WEIGHTED-DENSITY-FUNCTIONAL THEORY OF INHOMOGENEOUS LIQUIDS AND THE FREEZING TRANSITION
WEIGHTED-DENSITY-FUNCTIONAL THEORY OF INHOMOGENEOUS LIQUIDS AND THE FREEZING TRANSITION
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DOI：
10.1103/physreva.32.2909
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发表时间：
1985-01-01
影响因子：
2.9
通讯作者：
ASHCROFT, NW
中科院分区：
文献类型：
--
作者：
CURTIN, WA;ASHCROFT, NW
从非均匀经典液体亥姆霍兹自由能泛函的精确表达式出发，给出了依赖于物理密度加权平均的近似泛函。它保留了精确表达式的非局域性，但只需要均质液体的性质。根据均质液体的结构，对用于构造加权密度的权函数进行了物理选择。由此得到的加权密度近似(WDA)对应于在真自由能的密度泛函展开中对一些三阶和更高阶项的近似，而一、二阶和更高阶项的子集被精确地保留。在这方面，该理论与早期基于加权密度思想的泛函有很大的不同。作为WDA的一种应用，简单液体的冻结是在平均场理论的框架内考虑的，并与以前的理论作了简要的比较。特别是用WDA方法研究了硬球体系的冻结转变，得到的冻结参数和固体状态方程与计算机模拟结果吻合较好。
Starting from an exact expression for the Helmholtz free-energy functional of an inhomogeneous classical liquid, an approximate functional is presented which depends on a weighted average of the physical density. It retains the nonlocal character of the exact expression, but requires only the properties of the homogeneous liquid. A physical choice of the weighting function used to construct the weighted density is made by appealing to the structure of the homogeneous liquid. The resulting weighted-density approximation (WDA) corresponds to an approximation for some of the third-and higher-order terms in a density-functional expansion of the true free energy, the first-, second-, and a subset of higher-order terms being retained exactly. In this respect the theory differs crucially from earlier functionals based on weighted-density ideas. As an application of the WDA, the freezing of simple liquids is considered within the framework of mean-field theory and is briefly compared to previous theories. In particular, the freezing transition of the hard-sphere system is studied using the WDA formalism, the resulting freezing parameters and the equation of state for the solid being in good agreement with computer-simulation studies.