A complete OSV-MP2 analytical gradient theory for molecular structure and dynamics simulations

We propose an exact algorithm for computing the analytical gradient within the framework of the orbital-specific-virtual (OSV) second-order Moller-Plesset (MP2) theory in resolution-of-identity (RI) approximation. We implement the relaxation of perturbed OSVs through the explicit constraints of the perturbed orthonormality, the perturbed diagonality and the perturbed eigenvalue condition. We show that the rotation of OSVs within the retained OSV subspace makes no contribution to gradients, as long as the unperturbed Hylleraas energy functional reaches minimum. The OSV relaxation is solved as the perturbed non-degenerate eigenvalue problem between the retained and discarded OSV subspaces. The detailed derivation and preliminary implementations for gradient working equations are discussed. The coupled-perturbed localization method is implemented for meta-Lowdin localization function. The numerical accuracy of computed OSV-MP2 gradients is demonstrated for the geometries of selected molecules that are often ...