<i>n</i>th-nearest-neighbor distribution functions of an interacting fluid from the pair correlation function: A hierarchical approach

Abstract

The paper presents a general formalism for the $n\mathrm{t}\mathrm{h}\ensuremath{-}\mathrm{n}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}\ensuremath{-}\mathrm{n}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{b}\mathrm{o}\mathrm{r}\phantom{\rule{0ex}{0ex}}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}$ (NND) of identical interacting particles in a fluid confined in a $\ensuremath{\nu}$-dimensional space. The $n\mathrm{t}\mathrm{h}\ensuremath{-}\mathrm{N}\mathrm{N}\mathrm{D}$ functions, $W(n,\overline{r})$ (for $n=1,2,3,\dots{})$ in a fluid are obtained hierarchically in terms of the pair correlation function and $W(n\ensuremath{-}1,\overline{r})$ alone. The radial distribution function (RDF) profiles obtained from the molecular dynamics (MD) simulation of Lennard-Jones (LJ) fluid is used to illustrate the results. It is demonstrated that the collective structural information contained in the maxima and minima of the RDF profiles being resolved in terms of individual NND functions may provide more insights about the microscopic neighborhood structure around a reference particle in a fluid. Representative comparison between the results obtained from the formalism and the MD simulation data shows good agreement. Apart from the quantities such as $n\mathrm{t}\mathrm{h}\ensuremath{-}\mathrm{N}\mathrm{N}\mathrm{D}$ functions and $n\mathrm{t}\mathrm{h}\ensuremath{-}\mathrm{n}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}\ensuremath{-}\mathrm{n}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{b}\mathrm{o}\mathrm{r}$ distances, the average neighbor population number is defined. These quantities are evaluated for the LJ model system and interesting density dependence of the microscopic neighborhood shell structures are discussed in terms of them. The relevance of the NND functions in various phenomena is also pointed out.