On the time scale associated with Monte Carlo simulations

Abstract

Uniform-acceptance force-bias Monte Carlo (fbMC) methods have been shown to be a powerful technique to access longer timescales in atomistic simulations allowing, for example, phase transitions and growth. Recently, a new fbMC method, the time-stamped force-bias Monte Carlo (tfMC) method, was derived with inclusion of an estimated effective timescale; this timescale, however, does not seem able to explain some of the successes the method. In this contribution, we therefore explicitly quantify the effective timescale tfMC is able to access for a variety of systems, namely a simple single-particle, one-dimensional model system, the Lennard-Jones liquid, an adatom on the Cu(100) surface, a silicon crystal with point defects and a highly defected graphene sheet, in order to gain new insights into the mechanisms by which tfMC operates. It is found that considerable boosts, up to three orders of magnitude compared to molecular dynamics, can be achieved for solid state systems by lowering of the apparent activation barrier of occurring processes, while not requiring any system-specific input or modifications of the method. We furthermore address the pitfalls of using the method as a replacement or complement of molecular dynamics simulations, its ability to explicitly describe correct dynamics and reaction mechanisms, and the association of timescales to MC simulations in general.

Molecular Dynamics Simulations for Plasma‐Surface Interactions

“…In coupled or hybrid MD/MC simulations, reactive events are simulated in a MD module, while the system is relaxed by a subsequent MC simulation. Note, however, that unless the time scale in the MC simulations is carefully calibrated, no actual time scale can be assigned to the hybrid MD/MC simulation.…”

Nanoscale mechanisms of CNT growth and etching in plasma environment

“…Combined molecular dynamics / time-stamped force-bias Monte Carlo (MD/tfMC) simulations are used for simulation of the catalyzed CNT growth and hydrogenation/etching processes [41][42][43]. In tfMC calculations, all the atoms in the system are displaced at once in every time step with unit probability, and thus generate a system evolution in a MD-like fashion.…”

Multiscale Molecular Dynamics Simulation of Plasma Processing: Application to Plasma Sputtering

“…A tricky challenge is to use atomic scale simulation methods for enabling multiscale analysis. Kinetic Monte-Carlo methods are now relevant for describing a wide range of time and space scales [9,12,16,[22][23][24][25], including plasma materials processing reactors [26][27][28]. Recently Molecular Dynamics simulations (MDs), which are calculating all the trajectories of an ensemble of particle, have overcome the barrier of describing long time phenomena or rare infrequent events [29][30][31][32][33][34].…”