The analytical gradient of dual-basis resolution-of-the-identity second-order Møller–Plesset perturbation theory

In this work, we present the analytical gradient of dual-basis second-order Moller–Plesset perturbation theory within the resolution-of-the-identity approximation (DB-RI-MP2). Interestingly, analytical DB-RI-MP2 gradient theory involves significant changes to both the theory and computation of the coupled-perturbed self-consistent field equations (CPSCF). From a theoretical point of view, the number of orbital responses required in DB-RI-MP2 analytical gradient theory has been reduced to the product of the number of occupied and virtual orbitals determined by the rank of the small atomic orbital (AO) basis. From a computational point of view, the DB-CPSCF equations can be solved within this smaller space at a fraction of the computational cost. Additional computational savings can be obtained during the digestion of the four-centered AO integral derivatives and the efficient underlying DB-SCF procedure, which lead to a significant overall reduction in the computational cost necessary for treating molecula...