Electronic structure and quantum simulation of materials
Basic course given by Stefano de Gironcoli
Start: 01-10-2018 End: 20-12-2018 Room: 131
Schedule: Mon 11:00 - 13:30, Thu 14:00 - 16:30
The basic course will present fundamental concepts in the first-principles simulation of real materials at the nanoscale. Density Functional Theory will be introduced in its conceptual foundations and practical details of numerical atomistic simulations will be discussed. Strengths and shortcomings will be demonstrated in a number of case studies. Critical issues and open challenges will be introduced.
Evaluation will be based on course participation and performance in the two given assignments (one simpler and one more demanding).
Here follows the tentative list of lectures. The lecture of Thursday Nov 25th is moved to Wednesday Nov 24th at 2PM. No lecture on November 1st. The lecture of November 5th is moved to the afternoon due to the Welcome Day cerimony in the morning.
Where all begins: adiabatic approximation. (slides)
Electrons moving in an effective potential.(slides)
Variational principle for the electronic problem. The Hartree-Fock self-consistent equations.(slides)
Hund's rules. Koopmans' theorems. Building up the periodic table. (slides)
Density-Functional Theory. HK theorem, the KS equations. Jacob's ladder of xc functionals. (slides)
The standard model of DFT: LDA, GGA. Successes and problematic cases (slides)
.. continued (slides)
Band gap ''problem'' in DFT. The GW approximation.(slides)
.. continued (slides)
First assignment (text)
An almost free lunch: Hellmann-Feynman and Stress theorems. Structural optimization. Molecular Dynamics. Parrinello-Raman and Wentzcovitch dynamics. (slides) Car-Parrinello method. (slides) Examples (PW/examples/example02-example03-VCSexample; CPV/examples/example01-example02-example03)
Ab initio thermodynamics, catalysis, electrochemistry
Crystal Structure Prediction from first principles,.. and second principles
One step beyond: Density-Functional Perturbation Theory, general formulation.
Dielectric properties, effective charges. Piezoelectric constants. Examples
Phonons, temperature, quasi-harmonic approximation and its relevance for 'real life'.
Berry Phases and macroscopic polarization. Electric Fields, effective charges etc revisited.
DFT: I would rather be approximately right than exactly wrong (SIC, DFT+U and other 'advanced' functionals). Examples
DFT: when everything else fails read the manual (the van der Waals interaction and the Adiabatic-Connection Fluctuation-Dissipation approach). Examples
DFT: do the right thing (more ACFD stuff)
DFT: more functionals, Strictly Correlated Electrons, LIISA