Here, E 0 is the Hartree-Fock (HF) energy. We use i, j, . . . to indicate occupied MOs and a, b, . . . for virtual MOs, as determined by the HF reference state. Now suppose that two electronic states |Ψ I and |Ψ J become degenerate at a geometry R CX . It is possible to define the so-called "crude" adiabatic basis, 32