Rolf Lustig

Angle-average for the powers of the distance between two separated vectors

Closed analytical formulae are derived for the angle-average of arbitrary powers of the distance between two separated vectors. It is also shown how coefficients of an expansion in spherical harmonics can be obtained in a closed analytical form.

On the thermodynamics of liquid propane: A molecular dynamics study

A non-linear three-centre Lennard-Jones (3CLJ) model is used to simulate propane over the entire liquid region. If one uses the potential parameters recently derived through a thermodynamic perturbation theory by one of the authors, good overall agreement between simulation and experimental data for pressure, residual internal energy, and the derivative quantities heat capacity, adiabatic compressibility and thermal pressure coefficient is found. However, at high densities the simulated pressures are significantly higher than experiment. We demonstrate that the agreement can be greatly improved by readjusting the size parameter σ in the potential by less than 0·5 per cent. It is shown that three-body effects from triple dipole interactions have only a small influence on the thermodynamics of liquid propane. Since these results prove the consistency between experiment, theory and simulation we conclude that the 3CLJ potential used here is an excellent effective pair potential for fluid propane.

Statistical thermodynamics in the classical molecular dynamics ensemble. I. Fundamentals

The statistical thermodynamics of a classical system composed of rigid molecules is considered in the molecular dynamics ensemble. Accepting Boltzmann’s S=kB ln W as the basic assumption of statistical mechanics, exact formalisms for two classical choices of W are derived. Since there are no restrictions on the order of thermodynamic derivatives, any measurable quantity is directly accessible in this ensemble. Explicit statistical analogs are given for the derivatives of the Helmholtz energy including an approximation for the chemical potential. Basic phase space functions are identified and their properties are explored. It is shown that the complete thermodynamics is governed by small perturbations of these functions from universal behavior.

A molecular dynamics study of the thermodynamics of liquid ethane

Abstract Molecular dynamics (MD) calculations are reported in which ethane was simulated along four isochores spanning the entire liquid region. The molecules interact through a two-center Lennard-Jones (2CLJ) pair potential derived previously in a calculation based on the thermodynamic perturbation theory due to Kohler. Pressures, residual internal energies, and the fluctuation quantities as the residual specific heat and the thermal pressure coefficient obtained from this model agree with values given by an empirical equation of state within the combined uncertainty of both methods for all state points. This suggests that the 2CLJ potential used here is an excellent effective pair potential for fluid ethane.

Direct molecular NVT simulation of the isobaric heat capacity, speed of sound and Joule–Thomson coefficient

Explicit statistical analogues are given for the isobaric heat capacity, the speed of sound and the Joule–Thomson coefficient in the canonical ensemble. The results can directly serve as rigorous measuring prescriptions in existing molecular NVT simulation codes.

Statistical analogues for fundamental equation of state derivatives

A generalized methodology for statistical analogues of derivatives of the fundamental equation of state in the microcanonical and canonical ensembles is suggested. Those analogues include rigorous measuring prescriptions for any thermodynamic property in molecular NVE and NVT simulation. In particular, optimal data sets for exhaustive thermodynamic data correlation become rigorously accessible.

Microcanonical Monte Carlo simulation of thermodynamic properties

A rigorous sampling procedure in configurational phase space is used to simulate any thermodynamic property in the microcanonical ensemble. It is shown how two classical choices of W in Boltzmann’s S=kB ln W differ for small systems and become numerically equivalent in the thermodynamic limit. The same holds true for the comparison with classical molecular dynamics simulations. A comparison with the best empirical equations of state for the Lennard-Jones system shows that this Monte Carlo method is as accurate and reliable as any other simulation technique.

STATISTICAL THERMODYNAMICS IN THE CLASSICAL MOLECULAR DYNAMICS ENSEMBLE. II: APPLICATION TO COMPUTER SIMULATION

The statistical thermodynamics of the classical molecular dynamics ensemble is applied to computer simulation. The general formalism [J. Chem. Phys. 100, 3048 (1994)] is worked out for pairwise additive intermolecular potentials. Specific use is made of the multicenter n/m‐Mie interaction. Cutoff corrections for arbitrary thermodynamic functions are devised.

Equation of State for the Lennard-Jones Fluid

An empirical equation of state correlation is proposed for the Lennard-Jones model fluid. The equation in terms of the Helmholtz energy is based on a large molecular simulation data set and thermal virial coefficients. The underlying data set consists of directly simulated residual Helmholtz energy derivatives with respect to temperature and density in the canonical ensemble. Using these data introduces a new methodology for developing equations of state from molecular simulation. The correlation is valid for temperatures 0.5 < T/Tc < 7 and pressures up to p/pc = 500. Extensive comparisons to simulation data from the literature are made. The accuracy and extrapolation behavior are better than for existing equations of state.

Statistical thermodynamics in the classical molecular dynamics ensemble. III. Numerical results

The statistical thermodynamics of the classical molecular dynamics ensemble [J. Chem. Phys. 100, 3048 (1994); 100, 3060 (1994)] is used in preliminary simulations of systems composed of spherical, linear, and octahedral model molecules. The predicted behavior of general energy and volume derivatives of the classical phase space integrals are shown to hold true. A number‐of‐particles dependence cannot be detected for any of 12 different thermodynamic properties. It is shown that a curious error compensation makes it impossible to discriminate between two classical choices for W in Boltzmann’s entropy relation S=kB ln W.