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Laplacian.f90 File Reference

Defines utility routines for computing laplacian integrals between gaussian basis elements. More...

Functions/Subroutines

recursive real(kind=8) function c_laplacian_c (alpha1, r1, nx1, ny1, nz1, alpha2, r2, nx2, ny2, nz2)
 Two centers Laplacian integrals for Cubic Spherical Harmonics (C) More...
 
recursive real(kind=8) function y_laplacian_y (alpha1, r1, l1, m1, alpha2, r2, l2, m2)
 Two centers Laplacian integrals for Solid Spherical Harmonics (Y) More...
 

Detailed Description

Defines utility routines for computing laplacian integrals between gaussian basis elements.

Author: I. Duchemin July 2015

Function/Subroutine Documentation

recursive real(kind=8) function c_laplacian_c ( real(kind=8)  alpha1,
real(kind=8), dimension(3)  r1,
integer  nx1,
integer  ny1,
integer  nz1,
real(kind=8)  alpha2,
real(kind=8), dimension(3)  r2,
integer  nx2,
integer  ny2,
integer  nz2 
)

Two centers Laplacian integrals for Cubic Spherical Harmonics (C)

$ \int dr \, Y_{xyz}^{(1)}(r-R_1) \left(\nabla^2 \, Y_{xyz}^{(2)}(r-R_2)\right) $

nx+ny+nz must stay <= 6 for each spherical harmonics

Parameters
r1center for first spherical Harmonic
r2center for second spherical Harmonic
alpha1exponent for first spherical Harmonic
alpha2exponent for second spherical Harmonic
nx1x power for first cubic Harmonic
ny1y power for first cubic Harmonic
nz1z power for first cubic Harmonic
nx2x power for second cubic Harmonic
ny2y power for second cubic Harmonic
nz2z power for second cubic Harmonic
recursive real(kind=8) function y_laplacian_y ( real(kind=8)  alpha1,
real(kind=8), dimension(3)  r1,
integer  l1,
integer  m1,
real(kind=8)  alpha2,
real(kind=8), dimension(3)  r2,
integer  l2,
integer  m2 
)

Two centers Laplacian integrals for Solid Spherical Harmonics (Y)

$ \int dr \, Y_{lm}^{(1)}(r-R_1) \left(\nabla^2 \, Y_{lm}^{(2)}(r-R_2)\right) $

l must stay <= 6 for each spherical harmonics

Parameters
r1center for first spherical Harmonic
r2center for second spherical Harmonic
alpha1exponent for first spherical Harmonic
alpha2exponent for second spherical Harmonic
l1angular momentum for first spherical Harmonic
l2angular momentum for second spherical Harmonic
m1orbital momentum for first spherical Harmonic
m2orbital momentum for second spherical Harmonic