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Overlap.f90 File Reference

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

Functions/Subroutines

recursive real(kind=8) function c_overlap_c (alpha1, r1, nx1, ny1, nz1, alpha2, r2, nx2, ny2, nz2)
 Two centers overlap integral for Cubic Spherical Harmonics (C) More...
 
recursive real(kind=8) function y_overlap_y (alpha1, r1, l1, m1, alpha2, r2, l2, m2)
 Two centers overlap integral for Solid Spherical Harmonics (Y) More...
 
recursive real(kind=8) function cc_overlap_c (alpha1, r1, nx1, ny1, nz1, alpha2, r2, nx2, ny2, nz2, alpha3, r3, nx3, ny3, nz3)
 Three centers overlap integral for Cubic Spherical Harmonics (C) More...
 
recursive real(kind=8) function yy_overlap_y (alpha1, r1, l1, m1, alpha2, r2, l2, m2, alpha3, r3, l3, m3)
 Three centers overlap integral for Solid Spherical Harmonics (Y) More...
 

Detailed Description

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

Author: I. Duchemin July 2015

Function/Subroutine Documentation

recursive real(kind=8) function c_overlap_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 overlap integral for Cubic Spherical Harmonics (C)

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

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

Parameters
r1center for first cubic Harmonic
r2center for second cubic Harmonic
alpha1exponent for first cubic Harmonic
alpha2exponent for second cubic 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 cc_overlap_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,
real(kind=8)  alpha3,
real(kind=8), dimension(3)  r3,
integer  nx3,
integer  ny3,
integer  nz3 
)

Three centers overlap integral for Cubic Spherical Harmonics (C)

$ \int dr \, Y_{xyz}^{(1)}(r-R_1) Y_{xyz}^{(2)}(r-R_2) Y_{xyz}^{(3)}(r-R_3) $

l_tot must stay <= 14

Parameters
r1center for first cubic Harmonic
r2center for second cubic Harmonic
r3center for third cubic Harmonic
alpha1exponent for first cubic Harmonic
alpha2exponent for second cubic Harmonic
alpha3exponent for third cubic 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
nx3x power for third cubic Harmonic
ny3y power for third cubic Harmonic
nz3z power for third cubic Harmonic
recursive real(kind=8) function y_overlap_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 overlap integral for Solid Spherical Harmonics (Y)

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

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
recursive real(kind=8) function yy_overlap_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,
real(kind=8)  alpha3,
real(kind=8), dimension(3)  r3,
integer  l3,
integer  m3 
)

Three centers overlap integral for Solid Spherical Harmonics (Y)

$ \int dr \, Y_{lm}^{(1)}(r-R_1) Y_{lm}^{(2)}(r-R_2) Y_{lm}^{(3)}(r-R_3) $

l_tot must stay <= 14

Parameters
r1center for first spherical Harmonic
r2center for second spherical Harmonic
r3center for third spherical Harmonic
alpha1exponent for first spherical Harmonic
alpha2exponent for second spherical Harmonic
alpha3exponent for third spherical Harmonic
l1angular momentum for first spherical Harmonic
l2angular momentum for second spherical Harmonic
l3angular momentum for third spherical Harmonic
m1orbital momentum for first spherical Harmonic
m2orbital momentum for second spherical Harmonic
m3orbital momentum for third spherical Harmonic