Gibbs-Duhem integration: a new method for direct evaluation of phase coexistence by molecular simulation
TL;DR: In this article, a method that combines the best elements of thermodynamic integration and the Gibbs ensemble technique is proposed for the direct evaluation of phase equilibria by molecular simulation, given the conditions of coexistence at a single state point, simultaneous but independent NPT simulations of each phase are performed in succession along the saturation line.
Abstract: A method that combines the best elements of thermodynamic integration and the Gibbs ensemble technique is proposed for the direct evaluation of phase equilibria by molecular simulation. Given the conditions of coexistence at a single state point, simultaneous but independent NPT simulations of each phase are performed in succession along the saturation line. In each simulation, the pressure is adjusted to satisfy chemical potential equality according to the Gibbs-Duhem equation. Each coexistence point is determined by just one simulation, and particle insertions are never performed or attempted. Vapourliquid coexistence for the Lennard-Jones model is evaluated, and extensions are discussed.
Citations
More filters
TL;DR: A potential model intended to be a general purpose model for the condensed phases of water is presented, which gives excellent predictions for the densities at 1 bar with a maximum density at 278 K and an averaged difference with experiment of 7 x 10(-4) g/cm3.
Abstract: A potential model intended to be a general purpose model for the condensed phases of water is presented. TIP4P/2005 is a rigid four site model which consists of three fixed point charges and one Lennard-Jones center. The parametrization has been based on a fit of the temperature of maximum density (indirectly estimated from the melting point of hexagonal ice), the stability of several ice polymorphs and other commonly used target quantities. The calculated properties include a variety of thermodynamic properties of the liquid and solid phases, the phase diagram involving condensed phases, properties at melting and vaporization, dielectric constant, pair distribution function, and self-diffusion coefficient. These properties cover a temperature range from 123to573K and pressures up to 40000bar. The model gives an impressive performance for this variety of properties and thermodynamic conditions. For example, it gives excellent predictions for the densities at 1bar with a maximum density at 278K and an aver...
3,009 citations
TL;DR: The predictions for both the densities and the coexistence curves are better than for TIP4P, which previously yielded the best estimations of the ice properties.
Abstract: The ability of several water models to predict the properties of ices is discussed. The emphasis is put on the results for the densities and the coexistence curves between the different ice forms. It is concluded that none of the most commonly used rigid models is satisfactory. A new model specifically designed to cope with solid-phase properties is proposed. The parameters have been obtained by fitting the equation of state and selected points of the melting lines and of the coexistence lines involving different ice forms. The phase diagram is then calculated for the new potential. The predicted melting temperature of hexagonal ice (Ih) at 1 bar is 272.2 K. This excellent value does not imply a deterioration of the rest of the properties. In fact, the predictions for both the densities and the coexistence curves are better than for TIP4P, which previously yielded the best estimations of the ice properties.
1,033 citations
TL;DR: The results for the melting temperature from the direct coexistence simulations of this work are in agreement with those obtained previously by us from free energy calculations.
Abstract: In this work we present an implementation for the calculation of the melting point of ice Ih from direct coexistence of the solid-liquid interface. We use molecular dynamics simulations of boxes containing liquid water and ice in contact. The implementation is based on the analysis of the evolution of the total energy along NpT simulations at different temperatures. We report the calculation of the melting point of ice Ih at 1 bar for seven water models: SPC/E, TIP4P, TIP4P-Ew, TIP4P/ice, TIP4P/2005, TIP5P, and TIP5P-E. The results for the melting temperature from the direct coexistence simulations of this work are in agreement within the statistical uncertainty with those obtained previously by us from free energy calculations. By taking into account the results of this work and those of our free energy calculations, recommended values of the melting point of ice Ih at 1 bar for the above mentioned water models are provided. © 2006 American Institute of Physics. DOI: 10.1063/1.2183308
408 citations
TL;DR: In this paper, the phase diagram of a system consisting of hard particles with an attractive Yukawa interaction is computed by Monte Carlo simulation, and it is shown that the liquid-vapor coexistence curve disappears when the range of the attractive part of the Yukawa potential is less than approximately one sixth of the hard core diameter.
Abstract: The phase diagram of a system consisting of hard particles with an attractive Yukawa interaction is computed by Monte Carlo simulation. From the results of these simulations we can estimate that the liquid–vapor coexistence curve disappears when the range of the attractive part of the Yukawa potential is less than approximately one‐sixth of the hard‐core diameter. The results of the simulations are compared with predictions based on first order perturbation theory.
383 citations
TL;DR: The methodology proposed in this paper can be used to investigate the effect upon a coexistence line due to a change in the potential parameters and the location of the negative charge along the H-O-H bisector appears as a critical factor in the determination of the relative stability between the I(h) and II ice forms.
