I am trying to understand SCF cycle by trying to code up solved example from Quantum Chemistry by Levine (page 443, 5th edition). The problem is shown below:
One electron integrals are straight forward and I was able to get the correct answer, however I still can get correct values for two election integral, lets say
(11|11). Given below is my attempt in octave
clear all; N=2000; zeta1 = 1.45; zeta2 = 2.91; r = linspace(0.000001,10,N)'; dr = r(2)-r(1); chi = @(zetad,x) (2*zetad.^(3/2))*exp(-zetad*x).*x; chichi = 0; for i =1:N chichi = chichi + dr*(chi(zeta1,r(i))*chi(zeta1,r(i))*chi(zeta1,r')*(chi(zeta1,r)./((r(i)-r) + 0.000001))); end chichi*dr
However my values are way off in this case. Can anyone please shed a light on it? Value of
(11|11) = 5/8 zeta1 = 0.9062.
Two electron integrals are defined in the book as: