Metric tensor as the dynamical variable for variable-cell-shape molecular dynamics

We propose a variable-cell-shape molecular dynamics algorithm where the dynamical variables associated with the cell are the six independent dot products between the vectors defining the cell instead of the nine Cartesian components of those vectors. Our choice of the metric tensor as the dynamical variable automatically eliminates the cell orientation from the dynamics. Furthermore, choosing for the cell kinetic energy a simple scalar that is quadratic in the time derivatives of the metric tensor makes the dynamics invariant with respect to the choice of the simulation cell edges. Choosing the tensorial density of that scalar allows us to have a dynamics that obeys the virial theorem. We derive the equations of motion for the two conditions of constant external pressure and constant thermodynamic tension. We also show that using the metric as a variable is convenient for structural optimization under those two conditions. We use simulations for Ar with Lennard-Jones parameters and for Si with forces and stresses calculated from first principles of density-functional theory to illustrate the applications of the method.