Eur. Phys. J. Special Topics 200, 131-152 (2011)
https://doi.org/10.1140/epjst/e2011-01522-0

Regular Article

Stochastic-dynamical thermostats for constraints and stiff restraints

¹ Centrum Wiskunde & Informatica (CWI), PO Box 94079, 1090 GB Amsterdam, The Netherlands
² School of Mathematics and Maxwell Institute for Mathematical Sciences, The University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings, Mayfield Road, Edinburgh, Scotland EH9 3JZ, UK

^a e-mail: janis.bajars@cwi.nl
^b e-mail: jason@cwi.nl
^c e-mail: b.leimkuhler@ed.ac.uk

Received: 9 September 2011
Revised: 10 October 2011
Published online: 13 December 2011

Abstract

A broad array of canonical sampling methods are available for molecular simulation based on stochastic-dynamical perturbation of Newtonian dynamics, including Langevin dynamics, Stochastic Velo- city Rescaling, and methods that combine Nosé-Hoover dynamics with stochastic perturbation. In this article we discuss several stochastic-dynamical thermostats in the setting of simulating systems with holonomic constraints. The approaches described are easily implemented and facilitate the recovery of correct canonical averages with minimal disturbance of the underlying dynamics. For the purpose of illustrating our results, we examine the numerical application of these methods to a simple atomic chain, where a Fixman term is required to correct the thermodynamic ensemble.