The unitary-group formulation of the open-shell random-phase approximation

Abstract

Hartree-Fock stability equations for an open-shell configuration have been derived in the unitary-group formulation. These stability equations are used to compute a generalized open-shell random-phase approximation (OSRPA), where excited states are generated from the same multiplicity Hartree-Fock (HF) ground-state orbitals. This differs from conventional triplet RPA, where excited-state triplets are calculated from closed-shell singlet HF orbitals. OSRPA yields real excitation energies wherever the HF orbitals for the given multiplicity are stable, which is not the case for conventional triplet RPA. OSRPA treats excited states of any multiplicity, and for triplets yields more excited states than does conventional triplet RPA. We treat the ally1 doublet and butadiene singlet and triplet in detail using the Hiickel-Hubbard Hamiltonian and compare OSRPA with conventional triplet RPA for the butadiene triplet.