Fine tuning classical and quantum molecular dynamics using a generalized Langevin equation

Abstract

Generalized Langevin Equation (GLE) thermostats have been used very effectively as a tool to manipulate and optimize the sampling of thermodynamic ensembles and the associated static properties. Here we show that a similar, exquisite level of control can be achieved for the dynamical properties computed from thermostatted trajectories. We develop quantitative measures of the disturbance induced by the GLE to the Hamiltonian dynamics of a harmonic oscillator, and show that these analytical results accurately predict the behavior of strongly anharmonic systems. We also show that it is possible to correct, to a significant extent, the effects of the GLE term onto the corresponding microcanonical dynamics, which puts on more solid grounds the use of non-equilibrium Langevin dynamics to approximate quantum nuclear effects and could help improve the prediction of dynamical quantities from techniques that use a Langevin term to stabilize dynamics. Finally we address the use of thermostats in the context of approximate path-integral-based models of quantum nuclear dynamics. We demonstrate that a custom-tailored GLE can alleviate some of the artifacts associated with these techniques, improving the quality of results for the modeling of vibrational dynamics of molecules, liquids, and solids.

Hydrogen dynamics in solid formic acid: insights from simulations with quantum colored-noise thermostats

“…Though the result has been derived under a harmonic approximation, the predictions happen to be in excellent agreement with the exact VACF for system as anharmonic as liquid water [21]. It was shown that the post-processing deconvolution of the perturbed spectra can properly recover the unperturbed dynamic properties even in the case of heavily thermostatted cases, i.e.…”

“…where ζ(t) is a time-correlation function of the random force and K(t), is the memory kernel, introducing the dependence of the system evolution on its history in terms of a non-Markovian stochastic differential equation [21]. Such definition, however, requires the use of integrodifferential equations, leading to a serious numerical challenge.…”

“…where s is the vector of n additional degrees of freedom; ξ denotes a n+1 dimensional vector of uncorrelated Gaussian numbers [21]; a pp stands for a friction coefficient and b pp denotes the intensity of the random force, both linked by the so-called fluctuation…”

“…A remedy to this deficiency has been recently provided by Rossi, Kapil and Ceriotti [21], delivering an analytical scheme to extract the microcanonical velocity-velocity autocorrelation function (VACF) from the quantum-thermostated (GLE) trajectory. It is based on the idea that the exact VACF for a harmonic oscillator of frequency ω 0 , coupled to a GLE thermostat is:…”

“…For the details of the nomenclature and the matrices elements ([·] · ), we refer the reader to section 2 of [21]. For a system with a density of states given by g(ω), the VACF can be written in the harmonic limit as:…”