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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-)

  1. 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)

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

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

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

Adding interactions to band structure models

  1. Bare interactions: 4-index integrals, FCIDUMP
  2. RPA theory
  3. cRPA
  4. Double-counting problem
  5. GW+RPA (?)

Density matrix downfolding

  1. DMD theory: energy functional, relation between energy and DM expectation values.
  2. 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

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

DMD using QMC

TBD exactly.