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During one of my practical courses we had to do the Hartree-Fock-method "by hand". Part of that was to calculate the occurring two electron integrals.

With $$\chi_i(r) = 2 \cdot \alpha_i^{3/2} e^{-\alpha_i r} Y_0^0$$ we were given the following equation: $$\iint \frac{\chi_m(r_1)~\chi_n(r_1)~\chi_t(r_2)~\chi_u(r_2)}{|r_1-r_2|}~\mathrm d r_2 \mathrm d r_1$$ $$= 16\pi^2\int_0^{\infty}\int_0^{r_1} \chi_m(r_1)~\chi_n(r_1)~\chi_t(r_2)~\chi_u(r_2)~r_1~r_2^2~\mathrm d r_2 \mathrm d r_1$$ $$+ 16\pi^2\int_0^{\infty}\int_{r_1}^{\infty} \chi_m(r_1)~\chi_n(r_1)~\chi_t(r_2)~\chi_u(r_2)~r_1^2~r_2~\mathrm d r_2 \mathrm d r_1$$

What are the steps to come up with this? (At least I know where the $16\pi^2$ come from $\ldots$)

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    $\begingroup$ Take a look at: web.archive.org/web/20120907133630/http://www.files.chem.vt.edu/… $\endgroup$ – user1420303 Mar 7 '16 at 16:34
  • $\begingroup$ JFYI: Valeev Group page didn't disappear, it just have a bit different address. The notes on evaluation of molecular integrals were updated few times, the most current version (07.03.15) can be found in "teaching" section of the group site. $\endgroup$ – Wildcat Mar 9 '16 at 14:10
  • $\begingroup$ Thank you for the link. But could you tell me a little bit more about where they write about what I've written? I'm not very good at searching. $\endgroup$ – pH13 Mar 9 '16 at 14:57

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