A unified formulation of the constant temperature molecular dynamics methods

Three recently proposed constant temperature molecular dynamics methods by: (i) Nose (Mol. Phys., to be published); (ii) Hoover et al. [Phys. Rev. Lett. 48, 1818 (1982)], and Evans and Morriss [Chem. Phys. 77, 63 (1983)]; and (iii) Haile and Gupta [J. Chem. Phys. 79, 3067 (1983)] are examined analytically via calculating the equilibrium distribution functions and comparing them with that of the canonical ensemble. Except for effects due to momentum and angular momentum conservation, method (1) yields the rigorous canonical distribution in both momentum and coordinate space. Method (2) can be made rigorous in coordinate space, and can be derived from method (1) by imposing a specific constraint. Method (3) is not rigorous and gives a deviation of order N−1/2 from the canonical distribution (N the number of particles). The results for the constant temperature–constant pressure ensemble are similar to the canonical ensemble case.

[1]  Jerome K. Percus,et al.  Ensemble Dependence of Fluctuations with Application to Machine Computations , 1967 .

[2]  B. Alder,et al.  Studies in Molecular Dynamics. IV. The Pressure, Collision Rate, and Their Number Dependence for Hard Disks , 1967 .

[3]  L. V. Woodcock.  Isothermal molecular dynamics calculations for liquid salts , 1971 .

[4]  William G. Hoover,et al.  Lennard-Jones triple-point bulk and shear viscosities. Green-Kubo theory, Hamiltonian mechanics, and nonequilibrium molecular dynamics , 1980 .

[5]  M. Parrinello,et al.  Crystal structure and pair potentials: A molecular-dynamics study , 1980 .

[6]  H. C. Andersen.  Molecular dynamics simulations at constant pressure and/or temperature , 1980 .

[7]  M. Parrinello,et al.  Polymorphic transitions in single crystals: A new molecular dynamics method , 1981 .

[8]  William G. Hoover,et al.  High-strain-rate plastic flow studied via nonequilibrium molecular dynamics , 1982 .

[9]  W. G. Hoover.  Atomistic nonequilibrium computer simulations , 1982 .

[10]  S. Nosé,et al.  A study of solid and liquid carbon tetrafluoride using the constant pressure molecular dynamics technique , 1983 .

[11]  Gary P. Morriss,et al.  The isothermal/isobaric molecular dynamics ensemble , 1983 .

[12]  William G. Hoover,et al.  Nonequilibrium molecular dynamics via Gauss's principle of least constraint , 1983 .

[13]  A. Ladd,et al.  Plastic flow in close-packed crystals via nonequilibrium molecular dynamics , 1983 .

[14]  D. Heyes,et al.  MOLECULAR DYNAMICS AT CONSTANT PRESSURE AND TEMPERATURE , 1983 .

[15]  Roger Impey,et al.  Polymorphic phase transitions in alkali cyanide crystals , 1983 .

[16]  D. Wallace,et al.  Ensemble corrections for the molecular-dynamics ensemble , 1983 .

[17]  S. Nosé,et al.  Structural Transformations in Solid Nitrogen at High Pressure , 1983 .

[18]  Priya Vashishta,et al.  Structural Transitions in Superionic Conductors , 1983 .

[19]  R. Mountain,et al.  Phase relations and properties of lithium via molecular dynamics , 1983 .

[20]  J. Haile,et al.  Extensions of the molecular dynamics simulation method. II. Isothermal systems , 1983 .

[21]  Denis J. Evans,et al.  Computer ‘‘experiment’’ for nonlinear thermodynamics of Couette flow , 1983 .

[22]  S. Nosé,et al.  Constant pressure molecular dynamics for molecular systems , 1983 .

[23]  J. H. R. Clarke,et al.  A comparison of constant energy, constant temperature and constant pressure ensembles in molecular dynamics simulations of atomic liquids , 1984 .