Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-25T14:30:43.383Z Has data issue: false hasContentIssue false
  • English
  • Français

Molecular Simulation in the Canonical Ensemble and Beyond

Published online by Cambridge University Press:  16 June 2007

Zhidong Jia  and
Ben Leimkuhler
Zhidong Jia
Affiliation:
ICMSEC, P.O. Box 2719, Beijing 100080, China.
Ben Leimkuhler
Affiliation:
School of Mathematics and Maxwell Institute, University of Edinburgh, Edinburgh EH9 3JZ, UK.
Get access

Abstract

In this paper, we discuss advanced thermostatting techniques for sampling molecular systems in the canonical ensemble. We first survey work on dynamical thermostatting methods, including the Nosé-Poincaré method, and generalized bath methods which introduce a more complicated extended model to obtain better ergodicity. We describe a general controlled temperature model, projective thermostatting molecular dynamics (PTMD) and demonstrate that it flexibly accommodates existing alternative thermostatting methods, such as Nosé-Poincaré, Nosé-Hoover (with or without chains), Bulgac-Kusnezov, or recursive Nosé-Poincaré Chains. These schemes offer possible advantages for use in computing thermodynamic quantities, and facilitate the development of multiple time-scale modelling and simulation techniques. In addition, PTMD advances a preliminary step toward the realization of true nonequilibrium motion for selected degrees of freedom, by shielding the variables of interest from the artificial effect of thermostats. We discuss extension of the PTMD method for constant temperature and pressure models. Finally, we demonstrate schemes for simulating systems with an artificial temperature gradient, by enabling the use of two temperature baths within the PTMD framework.

Keywords

Molecular dynamicsconstant temperaturethermostatbarostatnonequilibrium simulation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 2: Special issue on Molecular Modelling , March 2007 , pp. 333 - 350
Copyright
© EDP Sciences, SMAI, 2007

