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Coulomb.f90 File Reference

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

Functions/Subroutines

recursive real(kind=8) function r_x_r (alpha1, r1, c1, l1max, alpha2, r2, c2, l2max)
 
recursive real(kind=8) function c_coulomb_c (alpha1, r1, nx1, ny1, nz1, alpha2, r2, nx2, ny2, nz2)
 Two centers Repulsion integrals for Cubic Spherical Harmonics (C) More...
 
recursive real(kind=8) function y_coulomb_y (alpha1, r1, l1, m1, alpha2, r2, l2, m2)
 Two centers Repulsion integrals for Solid Spherical Harmonics (Y) More...
 
recursive real(kind=8) function cc_coulomb_ion (alpha1, r1, nx1, ny1, nz1, alpha2, r2, nx2, ny2, nz2, rion)
 Two centers ionic integrals for Cubic Spherical Harmonics (C) More...
 
recursive real(kind=8) function yy_coulomb_ion (alpha1, r1, l1, m1, alpha2, r2, l2, m2, rion)
 Two centers ionic integrals for Solid Spherical Harmonics (Y) More...
 
recursive real(kind=8) function cc_coulomb_c (alpha1, r1, nx1, ny1, nz1, alpha2, r2, nx2, ny2, nz2, alpha3, r3, nx3, ny3, nz3)
 Three centers Repulsion integrals for Cubic Spherical Harmonics (C) More...
 
recursive real(kind=8) function yy_coulomb_y (alpha1, r1, l1, m1, alpha2, r2, l2, m2, alpha3, r3, l3, m3)
 Three centers Repulsion integrals for Solid Spherical Harmonics (Y) More...
 
recursive real(kind=8) function cc_coulomb_cc (alpha1, r1, nx1, ny1, nz1, alpha2, r2, nx2, ny2, nz2, alpha3, r3, nx3, ny3, nz3, alpha4, r4, nx4, ny4, nz4)
 Four centers Repulsion integrals for Cubic Spherical Harmonics (C) More...
 
recursive real(kind=8) function yy_coulomb_yy (alpha1, r1, l1, m1, alpha2, r2, l2, m2, alpha3, r3, l3, m3, alpha4, r4, l4, m4)
 Four centers Repulsion integrals for Solid Spherical Harmonics (Y) More...
 
recursive real(kind=8) function y_modcoulomb_y (acut, alpha1, r1, l1, m1, alpha2, r2, l2, m2)
 Two centers Modified Repulsion integrals for Solid Spherical Harmonics (Y) More...
 
recursive real(kind=8) function yy_modcoulomb_y (acut, alpha1, r1, l1, m1, alpha2, r2, l2, m2, alpha3, r3, l3, m3)
 Three centers Electron Modified Repulsion integrals for Solid Spherical Harmonics (Y) More...
 

Detailed Description

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

Author: I. Duchemin July 2015

Function/Subroutine Documentation

recursive real(kind=8) function c_coulomb_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 Repulsion integrals for Cubic Spherical Harmonics (C)

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

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_coulomb_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 Repulsion integrals for Cubic Spherical Harmonics (C)

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

Parameters
r1center for first cubic Harmonic
r2center for second cubic Harmonic
r3center for third cubic Harmonic
alpha1exponent for first spherical Harmonic
alpha2exponent for second spherical Harmonic
alpha3exponent for third 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
nx3x power for third cubic Harmonic
ny3y power for third cubic Harmonic
nz3z power for third cubic Harmonic
recursive real(kind=8) function cc_coulomb_cc ( 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,
real(kind=8)  alpha4,
real(kind=8), dimension(3)  r4,
integer  nx4,
integer  ny4,
integer  nz4 
)

Four centers Repulsion integrals for Cubic Spherical Harmonics (C)

$ \int dr \, dr' \, Y_{xyz}^{(1)}(r-R_1) Y_{xyz}^{(2)}(r-R_2) \frac{1}{|r-r'|} Y_{xyz}^{(3)}(r'-R_3) Y_{xyz}^{(4)}(r'-R_4) $

