Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.
H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom.
J Chem Phys. 2017 Jul 21;147(3):034501. doi: 10.1063/1.4993175.
In classical density functional theory (DFT), the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation. By considering the pair correlation function g(x) and structure factor S(k) of a one-dimensional model fluid, for which exact results are available, we show that the mean-field DFT, employed within the test-particle procedure, yields results much superior to those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that one should not judge the quality of a DFT based solely on the approximation it generates for the bulk pair direct correlation function.
在经典密度泛函理论（DFT）中，由粒子间吸引力引起的亥姆霍兹自由能泛函的一部分通常在平均场或范德华近似中处理。从表面上看，这是一种相当粗糙的处理方法，因为所得到的泛函为体相流体对直接相关函数生成了简单的随机相位近似（RPA）。我们解释了为什么基于这一观察，使用标准的平均场 DFT 来描述非均匀流体结构和热力学比人们预期的更准确。通过考虑一维模型流体的对关联函数 g(x)和结构因子 S(k)，我们展示了在测试粒子程序中使用的平均场 DFT 产生的结果远远优于体相奥恩斯坦-泽尔尼克方程的 RPA 封闭的结果。我们认为，不应该仅仅根据 DFT 为体相对直接相关函数生成的近似来判断 DFT 的质量。
