Summer School on Computational Materials Science
University of Illinois, Urbana-Champaign


Density Functional Theory

Richard Martin - - University of Illinois, Urbana-Champaign Physics Department, Computational Science and Engineering Program

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

Electrons in Material Density Function Theory
  Powerpoint presentation - www - download - (397 KB PPT)
More detailed information presented in lecture:
  Density Functional Theory for Electrons in Materials - (360 KB PDF)
  Pseudopotentials in Electronic Structure Theory - (145 KB PDF)

Lecture 2

Density Functional Theory for Electronics in Materials
  Powerpoint presentation - www - download - (296 KB PPT)
More detailed information presented in lecture:
  Electronic Bands in Crystals - (206 KB PDF)
  Iterative Methods - (198 KB PDF)

Lecture 3

Linear Scaling 'Order-N' Methods in Electronic Structure Theory
  Powerpoint presentation - www - download - (2.37 MB PPT)

Lab Exercises

Electron bands in crystals: calculations in a plane wave basis with empirical or model potentials
  Lab Information & Instructions
  Lab Solutions
  Lab Programs & Code - (952 KB TAR.GZ)


Last Updated July 24, 2001
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