Coulomb integral ($J_{ab}=\iint |a(1){|}^2|b(2){|}^2{r}_{12}^{-1}{d}^3{r}_1{d}^3{r}_2$)

In atomic units, the displayed integral is the direct electrostatic contribution between two normalized atomic orbitals $a,b$. It enters a two-electron energy expectation together with the exchange integral.