By Ilya Prigogine, Stuart A. Rice
Advances in Chemical Physics, quantity 127 covers contemporary advances on the innovative of analysis relative to chemical physics. The sequence, Advances in Chemical Physics, presents a discussion board for severe, authoritative reviews of advances in each region of the self-discipline.
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Computational strategies for mapping equilibrium phase diagrams 35 a conﬁguration of the other: Here the switch exchanges one lattice for another, while conserving the physical displacements with respect to lattice sites. The ﬁnal choice to be made is the form of the order parameter; in this case the default (built out of the energy function) deﬁned in Eq. (53) proves the right choice. Thus, making the phase labels explicit we take Ma~a ¼ Ea ðfug; cÞ À Ea~ ðfug; cÞ ð59Þ Figures 7 and 8 show results for the Lennard Jones (LJ) crystalline phases established with ESIT, on the basis of these choices .
The method has been successfully applied to calculate the phase diagrams of a number of simple ﬂuids and ﬂuid mixtures [79, 80]. 2. Critique The NPT-TP method is obviously designed to deal with the coexistence of ﬂuid phases: particle insertion into ordered structures is generally to be avoided. In this restricted context it is straightforward to implement, needing no more than the conventional apparatus of single-phase NPT simulation. 2). C. Beyond Equilibrium Sampling: Fast Growth Methods 1. Strategy The techniques discussed in this section might reasonably have been included in our collection of path-based strategies (Section IV).
The NPT and Test Particle Method 1. Strategy The NPT-TP method  locates phase coexistence at a prescribed temperature by ﬁnding that value of the pressure for which the chemical potentials of the two computational strategies for mapping equilibrium phase diagrams 41 phases are equal. The chemical potential m is identiﬁed with the difference between the Helmholtz free energies of systems containing N and N À 1 particles. Then the Zwanzig formula (, Eq. (54)) shows that m ¼ lnheÀ½EN ÀENÀ1 iNÀ1 ¼ mig þ lnheÀÁUN;NÀ1 iNÀ1 ð61Þ where ÁUN;NÀ1 is the additional conﬁguration energy associated with the insertion of a ‘‘test’’ particle into a system of N À 1 particles.