Downfolding school

Band structure using DFT (01/28)

1. Meaning of KS orbitals and energies. Kohn-Sham Hamiltonian.
2. The band Hamiltonian
3. Non-self-consistent calculations using the KS Hamiltonian. a) Exercise: h chain, convergence of non-self-consistent band structure as we increase kmesh

Discussion: 02/04 (present your work)

Localizing wave functions (02/18-)

4. Localization strategies: Wannier (note that there are also IAO, PAO) a) H chain: make localized orbitals (select active space, initial guess) (presentation: 02/18, discussion: 02/25)

5. Tight binding models from localized representations a) H chain: t(separation)

6. Band interpolation using localized representations (Wannier interpolation) a) Exercise: h chain, t convergence as we increase k-mesh -> band structure convergence

7. Transferability. a) Exercise: t for h chain, and t for a square of h atoms.

Adding interactions to band structure models

8. Bare interactions: 4-index integrals, FCIDUMP
9. RPA theory
10. cRPA
11. Double-counting problem
12. GW+RPA (?)

Density matrix downfolding

13. DMD theory: energy functional, relation between energy and DM expectation values.
14. DMD of FCI on H2, comparison to DFT-based downfolding, basis set extrapolation a) As you increase the basis in FCI, effective U tends to decrease.

QMC excited states

15. Excited state theory.
16. Example: get excited states for H2, compare to FCI
17. Analyzing excited states a) What type of excitations (spin vs orbital)

DMD using QMC

TBD exactly.