An extrapolation method for the efficient calculation of molecular response properties within Born―Oppenheimer molecular dynamics

The calculation of molecular response properties in dynamic molecular systems is a major challenge that requires sampling over many steps of, e.g., Born-Oppenheimer molecular dynamics (BO-MD) simulations. We present an extrapolation scheme to accelerate such calculations for multiple steps within BO-MD trajectories or equivalently within other sampling methods of conformational space. The extrapolation scheme is related to the one introduced by Pulay and Fogarasi [Chem. Phys. Lett., 2004, 386, 272] for self-consistent field (SCF) energy calculations. We extend the extrapolation to the quantities within our density matrix-based Laplace-transformed coupled perturbed SCF (DL-CPSCF) method that allows for linear-scaling calculations of response properties for large molecular systems. Here, we focus on the example of calculating NMR chemical shifts for which the number of required DL-CPSCF iterations reduces by roughly 40-70%.