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

Andersen, H.C., Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys. 72 (1980) 2384–2393. CrossRef
Barth, E.J., Laird, B.B. and Leimkuhler, B.J., Generating generalized distributions from dynamical simulation. J. Chem. Phys. 118 (2003) 5759–5768. CrossRef
E. Barth, B. Leimkuhler and C. Sweet, Approach to thermal equilibrium in biomolecular simulation, in New Algorithms for Macromolecular Simulation, B. Leimkuhler, C. Chipot, R. Elber, A. Laaksonen, A. Mark, T. Schlick, C. Schütte and R. Skeel Eds., Springer Lecture Notes in Computational Science and Engineering 49 (2006).
Boltzmann, L., On certain questions of the theory of gases. Nature 51 (1895) 413–415. CrossRef
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
Branka, A.C. and Wojciechowski, K.W., Generalization of Nosé and Nosé-Hoover isothermal dynamics. Phys. Rev. E 62 (2000) 3281–3292. CrossRef
Bulgac, A. and Kusnezov, D., Canonical ensemble averages from pseudomicrocanonical dynamics. Phys. Rev. A 42 (1990) 5045–5048. CrossRef
E. Cancés, F. Legoll and G. Stoltz, Theoretical and numerical comparison of some sampling methods for molecular dynamics. ESAIM: M2AN (to appear).
Car, R. and Parinello, M., Unified approach for molecular dynamics and density function theory. Phys. Rev. Lett. 55 (1985) 2471–2475. CrossRef
C. Chipot, Free energy calculations in biological systems: how useful are they in practice, in New Algorithms for Macromolecular Simulation, B. Leimkuhler, C. Chipot, R. Elber, A. Laaksonen, A. Mark, T. Schlick, C. Schütte and R. Skeel Eds., Springer Lecture Notes in Computational Science and Engineering 49 (2006).
Delhommelle, J., Correspondence between configurational temperature and molecular kinetic temperature thermostats. J. Chem. Phys. 117 (2002) 6016–602. CrossRef
Flekkøy, E.G. and Coveney, P.V., From molecular dynamics to dissipative particle dynamics. Phys. Rev. Lett. 83 (1999) 1775–1778. CrossRef
D. Frenkel and B. Smith, Understanding Molecular Simulation. Academic, London (1996).
Gill, S.P.A., Jia, Z., Leimkuhler, B. and Cocks, A.C.F., Rapid thermal equilibration in coarse-grained molecular dynamics. Phys. Rev. B 73 (2006) 184304. CrossRef
Hernandez, E., Metric-tensor flexible-cell for isothermal-isobaric molecular dynamics simulation. J. Chem. Phys. 115 (2001) 10282–10290. CrossRef
Hoover, W.G., Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 31 (1985) 1695–1697. CrossRef
W.G. Hoover, K. Aoki, C.G. Hoover and S.V. De Groot, Time reversible deterministic thermostats. Physica D (2004) 253–267.
Jeans, J.H., On the vibrations set up in molecules by collisions. Phil. Mag. 6 (1903) 279–286. CrossRef
Jeans, J.H., On the partition of energy between matter and ether. Phil. Mag. 10 (1905) 91–97. CrossRef
O.G. Jepps, G. Ayton and D.J. Evans, Microscopic expressions for the thermodynamic temperature. Phys. Rev. E, 62 (2000) 4757–4763.
Jia, Z. and Leimkuhler, B.J., A projective thermostatting dynamics technique. Multiscale Model. Simul. 4 (2005) 563–583. CrossRef
Kusnezov, D., Diffusive aspects of global demons. Phys. Lett. A 166 (1992) 315–320. CrossRef
F. Legoll, M. Luskin and R. Moeckel, Non-ergodicity of the Nosé-Hoover thermostatted harmonic oscillator, arXiv preprint (November 2005, math.DS/0511178). ARMA (to appear).
Leimkuhler, B.J. and Sweet, C.R., The canonical ensemble via symplectic integrators using Nosé and Nosé-Poincaré chains. J. Chem. Phys. 121 (2004) 108–116. CrossRef
Leimkuhler, B.J. and Sweet, C.R., Hamiltonian, A formulation for recursive multiple thermostats in a common timescale. SIAM J. Appl. Dyn. Sys. 4 (2005) 187–216. CrossRef
Liu, W.K., Karpov, E.G., Zhang, S. and Park, H.S., An introduction to computational nano-mechanics and materials. Comput. Meth. Appl. Mech. Eng. 193 (2004) 1529–1578. CrossRef
Liu, Y. and Tuckerman, M.E., Generalized Gaussian Moment Thermostatting: A new continuous dynamical approach to the canonical ensemble. J. Chem. Phys. 112 (2000) 1685–1700. CrossRef
Martyna, G.J., Tuckerman, M.E. and Klein, M.L., Nosé-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
Powles, J., Rickayzen, G. and Heyes, D.M., Temperature: old, new and middle-aged. Mol. Phys. 103 (2005) 1361–1373. CrossRef
Rosso, L., Mináry, P., Zhu, Z. and Tuckerman, M.E., On the use of the adiabatic molecular dynamics technique in the calculation of free energy profiles. J. Chem. Phys. 116 (2002) 4389–4402. CrossRef
Rugh, H.H., Dynamical approach to temperature. Phys. Rev. Lett. 78 (1997) 772–774. CrossRef
Schneider, T. and Stoll, E., Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions. Phys. Rev. B 17 (1978) 1302–1322. CrossRef
Sturgeon, J.B. and Laird, B.B., Symplectic algorithm for constant-pressure molecular-dynamics using a Nosé-Poincare thermostat. J. Chem. Phys. 112 (2000) 3474–3482. CrossRef
Tadmor, E.B., Ortiz, M. and Phillips, R., Quasicontinuum analysis of defects in solids. Philos. Mag. A 73 (1996) 1529–1563. CrossRef
Winkler, R.G., Kraus, V. and Reineker, P., Time-reversible and phase-conserving molecular dynamics at constant temperature. J. Chem. Phys. 102 (1995) 9018–9025. CrossRef