Analytical gradient for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory method (DLPNO-MP2)

Building upon our previously published work [P. Pinski and F. Neese, J. Chem. Phys. 148, 031101 (2018)], we derive the formally complete analytical gradient for the domain-based local pair natural orbital second order Møller-Plesset (MP2) perturbation theory method. Extensive testing of geometry optimizations shows that the deviations from resolution of the identity-based MP2 structures are small. Covalent bond lengths are reproduced to within 0.1 pm, whereas errors in interatomic distances between noncovalently interacting system parts do not exceed 1% with default truncation thresholds and 0.3% with tight thresholds. Moreover, we introduce a procedure to circumvent instabilities of the gradient caused by singular coupled-perturbed localization equations, as they occur for some symmetric systems with continuously degenerate localized orbitals. The largest system for which a geometry optimization was completed is a host-guest complex with over 200 atoms and more than 4000 basis functions (triple-zeta basis). The most demanding single-point gradient calculation was performed for the small protein crambin containing 644 atoms and over 12 000 basis functions.