## Coulomb repulsion

https://doi.org/10.1351/goldbook.CT07013
The potential energy component corresponding to the electrostatic interaction between each pair of charged particles: $V=\frac{1}{4\: \pi\: \varepsilon_{0}}\ \sum _{i}\sum _{j \lt i}e_{i}\ e_{j}\ \Delta r_{ij}$ where ε0 is the permittivity of a vacuum, Δrij is the distance between the two particles, and ei and ej are the charges on particles i and j. In molecular orbital theory, the electrostatic repulsion between the two electrons occupying the orbitals Ψi and Ψj. In the Hartree–Fock method, the mean Coulomb repulsion is determined by the value of the coulomb integral $J_{ij}=\int \int \Psi _{i\text{*}}\left(\mathbf{r}_{1}\right)\ \Psi _{i}\left(\mathbf{r}_{1}\right)\ \left(\frac{e^{2}}{r_{12}}\right)\ \Psi _{j\text{*}}\left(\mathbf{r}_{2}\right)\ \Psi _{j}\left(\mathbf{r}_{2}\right) \ \mathrm{d}\mathbf{r}_{1} \ \mathrm{d}\mathbf{r}_{2} = \lt ij|ij \gt$