Link to pdf file

Reading: Text: Chapters 8,9.

The purpose of this second lecture on DFT is to continue with the discussion of the Kohn-Sham ansatz.  This is the step that makes DFT so useful, and gets to the actual equations that are perhaps the most widely-used equations in the theory of materials.

1. The Kohn-Sham Equations (from last time)
1. Self-consistent independent-particle equations
2. Would lead to exact density and ground state energy of the interacting-electron system if:
• Exact density can be represented by non-interacting density
• One has the exact exchange-correlation functional
3. NO other properties are guaranteed to be given correctly by solution of Kohn-Sham equations
4. Exact exchange-correlation functional is not known - must make approximations
2. Key aspect of Kohn-Sham theory is the Exchange-Correlation Functional Exc[n]
1. Meaning of x-c energy in terms of many-body x-c hole
2. Approximations to Exc[n]
3. Local approximation (LDA) suggested in original paper of Kohn-Sham;  Uniquely determined by energy of homogeneous gas - known from quantum Monte Carlo calculations
4. Comparisons with many-body calculations on several systems
• Can be done by coupling constant integration
• Results for Atoms
• Crystalline silicon
1. Examples of results for total energies
1. Hydrogen atom
2. Hydrogen molecule
3. Other molecules
4. Semiconductor crystals
2. Beyond the local approximation
1. Gradient Corrections
2. Recent Forms that approach "chemical accuracy" -
   Finally the reason why Kohn won the 1998 Chemistry Nobel Prize!
3. The Harris Fowlkes Functional - variation on Kohn-Sham Functional
4. Conclusions