In an atomic orbital (AO)-based formalism relying solely on occupied MOs, {i, j, k, l, . . . }, and AOs, {µ, ν, κ, λ, . . . }, it furthermore has to be ensured that the excited-state eigenvector X is orthogonal to the ground-state (GS) MO coefficients C (Eq. ( )), a constraint introduced in the Lagrangian G via the Lagrange multiplier WX ,