Nonlinear molecular dynamics and Monte Carlo algorithms

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Abstract
Equations of motion for the molecular dynamics simulation of crystals are presented; the atomic degrees of freedom are coupled to a thermal reservoir to control temperature and to an elastic reservoir to control the deformation of the lattice, while satisfying a nonlinear stress-strain relation. The exact treatment of finite deformations of the lattice leads to a formulation of the tensorial virial theorem that accounts for the elastic response of the crystal to an inclusion of a new structural phase. A Metropolis Monte Carlo algorithm is presented that is completely consistent with the molecular dynamics method; this is achieved by extending the Monte Carlo procedure to include trials of both atomic positions and momenta. Computational results demonstrating the equivalence of the methods in satisfying the virial theorem in the nonlinear regime are presented.