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## Phys 498CQM Lecture # 10Wednesday, February 21, 2001Lecturer: Richard Martin |
Reading: Thijssen Ch. 5 |

- 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
- Atoms: See Atomic Reference Data for Electronic Structure Calculations at NIST
- Examples for solids in class and in Thijssen

- 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, ...

- Kohn-Sham approach: replace interacting problem with
independent-electron problem having the same density

Email question/comments/corrections to rmartin@uiuc.edu .