The energy defined in Eq. ( ) or ( ) is not suitable for the crossing region. The order of states is easily flipped near degeneracy, and the state-specific solvation model may exhibit discontinuities in the potential energy surface (PES). While OpenMolcas includes a feature that automatically selects the relevant state for applying solvent effects, the resulting energy remains non-invariant under rotations between crossing states, rendering the formulation unsuitable for exploring such regions. Therefore, an energy expression that remains invariant near degeneracy is required. To address this issue, the state-averaged energy in this study is defined as: (25) for crossing between states ϕ and χ (∈ P), where V