval_CGTO_pair_radial_grid	(	class(cgto_shell_pair_pw_expansion_obj)	this,
		real(kind=cfp), intent(in)	a,
		real(kind=cfp), dimension(2*n+1), intent(in)	x,
		real(kind=cfp), dimension(2*n+1), intent(in)	w,
		integer, intent(in)	n
	)

eval_CGTO_radial_grid()

subroutine cgto_pw_expansions_gbl::eval_CGTO_radial_grid	(	class(cgto_shell_pw_expansion_obj)	this,
		logical, intent(in)	only_on_bto_grid,
		class(legendre_grid_r1_r2_obj)	grid_r1_r2,
		real(kind=cfp), intent(in)	delta_r1,
		real(kind=cfp), dimension(2*n+1), intent(in)	x,
		real(kind=cfp), dimension(2*n+1), intent(in)	w,
		integer, intent(in)	n,
		integer, intent(in)	n_rng_knot,
		type(nucleus_type), dimension(:), optional	nuclei
	)

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eval_coulomb_integrals()

subroutine cgto_pw_expansions_gbl::eval_coulomb_integrals	(	class(cgto_shell_pair_pw_expansion_obj)	this,
		class(legendre_grid_r1_r2_obj)	grid_r1_r2
	)

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eval_exponential_grid()

subroutine cgto_pw_expansions_gbl::eval_exponential_grid	(	class(pw_expansion_obj)	this,
		real(kind=cfp), intent(in)	alp,
		integer, intent(in)	n
	)

Exponential grid on [0,1] with points accumulating towards 1.

eval_radial_GG_BB()

subroutine cgto_pw_expansions_gbl::eval_radial_GG_BB	(	class(cgto_shell_pair_pw_expansion_obj)	this,
		class(legendre_grid_r1_r2_obj)	grid_r1_r2
	)

Calculates the radial integral 2-electron integrals between all pairs of BTOs and all partial waves of the GG pair.

eval_regular_grid()

subroutine cgto_pw_expansions_gbl::eval_regular_grid	(	class(pw_expansion_obj)	this,
		real(kind=cfp), intent(in)	A,
		real(kind=cfp), intent(in)	B,
		real(kind=cfp), intent(in)	delta_r
	)

eval_Xlm_on_lebedev_grid()

subroutine cgto_pw_expansions_gbl::eval_Xlm_on_lebedev_grid	(	class(legendre_grid_r1_r2_obj)	this,
		integer, intent(in)	n
	)

eval_Xlm_x_pair_cgto_surface()

real(kind=cfp) function cgto_pw_expansions_gbl::eval_Xlm_x_pair_cgto_surface	(	class(xlm_x_pair_cgto_surface)	this,
		real(kind=cfp), intent(in)	x,
		real(kind=cfp), intent(in)	y
	)

Evaluates the product of CGTO and a real spherical harmonic at a given point in space. x,y are the spherical polar coordinates on the sphere.

eval_Y_l_BTO_BTO()

subroutine cgto_pw_expansions_gbl::eval_Y_l_BTO_BTO

(

class(legendre_grid_r1_r2_obj)

this

)

expand_pw_in_bsplines()

subroutine cgto_pw_expansions_gbl::expand_pw_in_bsplines	(	class(cgto_shell_pw_expansion_obj)	this,
		class(legendre_grid_r1_r2_obj)	grid_r1_r2,
		integer, intent(in)	cgto_m,
		integer, intent(in)	lm
	)

final()

subroutine cgto_pw_expansions_gbl::final

(

class(legendre_grid_r1_r2_obj)

this

)

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gto_pair_eval_R()

real(kind=cfp) function cgto_pw_expansions_gbl::gto_pair_eval_R	(	type(cgto_shell_data_obj), intent(in)	cgto_A,
		integer, intent(in)	m_A,
		type(cgto_shell_data_obj), intent(in)	cgto_B,
		integer, intent(in)	m_B,
		real(kind=cfp), intent(in)	x,
		real(kind=cfp), dimension(3), intent(in)	R
	)

Evaluates the product of a pair of CGTOs for the given m values at radial distance x and for angular direction given by vector R.

init_CGTO_pw_expansions_mod()

subroutine, public cgto_pw_expansions_gbl::init_CGTO_pw_expansions_mod	(	integer, intent(in)	inp_max_l_pw,
		integer, intent(in)	max_l_cgto
	)

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init_dbg()

subroutine, public cgto_pw_expansions_gbl::init_dbg

(

type(bspline_grid_obj)

bspline_grid

)

USED ONLY FOR DEBUGGING.

