We propose a new 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 densitary character 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 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.
In first-principles variable-cell-shape molecular dynamics simulations and structural optimizations of nitrogen at pressures of 0-500 GPa, the phase with lowest enthalpy at high pressures, BP, was found to transform at low pressures into a new, metastable, metallic phase with a chainlike structure. The latter may possibly be related to a metastable nonmolecular phase that was recently observed experimentally at low temperatures and pressures.
The electronic properties of the alkali trimers Li3, Na3, and K3 are studied using the pseudopotential and the local-spin-density approximations. More than 100 configurations were calculated for each trimer in order to obtain a complete picture of the adiabatic Born–Oppenheimer surfaces. The equilibrium geometry of the trimers are Jahn–Teller distortions of an equilateral triangle. Although the three surfaces are quite similar, Li3 is more affected than Na3 or K3 by the dynamical character of the Jahn–Teller distortion. The calculated ionization potentials agree very well with the experimental values and the qualitative features of the Born–Oppenheimer surface are confirmed by recent ESR experiments.
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