Low-Cost Molecular Excited States from a State-Averaged Resonating Hartree–Fock Approach

Quantum chemistry methods that describe excited states on the same footing as the ground state are generally scarce. In previous work, ( Gill J. Phys. Chem. A , 112 , 2008 , 13164 and later Sundstrom ; ; Head-Gordon J. Chem. Phys. , 140 , 2014 , 114103 ) considered excited states resulting from a nonorthogonal configuration interaction (NOCI) on stationary solutions of the Hartree-Fock equations. We build upon those contributions and present the state-averaged resonating Hartree-Fock (sa-ResHF) method, which differs from NOCI in that spin-projection and orbital relaxation effects are incorporated from the onset. Our results in a set of small molecules (alanine, formaldehyde, acetaldehyde, acetone, formamide, and ethylene) suggest that sa-ResHF excitation energies are a notable improvement over configuration interaction singles, at a mean-field computational cost. The orbital relaxation in sa-ResHF, carried out in the presence of a spin-projection operator, generally results in excitation energies that are closer to the EOM-CCSD and experimental values than the corresponding NOCI ones.