A nonorthogonal CI treatment of symmetry breaking in sigma formyloxyl radical

Spatial symmetry breaking can occur in Hartree–Fock wave functions when there are two or more close lying configurations that can mix strongly, such as in ${\mathrm{HCO}}_{\mathrm{2}},$ ${\mathrm{NO}}_{\mathrm{2}},$ and allyl radical. Like spin contamination, spatial symmetry breaking can cause sizeable errors when perturbation theory is used to estimate the correlation energy. With conventional methodology, very large MCSCF and MRCI calculations are necessary to overcome the spatial symmetry breaking problem. This paper explores an alternative approach in which a 2×2 nonorthogonal CI is used to recombine the two symmetry broken Hartree–Fock determinants. The necessary matrix elements closely resemble those used in the spin projection calculations. Second order perturbation theory is used to include electron correlation energy in this approach. With perturbative corrections for correlation energy, this approach predicts that the ${}^2{B}_2$ structure is a minimum, in agreement with the best available calculations.