State-dependent diffusion coefficients and free energies for nucleation processes from Bayesian trajectory analysis

Abstract

The rate of nucleation processes such as the freezing of a supercooled liquid or the condensation of supersaturated vapour is mainly determined by the height of the nucleation barrier and the diffusion coefficient for the motion across it. Here, we use a Bayesian inference algorithm for Markovian dynamics to extract simultaneously the free energy profile and the diffusion coefficient in the nucleation barrier region from short molecular dynamics trajectories. The specific example we study is the nucleation of vapour bubbles in liquid water under strongly negative pressures, for which we use the volume of the largest bubble as a reaction coordinate. Particular attention is paid to the effects of discretisation, the implementation of appropriate boundary conditions and the optimal selection of parameters. We find that the diffusivity is a linear function of the bubble volume over wide ranges of volumes and pressures, and is mainly determined by the viscosity of the liquid, as expected from the Rayleigh–Plesset theory for macroscopic bubble dynamics. The method is generally applicable to nucleation processes and yields important quantities for the estimation of nucleation rates in classical nucleation theory.

Position-Dependent Diffusion from Biased Simulations and Markov State Model Analysis

“…Eventually, one could consider the dynamic histogram analysis method extended to detailed balance (DHAMed), where the transition rates are used as parameters to build MSMs from biased trajectories sampled at finite observation intervals. However, this would require to systematically eliminate transitions between noncontiguous states to obtain a rate matrix consistent with a diffusive process, where no jump is allowed beyond the immediate neighbors of a state. ,, This roadmap will be considered in future work.…”

Free Energy Landscapes, Diffusion Coefficients, and Kinetic Rates from Transition Paths

“…We also remark that equilibrium properties are systematically recovered from out-of-equilibrium data: standard transition path sampling trajectories are the golden standard for the study of transformation mechanisms; however, since such a data set is a small subset of all possible (reactive and nonreactive) pathways, lacking Boltzmann distribution of the configurations, it cannot be used for the direct estimate of equilibrium histograms (i.e., free energies) and rate matrices (e.g., in Markov state models) by simple averaging. , Here we show that the contrary is true, provided bare transition paths are employed to train a suitable stochastic model (see also refs , , , and − for related or alternative ideas). Note that Langevin equations of motion, compared to other machine-learning tools, retain a direct physical interpretation, with the separation between a systematic average force and friction/noise effects describing the projected-out degrees of freedom (commonly referred to as “the bath”).…”

Free energy landscapes, diffusion coefficients and kinetic rates from transition paths

“…Here we show that the contrary is true, provided bare transition paths are employed to train a suitable stochastic model (see also Refs. [22,55,35,36,56,57] for related or alternative ideas). Note that Langevin equations of motion, compared to other machine-learning tools, retain a direct physical interpretation, with the separation between a systematic average force and friction/noise effects describing the projected-out degrees of freedom (commonly referred to as "the bath").…”