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Recent work from our research group has demonstrated that symmetry-projectedHartree--Fock (HF) methods provide a compact representation of molecular groundstate wavefunctions based on a superposition of non-orthogonal Slaterdeterminants. The symmetry-projected ansatz can account for static correlationsin a computationally efficient way. Here we present a variational extension ofthis methodology applicable to excited states of the same symmetry as theground state. Benchmark calculations on the C$_2$ dimer with a modest basisset, which allows comparison with full configuration interaction results,indicate that this extension provides a high quality description of thelow-lying spectrum for the entire dissociation profile. We apply the samemethodology to obtain the full low-lying vertical excitation spectrum offormaldehyde, in good agreement with available theoretical and experimentaldata, as well as to a challenging model $C_{2v}$ insertion pathway for BeH$_2$.The variational excited state methodology developed in this work has tworemarkable traits: it is fully black-box and will be applicable to fairly largesystems thanks to its mean-field computational cost.

Excited electronic states from a variational approach based on symmetry-projected Hartree--Fock configurations