# Density Functional Theory and Electronic structure

## Details

The lecture will be given in English by Prof. Blügel.

Content:

Ab initio simulations based on Density Functional Theory (DFT) enable the realistic, parameter free description of electronic properties of materials. When performing quantum mechanical simulations, DFT methods are the most accurate and effective for a large variety of systems ranging from larger molecules to periodic solids. Each year an increasing number of papers applying DFT calculations – 20.000 only in 2017 -- are reported worldwide. Such a large number of papers demonstrate the enormous field of applicability and relevance of ab initio computations. Thanks to their substantial impact, DFT numerical calculations are both a cornerstone and the key driving force of theoretical research in physics, chemistry, bio-physics, nano science, nano technology, nano-electronics and materials science.

The lecture introduces the foundations of density functional theory, the Hohenberg-Kohn theorem and the Kohn-Sham equations, and discusses different approximations for the exchange-correlation energy functional and their accuracy for calculating bond length in molecules and lattice structures in solids.

In addition, the course covers relativistic corrections, the mapping of the ab-initio total energies to model Hamiltonians to e.g. extract the finite temperature magnetic properties, and methods beyond the conventional the conventional exchange correlation approximations, such as LDA+U or Hubbard I approximation. Depending on time, different extensions on DFT will be discussed e.g. time-dependent density functional theory or many-body perturbation theory in the GW approximation of Hedin.

The DFT is realized in so-called quantum engines, i.e. electronic structure codes realising different electronic structure methods. Different possibilities or the computational implementation of DFT are introduced.

An important aspect of the lecture is the exercise which takes the partly the form of a tutorial. Some of which are used in hands-on exercises and tutorial to calculate e.g. Lattice constants, lattice structures, surface properties like surface energy and work functions, density of states and band structures of solids, local magnetic moments, magnetic exchange interactions and magnetic anisotropy and if time permits maybe non-collinear magnetic structures such as spin spirals. In this practical part of the lecture, we will employ the full-potential linearized augmented planewave method (FLAPW)-based code FLEUR.

**Previous Knowledge:**

It would be great if elementary knowledge of quantum mechanics , solid state physics, and computing (linux, a bit of graphics, fortran) would be available as well as a laptop with some storage with an updated operating system installed. The student should have also (at least) a student account on the Aachen Cluster.

**Objective:**

DFT is a central quantum mechanical tool with predictive and analytical power in many disciplines of science, where atoms, molecules, clusters, solids and liquids with and without surfaces and interfaces play a crucial role, with great potential in industry. Additional potential lies in high-throughput computing, exascale computing, in the computation of new properties enabled by the development of new exchange correlation functionals and extensions of electronic structure methods.

Aim of the lecture is a thorough introduction to the fundamentals of DFT, the spectrum of applications of DFT, the boundary of the validity of DFT in the present approximations, the choice of the DFT method in relation to the problem to be tackled and the proficiency of being able to use at least one electronic structure method, which in this lecture will be the FLEUR code (www.flapw.de).

**Teaching and Learning Method**:

Lecture with exercises

Please notice the Exercise / Tutorial is based on supervised work through a tutorial and takes place online. For this every Wednesday from 15:00 o'clock via video conference a short introduction to the respective tutorial section as well as a short discussion of the results so far and problems that have arisen. The working through the tutorial will then take place independently, whereby in the event of uncertainties and problems a support is available (via chat, email or video conference).

Time | Room | Start / Finish |
---|---|---|

Tuesday 08:30 - 12:00 am |
MBP2 015 (4272 / 015) |
October 11, 2022 - January 24, 2023 |