Langevin Dynamics in Constant Pressure Extended Systems
  The advantages of performing Langevin Dynamics in extended systems are discussed. A simple Langevin Dynamics scheme for producing the canonical ensemble is reviewed, and is then extended to the Hoover ensemble. We show that the resulting equations of motion generate the isobaric-isothermal ensemble. The Parrinello-Rahman ensemble is then discussed and we show that despite the presence of intrinsic probability gradients in this system, a Langevin Dynamics approach samples the extended phase space in the correct fashion. The implementation of these methods in the ab-initio plane wave density functional theory (DFT) code CASTEP [M. D. Segall, P. L. D. Lindan, M. J. Probert, C. J. Pickard, P. J. Hasnip, S. J. Clarke and M.C. Payne, J. Phys.: Cond. Matt. (11), 2717 (2003)] is demonstrated. 
D. Quigley, M.I.J Probert