Recent work from our research group has demonstrated that symmetry-projected
Hartree--Fock (HF) methods provide a compact representation of molecular ground
state wavefunctions based on a superposition of non-orthogonal Slater
determinants. The symmetry-projected ansatz can account for static correlations
in a computationally efficient way. Here we present a variational extension of
this methodology applicable to excited states of the same symmetry as the
ground state. Benchmark calculations on the C2 dimer with a modest basis
set, which allows comparison with full configuration interaction results,
indicate that this extension provides a high quality description of the
low-lying spectrum for the entire dissociation profile. We apply the same
methodology to obtain the full low-lying vertical excitation spectrum of
formaldehyde, in good agreement with available theoretical and experimental
data, as well as to a challenging model C2v insertion pathway for BeH2.
The variational excited state methodology developed in this work has two
remarkable traits: it is fully black-box and will be applicable to fairly large
systems thanks to its mean-field computational cost