 Exchange integral

For two orthonormal spatial atomic orbitals, the normalized symmetric and antisymmetric two-particle factors have Coulomb energies $J_{ab}+K_{ab}$ and $J_{ab}-K_{ab}$. With common orbitals, the fermionic singlet state and triplet state therefore differ by $2K_{ab}$. This is an exchange interaction resulting from the state symmetry and the Coulomb operator, rather than a separate classical force.