Accelerating the convergence of path integral dynamics with a generalized Langevin equation

Abstract

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.

High order path integrals made easy

“…19,20 : considering that for a classical oscillator q 2 = 1 /mβω 2 one can write the functional equation…”

“…This goal has been achieved by computing expensive parts of the potential on a reduced number of replicas 16,17 , by using a thermostat described by a generalized Langevin equation (GLE) to artificially generate the proper quantum fluctuations [18][19][20] , or by using a higher-order expansion of the quantum partition function -so-called "high-order path integral techniques" [21][22][23][24] . This latter approach is very appealing, particularly if low-temperature or high-accuracy are sought, since the convergence improves with the number of replicas P from P −2 of traditional methods to P −4 .…”

Nuclear Quantum Effects and Nonlocal Exchange-Correlation Functionals Applied to Liquid Hydrogen at High Pressure

“…and 1500 K utilized the accelerated PIMD method of Ceriotti, et al 44 , based on a generalized Langevin dynamics (GLE) and the Born-Oppenheimer approximation. The use of the PI+GLE method was carefully tested under the relevant pressure and temperature conditions, in order to guarantee proper convergence 45 .…”

Applications of the generalized Langevin equation: Towards a realistic description of the baths

“…A major step towards the solution of this problem for a realistic application has been recently given in Refs. [35,[41][42][43]45]. In particular, a very efficient algorithm has been developed in Ref.…”

“…The non-Markovian GLE represents a remarkably flexible framework which permits one to achieve a better control over the sampling properties of a molecular dynamics trajectory, to enhance its sampling efficiency for all the relevant time scales [35,[41][42][43], to control in a precise manner the disturbance of the dynamics for different frequency ranges, and to provide physical nonequilibrium trajectories for the study of nonequilibrium and/or relaxation processes.…”