Barostats

Keeping the pressure constant is a desirable feature for many applications of molecular dynamics. The concept of barostats and thus constant-pressure molecular dynamics was introduced in the framework of extended system dynamics by Andersen [30]. His method was devised to allow for isotropic fluctuations in the volume of the supercell. An extension of Andersen's method consists in allowing for changes of the shape of the computational cell to occur as a result of applying external pressure [29], including the possibility of non-isotropic external stress; the additional fictitious degrees of freedom in the Parrinello-Rahman approach [29] are the lattice vectors of the supercell. These variable-cell approaches make it possible to study dynamically structural phase transitions in solids at finite temperatures. The basic idea to allow for changes in the cell shape consists in constructing an extended Lagrangian where the lattice vectors ${\bf a}_1$ , ${\bf a}_2$ and ${\bf a}_3$ of the simulation cell are additional dynamical variables.

A modern formulation of barostats that combines the equation of motion also with thermostats was given by Martyna et al. [31].