Présents : Michele Amato, Salim Berrada, Arnaud Bournel, Philippe Dollfus, Jérôme Larroque, Mai Chung Nguyen, Jérôme Saint Martin, Su Li, Tran Van Truong, Adrien Vincent.

# Papers

Salim and Philippe with Plaçais group about Klein transistor nearly accepted (IOP 2D mat).

Monastir paper with Arnaud about optical effects in GeSn quantum wells accepted for JAP: « Wave-function engineering and absorption spectra in Si_{0.16}Ge_{0.84}/Ge_{0.94}Sn_{0.06}/Si_{0.16}Ge_{0.84} strained on relaxed Si_{0.10}Ge_{0.90} type I quantum well ». But not very original in comparison of a previous paper on Ge wells. Naima as 1^{st} author.

# Conferences

ISCAS of Adrien accepted! In Australia in June.

Next deadlines: tomorrow for E-MRS -> Michele has already submitted, Jérôme L. should write an abstract too. In Lille May 19-24.

Summer school Graphene 2014 -> Truong and Mai Chung (?). Deadline for the conference Graphene (Toulouse) = 1/2 -> Trung, Mai Chung.

IWCE, deadline 28/1. Same day as Comics lunch!

Ulis, February 3 but…

# Next Comics meetings

On Monday afternoon. About 1 per month.

# A (very) short introduction to Density Functional Theory, by Michele

(pdf here)

-> For atomic structure, thermodyn, chemical, electronic and scattering properties.

Nobel prize for DFT in chemistry. 1998: Walter Kohn and John Pople.

Semi-empirical methods (Hückel, based on Hartree-Fock formalism) -> good for large systems. Can fail if the computed molecule is not close to the database of parametrized molecules.

DFT -> very good scalability.

Many body problem -> N_{e} electrons, N_{n} nuclei, Schrödinger equation to solve… With kinetic energies and potential: repulsion between nuclei, between electrons and between electrons and nuclei. How to deal with 10^{23} particles?

Born-Oppenheimer separation -> nuclei frozen in their equilibrium positions. But wavefunctions remain very complex! And experimentally measurable. While electron density is observable, e.g.by X-rays.

Hohenberg-Kohn theorem I: the relation between the potential and the electron density is invertible. Then, the ground state expectation value of any observable depends only on the electron density.

Hohenberg-Kohn theorem II: the total energy functional has a minimum, the ground state energy E0, in correspondence to the ground state density r_{0} -> proof of the existence of the universal functional without determining it.

Kohn-Sham scheme -> r_{0} can be calculated thanks to an artificial system of non-interacting particles. Using one-particle orbitals which are not real wavefunctions. And Kohn-Sham potential = v_{ion}(r) + v_{H}(r) + v_{xc}(r) where v_{H} describes the classic electrostatic potential and v_{xc} is the exchange-correlation potential, for taking into account the effect of interactions between particles.

Approximation for v_{xc} -> local description.

Self consistent flow diagram to solve the Kohn-Sham scheme, as a function of the density.

De-freezing the nuclei… Cf. Feynman, Phys Rev 56 (4), 340 (1939) “Forces in molecules” (http://dx.doi.org/10.1103/PhysRev.56.340) -> Hellmann-Feynman theorem for an analytical solution. Wikipedia: proven independently by many authors, including Paul Güttinger (1932), Wolfgang Pauli (1933), Hans Hellmann (1937) and Richard Feynman (1939). This does not correspond to phonon problem!

For further development :

RevModPhys.71.1253 RMP_61_689 DFT_NATO g1