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Register a new userAutomatic, optimized interface placement in forward flux sampling simulations
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Forward flux sampling (FFS) provides a convenient and efficient way to simulate rare events in equilibrium or non-equilibrium systems. FFS ratchets the system from an initial state to a final state via a series of interfaces in phase space. The efficiency of FFS depends sensitively on the positions of the interfaces. We present two alternative methods for placing interfaces automatically and adaptively in their optimal locations, on-the-fly as an FFS simulation progresses, without prior knowledge or user intervention. These methods allow the FFS simulation to advance efficiently through bottlenecks in phase space by placing more interfaces where the probability of advancement is lower. The methods are demonstrated both for a single-particle test problem and for the crystallization of Yukawa particles. By removing the need for manual interface placement, our methods both facilitate the setting up of FFS simulations and improve their performance, especially for rare events which involve complex trajectories through phase space, with many bottlenecks.
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We used molecular dynamics simulations and the path sampling technique known as forward flux sampling to study homogeneous nucleation of NaCl crystals from supersaturated aqueous solutions at 298 K and 1 bar. Nucleation rates were obtained for a range of salt concentrations for the Joung-Cheatham NaCl force field combined with the SPC/E water model. The calculated nucleation rates are significantly lower than available experimental measurements. The estimates for the nucleation rates in this work do not rely on classical nucleation theory, but the pathways observed in the simulations suggest that the nucleation process is better described by classical nucleation theory than an alternative interpretation based on Ostwalds step rule, in contrast to some prior simulations of related models. In addition to the size of NaCl nucleus, we find that the crystallinity of a nascent cluster plays an important role in the nucleation process. Nuclei with high crystallinity were found to have higher growth probability and longer lifetimes, possibly because they are less exposed to hydration water.
Many processes in chemistry and physics take place on timescales that cannot be explored using standard molecular dynamics simulations. This renders the use of enhanced sampling mandatory. Here we introduce an enhanced sampling method that is based on constructing a model probability density from which a bias potential is derived. The model relies on the fact that in a physical system most of the configurations visited can be grouped into isolated metastable islands. To each island we associate a distribution that is fitted to a Gaussian mixture. The different distributions are linearly combined together with coefficients that are computed self consistently. Remarkably, from this biased dynamics, rates of transition between different metastable states can be straightforwardly computed.
Simulation of warm dense matter requires computational methods that capture both quantum and classical behavior efficiently under high-temperature, high-density conditions. Currently, density functional theory molecular dynamics is used to model electrons and ions, but this methods computational cost skyrockets as temperatures and densities increase. We propose finite-temperature potential functional theory as an in-principle-exact alternative that suffers no such drawback. We derive an orbital-free free energy approximation through a coupling-constant formalism. Our density approximation and its associated free energy approximation demonstrate the methods accuracy and efficiency.
When the cooling rate $v$ is smaller than a certain material-dependent threshold, the glass transition temperature $T_g$ becomes to a certain degree the material parameter being nearly independent on the cooling rate. The common method to determine $T_g$ is to extrapolate viscosity $ u$ of the liquid state at temperatures not far above the freezing conditions to lower temperatures where liquid freezes and viscosity is hardly measurable. It is generally accepted that the glass transition occurs when viscosity drops by $13leq nleq17$ orders of magnitude. The accuracy of $T_g$ depends on the extrapolation quality. We propose here an algorithm for a unique determining of $T_g$. The idea is to unambiguously extrapolate $ u(T)$ to low temperatures without relying upon a specific model. It can be done using the numerical analytical continuation of $ u(T)$-function from above $T_g$ where it is measurable, to $Tgtrsim T_g$. For numerical analytical continuation, we use the Pade approximant method.
Molecular dynamics are extremely complex, yet understanding the slow components of their dynamics is essential to understanding their macroscopic properties. To achieve this, one models the molecular dynamics as a stochastic process and analyses the dominant eigenfunctions of the associated Fokker-Planck operator, or of closely related transfer operators. So far, the calculation of the discretized operators requires extensive molecular dynamics simulations. The Square-root approximation of the Fokker-Planck equation is a method to calculate transition rates as a ratio of the Boltzmann densities of neighboring grid cells times a flux, and can in principle be calculated without a simulation. In a previous work we still used molecular dynamics simulations to determine the flux. Here, we propose several methods to calculate the exact or approximate flux for various grid types, and thus estimate the rate matrix without a simulation. Using model potentials we test computational efficiency of the methods, and the accuracy with which they reproduce the dominant eigenfunctions and eigenvalues. For these model potentials, rate matrices with up to $mathcal{O}(10^6)$ states can be obtained within seconds on a single high-performance compute server if regular grids are used.
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