  We propose an in-silico experiment to introduce classical density functional
theory (cDFT). Den- sity functional theories, whether quantum or classical,
rely on abstract concepts that are non- intuitive. 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. DFT is illustrated
here in its most simple and yet physically relevant form: the classical density
functional theory of an ideal fluid of classical particles. For illustration
purpose, 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. Students thus have to deal with (i) the
cDFT theory, (ii) some basic concepts of 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 one highlights the analogies between the quantum
and classical DFTs.
