Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations

Abstract

Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation (GLE), which can be rigorously derived by means of a linear projection (LP) technique. Within this framework a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied, usually by means of time-domain methods based on explicit molecular dynamics data. Here we discuss that this task is most naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importantly, we show that the rigid bond approach leads to a systematic underestimation of relaxation times, unless the system under study consists of a harmonic bath bi-linearly coupled to the relevant degrees of freedom. INTRODUCTIONStudying complex dynamics of many-particle systems has become one of the main goals in modern molecular physics. The fundamental understanding of the underlying microscopical processes requires the interplay of elaborate experimental techniques and sophisticated theoretical approaches. Experimentally, (non-)linear spectroscopy revealed itself as a powerful tool for probing the dynamics and for determining the characteristic timescales, such as dephasing/relaxation times and reaction rates to name but two. For interpreting the experimental spectra theoretical models are needed which can give insight into the atomistic dynamics. Often, a reduction of the description to few variables is convenient in many cases since this can not only ease the interpretation, but enable the identification of key properties [1]. Such a reduced description can formally be obtained from the so-called system-bath partitioning, where only a small subset of degrees of freedom (DOFs), referred to as system, is considered as important for describing a physical process under study. All the other DOFs, referred to as bath, are regarded as irrelevant in the sense that they might influence the time evolution of the system but do not explicitly enter any dynamical variable of interest. Practically, such a separation is often natural, for instance, when studying a reaction with a clearly defined reaction center or solute dynamics in a solvent environment. Further, reduced equations of motion (EOMs) for the system DOFs can be derived in which the influence of the bath is limited to dissipation and fluctuations.The most simple formulation of this idea is provided by the Markovian Langevin equation, where dissipation and fluctuations take the form of static friction and stochastic white noise, respectively [2][3][4]. Sit...

Vibrational spectroscopy via the Caldeira-Leggett model with anharmonic system potentials

“…(3.2) -(3.4) in Ref. [29]. It becomes apparent at this point that for anharmonic systems this procedure cannot be exploited anymore and one has to use both, the MAF and the MFC, to obtain the spectral densityξ(ω) directly via Eq.…”

“…for harmonic system potentials [29]; note that a similar in spirit but technically different method for linear GLEs was developed independently [46] and applied to quantum dynamics of hydrogen atoms on graphene [47,48]. In the following, we extend the method to the non-linear GLEs, Eq.…”

“…(12) comes along with two numerical issues that have been already encountered in the Fourier method for linear GLEs [29]. First, the Fourier transforms of the MAF and MFC should be calculated very accurately.…”

“…Further, we extend our recently suggested Fourier-based scheme for calculating memory kernels from explicit MD simulations for the harmonic cases [29] to the anharmonic ones. Since the resulting protocol is much more sensitive to the numerical accuracy of the input data than the one for the linear GLE, a comprehensive error analysis is provided as well.…”

“…Still, considering the somewhat artificial A 2 in A system adopted from Ref. [28] showed that it can be satisfactorily mapped onto the model [29].…”