AcceleratingAb InitioPath Integral Simulations via Imaginary Multiple-Timestepping

Abstract

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.

Nuclear quantum effects enter the mainstream

“…The original, and by far the most commonly employed contraction scheme [42][43][44][45][46][47][48], involves transforming to the normal mode representation of the free ring polymer and discarding the P − P highest normal modes and then transforming back to the Cartesian representation. More recently other procedures such as averaging contraction [49] and stride contraction [50] have occasionally also been used, although the latter leads to unstable dynamics in some cases. Once the forces have been evaluated on the contracted Preplica ring polymer they are projected back onto the full P -replica ring polymer, and combined with other force components before propagating the ring polymer dynamics.…”

Affordable Ab Initio Path Integral for Thermodynamic Properties via Molecular Dynamics Simulations Using Semiempirical Reference Potential

“…29 Markland and Manolopoulos proposed an approach to reduce the computational effort by separating the short-range interaction from the long-range one. 30 Cheng et al proposed the multiple-timestep molecular dynamics (MTS-MD) algorithm to accelerate the propagation by dividing the force into slowly oscillating part and quickly varying component, 31 but the former factor is still the efficiency bottleneck. Large integration time step can also be made possible by applying proper transformations, so the analytic integration over the high-frequency modes is allowed.…”

Using Machine Learning to Greatly Accelerate Path Integral Ab Initio Molecular Dynamics

“…In practice, the MTS and RPC can be both employed to accelerate the quantum simulation as formulated in refs. [18][19][20] One commonly used low level electronic structure method in MTS/RPC is the self-consistentcharge density-functional tight-binding (SCC-DFTB) method. [21][22] However, the SCC-DFTB approach is largely semi-empirical and known to have limitations, e.g., in describing the solvation structure and dynamics of liquid water and hydrated excess protons.…”