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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:

scf helium problem statement

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:

two electron integrals

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  • $\begingroup$ You replaced the 6-fold integration by one in spherical coordinates. Not sure if that can work as easily as you wrote it and I'm not an expert on that transformation, but I think that some multiplicative constants from the angle integrations are missing. $\endgroup$ – TAR86 May 29 at 17:43
  • $\begingroup$ If you improve the formatting (remove the screenshots and type in MathJax the specific integral you are having trouble with) this question might be well received on materials.stackexchange.com $\endgroup$ – user1271772 Jun 1 at 0:45
  • $\begingroup$ I never realized there is a material stackechange. thank you for your suggestion, let me try my luck there! $\endgroup$ – ipcamit Jun 1 at 5:36

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