The x and ŷ vectors (in atomic units) are obtained as a linear combination of the gradient difference and interstate coupling vectors following the definition given in Ref. 64, forming the branching plane. Although the PES of MS (Figure ) is considerably affected by artifacts and the surfaces are significantly distorted, those of the other CASPT2 variants (Figure and) are similar and exhibit no apparent irregularities. The local topology of MECIs can be identified using two parameters P and B, which represent the asymmetry of the CI -the relative tilt and its direction at the MECI structure. As per these parameters, the MECI at XMS, XDW, and RMS is a peaked single-path CI. This topological character agrees well with the plots shown in Figure . The MECI at MS is predicted to be peaked bifurcating; however, the PES is strongly distorted at this point, and so it is difficult to characterize it from Figure . Because the non-invariance character of MS, XDW, and RMS can be significant around the MECI structure obtained at the SA-CASSCF level of theory, it is important to verify the PES around that point. In Figure , the energy difference between the first two states (S 0 and S 1 ) is plotted as a function of displacement in the branching space around the MECI. Again, the PES of MS is unreliable. In particular, in the vicinity of this CI from SA-CASSCF (x = ŷ = 0.00), it exhibits a strong discontinuity. On the contrary, the other CASPT2 variants do not show any severe problems, even though a few discontinuities appear for RMS.