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.

12 pages, 10 figures

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• Emergence of molecular friction in liquids: bridging between the atomistic and hydrodynamic pictures
• On the Applicability of the Caldeira-Leggett Model to Condensed Phase Vibrational Spectroscopy
• Non-Markovian barrier crossing with two-time-scale memory is dominated by the faster memory component
• Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations
• Vibrational spectroscopy via the Caldeira-Leggett model with anharmonic system potentials
• Discretized hierarchical equations of motion in mixed Liouville--Wigner space for two-dimensional vibrational spectroscopies of liquid water
• Simulating two-dimensional correlation spectroscopies with third-order infrared and fifth-order infrared--Raman processes of liquid water
• Memory effects in colloidal motion under confinement and driving
• On Computing Spectral Densities from Classical, Semiclassical and Quantum Simulations
• Modelling a Bistable System Strongly Coupled to a Debye Bath: A Quasiclassical Approach Based on the Generalised Langevin Equation