Quasidegenerate scaled opposite spin second order perturbation corrections to single excitation configuration interaction.

Scaled opposite spin (SOS) second order perturbative corrections to single excitation configuration interaction (CIS) are extended to correctly treat quasidegeneracies between excited states. Two viable methods, termed as SOS-CIS(D(0)) and SOS-CIS(D(1)), are defined, implemented, and tested. Each involves one empirical parameter (plus a second for the SOS-MP2 ground state), has computational cost that scales with the fourth power of molecule size, and has storage requirements that are cubic, with only quantities of the rank of single excitations produced and stored during iterations. Tests on a set of low-lying adiabatic valence excitation energies and vertical Rydberg excitations of organic and inorganic molecules show that the empirical parameter can be acceptably transferred from the corresponding nondegenerate perturbation theories without any further fitting. Further tests on higher excited states show that the new methods correctly perform for surface crossings for which nondegenerate approaches fail. Numerical results show that SOS-CIS(D(0)) appears to treat Rydberg excitations in a more balanced way than SOS-CIS(D(1)) and is, therefore, likely to be the preferred approach. It should be useful for exploring excited state geometries, transition structures, and conical intersections for states of medium to large organic molecules that are dominated by single excitations.