lectures and exercises on DFT & related topics (G. B. Bachelet)

1^st hour (March 2, 2018)

Introduction to this part of the course and expected computationa tools: home-made atomic codes, Quantum Espresso (QE), Gaussian.

2^nd & 3^rd hour (March 12, 2018)

Getting familiar with periodic crystals: sc, fcc, bcc, diamond and zincblende structures with VESTA.

4^th & 5^th hour (March 19, 2018)

Bloch's theorem, plane waves, Hartree approximation: a refresher which implies perfect control of Fourier series and transforms. Why would a computer implementation of such a scheme be impractical, why and how core electrons are a problem.

6^th & 7^th hour (March 26, 2018)

Total electronic energy vs. sum of single-particle eigenvalues in the Hartree approximation: the example of ground-state He atom (here a complete set of theoretical-numerical tools)

Ewald sums (see e.g. here, here or here) and Brillouin-zone integration (see e.g. here or this quite good presentation).

First part of a QE tutorial: self-consistent calculation of the electronic density and the total energy of crystalline silicon at the experimental lattice constant based on plane waves and pseudopotentials (input and output analysis and visualization via XCrysden).

8^th & 9^th hour (April 9, 2018)

Second part of a QE tutorial: convergence tests, total energy versus plane-wave cutoff and Brillouin-zone sampling

10^th & 11^th hour (April 16, 2018)

Pseudopotential theory, first 27 out of 48 slides (~26 MB) NB: these slides are password protected and contain lots of useful links.

12^th & 13^th hour (April 23, 2018)

Pseudopotential theory (~26 MB), slides 28-47 NB: these slides are password protected and contain lots of useful links.

14^th & 15^th hour (May 7, 2018)

Introduction to HPC and parallel programming (dr. Fabio Affinito, CINECA)

16^th & 17^th hour (May 11, 2018)

Introduction to MARCONI (dr. Fabio Affinito, CINECA)

18^th & 19^th hour (May 14, 2018)

Esercitazione: i fononi del grafene (dr. Fabio Affinito, CINECA)

20^th & 21^th hour (May 21, 2018)

Density Functional Theory:
the homogeneous electron gas (jellium) model: kinetic and exchange energy, Wigner correlation energy
the Hohenberg-Kohn theorems (1964), beginning.

22^th & 23^th hour (May 28, 2018)

Density Functional Theory:
the Hohenberg-Kohn theorems (1964); the Kohn-Sham equations
the local density approximation, bad for the entire HK functional (=Thomas-Fermi-Dirac approximation) turns out to be good when applied to the exchange-correlation part only (see e.g. this Introduction to DFT and exchange-correlation energy functionals by R.O. Jones, 2006). Quick recap of the Kohn-Sham theory and the local-density approximation of the exchange-correlation energy (7 slides).

24^th & 25^th hour (June 4, 2018) - 4 hrs.

Practical hartree self-consistent calculations for the helium-ground state atom (first part of this)