A diagnostic for the applicability of the CIS and CIS(D) excitation energy methods

A ‘theta diagnostic’ is introduced that measures the reliability of the single excitation configuration interaction (CIS) approach to excitation energies, and a second order perturbation correction, CIS(D). This diagnostic characterizes the extent of mixing between CIS excited states due to electron correlation effects through second order in a Møller-Plesset expansion. Its evaluation requires negligible additional computation in a CIS(D) calculation. Calculations on ethylene, formaldehyde, nitric acid, chlorine nitrate, styrene and benzaldehyde are presented to show its utility. Small diagnostic values indicate the CIS states are stable to near-degeneracy effects.