which satisfies X † SX = I, where I is a unit matrix. Depending on the excitation class, the Hamiltonian (Eq. ( )) and overlap (Eq. ( )) have zero, two, four, or six indices of the active MO, but the explicit expression of the matrices is not essential in the derivation, so the indices are collectively written as η, ι, . . .: B ηι and S ηι . To distinguish between the two cases, the basis of the collective active MO (η, ι, . . .) is referred to as a non-orthogonal ICB in this study, whereas the orthonormalized basis is an orthogonal ICB and is indexed with υ and τ for linearly independent and dependent vectors, respectively. To generate orthogonal configurations, we have to solve the following generalized eigenvalue equation: