Literature recommendation for classical density functional theory (DFT) and fundamental measure theory (FMT)

Question

I'm very much interested in properly learning about density functional theory calculations (DFT) in classical settings, for example as used in the theory of liquids. Apart from the success of DFT applied to many-body QM systems, for classical​ systems it remains the main theoretical approach of the statistical physics of liquids and solids. Similarly, but more recently, applications of fundamental measure theory (FMT, which is a more geometric approach) can be noticed more and more.

In most current liquid state theory books, these approaches are only briefly introduced and almost never at depth (as they are often assumed known by the authors). Although I have the basics of statistical mechanics, I am very new to classical DFT calculations, and would be very much interested in any piece of literature, be they review papers, lecture notes or textbooks, that would softly and slowly introduce these techniques.

Answer 1

1. An excellent introduction to the field of classical DFT is Robert Evan's article Density functionals in the theory of nonuniform fluids (Fundamentals of inhomogeneous fluids 1 (1992): 85-176). It is a bit older, but very accessible and yet thorough. Some proofs are omitted, but references are provided for further information.

2. The standard textbook for liquid state theory, Theory of Simple Liquids by Jean-Pierre Hansen and Ian McDonald has a section on DFT and also discusses Fundamental Measure Theory. It is a great book but the presentation is quite terse, and makes numerous references to preceding sections that you will have to go through first. Nevertheless it a good starting point if you have the book lying around (as everyone interested in liquid theory should).

3. DFT is typically presented in terms of correlation functions of simple fluids, which means that one has to deal with complicated-looking integral equations. The article An introduction to inhomogeneous liquids, density functional theory, and the wetting transition by Hughes, Thiele and Archer presents an alternative introduction to DFT in terms of a simple (Ising) lattice model, which might be a good approach for those who have a more general statistical mechanics background.