Equation-of-motion regularized orbital-optimized second-order perturbation theory with the density-fitting approximation.

The density-fitted equation-of-motion (EOM) orbital-optimized second-order perturbation theory (DF-EOM-OMP2) method is presented for the first time. In addition, κ-DF-EOM-MP2 and κ-DF-EOM-OMP2 methods are implemented with the addition of κ-regularization. The accuracy of the DF-EOM-OMP2, κ-DF-EOM-MP2, and κ-DF-EOM-OMP2 methods are compared to the density-fitted EOM-MP2 (DF-EOM-MP2), EOM coupled-cluster (CC) singles and doubles (DF-EOM-CCSD), and EOM-CCSD with the triples excitation correction model [EOM-CCSD(fT)] for excitation energies of many closed- and open-shell chemical systems. The excitation energies computed using different test cases and methods were compared to the EOM-CCSD(fT) method and mean absolute errors (MAEs) are presented. The MAE values of closed- and open-shell cases (closed-shell organic chromophores set, open-shell set, peptide radicals set, and radical set) according to the EOM-CCSD(fT) method show that the κ-regularization technique yields highly accurate results for the first excited states. Our results indicate that the κ-DF-EOM-MP2 and κ-DF-EOM-OMP2 methods perform noticeably better than the DF-EOM-MP2 and DF-EOM-OMP2 methods. They approach the EOM-CCSD quality, at a significantly reduced cost, for the computation of excitation energies. Especially, the κ-DF-EOM-MP2 method provides outstanding results for most test cases considered. Overall, we conclude that the κ-versions of DF-EOM-MP2 and DF-EOM-OMP2 emerge as a useful computational tool for the study of excited-state molecular properties.