Measure-preserving integrators for molecular dynamics in the isothermal-isobaric ensemble derived from the Liouville operator

The Liouville operator approach is employed to derive a new measure-preserving geometric integrator for molecular dynamics simulations in the isothermal-isobaric (NPT) ensemble. Recently, we introduced such a scheme for NPT simulations with isotropic cell fluctuations in the absence of holonomic constraints [M.E. Tuckerman et al., J. Phys. A 39 (2006) 5629]. Here, we extend this approach to include both fully flexible cell fluctuations and holonomic constraints via a new and simpler formulation of the ROLL algorithm of Martyna et al. [Martyna et al., Mol. Phys. 87 (1996) 1117]. The new algorithm improves on earlier schemes in that it possesses a simpler mathematical structure and rigorously preserves the phase space metric. The new algorithm is illustrated on two example systems, ice and liquid n-decane.