# Solving two electron integral

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 $\ldots$)

• Mar 7, 2016 at 16:34
• 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. Mar 9, 2016 at 14:10
• 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.
– pH13
Mar 9, 2016 at 14:57