A simple and effective Verlet-type algorithm for simulating Langevin dynamics

An ab initio Langevin dynamics approach is developed based on stochastic density functional theory (sDFT) within a new embedded saturated fragment formalism, applicable to covalently bonded systems. The forces on the nuclei generated by sDFT contain a random component natural to Langevin dynamics and its standard deviation is used to estimate the friction term on each atom by satisfying the fluctuation-dissipation relation. The overall approach scales linearly with system size even if the density matrix is not local and is thus applicable to ordered as well as disordered extended systems. We implement the approach for a series of silicon nanocrystals (NCs) of varying size with a diameter of up to 3nm corresponding to N e = 3000 electrons and generate a set of configurations that are distributed canonically at a fixed temperature, ranging from cryogenic to room temperature. We also analyze the structure properties of the NCs and discuss the reconstruction of the surface geometry.

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“…We use the Verlet-like algorithm 39 for numerically integrating the LE of motion at a fixed temperature T and a predefined time-step ∆t. …”

Section: Langevin Dynamics Based On Efsdftmentioning

confidence: 99%

Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory

Arnon

Rabani

Neuhauser

et al. 2017

The Journal of Chemical Physics

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“…The trajectories are computed by numerically integrating Langevin's equation of motion (4). Denoting, respectively, by x n and v n the position and velocity of a particle at time t n , the integration is conducted using the G-JF algorithm that advances the system by one time step to t n+1 = t n + dt, using the following set of discrete-time equations [18,19]:…”

Section: B Langevin Dynamics Simulationsmentioning

confidence: 99%

“…This issue has considerable practical importance in numerical simulations where the time step dt is not infinitesimal. The results in the work are based on Langevin dynamics simulations employing the G-JF integrator [18,19] with a newly proposed "inertial" convention [12,13] (see details in section II B). This combination produces excellent results even for relatively large integration time steps.…”

Section: Introductionmentioning

confidence: 99%

Isothermal Langevin dynamics in systems with power-law spatially dependent friction

2016

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We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form D(x) ∼ |x| c , at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At large times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for c < 0, and superdiffusion for 0 < c < 1. For c > 1, the diffusion equation predicts that the particles accelerate. Here, we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially-dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit ( x 2 ∼ t 2 ). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin, and is correctly captured by Langevin's equation.

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“…This is rooted, in part, in the above-mentioned discrete-time artifact that momentum and position are not strictly mutually conjugated variables for dt > 0. Recently, a new and improved thermostat (a temporal discrete-time propagator of the Langevin equation) was introduced by Grønbech-Jensen and Farago (G-JF) [11], which reads…”

Section: Introductionmentioning

confidence: 99%

“…(1) and (2). The core of the G-JF method is that the fluctuationdissipation relationship is intact in discrete-time with respect to the balance between the energy lost by friction over the actual distance traveled and the accumulated noise over the time step [11]. This implies that the resulting discrete-time trajectory is thermodynamically sound.…”

Section: Introductionmentioning

confidence: 99%

The G‐JF Thermostat for Accurate Configurational Sampling in Soft‐Matter Simulations

Arad

Farago

Grønbech‐Jensen

2016

Israel Journal of Chemistry

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We implement the statistically sound G-JF thermostat for Langevin Dynamics simulations into the ESPREesSo molecular package for large-scale simulations of soft matter systems. The implemented integration method is tested against the integrator currently used by the molecular package in simulations of a fluid bilayer membrane. While the latter exhibits deviations in the sampling statistics that increase with the integration time step dt, the former reproduces near-correct configurational statistics for all dt within the stability range of the simulations. We conclude that, with very modest revisions to existing codes, one can significantly improve the performance of statistical sampling using Langevin thermostats.

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A simple and effective Verlet-type algorithm for simulating Langevin dynamics

Cited by 238 publications

References 14 publications

Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory

Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory

Isothermal Langevin dynamics in systems with power-law spatially dependent friction

The G‐JF Thermostat for Accurate Configurational Sampling in Soft‐Matter Simulations

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