Minimax-Ewald (MME) method for calculating 2-center and 3-center electron repulsion integrals (ERI) of periodic systems using a Hermite Gaussian basis. The method relies on analytical Fourier transforms of Cartesian and Hermite Gaussian functions and Poisson summation formula to represent ERIs as a discrete sum over direct lattice vectors or reciprocal lattice vectors. The reciprocal space potential 1/G^2 is approximated by a linear combination of Gaussians employing minimax approximation. Not yet implemented: 3c ERIs for nonorthogonal cells. More...

Functions/Subroutines
subroutine, public	eri_mme_2c_integrate (param, la_min, la_max, lb_min, lb_max, zeta, zetb, rab, hab, o1, o2, g_count, r_count, normalize, potential, pot_par)
	Low-level integration routine for 2-center ERIs.

subroutine, public	eri_mme_3c_integrate (param, la_min, la_max, lb_min, lb_max, lc_min, lc_max, zeta, zetb, zetc, ra, rb, rc, habc, o1, o2, o3, gg_count, gr_count, rr_count)
	Low-level integration routine for 3-center ERIs.

Detailed Description

Minimax-Ewald (MME) method for calculating 2-center and 3-center electron repulsion integrals (ERI) of periodic systems using a Hermite Gaussian basis. The method relies on analytical Fourier transforms of Cartesian and Hermite Gaussian functions and Poisson summation formula to represent ERIs as a discrete sum over direct lattice vectors or reciprocal lattice vectors. The reciprocal space potential 1/G^2 is approximated by a linear combination of Gaussians employing minimax approximation. Not yet implemented: 3c ERIs for nonorthogonal cells.

History: 2015 09 created

Author: Patrick Seewald

Function/Subroutine Documentation

◆ eri_mme_2c_integrate()

subroutine, public eri_mme_integrate::eri_mme_2c_integrate	(	type(eri_mme_param), intent(in)	param,
		integer, intent(in)	la_min,
		integer, intent(in)	la_max,
		integer, intent(in)	lb_min,
		integer, intent(in)	lb_max,
		real(kind=dp), intent(in)	zeta,
		real(kind=dp), intent(in)	zetb,
		real(kind=dp), dimension(3), intent(in)	rab,
		real(kind=dp), dimension(:, :), intent(inout)	hab,
		integer, intent(in)	o1,
		integer, intent(in)	o2,
		integer, intent(inout), optional	g_count,
		integer, intent(inout), optional	r_count,
		logical, intent(in), optional	normalize,
		integer, intent(in), optional	potential,
		real(kind=dp), intent(in), optional	pot_par
	)

Low-level integration routine for 2-center ERIs.

Parameters

param	...
la_min	...
la_max	...
lb_min	...
lb_max	...
zeta	...
zetb	...
rab	...
hab	...
o1	...
o2	...
G_count	...
R_count	...
normalize	calculate integrals w.r.t. normalized Hermite-Gaussians
potential	use exact potential instead of minimax approx. (for testing only)
pot_par	potential parameter

Definition at line 70 of file eri_mme_integrate.F.

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◆ eri_mme_3c_integrate()

subroutine, public eri_mme_integrate::eri_mme_3c_integrate	(	type(eri_mme_param), intent(in)	param,
		integer, intent(in)	la_min,
		integer, intent(in)	la_max,
		integer, intent(in)	lb_min,
		integer, intent(in)	lb_max,
		integer, intent(in)	lc_min,
		integer, intent(in)	lc_max,
		real(kind=dp), intent(in)	zeta,
		real(kind=dp), intent(in)	zetb,
		real(kind=dp), intent(in)	zetc,
		real(kind=dp), dimension(3), intent(in)	ra,
		real(kind=dp), dimension(3), intent(in)	rb,
		real(kind=dp), dimension(3), intent(in)	rc,
		real(kind=dp), dimension(:, :, :), intent(inout)	habc,
		integer, intent(in)	o1,
		integer, intent(in)	o2,
		integer, intent(in)	o3,
		integer, intent(inout), optional	gg_count,
		integer, intent(inout), optional	gr_count,
		integer, intent(inout), optional	rr_count
	)

Low-level integration routine for 3-center ERIs.