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Phys 498CQM Lecture # 10

Wednesday, February 21, 2001
Lecturer: Richard Martin
Reading:
Thijssen Ch. 5

Outline

Continue Density Functional Theory, the Kohn-Sham Approach, and actual programs for calculations for atoms
  • A postscript file with lecture notes on Density Functional Theory to accompany lectures 9 and 10 is available.
  • See Atomic Reference Data for Electronic Structure Calculations at NIST for descriptions of the equations and many results on atoms
    1. Density Functional Theory continued
      • Kohn-Sham approach: replace interacting problem with independent-electron problem having the same density
        • Leads to self-consistent sets of independent-particle Schroedinger-like Eqs.
        • In principle sovles interacting problem!
        • In practice must aproximate exchange and correlation functional Exc[n]
      • Examples of functionals for exchange and correlation
        • Local Density Approximation
        • Energy at each point same as a homogeneous elec. gas
        • Slater Local exchange - (inconsistent)
        • Kohn-Sham variational Local exchange - simple expression!
        • Wigner interpolation for correlation - simple form!
        • Ceperley-Alder correlation calculated by a many-body calculation on the homogeneous electron gas - fit to analytic expressions
        • Spin density functionals
        • Beyond the local approximation
      • Density Functional programs
        • Simpler than Hartree-Fock!
        • Obvious method - use the Numerov & Shooting methods
        • F90 program using the steps built up in our class
        • Examples
      • Results using the Kohn-Sham Ansatz and simple approximations for Exc
      • Beyond the usual simple approximations for Exc
        • OEP - optimized effective potential - local potential that is gives the optimal energy for a functional such as the Hartree-Fock exchange functional of the wavefunctions
      • Possible problems for projects: relativistic programs that will work for heavy atoms, OEP calculations, ...
    Last Modified Feb. 20
    Email question/comments/corrections to rmartin@uiuc.edu .