The one-electron part requires only one-electron transition density matrix for the final SOC matrix elements. The two-electron part requires the SO two-electron integrals and twoelectron transition densities, which makes the full calculation expensive. However, the twoelectron contribution can be effectively approximated by considering only the separable part of the two-electron transition density, such that the two-electron SO integrals are first contracted with the density of the reference determinant (usually Hartree-Fock determinant), and the resulting mean-field-like one-electron operator is then folded into the one-electron part. This spin-orbit mean-field approximation (SOMF) is commonly used in calculations of SOCs ; it is described in Section II D.