Lecturer: Prof. Emilio Artacho

This course covers the fundamentals and main approximations of DFT ( Density Functional Theory Calculations)-based electronic structure. Practicals will be based on SIESTA, ONETEP, and CASTEP.

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.

Students who have not covered the necessary background for this course in their previous studies may wish to attend Professor Artacho’s Foundation Course in QM.

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

Picture credits:

• Electronic structure of DNA (top image) – Emilio Artacho
• Electronic structure of pilin protein – Gustavo Troiano Feliciano
• Protons in diamond – Jessica Halliday