with X N sing and X N trip referring to the spin-adapted singlet and triplet excitation amplitudes and a, b, c, d, . . . indicating virtual orbitals. |Ψ 0 denotes the KS reference Slater determinant built from the ground-state KS orbitals φ iσ . As noted by Marian , Eqs. ( )-( ) can be obtained by choosing the AMEW with maximum spin quantum number and generating the remaining states by applying the Wigner-Eckhart theorem.