Outline of Lecture

1. Basic Density Functional Theory & Bands in Crystals
   1. Hohenberg-Kohn theorems
   2. Meaning for the functional - Levy-Lieb variational principle
   3. Practical DFT: the KOhn-Sham approach
   4. Solving the self-consistent Kohn-Sham equations
   5. Examples of results for simple systems - successes, failures
2. Pseudopotentials and efficient iterative methods for calculations
   1. Calculations for atoms; generation of ab into pseudopotentials Semilocal and Kleinman-Bylander non-local separable operators
   2. Bloch theorem and bands for electrons in periodic crystals Definition of the crystal stucture and Brillouin zone in programs the will be used in the lab
   3. Plane wave DFT codes Empirical pseudopotentials: examples of band structures Ab into pseudopotential calculations achieving self-consistency examples of ab intio results
   4. Iterative methods General aspects: Krylov subspaces; iterative solutions Solution by minmization: Conjugate gradradient methods Must impose constraint of orthonormality Solution by residual minimization (Connection to VASP code that will be used by Tuttle)
   5. Car-Parrinello quantum molecular dynamics
3. Order-N methods
   1. Locality and quantum mechanics the density matrix Wannier functions (generalized)
   2. Methods for solving equations taking advantage of locality A new functional that can be minimized without the constraint of orthonormality Density matrix methods - "McWeeny purification" Fermi operator projection methods Combinations of the methods
   3. Examples of results Giant Fullerenes Simulation of fullerenes crahing into diamond surfaces Hot metals A complete turn of DNA
4. Lab: Working with simple codes for atoms, empirical pseudopotential and tight-binding. Application to Si, GaAs.
   1. Structure of modular F90 code
   2. Physical problems: Changes in the bands with volume Phonon displacenents

Background Article

"Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients", M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Rev. Mod. Phys. 64, 1045-1097 (1992).

"Pseudopotential Methods in Condensed Matter Applications", W. E. Pickett, Computer Physics Reports 9, 115 (1989).

More specialized article: "Linear Scaling Electronic Structure Methods ", S. Goedecker, Rev. Mod. Phys. 71, 1085-1123 (1999).

Lecture 1

Lecture 2

Lecture 3

Lab Exercises