## Program

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).

If/when lectures are given in on-line or in hybrid format the following permanent zoom link will be used https://sissa-it.zoom.us/j/5044742140

8/10 Where all begins: adiabatic approximation. (slides,video)

10/10 Electrons moving in an effective potential.(slides, video)

15/10 Variational principle for the electronic problem. The Hartree-Fock self-consistent equations.(slides, video ,video 2022-10-12 )

17/10 Hund's rules. Koopmans' theorems. (slides, video, video 2022-10-13

22/10 Building up the periodic table. Homogeneous electron gas.(slides, video , video 2022-10-18 )

24/10 Band magnetism Wigner Crystal (slides)** ** (video) video 2022-10-20

29/10 Discussion of the numerical exexcse (due by 8/11) : **Simple 1D Examples **(Examples_1, slides)

31/10 Density-Functional Theory. HK theorem, the KS equations. Jacob's ladder of xc functionals. (slides) (video) video 2022-10-26

05/11 The standard model of DFT: LDA, GGA. Successes and problematic cases (slides) (video) (slides2) video 2022-10-27

07/11 end of previous topic-> beginning of Band gap ''problem'' in DFT. The GW approximation.(slides) video 2022-11-02

12/11 end of previous topic -> beginning of Electronic structure of solids: Bloch theorem, basis set expansions, spectral methods (FFT), k-point sampling, pseudopotentials and the like. (slides) (video) video 2022-11-08

14/11 continuation of Electronic structure of solids: Bloch theorem, basis set expansions, spectral methods (FFT), k-point sampling, pseudopotentials and the like. (slides) video 2020-11-10

19/11 continuation of Electronic structure of solids: Bloch theorem, basis set expansions, spectral methods (FFT), k-point sampling, pseudopotentials and the like. (slides) video 2022-11-22

21/11 end of previous topic -> Don't panic .... introduction to QE (slides,JPCM_2009,JPCM-2017) (video) video 2022-11-24

26/11 An almost free lunch: Hellmann-Feynman and Stress theorems. Structural optimization. Molecular Dynamics. Parrinello-Raman and Wentzcovitch dynamics. (slides) (video) ** ****video 2022-11-29**

28/11 Car-Parrinello method. (slides) **Examples** (PW/examples/example02-example03-VCSexample; CPV/examples/example01-example02-example03) (video)

Ab initio thermodynamics, catalysis,... (slides)

Crystal Structure Prediction from first principles, (slides)... and second principles