A Doubles Correction to Electronic Excited States from Configuration Interaction in the Space of Single Substitutions

A perturbative correction to the method of configuration interaction with single substitutions (CIS) is presented. This CIS(D) correction approximately introduces the effect of double substitutions which are absent in CIS excited states. CIS(D) is a second-order perturbation expansion of the coupled-cluster excited state method, restricted to single and double substitutions, in a series in which CIS is zeroth order, and the first-order correction vanishes. CIS (D) excitation energies are size consistent and the calculational complexity scales with the fifth power of molecular size, akin to second-order Moller-Plesset theory for the ground state. Calculations on singlet excited states of ethylene, formaldehyde, acetaldehyde, butadiene and benzene show that CIS (D) is a uniform improvement over CIS. CIS(D) appears to be a promising method for examining excited states of large molecules, where more accurate methods are not feasible.