Advances in Chemical Physics (Volume 127) by Ilya Prigogine, Stuart A. Rice

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, offers a discussion board for serious, authoritative reviews of advances in each region of the self-discipline.

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By appropriate choice of the operations t, it is possible [71] to implement a switch that, instead, conserves a set of Fourier coordinates, and therefore the harmonic contributions to the energy of the configurations of each phase; the determinant in Eq. (47) then captures the harmonic contribution to the free-energy difference, leaving the computational problem focused on the anharmonic contributions that (alone) are left in R. This strategy greatly enhances the overlap between the two branches of the order parameter distribution; but the associated efficiency gains (resulting from the reduced length of ‘‘path’’ through M-space) are offset by the greatly increased computational cost of the mapping itself [71].

Bruce and nigel b. wilding VI. DETERMINING THE PHASE BOUNDARY: EXTRAPOLATION, TRACKING, AND THE THERMODYNAMIC LIMIT The path-based methods exemplified in the preceding section provide us with ways of estimating the difference between the free energies of the two phases, ÁFa~a ðflg; NÞ [Eq. (10)] at some point c  flg in the space of the controlling fields [88], for a system whose size N (which we shall occasionally make explicit in this section) is computationally manageable. 1 N ÁFa~a ðflgx ; NÞ ¼ 0 ð67Þ We divide this program into three parts.

It is helpful to assess its strengths and weaknesses armed with an explicit example. We shall consider what is arguably the archetypal example of the NIRM strategy: the Einstein Solid Method (ESM) [28]. The ESM provides a simple way of computing the free energies of crystalline phases and therefore addresses questions of the relative stability of competing crystalline structures. We describe its implementation for the simplest case where the interparticle interaction is of hard-sphere form; it is readily extended to deal with particles interacting through soft potentials [29].

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