Link to pdf file that provides a summary of material used the two lectures on DFT

Reading: Text: Chapters 6,7.

What is so important about DFT that it led to the 1998 Nobel Prize in Chemistry for Walter Kohn?  Why did it happen in 1998? Why in Chemistry? 

DFT is by far the main method used for realistic calculations in solids.  Under what circumstances does it appear to be successful?  When are present approximations not successful?  This lecture and the next are devoted to the theory and description of some typical results.

1. The Hohenberg-Kohn Theorems
1. These are exact theorems that ALL properties of electron systems are functionals of the density
2. Holds the promise of solving many-electron problems WITHOUT dealing with the full many-body wave-function
3. But no hint of how to accomplish this!
4. Exact expressions in terms of many-body expectation values, but is this useful?
2. Kohn-Sham Ansatz
1. Replace interacting-electron problem with non-interacting particle problem
2. Require the density be the same as interacting-electron system (not proven in general that this is possible)
3. Leads to density and ground state energy of the interacting-electron system by solving appropriate non-interacting particle equations called the Kohn-Sham equations
4. NO other properties are guaranteed to be given correctly by solution of Kohn-Sham equations
3. 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
4. Uniquely determined by energy of homogeneous gas - known from quantum Monte Carlo calculations
5. More on other approximations later
4. Examples of results
1. Hydrogen molecule
2. Semiconductor crystals
5. Conclusions