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.
Similar content being viewed by others
References
G. Bussi, D. Donadio, M. Parrinello, J. Chem. Phys. 126, 014101 (2007)
G. Bussi, M. Parrinello, Comp. Phys. Comm. 179, 26 (2008)
W.K. den Otter, W. Briels, J. Chem. Phys. 106, 13 (1997)
M. Cassandro, G. Ciccotti, V. Rosato, J.P. Ryckaert, Statistical mechanics of rigid systems: an atomic description, unpublished note
G. Ciccotti, J.P. Ryckaert, Comp. Phys. Reports 4, 346 (1986)
G. Ciccotti, R. Kapral, E. Vanden-Eijnden, Chem. Phys. Chem. 6, 1809 (2005)
E. Darve, Ph.D. thesis, Université Paris VI (1999)
W.E.W. Ren, E. Vanden-Eijnden, Phys. Rev. B 66, 052301 (2002)
M. Fixman, P. Nat. Acad. Sci. 71, 3050 (1974)
M. Fixman, J. Chem. Phys. 69, 1527 (1978)
J. Frank, G.A. Gottwald, J. Stat. Phys. 143, 715 (2011)
N. Go, H.A. Scheraga, J. Chem. Phys. 51, 4751 (1969)
N. Go, H.A. Scheraga, Macromolecules 9, 535 (1976)
A. Jones, B. Leimkuhler (2011) (submitted)
N.G. van Kampen, Appl. Sci. Res. 37, 67 (1981)
N.G. van Kampen, J.J. Lodder, Am. J. Phys. 52, 419 (1984)
B. Leimkuhler, S. Reich, Math. Comp. 63, 598 (1994)
B. Leimkuhler, Phys. Rev. E 81, 026703 (2010)
B. Leimkuhler, E. Noorizadeh, O. Penrose, J. Stat. Phys. 143, 921 (2011)
B. Leimkuhler, E. Noorizadeh, F. Theil, J. Stat. Phys. 135, 261 (2009)
T. Lelièvre, M. Rousset, G. Stoltz (preprint) (2010)
A. Samoletov, M.A.J. Chaplain, C.P. Dettmann, J. Stat. Phys. 128, 1321 (2007)
J.A. Izaguirre, D.P. Catarello, J.M. Wozniak, R.D. Skeel, J. Chem. Phys. 114, 2090 (2001)
P. Minary, G.J. Martyna, M.E. Tuckerman, Phys. Rev. Lett. 93, 150201 (2004)
S. Reich, Physica D. 89, 28 (1995)
C. Hartmann, Constraints in Molecular Simulation 2010, Zaragosa, slides, http://neptuno.unizar.es/events/constraints2010/files/Carsten_Hartmann.pdf
S. Melchionna, J. Chem. Phys. 127, 044108 (2007)
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Bajars, J., Frank, J. & Leimkuhler, B. Stochastic-dynamical thermostats for constraints and stiff restraints. Eur. Phys. J. Spec. Top. 200, 131–152 (2011). https://doi.org/10.1140/epjst/e2011-01522-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2011-01522-0