State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200238, China.
J Chem Phys. 2013 Aug 14;139(6):064509. doi: 10.1063/1.4817784.
Direct correlation functions (DCFs) play a pivotal role in the applications of classical density functional theory (DFT) to addressing the thermodynamic properties of inhomogeneous systems beyond the local-density or mean-field approximations. Whereas numerous studies have been dedicated to the radial distribution functions of liquid water--the most important solvent on earth, relatively little attention has been given to the site-site DCFs. The water DCFs are long-ranged and difficult to calculate directly by simulation, and the predictions from conventional liquid-state theories have been rarely calibrated. Here we report a computational procedure for accurate evaluation of the site-site DCFs of liquid water based on three popular molecular models (viz., SPC, SPC∕E, and TIP3P). The numerical results provide a benchmark for calibration of conventional liquid-state theories and fresh insights into development of new DFT methods. We show that: (1) the long-range behavior of the site-site DCFs depends on both the molecular model and the thermodynamic condition; (2) the asymptotic limit of DCFs at large distance does not follow the mean-spherical approximation (MSA); (3) individual site-site DCFs are long ranged (40 nm) but a summation of all DCF pairs exhibits only short-range behavior (1 nm or a few water diameters); (4) the site-site bridge correlation functions behave as the DCFs, i.e., they are also long-ranged while the summation of all bridge correlation functions is short ranged. Our analytical and numerical analyses of the DCFs provide some simple strategies for possible improvement of the numerical performance of conventional liquid-state theories.
直接相关函数（DCF）在经典密度泛函理论（DFT）应用于解决非均匀体系热力学性质方面发挥着关键作用，超越了局部密度或平均场近似。虽然已经有许多研究致力于液体水的径向分布函数，液体水是地球上最重要的溶剂，但相对较少关注的是位相关 DCF。水的 DCF 是长程的，很难通过模拟直接计算，并且传统液体状态理论的预测很少经过校准。在这里，我们报告了一种基于三种流行的分子模型（即 SPC、SPC∕E 和 TIP3P）准确评估液体水的位相关 DCF 的计算程序。数值结果为传统液体状态理论的校准提供了基准，并为新 DFT 方法的发展提供了新的见解。我们表明：（1）位相关 DCF 的长程行为取决于分子模型和热力学条件；（2）在大距离处 DCF 的渐近极限不符合均方球近似（MSA）；（3）单个位相关 DCF 是长程的（40nm），但所有 DCF 对的总和仅表现出短程行为（1nm 或几个水分子直径）；（4）位相关桥联相关函数与 DCF 一样，也是长程的，而所有桥联相关函数的总和是短程的。我们对 DCF 的分析和数值分析为可能改进传统液体状态理论的数值性能提供了一些简单的策略。
