Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T20:12:01.818Z Has data issue: false hasContentIssue false
  • English
  • Français

A Metropolis adjusted Nosé-Hoover thermostat

Published online by Cambridge University Press:  08 July 2009

Benedict Leimkuhler  and
Sebastian Reich
Benedict Leimkuhler
Affiliation:
The Maxwell Institute and School of Mathematics, University of Edinburgh, Edinburgh, EH9 3JZ, UK. [email protected]
Sebastian Reich
Affiliation:
Universität Potsdam, Institut für Mathematik, 14469 Potsdam, Germany.
Get access

Abstract

We present a Monte Carlo technique for sampling from thecanonical distribution in molecular dynamics. The method is built uponthe Nosé-Hoover constant temperature formulation and the generalizedhybrid Monte Carlo method. In contrast to standard hybrid Monte Carlo methodsonly the thermostat degree of freedom is stochastically resampled during a Monte Carlo step.

Keywords

Molecular dynamicsthermostatshybrid Monte Carlocanonical ensemble.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 4: Special issue on Numerical ODEs today , July 2009 , pp. 743 - 755
Copyright
© EDP Sciences, SMAI, 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akhmatskaya, E. and Reich, S., GSHMC: An efficient method for molecular simulations. J. Comput. Phys. 227 (2008) 4934–4954. CrossRef
Akhmatskaya, E., Bou-Rabee, N. and Reich, S., Generalized hybrid Monte Carlo methods with and without momentum flip. J. Comput. Phys. 227 (2008) 4934–4954. CrossRef
M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids. Clarendon Press, Oxford (1987)
Bond, S.D., Leimkuhler, B.J. and Laird, B.B., The Nosé-Poincaré method for constant temperature molecular dynamics. J. Comput. Phys. 151 (1999) 114–134. CrossRef
Bussi, G., Donadio, D. and Parrinello, M., Canonical sampling through velocity rescaling. J. Chem. Phys. 126 (2007) 014101. CrossRef
Duane, S., Kennedy, A.D., Pendleton, B.J. and Roweth, D., Hybrid Monte-Carlo. Phys. Lett. B 195 (1987) 216–222. CrossRef
D. Frenkel and B. Smit, Understanding Molecular Simulation. Academic Press, New York (1996).
Hoover, W.G., Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 31 (1985) 1695–1697. CrossRef
Horowitz, A.M., A generalized guided Monte-Carlo algorithm. Phys. Lett. B 268 (1991) 247–252. CrossRef
Izaguirre, J.A. and Hampton, S.S., Shadow Hybrid Monte Carlo: An efficient propagator in phase space of macromolecules. J. Comput. Phys. 200 (2004) 581–604. CrossRef
Kennedy, A.D. and Pendleton, B., Cost of the generalized hybrid Monte Carlo algorithm for free field theory. Nucl. Phys. B 607 (2001) 456–510. CrossRef
Klein, P., Pressure and temperature control in molecular dynamics simulations: a unitary approach in discrete time. Modelling Simul. Mater. Sci. Eng. 6 (1998) 405–421. CrossRef
Legoll, F., Luskin, M. and Moeckel, R., Non-ergodicity of the Nose-Hoover thermostatted harmonic oscillator. Arch. Ration. Mech. Anal. 184 (2007) 449–463. CrossRef
Leimkuhler, B. and Sweet, C., Hamiltonian, A formulation for recursive multiple thermostats in a common timescale. SIAM J. Appl. Dyn. Syst. 4 (2005) 187–216. CrossRef
B. Leimkuhler, E. Noorizadeh and F. Theil, A gentle ergodic thermostat for molecular dynamics. J. Stat. Phys. (2009), doi: 10.1007/s10955-009-9734-0. CrossRef
J.S. Liu, Monte Carlo Strategies in Scientific Computing. Springer-Verlag, New York (2001).
Martyna, G.J., Klein, M.L. and Tuckerman, M., Nose-Hoover chains: The canonical ensemble via continuous dynamics. J. Chem. Phys. 97 (1992) 2635–2643. CrossRef
Nosé, S., A unified formulation of the constant temperature molecular-dynamics methods. J. Chem. Phys. 81 (1984) 511–519. CrossRef
B. Oksendal, Stochastic Differential Equations. 5th Edition, Springer-Verlag, Berlin-Heidelberg (2000).
Ryckaert, J.-P. and Bellemans, A., Molecular dynamics of liquid alkanes. Faraday Discussions 66 (1978) 95–107. CrossRef
Samoletov, A., Chaplain, M.A.J. and Dettmann, C.P., Thermostats for “slow" configurational modes. J. Stat. Phys. 128 (2007) 1321–1336. CrossRef