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... | |
Defines utility routines for computing coulomb integrals between gaussian basis elements.
Author: I. Duchemin July 2015
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)
r1 | center for first cubic Harmonic |
r2 | center for second cubic Harmonic |
alpha1 | exponent for first cubic Harmonic |
alpha2 | exponent for second cubic Harmonic |
nx1 | x power for first cubic Harmonic |
ny1 | y power for first cubic Harmonic |
nz1 | z power for first cubic Harmonic |
nx2 | x power for second cubic Harmonic |
ny2 | y power for second cubic Harmonic |
nz2 | z 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)
r1 | center for first cubic Harmonic |
r2 | center for second cubic Harmonic |
r3 | center for third cubic Harmonic |
alpha1 | exponent for first spherical Harmonic |
alpha2 | exponent for second spherical Harmonic |
alpha3 | exponent for third spherical Harmonic |
nx1 | x power for first cubic Harmonic |
ny1 | y power for first cubic Harmonic |
nz1 | z power for first cubic Harmonic |
nx2 | x power for second cubic Harmonic |
ny2 | y power for second cubic Harmonic |
nz2 | z power for second cubic Harmonic |
nx3 | x power for third cubic Harmonic |
ny3 | y power for third cubic Harmonic |
nz3 | z 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)
r1 | center for first cubic Harmonic |
r2 | center for second cubic Harmonic |
r3 | center for third cubic Harmonic |
r4 | center for fourth cubic Harmonic |
alpha1 | exponent for first spherical Harmonic |
alpha2 | exponent for second spherical Harmonic |
alpha3 | exponent for third spherical Harmonic |
alpha4 | exponent for fourth spherical Harmonic |
nx1 | x power for first cubic Harmonic |
ny1 | y power for first cubic Harmonic |
nz1 | z power for first cubic Harmonic |
nx2 | x power for second cubic Harmonic |
ny2 | y power for second cubic Harmonic |
nz2 | z power for second cubic Harmonic |
nx3 | x power for third cubic Harmonic |
ny3 | y power for third cubic Harmonic |
nz3 | z power for third cubic Harmonic |
nx4 | x power for fourth cubic Harmonic |
ny4 | y power for fourth cubic Harmonic |
nz4 | z 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)
r1 | center for first cubic Harmonic |
r2 | center for second cubic Harmonic |
rion | ion position |
alpha1 | exponent for first cubic Harmonic |
alpha2 | exponent for second cubic Harmonic |
nx1 | x power for first cubic Harmonic |
ny1 | y power for first cubic Harmonic |
nz1 | z power for first cubic Harmonic |
nx2 | x power for second cubic Harmonic |
ny2 | y power for second cubic Harmonic |
nz2 | z 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 | ||
) |
r1 | center for first cubic Harmonic |
r2 | center for second cubic Harmonic |
alpha1 | exponent for first cubic Harmonic |
alpha2 | exponent for second cubic Harmonic |
l1max | max order for first cubic Harmonic |
l2max | max order for second cubic Harmonic |
c1 | coefficients of first cubic Harmonic in the R basis |
c2 | coefficients 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)
r1 | center for first spherical Harmonic |
r2 | center for second spherical Harmonic |
alpha1 | exponent for first spherical Harmonic |
alpha2 | exponent for second spherical Harmonic |
l1 | angular momentum for first spherical Harmonic |
l2 | angular momentum for second spherical Harmonic |
m1 | orbital momentum for first spherical Harmonic |
m2 | orbital 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) /
r1 | center for first spherical Harmonic |
r2 | center for second spherical Harmonic |
acut | exponent for cutoff spherical Harmonic |
alpha1 | exponent for first spherical Harmonic |
alpha2 | exponent for second spherical Harmonic |
l1 | angular momentum for first spherical Harmonic |
l2 | angular momentum for second spherical Harmonic |
m1 | orbital momentum for first spherical Harmonic |
m2 | orbital 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)
r1 | center for first spherical Harmonic |
r2 | center for second spherical Harmonic |
rion | ion position |
alpha1 | exponent for first spherical Harmonic |
alpha2 | exponent for second spherical Harmonic |
l1 | angular momentum for first spherical Harmonic |
l2 | angular momentum for second spherical Harmonic |
m1 | orbital momentum for first spherical Harmonic |
m2 | orbital 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)
r1 | center for first spherical Harmonic |
r2 | center for second spherical Harmonic |
r3 | center for third spherical Harmonic |
alpha1 | exponent for first spherical Harmonic |
alpha2 | exponent for second spherical Harmonic |
alpha3 | exponent for third spherical Harmonic |
l1 | angular momentum for first spherical Harmonic |
l2 | angular momentum for second spherical Harmonic |
l3 | angular momentum for third spherical Harmonic |
m1 | orbital momentum for first spherical Harmonic |
m2 | orbital momentum for second spherical Harmonic |
m3 | orbital 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)
r1 | center for first spherical Harmonic |
r2 | center for second spherical Harmonic |
r3 | center for third spherical Harmonic |
r4 | center for third spherical Harmonic |
alpha1 | exponent for first spherical Harmonic |
alpha2 | exponent for second spherical Harmonic |
alpha3 | exponent for third spherical Harmonic |
alpha4 | exponent for third spherical Harmonic |
l1 | angular momentum for first spherical Harmonic |
l2 | angular momentum for second spherical Harmonic |
l3 | angular momentum for third spherical Harmonic |
l4 | angular momentum for third spherical Harmonic |
m1 | orbital momentum for first spherical Harmonic |
m2 | orbital momentum for second spherical Harmonic |
m3 | orbital momentum for third spherical Harmonic |
m4 | orbital 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) /
r1 | center for first spherical Harmonic |
r2 | center for second spherical Harmonic |
r3 | center for third spherical Harmonic |
acut | exponent for cutoff spherical Harmonic |
alpha1 | exponent for first spherical Harmonic |
alpha2 | exponent for second spherical Harmonic |
alpha3 | exponent for third spherical Harmonic |
l1 | angular momentum for first spherical Harmonic |
l2 | angular momentum for second spherical Harmonic |
l3 | angular momentum for third spherical Harmonic |
m1 | orbital momentum for first spherical Harmonic |
m2 | orbital momentum for second spherical Harmonic |
m3 | orbital momentum for third spherical Harmonic |