eri_mme_gaussian Module Reference

Methods related to properties of Hermite and Cartesian Gaussian functions. More...

Functions/Subroutines
pure subroutine, public	create_hermite_to_cartesian (zet, l_max, h_to_c)
	Create matrix to transform between cartesian and hermite gaussian basis functions. More...
pure real(kind=dp) function, public	hermite_gauss_norm (zet, l)
	Norm of 1d Hermite-Gauss functions. More...
subroutine, public	get_minimax_coeff_v_gspace (n_minimax, cutoff, G_min, minimax_aw, potential, pot_par, err_minimax)
	Get minimax coefficient a_i and w_i for approximating 1/G^2 by sum_i w_i exp(-a_i G^2) More...
pure subroutine, public	create_gaussian_overlap_dist_to_hermite (l, m, a, b, R1, R2, H_or_C_product, E)
	Expand 1d product of cartesian (or hermite) gaussians into single hermite gaussians: Find E_t^{lm} s.t. F(l, a, r-R1) * F(m, b, r-R2) = sum_{t=0}^{l+m} E_t^{lm} H(t, p, r-R_P) with p = a + b, R_P = (a*R1 + b*R2)/p. The function F can be either Cartesian Gaussian or Hermite Gaussian. More...

Variables
integer, parameter, public	eri_mme_coulomb = 1
integer, parameter, public	eri_mme_yukawa = 2
integer, parameter, public	eri_mme_longrange = 3

Detailed Description

Methods related to properties of Hermite and Cartesian Gaussian functions.

History

2015 09 created

Author

Patrick Seewald

Function/Subroutine Documentation

create_hermite_to_cartesian()

pure subroutine, public eri_mme_gaussian::create_hermite_to_cartesian	(	real(kind=dp), intent(in)	zet,
		integer, intent(in)	l_max,
		real(kind=dp), dimension(:, :), intent(out), allocatable	h_to_c
	)

Create matrix to transform between cartesian and hermite gaussian basis functions.

Parameters

zet	exponent
l_max	...
h_to_c	transformation matrix with dimensions (0:l_max, 0:l_max)

Note

is idempotent, so transformation is the same in both directions.

Definition at line 50 of file eri_mme_gaussian.F.

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hermite_gauss_norm()

pure real(kind=dp) function, public eri_mme_gaussian::hermite_gauss_norm	(	real(kind=dp), intent(in)	zet,
		integer, dimension(3), intent(in)	l
	)

Norm of 1d Hermite-Gauss functions.

Parameters

zet	...
l	...

Returns

...

Definition at line 75 of file eri_mme_gaussian.F.

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get_minimax_coeff_v_gspace()

subroutine, public eri_mme_gaussian::get_minimax_coeff_v_gspace	(	integer, intent(in)	n_minimax,
		real(kind=dp), intent(in)	cutoff,
		real(kind=dp), intent(in)	G_min,
		real(kind=dp), dimension(:), intent(out)	minimax_aw,
		integer, intent(in), optional	potential,
		real(kind=dp), intent(in), optional	pot_par,
		real(kind=dp), intent(out), optional	err_minimax
	)

Get minimax coefficient a_i and w_i for approximating 1/G^2 by sum_i w_i exp(-a_i G^2)

Parameters

n_minimax	Number of minimax terms
cutoff	Plane Wave cutoff
G_min	Minimum absolute value of G
minimax_aw	Minimax coefficients a_i, w_i
potential	potential to use. Accepts the following values: 1: coulomb potential V(r)=1/r 2: yukawa potential V(r)=e(-a*r)/r 3: long-range coulomb erf(a*r)/r
pot_par	potential parameter a for yukawa V(r)=e(-a*r)/r or long-range coulomb V(r)=erf(a*r)/r
err_minimax	Maximum error MAX (|1/G^2-\sum_i w_i exp(-a_i G^2)|)

Definition at line 98 of file eri_mme_gaussian.F.

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create_gaussian_overlap_dist_to_hermite()

pure subroutine, public eri_mme_gaussian::create_gaussian_overlap_dist_to_hermite	(	integer, intent(in)	l,
		integer, intent(in)	m,
		real(kind=dp), intent(in)	a,
		real(kind=dp), intent(in)	b,
		real(kind=dp), intent(in)	R1,
		real(kind=dp), intent(in)	R2,
		integer, intent(in)	H_or_C_product,
		real(kind=dp), dimension(-1:l+m+1, -1:l, -1:m), intent(out)	E
	)

Expand 1d product of cartesian (or hermite) gaussians into single hermite gaussians: Find E_t^{lm} s.t. F(l, a, r-R1) * F(m, b, r-R2) = sum_{t=0}^{l+m} E_t^{lm} H(t, p, r-R_P) with p = a + b, R_P = (a*R1 + b*R2)/p. The function F can be either Cartesian Gaussian or Hermite Gaussian.

Parameters

l	...
m	...
a	...
b	...
R1	...
R2	...
H_or_C_product	1: cartesian product, 2: hermite product
E	...

Definition at line 193 of file eri_mme_gaussian.F.

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Variable Documentation

eri_mme_coulomb

integer, parameter, public eri_mme_gaussian::eri_mme_coulomb = 1

Definition at line 29 of file eri_mme_gaussian.F.

eri_mme_yukawa

integer, parameter, public eri_mme_gaussian::eri_mme_yukawa = 2

Definition at line 29 of file eri_mme_gaussian.F.

eri_mme_longrange

integer, parameter, public eri_mme_gaussian::eri_mme_longrange = 3

Definition at line 29 of file eri_mme_gaussian.F.