Stochastic thermostats and temperature expressions

Abstract Molecular dynamics (MD) is in the core of fundamental research for a range of disciplines in natural sciences and is known for its applications in the design of new functional materials and the drug discovery. MD simulations are performed under certain thermodynamic conditions, typically at fixed temperature and pressure. The thermodynamic variables in the MD are modeled using equations that are called thermostats. Many different thermostats have been proposed. Recently (Samoletov A and Vasiev B 2017 J. Chem. Phys. 147 204106), we have shown that a range of thermostats can be derived in the framework of a unified approach based on the fundamental principles of statistical physics, so that the relevant dynamic schemes are based on the concept of temperature expression (in short, ϑ-expression). However, only a few specific ϑ-expressions have been used so far and reported in the literature. In this paper, we are using a wider set of ϑ-expressions and their mathematical properties that allow us to modify the known and offer new thermostats with improved computational efficiency and ergodicity. We focus on the Nosé-Hoover-Langevin stochastic scheme and extend it with additional temperature control tools. Simultaneous thermostatting of all phase space variables with minimal additional computational costs is an advantage of the modified dynamics.