David MacGowan

Large Timesteps in Molecular Dynamics Simulations

Abstract Both equilibrium and nonequilibrium molecular dynamics simulations are carried out for two state points of the Lennard-Jones fluid, using leapfrog algorithms. In the equilibrium simulations we obtain internal energies, pressures, radial distribution functions and velocity autocorrelation functions. In the nonequilibrium simulations we obtain the relevant transport coefficients; additionally, the radial distribution function and velocity autocorrelation function in a shearing fluid are computed. It is found that, provided the accuracy of the particle trajectories is fully utilised in calculating their velocities, much larger timesteps than are customary can be used without significant drift in the results. We are thus able to take full advantage of the well known stability of the leapfrog algorithm and also of the even greater stability of its modifications for isokinetic simulations.

Solution of the SSOZ equation for molecules of arbitrary symmetry

We present a flexible and efficient method of solving site-site integral equations for polar molecular fluids. The numerical method is based on a combination of Newton-Raphson and Picard schemes first proposed by Gillan, together with the Ng method for handling Coulomb potentials. It is completely general and can be used with any closure or potential to solve for molecules of arbitrary symmetry. We apply the method to several model systems and demonstrate its superiority to the usual renormalization technique. For quadrupolar hard dumb-bells we find that, in contrast to the situation for neutral dumb-bells, approximate integral equation results depend strongly on the physically irrelevant hard core diameter associated with the centre of the dumb-bell.

Thermodynamics of homonuclear diatomic fluids from the angular median potential

The use of the angular median potential as a temperature‐independent spherical reference system for approximating molecular fluids is tested for its predictions of thermodynamics. Calculations have been carried out for a wide range of homonuclear diatomics with continuous atom–atom potentials believed to be representative of the full range of simulation data available for such systems. The results for the pressure are surprisingly good both in the detonation regime and around the triple point. In the latter case, however, the internal energies for highly elongated molecules with attractive potential wells are considerably too positive. Comparison with other perturbation theories indicates that the median reference system gives better pressures but poorer energies than RAM, and that in many cases, especially for purely repulsive potentials, it gives results of comparable accuracy to those obtained with nonspherical reference systems.

A comparison of NEMD algorithms for thermal conductivity

Abstract We compare carefully the Evans and Gillan NEMD algorithms for thermal conductivity which have hitherto been regarded as essentially identical. Despite significant differences between them, both algorithms give correct results.

Effective spherical potentials for the thermodynamics of homonuclear diatomic Lennard‐Jones liquids

The predictions of several effective spherical potentials for thermodynamic properties of symmetric diatomic Lennard‐Jones molecules are examined. The effective potentials are obtained by splitting the molecular potential in various ways followed by adding the separate angular medians of the two parts. Luckily, the best results are obtained when each site–site interaction is divided into its individual power law terms. It is therefore possible to obtain quite accurate thermodynamic properties over a continuous range of elongations using linear combinations of just two spherical potentials for which accurate analytic fitting functions are provided.

Simulation of diffusion coefficients in binary liquid mixtures

The mutual diffusion coefficient and self diffusion coefficients in a binary argon-krypton mixture with Lennard-Jones interactions are investigated using nonequilibrium molecular dynamics simulations. Compared to the results obtained by Schoen and Hoheisel on the basis of equilibrium simulations, the present values of all the diffusion coefficients are significantly lower, by similar fractional amounts. Consequently, both methods agree on the relative importance of dynamical cross correlations though neither gives better than a rough estimate of this quantity.

The self-consistent mean spherical approximation for the one-component plasma

The consequences of choosing the adjustable hard-core diameter in the mean spherical approximation for the one-component plasma so as to achieve thermodynamic consistency between the energy and compressibility equations are investigated. Such a choice is found to be possible only for Γ>8.5 and, although the resulting correlation functions are discontinuous, the height of the main peak in the static structure factor is remarkably accurate. Two especially noteworthy aspects of the thermodynamic results are that the compressibility equation is much more accurate than in any previous approximation free of input from computer simulations and that the nonstatic part of the internal energy has a Γ1/4 dependence in the strong coupling limit in agreement with Monte Carlo data.

Angular correlations in dense hot diatomic fluids

Molecular dynamics (MD) simulation data for rigid diatomic models of N2 and CO2 under conditions of extremely high density and temperature are analyzed for static correlation functions. The results show some significant qualitative differences from those for diatomic fluids at normal densities and temperatures (i.e., near the triple point). For a single thermodynamic state of N2, the radial distribution functions (RDFs) of the (spherical) RAM and median potentials are found, also by MD. Whereas the median gives good thermodynamic results and poor centers correlation functions, RAM produces just the opposite. Thus no explanation in terms of distribution functions is found for the success of the median for thermodynamics although an empirical correlation is found between the breakdown of median thermodynamics for CO2 and a distinctive feature of the molecular correlation functions.

Van der waals one-fluid theory : justification and generalisation

Abstract We describe an approach to van der Waals one-fluid theory based on thermodynamic consistency and propose a method for generalising it to non-conformal fluids.

Limitations on the usefulness of the angular median and related potentials

The use of the angular median and related effective spherical potentials to predict thermodynamic properties of nonpolar homonuclear diatomic liquids has recently been shown to be efficient and accurate. Here we compare the results obtained from median-like methods for some other molecular liquids with simulation data. We find impressive agreement for linear triatomic molecules but results for tetrahedral molecules and for the overlap potential are very poor. The characteristic shape of potential energy frequency distributions at fixed separations is suggested as a criterion for the success or otherwise of the median potential.