Accelerated path-integral simulations using ring-polymer interpolation

Abstract

Path-integral (PI) molecular simulations can be used to calculate exact quantum statistical mechanical properties for complex systems containing many interacting atoms and molecules. The limiting computational factor in a PI simulation is typically the evaluation of the potential energy surface (PES) and forces at each ring-polymer "bead"; for an n-bead ring-polymer, a PI simulation is typically n times greater than the corresponding classical simulation. To address the increased computational effort of PI simulations, several approaches have been developed recently, most notably based on the idea of ring-polymer contraction (RPC) which exploits either the separation of the PES into short-range and long-range contributions or the availability of a computationally-inexpensive PES which can be incorporated to effectively smooth the ringpolymer PES; neither approach is satisfactory in applications to systems described by ab initio PESs. In this Article, we describe a new method, ring-polymer interpolation (RPI), which can be used to accelerate PI simulations without any prior assumptions about the PES. In simulations of liquid water under ambient conditions, where quantum effects are known to play a subtel role in influencing experimental observables such as diffusion coefficients and radial distribution functions, we find that RPI can accurately reproduce the results of fully-converged PI simulations, albeit with far fewer PES evaluations; this approach therefore opens up the possibility of large-scale PI simulations on ab initio PESs at lower computational effort than current methods.

Static and Dynamic Statistical Correlations in Water: Comparison of Classical Ab Initio Molecular Dynamics at Elevated Temperature With Path Integral Simulations at Ambient Temperature

“…1 Though NQEs appear to be minimal for the calculated intermolecular properties in some water simulations, 2-3 they were found to be non-negligible in other cases [4][5] as demonstrated by the differences in thermodynamic properties between light and heavy water. 1 In principle, Feynman's imaginary-time path-integral formalism 6 enables the modeling of NQEs in liquid water to numerical accuracy, but the associated high computational cost has hindered widespread application of path-integral molecular dynamics (PIMD) simulations until recent developments of more efficient approximations, 7 such as the ring-polymer contraction (RPC), 8 the ring-polymer interpolation, 9 and the combined path-integral and generalized Langevin equation (PI+GLE) approach. 10 The computational cost of a PIMD simulation of liquid water significantly increases when the underlying Born-Oppenheimer potential energy surface is calculated "on the fly" as in ab initio molecular dynamics (AIMD) simulations 11 where Kohn-Sham density functional theory 12 (KS-DFT) is generally used to solve the (electronic) Schrödinger equation at each step of the dynamical trajectory.…”

Classical Ab Initio Molecular Dynamics Run at an Elevated Temperature is Not a Good Model for the Nuclear Quantum Effects in Water at Ambient Temperature

“…1 Though NQEs appear to be minimal for the calculated intermolecular properties in some water simulations, 2, 3 they were found to be non-negligible in other cases 4,5 as demonstrated by the differences in thermodynamic properties between light and heavy water. 1 In principle, Feynman's imaginary-time path-integral formalism 6 enables the modeling of NQEs in liquid water to numerical accuracy, but the associated high computational cost has hindered widespread application of path-integral molecular dynamics (PIMD) simulations until recent developments of more efficient approximations, 7 such as the ring-polymer contraction (RPC), 8 the ring-polymer interpolation, 9 and the combined path-integral and generalized Langevin equation (PI+GLE) approach. 10 The computational cost of a PIMD simulation of liquid water significantly increases when the underlying Born-Oppenheimer potential energy surface is calculated "on the fly" as in ab initio molecular dynamics (AIMD) simulations 11 where Kohn-Sham density functional theory 12 (KS-DFT) is generally used to solve the (electronic) Schrödinger equation at each step of the dynamical trajectory.…”

Progress and Challenges in Ab Initio Simulations of Quantum Nuclei in Weakly Bonded Systems

“…Quantum mechanical simulations with atomistic resolution are currently reaching length and time scales that had been almost unimaginable only a few decades ago. The reasons for this impressive progress can be attributed to a number of conspiring factors including the increase of the availability of high performance computers, improved algorithms in many community software packages [1][2][3] , and the sympatico relationship of machine learning with quantum mechanical methods [4][5][6][7] .…”