Introduction to Classical Density Functional Theory by a Computational Experiment

We propose an in silico experiment to introduce the classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely on abstract concepts that are nonintuitive; however, they are at the heart of powerful tools and active fields of research in both physics and chemistry. They led to the 1998 Nobel Prize in chemistry. A DFT is illustrated here in its most simple and yet physically relevant form: the cDFT of an ideal fluid of classical particles. For illustration purposes, it is applied to the prediction of the molecular structure of liquid neon. The numerical experiment proposed therein is built around the writing of a cDFT code by students in Mathematica software. Students thus must deal with (i) the cDFT theory, (ii) some basic concepts of the statistical mechanics of simple fluids, (iii) functional minimization, and (iv) a useful functional programming language. This computational experiment is proposed during a molecular simulation class but may also be of interest in a quantum chemistry class to illustrate electronic DFT if the instruction highlights the analogies between quantum and classical DFTs.