Orbital-Optimized Second-Order Perturbation Theory with Density-Fitting and Cholesky Decomposition Approximations: An Efficient Implementation.

An efficient implementation of the orbital-optimized second-order perturbation theory with the density-fitting (DF-OMP2) and Cholesky decomposition (CD-OMP2) approaches is presented. The DF-OMP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost with the conventional orbital-optimized MP2 (OMP2) [Bozkaya, U.; Turney, J. M.; Yamaguchi, Y.; Schaefer, H. F.; Sherrill, C. D. J. Chem. Phys. 2011, 135, 104103] and the orbital-optimized MP2 with the resolution of the identity approach (OO-RI-MP2) [Neese, F.; Schwabe, T.; Kossmann, S.; Schirmer, B.; Grimme, S. J. Chem. Theory Comput. 2009, 5, 3060-3073]. Our results demonstrate that the DF-OMP2 method provides substantially lower computational costs than OMP2 and OO-RI-MP2. Further application results show that the orbital-optimized methods are very beneficial for the computation of open-shell noncovalent interactions. Considering both computational efficiency and the accuracy of the DF-OMP2 method, we conclude that DF-OMP2 is very promising for the study of weak interactions in open-shell molecular systems.