Re-integration with anchor points algorithm for ab initio molecular dynamics

A new integration scheme for ab initio molecular dynamics (MD) is proposed in this work for efficient propagation using large time steps (e.g., 2.0 fs or a larger time step with one ab initio evaluation of gradients for the dynamics point and one additional evaluation for the anchor point per dynamics step). This algorithm is called re-integration with anchor points (REAP) integrator. The REAP integrator starts from a quadratic potential energy surface based on the updated Hessian to propagate the system to the halfway of the MD step that is called the anchor point. Then, an approximate dynamics position for this step is obtained by the propagation based on an interpolated surface using the anchor point and the previous MD point. The approximate dynamics step can be further improved by the re-integration steps, i.e., integration based on the interpolated surface using the calculated energies, gradients, and updated Hessians of the previous step, the anchor point, and the approximate current step. A trajectory only needs one analytical Hessian calculation at the initial geometry, and thereafter, only calculations of gradients are required. This integrator can be considered either as a generalization of Hessian-based predictor-corrector integration with substantial improvement of accuracy and efficiency or as a dynamics on interpolated surfaces that are built on the fly. An automatic correction scheme is implemented by comparing the interpolated energies and gradients to the actual ones to ensure the quality of the interpolations at a certain level. The tests in this work show that the REAP method can increase computational efficiency by more than one order of magnitude than that of the velocity Verlet integrator and more than twice that of Hessian-based predictor-corrector integration.