Présents : Michele Amato, Salim Berrada, Arnaud Bournel, Philippe Dollfus, Jérôme Larroque, Mai Chung Nguyen, Jérôme Saint Martin, Su Li, Tran Van Truong, Adrien Vincent.
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 Si0.16Ge0.84/Ge0.94Sn0.06/Si0.16Ge0.84 strained on relaxed Si0.10Ge0.90 type I quantum well ». But not very original in comparison of a previous paper on Ge wells. Naima as 1st author.
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
-> 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 -> Ne electrons, Nn nuclei, Schrödinger equation to solve… With kinetic energies and potential: repulsion between nuclei, between electrons and between electrons and nuclei. How to deal with 1023 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 r0 -> proof of the existence of the universal functional without determining it.
Kohn-Sham scheme -> r0 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 = vion(r) + vH(r) + vxc(r) where vH describes the classic electrostatic potential and vxc is the exchange-correlation potential, for taking into account the effect of interactions between particles.
Approximation for vxc -> 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 :