Verlet-like algorithms for Car-Parrinello molecular dynamics with unequal electronic occupations.

ABSTRACT

The ab initio molecular dynamics simulations of metallic, charged, and electrochemical systems require, in principle, the inclusion of unequally occupied electronic states. In this contribution, the general approach to work with fixed but arbitrary occupations within the Car-Parrinello molecular dynamics scheme is revisited, focusing on the procedure which is required to maintain the orthonormality constraints in the commonly used position-Verlet integrator. Expressions to constrain also the orbital velocities, as it is demanded by a velocity-Verlet integrator, are then derived. The generalized unequal-occupation SHAKE algorithm is compared with the standard procedure for damped dynamics (energy optimization) of systems including fully unoccupied electronic states. In turn, the proposed unequal-occupation RATTLE algorithm is validated by the corresponding microcanonical ensemble simulations. It is shown that only with the proper orthogonalization method, a correct ordering of states and energy conserving dynamics can be achieved.