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 Møller–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 nondegenerate 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-Löwdin localization function. The numerical accuracy of computed OSV-MP2 gradients is demonstrated for the geometries of selected molecules that are often discussed in other theories. From OSV-MP2 with the normal OSV selection, the canonical RI-MP2/def2-TZVP gradients can be reproduced within 10–4au. The OSV-MP2/def2-TZVPP covalent bond lengths, angles, and dihedral angles are in good agreement with canonical RI-MP2 structures by 0.017 pm, 0.03°, and 0.2°, respectively. No particular accuracy gains have been observed for molecular geometries compared to the recent local pair-natural-orbital MP2 by using the predefined orbital domains. Moreover, the OSV-MP2 analytical gradients can generate atomic forces that are utilized to drive the Born–Oppenheimer molecular dynamics (BOMD) simulation for studying structural and vibrational properties with respect to OSV selections. By performing the OSV-MP2 NVE BOMD calculation using the normal OSV selection, the structural and vibrational details of protonated water cations are well reproduced. The 200 ps NVT well-tempered metadynamics at 300 K has been simulated to compute the OSV-MP2 rotational free-energy surface of coupled hydroxyl and methyl rotors for ethanol molecule.