Density Functional Theory for Periodic Systems

Monday, July 30, 2007 - 2:30pm - 3:30pm
EE/CS 3-180
Eric Cances (CERMICS)
By means of thermodynamic limit arguments, the Kohn-Sham model can be extended to the case when the nuclear configuration is periodic. The resulting periodic Kohn-Sham model is very useful to understand the electronic structure of perfect crystals, but also to simulate the condensed phase by means of artificial periodic boundary conditions. In the latter case, the periodic cell may contain a very large number of nuclei and electrons.

In the first part of the lecture, I will present the Bloch theory of periodic Schrdinger operators, and recall how the band structure of their spectrum can be related to the insulating or conducting character of the underlying material. I will also present the concept of Wannier functions, which is of growing importance in various applications (computation of dielectric and magnetic properties, local correlation methods, electronic structure of crystals with defects, ...).

In the second part of the lecture, I will focus on the discretization of the periodic Kohn-Sham model in plane-wave (PW) basis sets.