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omp_calculate_CGTO_pair_pw_coefficients_analytic()

subroutine cgto_pw_expansions_gbl::omp_calculate_CGTO_pair_pw_coefficients_analytic	(	integer, intent(in)	max_l,
		type(cgto_shell_data_obj), intent(in)	cgto_A,
		type(cgto_shell_data_obj), intent(in)	cgto_B,
		real(kind=cfp), dimension(:), allocatable	r_points,
		real(kind=cfp), dimension(:,:,:), allocatable	angular_integrals
	)

Calculates the partial wave expansion of a product of two CGTOs up to partial wave L=max_l and on the grid of radial points r_points.

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omp_calculate_CGTO_pw_coefficients_analytic()

subroutine cgto_pw_expansions_gbl::omp_calculate_CGTO_pw_coefficients_analytic	(	real(kind=cfp), intent(in)	threshold,
		integer, intent(in)	max_l_inp,
		integer, intent(in)	max_lp,
		type(cgto_shell_data_obj), intent(in)	cgto_shell,
		real(kind=cfp), dimension(:), allocatable	r_points,
		real(kind=cfp), dimension(:,:), allocatable	angular_integrals,
		integer, dimension(:,:), allocatable	non_neg_indices_l,
		real(kind=cfp), dimension(:,:), allocatable	gaunt_angular_integrals,
		integer, dimension(:,:,:), allocatable	non_neg_indices_l_lp
	)

Calculates the partial wave expansion of CGTO up to partial wave L=max_l_inp and on the grid of radial points r_points. From this it generates the double angular projections for X_lm up to l=max_lp. It uses auxiliary arrays declared on top of this routine.

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precalculate_pair_solh_translation_coeffs()

subroutine cgto_pw_expansions_gbl::precalculate_pair_solh_translation_coeffs	(	integer, intent(in)	CGTO_A_L,
		real(kind=cfp), intent(in)	RA_A,
		real(kind=cfp), dimension(:), allocatable	Xlm_CGTO_A_center,
		integer, intent(in)	CGTO_B_L,
		real(kind=cfp), intent(in)	RA_B,
		real(kind=cfp), dimension(:), allocatable	Xlm_CGTO_B_center,
		real(kind=cfp), dimension(:,:,:,:,:), allocatable	transl_cfs_AB
	)

Warning

Requires precalculated values of the real spherical harmonics at the position of the CGTO nucleus. The coupling coefficients should also be precalculated for performance reasons.

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precalculate_solh_translation_coeffs()

subroutine cgto_pw_expansions_gbl::precalculate_solh_translation_coeffs	(	integer, intent(in)	CGTO_L,
		real(kind=cfp), intent(in)	RA,
		real(kind=cfp), dimension(:), allocatable	Xlm_CGTO_center,
		real(kind=cfp), dimension(:,:,:), allocatable	transl_cfs
	)

Warning

Requires precalculated values of the real spherical harmonics at the position of the CGTO nucleus. The coupling coefficients should also be precalculated for performance reasons.

precalculate_Xlm_for_CGTO_center()

subroutine cgto_pw_expansions_gbl::precalculate_Xlm_for_CGTO_center	(	real(kind=cfp), dimension(3), intent(in)	RA,
		integer, intent(in)	max_l,
		real(kind=cfp), dimension(:), allocatable	Xlm_CGTO_center
	)

Calculates the real spherical harmonics for all l,m up to l=max_l for directions corresponding to the nuclear positions.

precalculate_Xlm_for_CGTO_product_center()

subroutine cgto_pw_expansions_gbl::precalculate_Xlm_for_CGTO_product_center	(	integer, intent(in)	n_contr_pairs,
		real(kind=cfp), dimension(3,n_contr_pairs), intent(in)	RA,
		integer, intent(in)	max_l,
		real(kind=cfp), dimension(:), allocatable	Xlm_product_CGTO_center
	)

precalculate_Xlm_for_nuclei()

subroutine, public cgto_pw_expansions_gbl::precalculate_Xlm_for_nuclei	(	type(nucleus_type), dimension(:), intent(in)	nuclei,
		integer, intent(in)	max_l,
		real(kind=cfp), dimension(:), allocatable	Xlm_nuclei,
		integer, intent(out)	n_Xlm_nuclei
	)

