Shuichi Nosé

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.

Constant pressure molecular dynamics for molecular systems

Technical aspects of the constant pressure molecular dynamics (MD) method proposed by Andersen and extended by Parrinello and Rahman to allow changes in the shape of the MD cell are discussed. The new MD method is extended to treat molecular systems and to include long range charge-charge interactions. Results on the conservation laws, the frequency of oscillation of the MD cell, and the equations which constrain the shape of the MD cell are also given. An additional constraint is introduced to stop the superfluous MD cell rotation which would otherwise complicate the analysis of crystal structures. The method is illustrated by examining the behaviour of solid nitrogen at high pressure.

Constant Temperature Molecular Dynamics Methods

How the canonical distribution is realized in simulations based on deterministic dynamical equations is explained in this review. Basic formulations and their recent extensions of two constant temperature molecular dynamics methods; the constraint and the extended system methods, are discussed. In both methods, the canonical distribution is derived analytically as a stationary solution of a generalized Liouvilles equation which expresses the conservation of probability in a phase space. In the constraint method, the total kinetic energy of a system is kept to a constant by imposing a constraint

Glass Transition

Computer simulations of melting, crystallization, glass transition, and annealing for a model system of 864 Lennard-Jones (LJ) atoms under a periodic boundary condition are carried out using constant-pressure molec ular dynamics techniques with temperature control. When an fcc crystal of LJ atoms is heated, melting occurs; however, an LJ liquid, when quenched slowly, crystallizes into layers with stacking faults. Each layer forms a two-dimensional, close-packed structure with occasional point defects but without dislocations. When the quench rate is high enough, an LJ liquid transforms into a disordered structure without a discontinuous change in volume. The dependence of the glass transi tion on the quench rate is determined by examining macroscopically observable physical features. Several microscopic structure parameters are introduced to ana lyze, at the atomic level, the structures of glasses pro duced by different quench rates. When annealed, a glass made with a low enough quench rate is stable against crystallization. Identifying the number of atoms in the system having local icosahedral symmetry is a prom ising method of characterizing the glasss stability. The microscopic structural changes in the annealing pro cesses are presented in the companion video to this paper.

Isothermal–isobaric computer simulations of melting and crystallization of a Lennard‐Jones system

By means of constant‐temperature, constant‐pressure molecular dynamics techniques, we simulate the melting and crystallization processes of a model system composed of 864 Lennard‐Jones (LJ) particles under periodic boundary conditions. On heating an fcc crystal of LJ particles, it is ascertained that melting takes place. On the other hand, a LJ liquid, when quenched slowly, crystallizes into a stacking of layers with stacking faults where each layer forms a close‐packed structure with occasional point defects. The atomic configuration is not always nucleated into a completely ordered structure. A large hysteresis in the volume‐temperature curve is observed. The volume contraction at the transition is characterized by two different growth rates, relatively slow at the first stage and relatively fast at the final stage. The critical cooling rate which separates the crystal‐forming cooling rates and the glass‐forming cooling rates is between 4×1010 and 4×1011 K/s for argon. On taking advantage of computer si...

A study of solid and liquid carbon tetrafluoride using the constant pressure molecular dynamics technique

The constant pressure molecular dynamics technique originally proposed by Andersen to study fluids and subsequently generalized by Parrinello and Rahman to deal with crystals of arbitrary symmetry has been further extended to treat molecular systems. As a pedagogical example designed to illustrate the utility of this approach, we have investigated the properties of carbon tetrafluoride in its condensed phases using an intermolecular potential based upon atom–atom interactions. In particular, we have explored the effect of changes in temperature and pressure on the orientationally ordered low temperature monoclinic solid. As in the real crystal, isobaric heating to sufficiently high temperature causes the ordered phase to transform spontaneously to a noncubic orientationally disordered phase. The properties of this disordered phase are also examined along with those of the liquid. The atom–atom potential appears to correlate a wide range of experimental data. The possible role of the electrostatic octopole...

Constant-temperature molecular dynamics

A review is given of how molecular dynamics methods have been modified to perform simulations in the constant-temperature condition. One usually considers a system which is thermally connected with a huge external system (a heat reservoir) to describe a canonical ensemble in statistical mechanics. The way in which this situation is reflected is a key factor for simulations under isothermal conditions. The total kinetic energy is kept to a constant value in constraint methods. In stochastic methods, interactions with a heat bath are treated as random collisions with hypothetical atoms or random forces acting on particles. In the extended-system method, a degree of freedom which mimics a heat bath is introduced, and the total energy of a physical system is allowed to fluctuate.

An Improved Symplectic Integrator for Nosé-Poincaré Thermostat

Simple, completely explicit symplectic integration formula are obtained for the Nose-Poincare thermostat; a Hamiltonian dynamics version of the Nose-Hoover thermostat. The time reversibility holds in each of recursion relations.

Molecular Dynamics Simulations at Constant Temperature and Pressure

It is explained how the molecular dynamics methods have been modified to carry out simulations at constant temperature and pressure. The limitations and inconveniences encountered in the ordinary molecular dynamics simulations due to the use of the microcanonical ensemble and the difference between the statistical ensembles are pointed out. We discuss in detail three typical methods ( extended system, constraint, and stochastic methods) developed to resolve the problem. The integration algorithms, the choice of an appropriate value for a mass parameter introduced in the extended system method, and the dynamical properties are also discussed.

Computer Simulations of the Glass Transition

via a glass transition. We monitor the occurrence of the glass transition by examining the macroscopically-observable physical properties such as thermodynamic, structural and dynamical properties. When the quench rate is high enough to form a glass, the larger the quench rate, the higher the glass-transition temperature. We also introduce several microscopic structure parameters in order to analyze,