Monday, July 4, 2016

Learning notes on DFT

I learn this to prepare for an interview. A very abstract theory. I will learn it anyway.DFT is an acronym for density functional theory, which is widely used in computational physics and computational chemistry to study the fundamental property of material. Density is for the density of electrons. Functional is a mathematical term, meaning "function of a function", e.g. F[f(x)]. There is a particular maths course called "functional analysis".
DFT was initially developed in Thomas and Fermi in 1920s, but hadn't achieve a good theoretical foundation until 1960s. Hohenberg-Kohn theorem demonstrated that the ground state properties of a many-electron system are uniquely determined by an electron density with only 3 spatial coordinates, and the correct ground state electron density minimizes the energy functional of the system. Later, Kohn-Sham equation provides a method to specifically describe the potential term. The effective potential is divided into external potential, and Coulomb interaction effect (exchange and correlation interaction). The interaction terms are difficult to model, and are treated by local-density approximation (LDA).

A real calculation by classical DFT on liquid Neon [^1] is a best way to dive in. This is done by a few lines of Mathematica codes revealed in its supplemental material.
A review paper on DFT by Burke's group [^2] provides in-depth overview, including its development, two most popular choices of functionals (empirical and nonempirical approaches) and the research trend.
[^1]: Jeanmairet, G., et al. (2014). "Introduction to Classical Density Functional Theory by a Computational Experiment." Journal of Chemical Education 91(12): 2112-2115.
[^2]: Pribram-Jones, A., et al. (2015). "DFT: A Theory Full of Holes?" Annual Review of Physical Chemistry 66(1): 283-304.