Communication: Adjusting charge transfer state energies for configuration interaction singles: Without any parameterization and with minimal cost

In a recent article, we showed that configuration interaction singles (CIS) has a systematic bias against charge-transfer (CT) states: CT vertical excitation energies are consistently too high (by 1-2 eV) as compared with non-CT energies [J. E. Subotnik, J. Chem. Phys. 137, 071104 (2011)]. We now show that this CIS error can be corrected approximately by performing a single Newton-Raphson step to reoptimize orbitals, thus establishing a new set of orbitals which better balances ground and excited state energies. The computational cost of this correction is exactly that of one coupled-perturbed Hartree-Fock calculation, which is effectively the cost of the CIS calculation itself. In other words, for twice the computational cost of a standard CIS calculation, or roughly the same cost as a linear-response time-dependent Hartree-Fock calculation, one can achieve a balanced, size-consistent description of CT versus non-CT energies, ideally with the accuracy of a much more expensive doubles CIS(D) calculation.