Invariance of Parrinello-Rahman molecular dynamics and its relation to continuum mechanics



Parrinello-Rahman molecular dynamics has proved to be a reliable technique for the investigation of phase transitions in solids. This type of molecular dynamics may lead to a proper description of the atomistic scale in multi-scale analysis of engineering problems. However, the employed Lagrangian is proposed without a derivation and lacks invariance under modular transformations. A re-interpretation of the Lagrangian in terms of continuum mechanics was recently developed. The new formulation is derived in a consistent physical manner and only quantities native to continuum mechanics are incorporated into this Lagrangian. Based on this recent continuum-related derivation, the invariance of the new Lagrangian under modular transformations is investigated. The implication that the obtained dynamics is invariant to the chosen unit cell corroborates with results in solid state physics and is a mandatory requirement for the suitability of multi-scale analysis. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)