γ . Once SCF convergence is achieved, the conventional SA-MCSCF energy (in the gas phase) remains invariant with respect to internal and external state rotations. However, when applying the formulation from the previous section, this invariance does not hold for states γ ̸ = ϕ . Moreover, due to the unequal averaging of the solute density for polarizing the ASCs, the SA-MCSCF energy is not invariant under rotations between internal states. While the following formulation and implementation are valid for γ ̸ = ϕ , in this study, we restrict calculations to cases where γ = ϕ , as the energy for γ ̸ = ϕ lacks physical significance.