Accelerating Ab Initio Path Integral Simulations via Imaginary Multiple-Timestepping

This work investigates the use of multiple-timestep schemes in imaginary time for computationally efficient ab initio equilibrium path integral simulations of quantum molecular motion. In the simplest formulation, only every n(th) path integral replica is computed at the target level of electronic structure theory, whereas the remaining low-level replicas still account for nuclear motion quantum effects with a more computationally economical theory. Motivated by recent developments for multiple-timestep techniques in real-time classical molecular dynamics, both 1-electron (atomic-orbital basis set) and 2-electron (electron correlation) truncations are shown to be effective. Structural distributions and thermodynamic averages are tested for representative analytic potentials and ab initio molecular examples. Target quantum chemistry methods include density functional theory and second-order Møller-Plesset perturbation theory, although any level of theory is formally amenable to this framework. For a standard two-level splitting, computational speedups of 1.6-4.0x are observed when using a 4-fold reduction in time slices; an 8-fold reduction is feasible in some cases. Multitiered options further reduce computational requirements and suggest that quantum mechanical motion could potentially be obtained at a cost not significantly different from the cost of classical simulations.