Molecular simulation in the canonical ensemble and beyond

In this paper, we discuss advanced thermostatting techniques for sampling molecular systems in the canonical ensemble. We first survey work on dynamical thermostatting methods, including the Nosé-Poincaré method, and generalized bath methods which introduce a more complicated extended model to obtain better ergodicity. We describe a general controlled temperature model, projective thermostatting molecular dynamics (PTMD) and demonstrate that it flexibly accommodates existing alternative thermostatting methods, such as Nosé-Poincaré, Nosé-Hoover (with or without chains), Bulgac-Kusnezov, or recursive Nosé-Poincaré Chains. These schemes offer possible advantages for use in computing thermodynamic quantities, and facilitate the development of multiple time-scale modelling and simulation techniques. In addition, PTMD advances a preliminary step toward the realization of true nonequilibrium motion for selected degrees of freedom, by shielding the variables of interest from the artificial effect of thermostats. We discuss extension of the PTMD method for constant temperature and pressure models. Finally, we demonstrate schemes for simulating systems with an artificial temperature gradient, by enabling the use of two temperature baths within the PTMD framework.