Although XMS can produce smooth PESs, using the state-averaged density matrix in Ĥ(0) may in general decrease the accuracy compared to MS. The idea of interpolating between them has motivated the development of XDW and RMS. First, similarly to XMS, the Fock operator is diagonalized to produce a set of rotated reference states (Eq. ( )). In this transformation, the (equally) state-averaged Fock operator is used; therefore, it is totally equivalent to XMS. In XDW, the density matrix used in the construction of the Fock operator for the perturbed state α is averaged using dynamical weights ω β α as follows: