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Consistent integral equations for two- and three-body-force models: Application to a model of silicon
Laird, Brian Bostian Wang, Jun Haymet, A. D. J.
Laird, Brian Bostian
Wang, Jun
Haymet, A. D. J.
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Abstract
Functional differentiation of systematic expansions for the entropy, in the grand ensemble [B. B. Laird and A. D. J. Haymet, Phys. Rev. A 45, 5680 (1992)], leads directly to consistent integral equations for classical systems interacting via two-body, three-body, and even higher-order forces. This method is both a concise method for organizing existing published results and for deriving previously unpublished, higher-order integral equations. The equations are automatically consistent in the sense that all thermodynamic quantities may be derived from a minimum on an approximate free-energy surface, without the need to introduce weighting functions or numerically determined crossover functions. A number of existing approximate theories are recovered by making additional approximations to the equations. For example, the Kirkwood superposition approximation is shown to arise from a particular approximation to the entropy. The lowest-order theory is then used to obtain integral-equation predictions for the well-known Stillinger-Weber model for silicon, with encouraging results. Further connections are made with increasingly popular density-functional methods in classical statistical mechanics.
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This is the publisher's version, also available electronically from http://journals.aps.org/pre/abstract/10.1103/PhysRevE.47.2491.
Date
1993-04-01
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American Physical Society
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Laird, Brian Bostian; Wang, Jun; Haymet, A. D. J. (1993). "Consistent integral equations for two- and three-body-force models: Application to a model of silicon." Physical Review E, 47:2491. http://dx.doi.org/10.1103/PhysRevE.47.2491