Abstract
Substantial acceleration of research and more efficient utilization of resources can be achieved in modelling investigated phenomena by identifying the limits of system's accessible states instead of tracing the trajectory of its evolution. The proposed strategy uses the Metropolis-Hastings Monte-Carlo sampling of the configuration space probability distribution coupled with physically-motivated prior probability distribution. We demonstrate this general idea by presenting a high performance method of generating configurations for lattice dynamics and other computational solid state physics calculations corresponding to non-zero temperatures. In contrast to the methods based on molecular dynamics, where only a small fraction of obtained data is used, the proposed scheme is distinguished by a considerably higher, reaching even 80%, acceptance ratio and much lower amount of computation required to obtain adequate sampling of the system in thermal equilibrium at non-zero temperature.
Highlights
Every system can be successfully studied by methodical observation of its behaviour for a long enough time
A number of problems in solid state physics connected with lattice dynamics can be effectively addressed with inter-atomic potential models constructed using data obtained from quantum mechanical calculations (e.g. Density Functional Theory – DFT)
It is usually comprised of atomic positions as well as resulting energies and forces calculated with some quantum mechanical (e.g. DFT) or even effective potential method
Summary
Every system can be successfully studied by methodical observation of its behaviour for a long enough time. The data set should correspond to the system at thermal equilibrium or other physical state It is usually comprised of atomic positions as well as resulting energies and forces calculated with some quantum mechanical (e.g. DFT) or even effective potential method. Molecular dynamics is often used to investigate systems at non-zero temperature in thermal equilibrium This is done either directly – by analysis of the MD trajectory – or as a source of configurations for building the mentioned effective models of the inter-atomic potential to be used in further analysis (e.g. with programs like ALAMODE [10,11] or TDEP [7]). We indicate its possible application to some additional cases like disordered systems or large, complicated systems
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