Reformulation of Ensemble Averages via Coordinate Mapping.
Reformulation of Ensemble Averages via Coordinate Mapping.
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DOI：
10.1021/acs.jctc.6b00018
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发表时间：
2016-03
影响因子：
5.5
通讯作者：
A. Schultz;Sabry G. Moustafa;Weisong Lin;S. J. Weinstein;D. Kofke
中科院分区：
文献类型：
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作者：
A. Schultz;Sabry G. Moustafa;Weisong Lin;S. J. Weinstein;D. Kofke
建立了统计力学中常见的系综平均公式的一般框架。这种“映射平均”方案允许从统计力学中得到的近似理论结果重新引入到潜在的形式体系中，产生新的集合平均，精确地表示理论中的误差。结果代表了一个独特的替代微扰理论有条理地采用可处理系统作为起点来描述复杂系统。分子模拟被证明为利用这一进步提供了一个有吸引力的途径。通过分子模拟计算重新表述的平均值可以不受近似理论已经捕获的行为所产生的噪声的污染。因此，可以在使用较少的计算工作量的同时获得准确和精确的属性值，在有利的情况下，可以减少许多数量级。本文用三个例子说明了这种处理方法：(1)铁嵌入原子模型的热容计算，(2)偶极分子的Stockmayer模型的介电常数计算，以及(3)Lennard-Jones流体的压力计算。可以观察到，计算效率的提高与所模拟条件的基础理论的适当性有关；然而，结果的准确性不受此影响。该框架为进一步发展开辟了许多途径，既可以作为改进模拟方法的手段，也可以作为发展热物理性质理论的新基础。
A general framework is established for reformulation of the ensemble averages commonly encountered in statistical mechanics. This "mapped-averaging" scheme allows approximate theoretical results that have been derived from statistical mechanics to be reintroduced into the underlying formalism, yielding new ensemble averages that represent exactly the error in the theory. The result represents a distinct alternative to perturbation theory for methodically employing tractable systems as a starting point for describing complex systems. Molecular simulation is shown to provide one appealing route to exploit this advance. Calculation of the reformulated averages by molecular simulation can proceed without contamination by noise produced by behavior that has already been captured by the approximate theory. Consequently, accurate and precise values of properties can be obtained while using less computational effort, in favorable cases, many orders of magnitude less. The treatment is demonstrated using three examples: (1) calculation of the heat capacity of an embedded-atom model of iron, (2) calculation of the dielectric constant of the Stockmayer model of dipolar molecules, and (3) calculation of the pressure of a Lennard-Jones fluid. It is observed that improvement in computational efficiency is related to the appropriateness of the underlying theory for the condition being simulated; the accuracy of the result is however not impacted by this. The framework opens many avenues for further development, both as a means to improve simulation methodology and as a new basis to develop theories for thermophysical properties.