Classical Monte Carlo simulations have been carried out for liquid water in the NPT ensemble at 25 °C and 1 atm using six of the simpler intermolecular potential functions for the water dimer: Bernal–Fowler (BF), SPC, ST2, TIPS2, TIP3P, and TIP4P. Comparisons are made with experimental thermodynamic and structural data including the recent neutron diffraction results of Thiessen and Narten. The computed densities and potential energies are in reasonable accord with experiment except for the original BF model, which yields an 18% overestimate of the density and poor structural results. The TIPS2 and TIP4P potentials yield oxygen–oxygen partial structure functions in good agreement with the neutron diffraction results. The accord with the experimental OH and HH partial structure functions is poorer; however, the computed results for these functions are similar for all the potential functions. Consequently, the discrepancy may be due to the correction terms needed in processing the neutron data or to an effect uniformly neglected in the computations. Comparisons are also made for self‐diffusion coefficients obtained from molecular dynamics simulations. Overall, the SPC, ST2, TIPS2, and TIP4P models give reasonable structural and thermodynamic descriptions of liquid water and they should be useful in simulations of aqueous solutions. The simplicity of the SPC, TIPS2, and TIP4P functions is also attractive from a computational standpoint.

Comparison of simple potential functions for simulating liquid water

Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling

A methodology is presented for Monte Carlo simulation of fluids in a new ensemble that can be used to obtain phase coexistence properties of multicomponent systems from a single computer experiment. The method is based on performing a simulation simultaneously in two distinct physical regions of generally different densities and compositions. Three types of perturbations are performed, a random displacement of molecules that ensures equilibrium within each region, an equal and opposite change in the volume of the two regions that results in equality of pressures, and random transfers of molecules that equalize the chemical potentials of each component in the two regions. The method is applied to the calculation of the liquid-gas coexistence envelope for the pure Lennard-Jones (6, 12) fluid for several reduced temperatures from the vicinity of the triple point to close to the critical point (T* = 0·75 to T* = 1·30). Good overall agreement with previously available literature results is obtained, with some ...

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Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble

We review the existing simulation data and equations of state for the Lennard-Jones (LJ) fluid, and present new simulation results for both the cut and shifted and the full LJ potential. New parameters for the modified Benedict-Webb-Rubin (MBWR) equation of state used by Nicolas, Gubbins, Streett and Tildesley are presented. In contrast to previous equations, the new equation is accurate for calculations of vapour-liquid equilibria. The equation also accurately correlates pressures and internal energies from the triple point to about 4·5 times the critical temperature over the entire fluid range. An equation of state for the cut and shifted LJ fluid is presented and compared with the simulation data of this work, and previously published Gibbs ensemble data. The MBWR equation of state can be extended to mixtures via the van der Waals one-fluid theory mixing rules. Calculations for binary fluid mixtures are found to be accurate when compared with Gibbs ensemble simulations.

The Lennard-Jones equation of state revisited

The effective interactions of ions, dipoles and higher-order multipoles under periodic boundary conditions are calculated where the array of periodic replications forms an infinite sphere surrounded by a vacuum. Discrepancies between the results of different methods of calculation are resolved and some shape-dependent effects are discussed briefly. In a simulation under these periodic boundary conditions, the net Hamiltonian contains a positive term proportional to the square of the net dipole moment of the configuration. Surrounding the infinite sphere by a continuum of dielectric constant e.9 changes this positive term, the coefficient being zero as e9 ->∞ . We report on the simulation of a dense fluid of hard spheres with embedded point dipoles; simulations are made for different values of showing how the Kirkwood gr-factor and the long-range part of hA (r) depend on e9 in a finite simulation. We show how this dependence on e9 nonetheless leads to a dielectric constant for the system that is independent of e . In particular, the Clausius-Mosotti and Kirkwood formulae for the dielectric constant e of the system give consistent e values.

Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants.

A Monte Carlo method for the calculation of thermodynamic properties in the isothermal-isobaric ensemble is described. Application is made to the calculation of excess thermodynamic properties (enthalpy, volume and Gibbs free energy) of binary mixtures of Lennard-Jones 12–6 liquids. Comparison is made with the predictions of a number of theories of liquid mixtures; the so-called van der Waals one-fluid model and the variational theory of Mansoori and Leland are both found to give excellent results. The accuracy attainable in estimates of the excess properties is discussed in terms of statistical fluctuations in various calculated quantities and the advantages and disadvantages of the method are examined in relation to calculations by the more familiar constant-volume method.

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NpT-ensemble Monte Carlo calculations for binary liquid mixtures

An empirical formula for the Helmholtz free energy of a system of particles interacting through the Lennard-Jones 12-6 potential is derived on the basis of Monte Carlo computations of the internal energy and pressure. The calculations cover the reduced temperature range from [Ttilde] = 0·551 to [Ttilde] = 1·237 and reduced pressures up to [ptilde] = 1·6. The results are used to assess the adequacy of the 12-6 potential model for a number of simple liquids (Ar, Kr, Xe, CH4, N2, O2, CO) and values of the effective 12-6 potential parameters are proposed for each.

An equation of state for simple liquids

Monte Carlo results are presented for the free energy and dielectric constant of systems of permanent dipoles disposed on the sites of simple cubic and face-centred cubic lattices as functions of the parameter ϑ = μ2ρ/kT. Alternative schemes are considered for taking account of the long-range character of the dipolar interaction, based on an Ewald-type sum or a reaction-field approximation; use of such a procedure is essential if the system is to have the correct dielectric properties. Different methods of calculating the dielectric constant are also compared. It is shown that the two methods of treating the long-range contribution to the energy lead to similar results for the dielectric constant, but use of the Ewald method apparently introduces a small but systematic error. The results on both free energy and dielectric constant are discussed in the light of predictions of a number of analytical approaches. In the case of the simple cubic lattice the general trend in the computed dielectric constant as ...

Thermodynamic and dielectric properties of polar lattices

The conformal solution approach is used to relate the distribution functions g αβ(r) for a fluid mixture to those of a pure fluid, g x(r). The procedure is to expand g αβ(r) about the corresponding function for an ideal solution, using σ αβ 3 and eαβσαβ 3 as expansion parameters; the expansion of the function y αβ(r) is also considered. Molecular dynamics results are reported for the tg αβ for argon-krypton liquid mixtures using the Lennard-Jones (12, 6) potential. These results are used to test the conformal solution expansions to first order; the g αβ expansion is found to be superior to that for y αβ for most r values of interest. The second order term in the conformal solution expansion for the Helmholtz free energy is also calculated for argon-krypton mixtures, and found to be about 10 per cent of the value of A E given by the van der Waals 1 theory.

The radial distribution function in fluid mixtures: Conformal solution theory and molecular dynamics results

The results of Monte Carlo calculations in the isothermal-isobaric ensemble are reported for a series of binary mixtures of Lennard-Jones liquids at zero pressure and a temperature of 115·8 K. In the case of equimolar mixtures comparison is made with the predictions of several recently developed theories of liquid mixtures. Particularly good results for excess Gibbs free energy and enthalpy are obtained from the variational theory of Mansoori and Leland and for excess volume from the one-fluid version of the so-called van der Waals model.

I.R. McDonald

Papers

NpT-ensemble Monte Carlo calculations for binary liquid mixtures

An equation of state for simple liquids

Thermodynamic and dielectric properties of polar lattices

The radial distribution function in fluid mixtures: Conformal solution theory and molecular dynamics results

Excess thermodynamic properties of mixtures of Lennard-Jones liquids