Adaptive accuracy control for Car-Parrinello simulations

The Car-Parrinello (CP) approach to ab initio molecular dynamics serves as an approximation to time-dependent Born-Oppenheimer (BO) calculations. It replaces the explicit minimization of the energy functional by a fictitious Newtonian dynamics and therefore introduces an artificial mass parameter μ which controls the electronic motion. A recent theoretical investigation shows that the CP-error, i.e., the deviation of the CP-solution from the BO-solution decreases like μ^1/2 asymptotically. Since the computational effort increases like μ^-1/2, the choice of μ has to find a compromise between efficiency and accuracy. The asymptotical result is used in this paper to construct an easily implemented algorithm which automatically controls μ: the parameter μ is repeatedly adapted during the simulation by choosing μ, as large as possible while pushing an error measure below a user-given tolerance. The performance and reliability of the algorithm is illustrated by a typical example.