Calculates the real spherical harmonics for all l,m up to l=max_l for directions corresponding to the nuclear positions.

radial_grid()

subroutine cgto_pw_expansions_gbl::radial_grid	(	real(kind=cfp), dimension(:), intent(in)	centers,
		logical, intent(in)	only_on_bto_grid,
		real(kind=cfp), intent(in)	R_min,
		real(kind=cfp), intent(in)	R_max,
		type(bspline_grid_obj), intent(in)	bspline_grid,
		real(kind=cfp), intent(in)	delta_cgto_grid,
		real(kind=cfp), dimension(2*n+1), intent(in)	x,
		real(kind=cfp), dimension(2*n+1), intent(in)	w,
		integer, intent(in)	n,
		integer, intent(in)	n_rng_knot,
		real(kind=cfp), dimension(:), allocatable	r_points,
		real(kind=cfp), dimension(:), allocatable	weights,
		integer, intent(out)	n_total_points
	)

Determines the radial grid needed to describe, integrals involving the CGTO and the B-splines on the given grid. We assume that if the CGTO spanned the whole B-spline grid it would be sufficient to use the given quadrature rule (x,w,n) within each knot interval. For CGTOs whose radial extent is smaller than the range of the B-spline grid the number of quadrature points within each knot interval is expanded by the factor ceiling(n_int/R), where R is the extent of the CGTO (determined to coincide with the nearest larger knot) and n_int is the number of distinct intervals of knots in the B-spline basis.

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radial_grid_CGTO_pair()

subroutine cgto_pw_expansions_gbl::radial_grid_CGTO_pair	(	type(cgto_shell_data_obj), intent(in)	cgto_A,
		type(cgto_shell_data_obj), intent(in)	cgto_B,
		real(kind=cfp), intent(in)	R_min,
		real(kind=cfp), intent(in)	R_max,
		real(kind=cfp), dimension(2*n+1), intent(in)	x,
		real(kind=cfp), dimension(2*n+1), intent(in)	w,
		integer, intent(in)	n,
		real(kind=cfp), intent(in)	delta_cgto_grid,
		real(kind=cfp), dimension(:), allocatable	r_points,
		real(kind=cfp), dimension(:), allocatable	weights,
		integer, intent(out)	n_total_points
	)

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radial_grid_mo()

subroutine cgto_pw_expansions_gbl::radial_grid_mo	(	real(kind=cfp), dimension(:), intent(in)	centers,
		real(kind=cfp), intent(in)	R_min,
		real(kind=cfp), intent(in)	R_max,
		type(bspline_grid_obj), intent(in)	bspline_grid,
		real(kind=cfp), intent(in)	delta_cgto_grid,
		real(kind=cfp), dimension(2*n+1), intent(in)	x,
		real(kind=cfp), dimension(2*n+1), intent(in)	w,
		integer, intent(in)	n,
		real(kind=cfp), dimension(:), allocatable	r_points,
		real(kind=cfp), dimension(:), allocatable	weights,
		integer, intent(out)	n_total_points
	)

Radial grid used when integrating over the molecular orbitals purely numerically.

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write_CGTO_shell_pw_expansion_obj()

subroutine cgto_pw_expansions_gbl::write_CGTO_shell_pw_expansion_obj

(

class(cgto_shell_pw_expansion_obj)

this

)

write_Y_lm_to_file()

subroutine cgto_pw_expansions_gbl::write_Y_lm_to_file	(	class(cgto_shell_pw_expansion_obj)	this,
		character(len=line_len), intent(in)	scratch_directory
	)

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Variable Documentation

cpl

type(couplings_type), public cgto_pw_expansions_gbl::cpl

Used to evaluate various coupling coefficients.

dbg_cgto

type(cgto_shell_data_obj), dimension(n_alp), public cgto_pw_expansions_gbl::dbg_cgto