A Metropolis adjusted Nosé-Hoover thermostat
ESAIM: Modélisation mathématique et analyse numérique, Special issue on Numerical ODEs today, Tome 43 (2009) no. 4, pp. 743-755.

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

DOI : 10.1051/m2an/2009023
Classification : 65C05, 65C20, 65C60, 82B80, 60H30
Mots-clés : molecular dynamics, thermostats, hybrid Monte Carlo, canonical ensemble 
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     title = {A {Metropolis} adjusted {Nos\'e-Hoover} thermostat},
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Leimkuhler, Benedict; Reich, Sebastian. A Metropolis adjusted Nosé-Hoover thermostat. ESAIM: Modélisation mathématique et analyse numérique, Special issue on Numerical ODEs today, Tome 43 (2009) no. 4, pp. 743-755. doi : 10.1051/m2an/2009023. http://archive.numdam.org/articles/10.1051/m2an/2009023/

[1] E. Akhmatskaya and S. Reich, GSHMC: An efficient method for molecular simulations. J. Comput. Phys. 227 (2008) 4934-4954. | MR | Zbl

[2] E. Akhmatskaya, N. Bou-Rabee and S. Reich, Generalized hybrid Monte Carlo methods with and without momentum flip. J. Comput. Phys. 227 (2008) 4934-4954. | MR | Zbl

[3] M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids. Clarendon Press, Oxford (1987) | Zbl

[4] S.D. Bond, B.J. Leimkuhler and B.B. Laird, The Nosé-Poincaré method for constant temperature molecular dynamics. J. Comput. Phys. 151 (1999) 114-134. | MR | Zbl

[5] G. Bussi, D. Donadio and M. Parrinello, Canonical sampling through velocity rescaling. J. Chem. Phys. 126 (2007) 014101.

[6] S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Hybrid Monte-Carlo. Phys. Lett. B 195 (1987) 216-222.

[7] D. Frenkel and B. Smit, Understanding Molecular Simulation. Academic Press, New York (1996). | Zbl

[8] W.G. Hoover, Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 31 (1985) 1695-1697.

[9] A.M. Horowitz, A generalized guided Monte-Carlo algorithm. Phys. Lett. B 268 (1991) 247-252.

[10] J.A. Izaguirre and S.S. Hampton, Shadow Hybrid Monte Carlo: An efficient propagator in phase space of macromolecules. J. Comput. Phys. 200 (2004) 581-604. | Zbl

[11] A.D. Kennedy and B. Pendleton, Cost of the generalized hybrid Monte Carlo algorithm for free field theory. Nucl. Phys. B 607 (2001) 456-510. | MR | Zbl

[12] P. Klein, Pressure and temperature control in molecular dynamics simulations: a unitary approach in discrete time. Modelling Simul. Mater. Sci. Eng. 6 (1998) 405-421.

[13] F. Legoll, M. Luskin and R. Moeckel, Non-ergodicity of the Nose-Hoover thermostatted harmonic oscillator. Arch. Ration. Mech. Anal. 184 (2007) 449-463. | MR | Zbl

[14] B. Leimkuhler and C. Sweet, A Hamiltonian formulation for recursive multiple thermostats in a common timescale. SIAM J. Appl. Dyn. Syst. 4 (2005) 187-216. | MR | Zbl

[15] 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. | MR

[16] J.S. Liu, Monte Carlo Strategies in Scientific Computing. Springer-Verlag, New York (2001). | MR | Zbl

[17] G.J. Martyna, M.L. Klein and M. Tuckerman, Nose-Hoover chains: The canonical ensemble via continuous dynamics. J. Chem. Phys. 97 (1992) 2635-2643.

[18] S. Nosé, A unified formulation of the constant temperature molecular-dynamics methods. J. Chem. Phys. 81 (1984) 511-519.

[19] B. Oksendal, Stochastic Differential Equations. 5th Edition, Springer-Verlag, Berlin-Heidelberg (2000). | Zbl

[20] J.-P. Ryckaert and A. Bellemans, Molecular dynamics of liquid alkanes. Faraday Discussions 66 (1978) 95-107.

[21] A. Samoletov, M.A.J. Chaplain and C.P. Dettmann, Thermostats for “slow'' configurational modes. J. Stat. Phys. 128 (2007) 1321-1336. | MR | Zbl

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