Two-electron exchange integral ($K_{pq}$)

For real spatial orbitals, $K_{pq}=\iint {\varphi }_p(1){\varphi }_q(1)r_{12}^{-1}{\varphi }_q(2){\varphi }_p(2)d1d2$ in atomic units. It enters the energy of a Slater determinant through antisymmetry and becomes small for well-separated localized orbitals.