It would be informative to compare the computational cost for the four MS-CASPT2 variants in the nuclear gradient calculation. There are three sources of difference. First, we need the derivative of the weight (Eq. ( )) for XDW, but this step is negligible, so the computational cost for XDW and RMS is almost identical. Second, XMS, XDW, and RMS require additional evaluations that arise from the rotation of the reference states. This evaluation is not negligible, but it is needed only once, so the cost is relatively small. Third, the Fock matrix at the MS, XDW, and RMS levels is defined with a state-dependent density matrix, while the one at the SCF level with the state-averaged density matrix. Due to this difference, the derivative of the Fock matrix at the PT2 level cannot be computed in a similar fashion to the one at the SCF level. To be specific, the derivative of the g pq (D) for the state-dependent Fock matrix is split following the equality: