Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. I. Thermodynamic properties in the bulk and at the liquid-vapor phase boundary.

The Wang-Landau sampling is a powerful method that allows for a direct determination of the density of states. However, applications to the calculation of the thermodynamic properties of realistic fluids have been limited so far. By combining the Wang-Landau method with expanded grand-canonical simulations, we obtain a high-accuracy estimate for the grand-canonical partition function for atomic and molecular fluids. Then, using the formalism of statistical thermodynamics, we are able to calculate the thermodynamic properties of these systems, for a wide range of conditions spanning the single-phase regions as well as the vapor-liquid phase boundary. Excellent agreement with prior simulation work and with the available experimental data is obtained for argon and CO(2), thereby establishing the accuracy of the method for the calculation of thermodynamic properties such as free energies and entropies.

[1]  Fernando A Escobedo,et al.  A general framework for non-Boltzmann Monte Carlo sampling. , 2006, The Journal of chemical physics.

[2]  Vargaftik,et al.  Handbook of Physical Properties of Liquids and Gases , 1983 .

[3]  A. Malakis,et al.  Multicritical points and crossover mediating the strong violation of universality: Wang-Landau determinations in the random-bond d=2 Blume-Capel model. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  V. K. Shen,et al.  Direct evaluation of multicomponent phase equilibria using flat-histogram methods. , 2005, The Journal of chemical physics.

[5]  Athanassios Z Panagiotopoulos,et al.  Generalization of the Wang-Landau method for off-lattice simulations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  G. Ganzenmuller,et al.  Phase behaviour and dynamics in primitive models of molecular ionic liquids , 2012, 1202.4279.

[7]  Yuko Okamoto,et al.  Generalized-ensemble algorithms: enhanced sampling techniques for Monte Carlo and molecular dynamics simulations. , 2003, Journal of molecular graphics & modelling.

[8]  F. Escobedo,et al.  Multicanonical schemes for mapping out free-energy landscapes of single-component and multicomponent systems. , 2005, The Journal of chemical physics.

[9]  Kurt Binder,et al.  Transitions of tethered polymer chains: a simulation study with the bond fluctuation lattice model. , 2008, The Journal of chemical physics.

[10]  A. Lyubartsev,et al.  New approach to Monte Carlo calculation of the free energy: Method of expanded ensembles , 1992 .

[11]  Fernando A Escobedo,et al.  Optimization of expanded ensemble methods. , 2008, The Journal of chemical physics.

[12]  F. Escobedo.  Optimized expanded ensembles for simulations involving molecular insertions and deletions. II. Open systems. , 2007, The Journal of chemical physics.

[13]  G. Ganzenmüller,et al.  Applications of Wang-Landau sampling to determine phase equilibria in complex fluids. , 2007, The Journal of chemical physics.

[14]  Jeffrey R Errington.  Evaluating surface tension using grand-canonical transition-matrix Monte Carlo simulation and finite-size scaling. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  J. Delhommelle,et al.  Phase equilibria of polyaromatic hydrocarbons by hybrid Monte Carlo Wang–Landau simulations , 2010 .

[16]  P. Debenedetti,et al.  Flat-histogram dynamics and optimization in density of states simulations of fluids , 2004 .

[17]  Wei Shi,et al.  Improvement in molecule exchange efficiency in Gibbs ensemble Monte Carlo: Development and implementation of the continuous fractional component move , 2008, J. Comput. Chem..

[18]  John S. Rowlinson,et al.  Liquids and liquid mixtures , 1959 .

[19]  Berg,et al.  Multicanonical ensemble: A new approach to simulate first-order phase transitions. , 1992, Physical review letters.

[20]  Thomas F. Miller,et al.  Symplectic quaternion scheme for biophysical molecular dynamics , 2002 .

[21]  D. Landau,et al.  Efficient, multiple-range random walk algorithm to calculate the density of states. , 2000, Physical review letters.

[22]  D. Landau,et al.  Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  J. Singh,et al.  Calculation of phase coexistence properties and surface tensions of n-alkanes with grand-canonical transition-matrix monte carlo simulation and finite-size scaling. , 2006, The journal of physical chemistry. B.

[24]  A. Ghoufi,et al.  Surface tension of water and acid gases from Monte Carlo simulations. , 2008, The Journal of chemical physics.

[25]  P. G. Debenedetti,et al.  An improved Monte Carlo method for direct calculation of the density of states , 2003 .

[26]  A. D. Mackie,et al.  Vapour-liquid coexistence curves of the united-atom and anisotropic united-atom force fields for alkane mixtures , 1999 .

[27]  N. B. Wilding.  Computer simulation of fluid phase transitions , 2001 .

[28]  J. Delhommelle,et al.  Phase equilibria of molecular fluids via hybrid Monte Carlo Wang-Landau simulations: applications to benzene and n-alkanes. , 2009, The Journal of chemical physics.

[29]  Juan J. de Pablo,et al.  Expanded grand canonical and Gibbs ensemble Monte Carlo simulation of polymers , 1996 .

[30]  Chenggang Zhou,et al.  Understanding and improving the Wang-Landau algorithm. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  T. Aleksandrov,et al.  Optimisation of multiple time-step hybrid Monte Carlo Wang–Landau simulations in the isobaric–isothermal ensemble for the determination of phase equilibria , 2010 .

[32]  D. Huse,et al.  Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  J. Pablo,et al.  Calculation of interfacial tension from density of states , 2003 .

[34]  W. Paul,et al.  Measuring the chemical potential of polymer solutions and melts in computer simulations , 1994 .

[35]  J. Ilja Siepmann,et al.  Vapor–liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen , 2001 .

[36]  T. Aleksandrov,et al.  Vapor–liquid equilibria of copper using hybrid Monte Carlo Wang—Landau simulations , 2010 .

[37]  A. Panagiotopoulos.  Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble , 1987 .

[38]  C. Abreu,et al.  On the use of transition matrix methods with extended ensembles. , 2006, The Journal of chemical physics.

[39]  Kurt Binder,et al.  Monte Carlo calculation of the surface tension for two- and three-dimensional lattice-gas models , 1982 .

[40]  R. Kaminsky.  Monte Carlo evaluation of ensemble averages involving particle number variations in dense fluid systems , 1994 .

[41]  Andrew S. Paluch,et al.  Comparing the Use of Gibbs Ensemble and Grand-Canonical Transition-Matrix Monte Carlo Methods to Determine Phase Equilibria , 2008 .

[42]  Jeffrey R. Errington,et al.  Direct calculation of liquid–vapor phase equilibria from transition matrix Monte Carlo simulation , 2003 .