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Electronic structure and DFT [M10]

Main purpose: Fundamentals and main approximations of DFT ( Density Functional Theory Calculations)-based electronic structure; students should leave the course knowing: how to run DFT calculations from a pre-existing programme; how to converge the results with respect to technical parameters; the capabilities and limitations of the methods, addressing the different approximations separately. Practicals will be based on SIESTA, ONETEP, and CASTEP.

Lectures:

  1. Many particle problem. Born Oppenheimer, Independent particles; Practical: Time for Mini-project coming from foundation course (see below). For students not doing the foundation course, exercise: 1D tight-binding ionic chain.
  2. Indistinguishable particles, Spin, Pauli, Aufbau; Practical: Continue as in 1.
  3. Hartree, SCF, double counting, Hartree-Fock, exchange, correlation; Practical: Band structure of diamond. Visualise: tools and graphics.
  4. Correlation: CI & QC direction. Complexity exponential wall (Kohn RMP & Phys Today). Practical: Siesta: k-point sampling; Converging & DOS: Diamond, Al.
  5. DFT: Intro; definition of density; local potential; Hohenberg-Kohn and Levy construction (Jones-Gunnarson). Practical: Siesta E(V) Diamond and Al. P(V). Murnaghan.
  6. Kohn-Sham. LDA, Ceperly Alder; GGAs. Bands. Band-gap problem. Practical: Siesta E(V) Diamond and Al: compare LDA, PBE, WC
  7. Forces, stress. -> MD & Relaxations. Hellman-Feynman. Variable cell; Practical: Siesta: relax H2O molecule & cell for MgSiO3 under strain (Ferro)?
  8. Pseudos; atom: generate C pseudo Practical: Generate Pseudo. Test it within atom and in bulk
  9. Bases; generate basis and plot. Practical: Generate basis. Test in bulk
  10. PBC: cells & supercells. Practical calculations. Accuracies, limits (highly correlated, dispersion interactions); Practical: Start Mini-Project

The course can be complemented by (e.g. one lecture each)

  • Quantum Monte Carlo
  • Plane waves
  • Excitations
  • Transport
  • Molecular dynamics