XMS, XDW, and RMS are regulated using the ζ parameter in Eq. (21). At the limit ζ → 0, XDW corresponds to XMS, whereas at the limit ζ → ∞ to RMS. As ζ → 0, the density matrix used in the Fock operator (Eq. ( )) is averaged with equal weights for all states in the perturbation calculation. Consequently, the zeroth-order Hamiltonian (Eq. ( ))