We next consider how the basis of matrix B (indices for the excitation class and perturbed state γ are omitted) is transformed in the computation procedure to further analyze the noninvariance of CASPT2-IPEA. B is initially computed in the active MO basis (see Eq. ( ), for instance). However, the basis is generally non-orthonormal and can be linearly dependent, so we have to diagonalize the overlap matrix in the non-orthogonal basis first: