Variational boundary conditions for molecular dynamics simulations of crystalline solids at finite temperature

Treatment of the thermal bath

Xiantao Li, Weinan E

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

This paper presents a systematic approach for finding efficient boundary conditions for molecular dynamics simulations of crystalline solids. These boundary conditions effectively eliminate phonon reflection at the boundary and at the same time allow the thermal energy from the bath to be introduced to the system. Our starting point is the Mori-Zwanzig formalism for eliminating the thermal bath, but we take the crucial next step that goes beyond this formalism in order to obtain memory kernels that decay faster. An equivalent variational formulation allows us to find the optimal approximate boundary conditions, after specifying the spatial-temporal domain of dependence for the positions of the boundary atoms. Application to a one-dimensional chain, a two-dimensional Lennard-Jones system, and a three-dimensional model of α -iron with embedded atom potential is presented to demonstrate the effectiveness of this approach.

Original languageEnglish (US)
Article number104107
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume76
Issue number10
DOIs
StatePublished - Sep 18 2007

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Molecular dynamics
baths
Boundary conditions
boundary conditions
molecular dynamics
Crystalline materials
Computer simulation
formalism
Atoms
simulation
three dimensional models
Thermal energy
thermal energy
Temperature
temperature
atoms
Iron
formulations
Data storage equipment
iron

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

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AB - This paper presents a systematic approach for finding efficient boundary conditions for molecular dynamics simulations of crystalline solids. These boundary conditions effectively eliminate phonon reflection at the boundary and at the same time allow the thermal energy from the bath to be introduced to the system. Our starting point is the Mori-Zwanzig formalism for eliminating the thermal bath, but we take the crucial next step that goes beyond this formalism in order to obtain memory kernels that decay faster. An equivalent variational formulation allows us to find the optimal approximate boundary conditions, after specifying the spatial-temporal domain of dependence for the positions of the boundary atoms. Application to a one-dimensional chain, a two-dimensional Lennard-Jones system, and a three-dimensional model of α -iron with embedded atom potential is presented to demonstrate the effectiveness of this approach.

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