论文标题
经典密度功能理论应用于固态
Classical Density Functional Theory applied to the solid state
论文作者
论文摘要
配对电势的经典密度功能理论的标准模型由硬球功能和均值范围的均值学期核算组成。但是，大多数使用复杂的基本测量硬球功能的实现是由于功能本身可能的不稳定性而遭受了潜在的数值不稳定性，或者由于实现了不一致的实现和傅立叶空间组件的实现。在这里，我们提出了一个基于明显稳定的硬球功能的新实现，该功能以完全一致的方式实现。目前的工作不取决于近似球形整合方案，因此比以前的算法更强大。通过使用标准的Lennard-Jones电位以及Wang等人最近提出的新的一类新电位来计算固态的相图（Phys。Chem。Chem。Chem。24，10624（2020））。后者仅通过改变参数，从小分子的电势到适合胶体系统的电势。我们验证CDFT能够在所有情况下都能半定量重现该相图。我们还表明，对于这些问题，计算上便宜的高斯近似值几乎与基于有限差异的完全最小化一样好。
The standard model of classical Density Functional Theory for pair potentials consists of a hard-sphere functional plus a mean-field term accounting for long ranged attraction. However, most implementations using sophisticated Fundamental Measure hard-sphere functionals suffer from potential numerical instabilities either due to possible instabilities in the functionals themselves or due to implementations that mix real- and Fourier-space components inconsistently. Here, we present a new implementation based on a demonstrably stable hard-sphere functional that is implemented in a completely consistent manner. The present work does not depend on approximate spherical integration schemes and so is much more robust than previous algorithms. The methods are illustrated by calculating phase diagrams for the solid state using the standard Lennard-Jones potential as well as a new class of potentials recently proposed by Wang et al (Phys. Chem. Chem. Phys. 22, 10624 (2020)). The latter span the range from potentials for small molecules to those appropriate to colloidal systems simply by varying a parameter. We verify that cDFT is able to semi-quantitatively reproduce the phase diagram in all cases. We also show that for these problems computationally cheap Gaussian approximations are nearly as good as full minimization based on finite differences.
