Solid–fluid coexistence of the Lennard-Jones system from absolute free energy calculations

Barroso, M.; Ferreira, A. L.

doi:10.1063/1.1464828

Cited by 84 publications

(97 citation statements)

References 33 publications

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“…The Einstein crystal method was proposed by Frenkel and Ladd in the year 1984 [27] and, since then, it has become the standard method to compute the free energy of solids [32,41,42,142,29,143,62,44,144,63]. In this method an ideal Einstein crystal is used as the reference system to compute the free energy of a solid.…”

Section: Widom Test Particle Methodsmentioning

confidence: 99%

Determination of phase diagrams via computer simulation: methodology and applications to water, electrolytes and proteins

Vega¹,

Sanz

Abascal

et al. 2008

J. Phys.: Condens. Matter

275

452

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Abstract. In this review we focus on the determination of phase diagrams by computer simulation with particular attention to the fluid-solid and solid-solid equilibria. The methodology to compute the free energy of solid phases will be discussed. In particular, the Einstein crystal and Einstein molecule methodologies are described in a comprehensive way. It is shown that both methodologies yield the same free energies and that free energies of solid phases present noticeable finite size effects. In fact this is the case for hard spheres in the solid phase. Finite size corrections can be introduced, although in an approximate way, to correct for the dependence of the free energy on the size of the system. The computation of free energies of solid phases can be extended to molecular fluids. The procedure to compute free energies of solid phases of water (ices) will be described in detail. The free energies of ices Ih, II, III, IV, V, VI, VII, VIII, IX, XI and XII will be presented for the SPC/E and TIP4P models of water. Initial coexistence points leading to the determination of the phase diagram of water for these two models will be provided. Other methods to estimate the melting point of a solid, as the direct fluid-solid coexistence or simulations of the free surface of the solid will be discussed. It will be shown that the melting points of ice Ih for several water models, obtained from free energy calculations, direct coexistence simulations and free surface simulations, agree within their statistical uncertainty. Phase diagram calculations can indeed help to improve potential models of molecular fluids. For instance, for water, the potential model TIP4P/2005 can be regarded as an improved version of TIP4P. Here we will review some recent work on the phase diagram of the simplest ionic model, the restricted primitive model. Although originally devised to describe ionic liquids, the model is becoming quite popular to describe the behaviour of charged colloids. Besides the possibility of obtaining fluid-solid equilibria for simple protein models will be discussed. In these primitive models, the protein is described by a spherical potential with certain anisotropic bonding sites (patchy sites).

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Section: Widom Test Particle Methodsmentioning

confidence: 99%

Determination of phase diagrams via computer simulation: methodology and applications to water, electrolytes and proteins

Vega¹,

Sanz

Abascal

et al. 2008

J. Phys.: Condens. Matter

275

452

View full text Add to dashboard Cite

show abstract

“…The simplest way to determine fluid-solid coexistence comprises an independent determination of the free energy of the fluid and the solid phase via thermodynamic integration 7,8 or more advanced techniques. [9][10][11] This is achieved via a series of simulations starting from a state of known free energy (usually an ideal gas state). The solid phase is modeled as a constrained system in which each particle is confined to move in a Wigner-Seitz cell 7 or as an Einstein crystal.…”

mentioning

confidence: 99%

Communication: A simple method for simulation of freezing transitions

Orkoulas

Nayhouse

2011

The Journal of Chemical Physics

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Despite recent advances, precise simulation of freezing transitions continues to be a challenging task. In this work, a simulation method for fluid-solid transitions is developed. The method is based on a modification of the constrained cell model which was proposed by Hoover and Ree [J. Chem. Phys. 47, 4873 (1967)]10.1063/1.1701730. In the constrained cell model, each particle is confined in a single Wigner-Seitz cell. Hoover and Ree pointed out that the fluid and solid phases can be linked together by adding an external field of variable strength. High values of the external field favor single occupancy configurations and thus stabilize the solid phase. In the present work, the modified cell model is simulated in the constant-pressure ensemble using tempering and histogram reweighting techniques. Simulation results on a system of hard spheres indicate that as the strength of the external field is reduced, the transition from solid to fluid is continuous at low and intermediate pressures and discontinuous at high pressures. Fluid-solid coexistence for the hard-sphere model is established by analyzing the phase transition of the modified model in the limit in which the external field vanishes. The coexistence pressure and densities are in excellent agreement with current state-of-the-art techniques.

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“…This indicates that the present model can reproduce the phase diagram in a real system, at least qualitatively. figure 9 shows the temperature-number density phase boundaries by vdW EOS and a comparison of the calculated result with that for the LJ system [6,22]. The sign of the tangent of the solidliquid phase boundaries in figure 9 is different from that for the LJ system.…”

Section: Phase Equilibrium Pointsmentioning

confidence: 96%

“…The potential parameters for argon are given in Table 2. 6 PhaSE DIaGram figure 8 shows a comparison of the phase diagram in (p, T) space by vdW EOS with the experimental [15,16], molecular dynamics [17][18][19][20][21] and free energy calculations [22,23] for the LJ system. The calculated phase diagram is similar to that observed for argon and the LJ system.…”

Section: Phase Equilibrium Pointsmentioning

confidence: 99%

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Thermodynamics of Three-phase Equilibrium by Van Der Waals Equation of State

Kataoka

2017

Journal of Computer Chemistry, Japan -International Edition

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The phase diagram for a three-phase equilibrium was derived using van der Waals (vdW) equation of state (EOS) with respect to pressure. Aside from the typical liquid-gas vdW EOS, a new solid-gas vdW EOS was introduced. The new vdW EOS had the same functional form as the original equation of state and only the van der Waals coefficients were different. The thermodynamic EOSs were integrated to obtain the internal energy and the integral constants were given explicitly. The calculated phase diagram was consistent with that for argon and the Lennard-Jones system.

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Solid–fluid coexistence of the Lennard-Jones system from absolute free energy calculations

Cited by 84 publications

References 33 publications

Determination of phase diagrams via computer simulation: methodology and applications to water, electrolytes and proteins

Determination of phase diagrams via computer simulation: methodology and applications to water, electrolytes and proteins

Communication: A simple method for simulation of freezing transitions

Thermodynamics of Three-phase Equilibrium by Van Der Waals Equation of State

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