Parameters
r1center for first cubic Harmonic
r2center for second cubic Harmonic
r3center for third cubic Harmonic
r4center for fourth cubic Harmonic
alpha1exponent for first spherical Harmonic
alpha2exponent for second spherical Harmonic
alpha3exponent for third spherical Harmonic
alpha4exponent for fourth 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
nx3x power for third cubic Harmonic
ny3y power for third cubic Harmonic
nz3z power for third cubic Harmonic
nx4x power for fourth cubic Harmonic
ny4y power for fourth cubic Harmonic
nz4z power for fourth cubic Harmonic
recursive real(kind=8) function cc_coulomb_ion ( 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), dimension(3)  rion 
)

Two centers ionic integrals for Cubic Spherical Harmonics (C)

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

Parameters
r1center for first cubic Harmonic
r2center for second cubic Harmonic
rionion position
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 r_x_r ( real(kind=8)  alpha1,
real(kind=8), dimension(3)  r1,
real(kind=8), dimension(455)  c1,
integer  l1max,
real(kind=8)  alpha2,
real(kind=8), dimension(3)  r2,
real(kind=8), dimension(455)  c2,
integer  l2max 
)
Parameters
r1center for first cubic Harmonic
r2center for second cubic Harmonic
alpha1exponent for first cubic Harmonic
alpha2exponent for second cubic Harmonic
l1maxmax order for first cubic Harmonic
l2maxmax order for second cubic Harmonic
c1coefficients of first cubic Harmonic in the R basis
c2coefficients of second cubic Harmonic in the R basis
recursive real(kind=8) function y_coulomb_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 Repulsion integrals for Solid Spherical Harmonics (Y)

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

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 y_modcoulomb_y ( real(kind=8)  acut,
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 Modified Repulsion integrals for Solid Spherical Harmonics (Y)

/ compute | dr1 dr2 Ylm1(r1-R1) * Y00(r1-R2) * 1/|r1-r2| * Ylm2(r2-R2) /

Parameters
r1center for first spherical Harmonic
r2center for second spherical Harmonic
acutexponent for cutoff 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_coulomb_ion ( 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), dimension(3)  rion 
)

Two centers ionic integrals for Solid Spherical Harmonics (Y)

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

Parameters
r1center for first spherical Harmonic
r2center for second spherical Harmonic
rionion position
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_coulomb_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 Repulsion integrals for Solid Spherical Harmonics (Y)

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

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
recursive real(kind=8) function yy_coulomb_yy ( 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,
real(kind=8)  alpha4,
real(kind=8), dimension(3)  r4,
integer  l4,
integer  m4 
)

Four centers Repulsion integrals for Solid Spherical Harmonics (Y)

$ \int dr \, dr' \, Y_{lm}^{(1)}(r-R_1) Y_{lm}^{(2)}(r-R_2) \frac{1}{|r-r'|} Y_{lm}^{(3)}(r'-R_3) Y_{lm}^{(4)}(r'-R_4) $

Parameters
r1center for first spherical Harmonic
r2center for second spherical Harmonic
r3center for third spherical Harmonic
r4center for third spherical Harmonic
alpha1exponent for first spherical Harmonic
alpha2exponent for second spherical Harmonic
alpha3exponent for third spherical Harmonic
alpha4exponent for third spherical Harmonic
l1angular momentum for first spherical Harmonic
l2angular momentum for second spherical Harmonic
l3angular momentum for third spherical Harmonic
l4angular momentum for third spherical Harmonic
m1orbital momentum for first spherical Harmonic
m2orbital momentum for second spherical Harmonic
m3orbital momentum for third spherical Harmonic
m4orbital momentum for third spherical Harmonic
recursive real(kind=8) function yy_modcoulomb_y ( real(kind=8)  acut,
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 Electron Modified Repulsion integrals for Solid Spherical Harmonics (Y)

/ compute | dr1 dr2 Ylm1(r1-R1) * Ylm2(r1-R2) * Y00(r1-R3) * 1/|r1-r2| * Ylm3(r2-R3) /

Parameters
r1center for first spherical Harmonic
r2center for second spherical Harmonic
r3center for third spherical Harmonic
acutexponent for cutoff 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