Accelerated path integral methods for atomistic simulations at ultra-low temperatures

Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear quantum effects are often significant for light nuclei already at room temperature, but become crucial at cryogenic temperatures such as those provided by superfluid helium as a solvent. Unfortunately, the cost of converged path integral simulations increases significantly upon lowering the temperature so that the computational burden of simulating matter at the typical superfluid helium temperatures becomes prohibitive. Here we investigate how accelerated path integral techniques based on colored noise generalized Langevin equations, in particular the so-called path integral generalized Langevin equation thermostat ( PIGLET) variant, perform in this extreme quantum regime using as an example the quasi-rigid methane molecule and its highly fluxional protonated cousin, CH5+. We show that the PIGLET technique gives a speedup of two orders of magnitude in the evaluation of structural observables and quantum kinetic energy at ultralow temperatures. Moreover, we computed the spatial spread of the quantum nuclei in CH4 to illustrate the limits of using such colored noise thermostats close to the many body quantum ground state. Published by AIP Publishing.