Efficient and general algorithms for path integral Car–Parrinello molecular dynamics

In path integral molecular dynamics, efficient sampling of the phase space is not guaranteed due to the stiff harmonic part of the action arising from the quantum kinetic energy. This problem has been eliminated by incorporating a sufficient number of thermostats into the dynamical scheme and by introducing a transformation of the path ‘‘bead’’ variables. In this paper, an efficient Car–Parrinello path integral molecular dynamics algorithm, sufficiently general to include the use of ultrasoft pseudopotentials is introduced. Difficulties encountered when combining thermostats and transformations of the Cartesian ‘‘bead’’ coordinates with the generalized orthonormality condition are circumvented by employing a constrained nonorthogonal orbital method.