We have located the MECP along the conical seam between the S 0 and S 1 states of PSB3 at the CIS/6-31G* level of theory. The energy difference between the two states is less than 10 -7 Ha. Taking this MECP as the origin, we carried out single-point energy scans for an arbitrary choice of R, with z constructed from R according to Eq. (B1). The S 1 /S 0 energy gap is plotted in Fig. as the red curve. It can be seen that the degeneracy between the two states is lifted even in the very near vicinity of the MECP. This indicates that the g vector itself is not sufficient to determine the branching space.