The lecture follows the Classnotes on Periodic Crystals discussed in the previous lectures, Classnotes on Mathieu Equation and the F90 program given in the Fortran Directory for the class.

Outline

1. Homework 3 Due 3-21.
2. Program for Plane wave calculations is on the WWW pages.
3. Bands in crystals: What to expect
   • One dimensional examples - Mathieu Equation
   • Nearly free electron metals
   • Insulators like He
   • Semiconductors like silicon, diamond
   • Examples of bands - empirical fitting by Chelikowsky & Cohen
   • General features of metals, insulators
4. Issues involved in plane calculations
   • How many plane waves are needed?
   • Huge numbers for core electrons!
   • Sucessful only because of pseudopotentials
   • Theory of pseudopotentials - PROJECT FOR SOMEONE
   • Semi-empirical pseudopotentials used in our programs
5. Codes for generation of "ab intio" "norm-conserving" pseudopotentials from atomic calculations available at
   http://bohr.inesc.pt/~jlm/research.html
6. Issues involved in getting the total DFT potental
   • External (nuclei) + Hartree + exchange-correlation
   • Requires self-consistent calculation - like in atom
   • Simple approximation: screening - V_ext(r)/epsilon(r)
   • Example for He - from ordinary conditions to Planetary conditions
7. Full self self-consistent DFT plane wave pseudopotential codes available in many places including
   http://www.pcpm.ucl.ac.be/ABINIT
8. Tight-binding formulation
   • Simplified version of general localized description of electronic states
   • Tight binding codes and description available at
     http://cst-www.nrl.navy.mil/bind/dodtb/