Multiple Scattering Theory

The idea behind Multiple Scattering Theory (MST) for density functional theory (DFT) is that you can solve the solution to Kohn-Sham equations using a multi-center spherical-harmonic expansion.  Basically, you pick expansion centers that are convenient for the problem and define 'cells' that each contain one of these centers.  Inside each of these cells you solve the Kohn-Sham radial equations numerically, then MST tells you how to join the solutions in each of the centers together in a rigorous procedure.

The single-cell solutions are similar to average atom like calculations, and give a t-matrix for each of the cells.  The positions of the expansion centers lead to a matrix known as the structure constants matrix.  Together these are used in Dyson's equation.  The result is a multi-center solution that can be used to construct the electron density, or other quantities of interest. 

The MST method uses the Green's function in place of the more common wavefunctions.  This allow us to carry out energy integrals in the complex energy plane.  The advantage is two-fold -- you don't need to find eigensolutions, and the integrands are much smoother in the complex plane, allowing easy numerical integration.

The MST method has a very long history, and in fact predates DFT.  It was originally developed by Korringa in 1947, and independently by Kohn and Rostoker in 1954.  The method has been much developed since then.  Our contribution was to adapt the method to warm and hot dense plasmas.  Such a possibility was first pointed out by Wilson et al.  We first showed that the method was practical and accurate for hot electrons in a crystal lattice here.  Then, through the introduction of additional expansion centers, we adapted the method to disordered plasmas.  The accuracy of a simpler-to-implement cluster approximation was demonstrated here.

The origin of the name, multiple scattering theory, is presumably because, by solving Dyson's equation, you are taking into account quantum diffraction - the scattering of an electron wave by more than one center at a time.