## exchange repulsion

Also contains definition of: exchange integral
https://doi.org/10.1351/goldbook.ET07034
The correction to the @CT07013@ between two electrons in orbitals $$\Psi _{i}$$ and $$\Psi _{j}$$ for the case when the electrons possess parallel spins. It is to be subtracted from the @CT07013@ to give the total energy of the electron–electron interaction. In the @H02747@–Fock theory the magnitude of the exchange repulsion is given by the exchange integral $K_{ij}=\int \int \Psi _{i}^{\text{*}}\left(\mathbf{r}_{1}\right)\ \Psi _{j}^{\text{*}}\left(\mathbf{r}_{1}\right)\ \left(\frac{e^{2}}{r_{12}}\right)\ \Psi _{i}\left(\mathbf{r}_{2}\right)\ \Psi _{j}\left(\mathbf{r}_{2}\right) \ \mathrm{d}\mathbf{r}_{1} \ \mathrm{d}\mathbf{r}_{2}=\lt ij|ji \gt$ For the case of electrons with opposite spins $$K_{ij}$$ vanishes.
Source:
PAC, 1999, 71, 1919. (Glossary of terms used in theoretical organic chemistry) on page 1938 [Terms] [Paper]