Cell dynamics based on the metric tensor as extended variable for isothermal–isobaric molecular dynamics simulations

An extended Hamiltonian approach to conduct isothermal–isobaric molecular dynamics simulations with full cell flexibility is described. The components of the metric tensor of the simulation cell are used as the fictitious degrees of freedom, which avoids the problem of spurious cell rotations and artificial symmetry breaking effects present in the original Parrinello–Rahman scheme. This is combined with the Nosé–Poincaré approach for isothermal sampling, thus leading to equations of motion that are Hamiltonian in structure, and which can be solved numerically using recently developed powerful symplectic integrators. One such integrator, the generalised leap-frog, is employed to provide a numerical algorithm for integrating the isothermal–isobaric equations of motion obtained. The method is illustrated with applications to crystalline Si in the diamond structure (d-Si) systems simulated with a tight-binding Hamiltonian, and to carbon nanotube bundles simulated using the Tersoff empirical potential.