  Ehrenfest and Car-Parrinello molecular dynamics are computational
alternatives to approximate Born-Oppenheimer molecular dynamics without solving
the electron eigenvalue problem at each time-step. A non-trivial issue is to
choose the artificial electron mass parameter appearing in the Car-Parrinello
method to achieve both good accuracy and high computational efficiency. In this
paper, we propose an algorithm, motivated by the Landau-Zener probability, to
systematically choose an artificial mass dynamically, which makes the
Car-Parrinello and Ehrenfest molecular dynamics methods dependent only on the
problem data. Numerical experiments for simple model problems show that the
time-dependent adaptive artificial mass parameter improves the efficiency of
the Car-Parrinello and Ehrenfest molecular dynamics.