Abstract: The melting temperature of ice Ih for several commonly used models of water sSPC, SPC/ E,TIP3P,TIP4P, TIP4P/Ew, and TIP5Pd is obtained from computer simulations at p= 1 bar. Since the melting temperature of ice I h for the TIP4P model is now known fE. Sanz, C. Vega, J. L. F. Abascal, and L. G. MacDowell, Phys. Rev. Lett. 92, 255701 s2004dg, it is possible to use the Gibbs‐Duhem methodology fD. Kofke, J. Chem. Phys. 98, 4149 s1993dg to evaluate the melting temperature of ice I h for other potential models of water. We have found that the melting temperatures of ice I h for SPC, SPC/E, TIP3P, TIP4P, TIP4P/Ew, and TIP5P models are T= 190 K, 215 K, 146 K, 232 K, 245 K, and 274 K, respectively. The relative stability of ice I h with respect to ice II for these models has also been considered. It turns out that for SPC, SPC/E, TIP3P, and TIP5P the stable phase at the normal melting point is ice II sso that ice Ih is not a thermodynamically stable phase for these modelsd. For TIP4P and TIP4P/Ew, ice Ih is the stable solid phase at the standard melting point. The location of the negative charge along the H‐O‐H bisector appears as a critical factor in the determination of the relative stability between the I h and II ice forms. The methodology proposed in this paper can be used to investigate the effect upon a coexistence line due to a change in the potential parameters. © 2005 American Institute of Physics . fDOI: 10.1063/1.1862245g
350 citations
References
More filters
Book•
11 Feb 1988TL;DR: In this paper, the gear predictor -corrector is used to calculate forces and torques in a non-equilibrium molecular dynamics simulation using Monte Carlo methods. But it is not suitable for the gear prediction problem.
Abstract: Introduction Statistical mechanics Molecular dynamics Monte Carlo methods Some tricks of the trade How to analyse the results Advanced simulation techniques Non-equilibrium molecular dynamics Brownian dynamics Quantum simulations Some applications Appendix A: Computers and computer simulation Appendix B: Reduced units Appendix C: Calculation of forces and torques Appendix D: Fourier transforms Appendix E: The gear predictor - corrector Appendix F: Programs on microfiche Appendix G: Random numbers References Index.
21,073 citations
Book•
01 Sep 1971
4,078 citations
TL;DR: In this article, 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.
Abstract: 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 ...
1,846 citations
TL;DR: In this article, the Gibbs-ensemble Monte Carlo simulation methodology for phase equilibrium calculations proposed by Panagiotopoulos is generalized and applied to mixture and membrane equilibria, and an alternative derivation of the Gibbs simulation criteria based on the limiting distributions for the appropriate statistical mechanical ensembles is presented.
Abstract: The Gibbs-ensemble Monte Carlo simulation methodology for phase equilibrium calculations proposed by Panagiotopoulos [1] is generalized and applied to mixture and membrane equilibria. An alternative derivation of the Gibbs simulation criteria based on the limiting distributions for the appropriate statistical mechanical ensembles is presented. The method is then generalized for the calculation of phase equilibria of mixtures by simulation in a constantpressure Gibbs ensemble and the calculation of equilibria across semipermeable membranes with an imposed osmotic pressure difference. The method is used to calculate phase equilibria for binary mixtures of Lennard-Jones molecules. Good agreement is found with published results obtained using other simulation techniques. The computer time required for the Gibbs method is only a small fraction of the corresponding requirement for previously available simulation techniques. Calculations for simple osmotic systems are performed for the first time by simulation, ...
1,049 citations
TL;DR: Gibbs Ensemble Monte Carlo (GEMC) as mentioned in this paper is a widely used Monte Carlo method for direct determination of phase coexistence in fluids, which requires only a single simulation per coexistence point.
Abstract: This paper provides an extensive review of the literature on the Gibbs ensemble Monte Carlo method for direct determination of phase coexistence in fluids. The Gibbs ensemble technique is based on performing a simulation in two distinct regions in a way that ensures that the conditions of phase coexistence are satisfied in a statistical sense. Contrary to most other available techniques for this purpose, such as thermodynamic integration, grand canonical Monte Carlo or Widom test particle insertions, the Gibbs ensemble technique involves only a single simulation per coexistence point. A significant body of literature now exists on the method, its theoretical foundations, and proposed modifications for efficient determination of equilibria involving dense fluids and complex intermolecular potentials. Some practical aspects of Gibbs ensemble simulation are also discussed in this review. Applications of the technique to date range from studies of simple model potentials (for example Lennard–Jones, s...
314 citations