On the “killer condition’' in the equation-of-motion method: ionization potentials from multi-reference wave functions

The ionization operator Ω in the equation-of-motion (EOM) method is written in a form that satisfies the “killer condition ” ΩT∣Ψ0〉 = 0 for arbitrary multiconfigurational reference states. The resulting equation for ionization potentials is equivalent to traditional EOM equation only if the reference state is an exact eigenfunction of the Hamiltonian. The new equation is insensitive to specifying either a simple metric or the “commutator metric”, and it represents a Hermitian formulation even for partially optimized wave functions. It is, however, equivalent to a multi-reference CI equation for the ionized state using the extended Koopmans ansatz.