= Exchange integral
{title2=$K_{ab}=\iint a^*(1)b(1)b^*(2)a(2)r_{12}^{-1}\,d^3r_1d^3r_2$}
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.
Back to article page
