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**Abstract:
**

The school taught PhD students from all over the world the basic and more advanced concepts in modern electronic structure theory including ground state density functional theory (DFT) and many-body methods. Emphasis was put on the methodology applied “on-top” of ab-initio calculations which is essential for the computational design of new functional materials. This was achieved through a combination of lectures given by world leading experts and hands-on computer exercises.

**Scientific summary:**

The primary purpose of this summer school was to teach the students how electronic structure theory can be used for materials design. An introduction to density functional theory (DFT) with particular emphasis on practical methodology and implementation aspects was given. Extensions beyond the standard DFT formalism including time-dependent DFT, non-collinear spin, spin-orbit coupling, Berry phases and Many-body perturbation theory was discussed. The subjects provided the students with a basic toolbox that will allow them to perform first principles analysis of a large variety of problems in physics and chemistry. For example, quasiparticle excitations in the GW approximation, excitons from the Bethe-Salpeter Equation (BSE), time-dependent density functional theory (TDDFT), Berry phases and topological insulators, heterogeneous catalysis, electrochemistry and magnetism. The students were taught how to embed electronic structure calculations in a framework that facilitates design of materials with specific properties. For this purpose, there was introductory lectures on machine learning, materials databases, and materials informatics and it was shown how to perform materials design using data mining from materials databases and machine learning.

The summer school consisted of lectures by international experts in the field followed by computer exercises giving hands-on-experience with the concepts discussed in the lectures. The lectures were divided in tutorial lectures, covering the basic theory on specific subjects and applied lectures, where it was demonstrated how to apply the methodology to tackle cutting edge research problems. The computer exercises were based on the electronic structure code GPAW and the Atomic Simulation Environment (ASE). GPAW is based on the projector-augmented wave methodology and can perform computations on real space grids, plane waves or localized atomic orbitals. Besides ground state DFT, GPAW can perform various post-DFT electronic structures calculations such as GW, BSE, and TDDFT – all exemplified by pedagogical exercises. The ASE is a general purpose open source simulation environment that can be used to setup, control, and analyze electronic structure simulations carried out in a variety of electronic structure codes, e.g. including VASP, Octopus, GPAW, Dacapo, AbInit, ASAP, and Siesta. The exercises were supervised by expert users of ASE and GPAW.

During the exercises the students worked in small groups with the focus on learning to produce publication quality simulations on the local computer-cluster. There was a set of introductory exercises, which served to introduce the students to the codes as well as to give the basic hands-on experience with DFT calculations. After completing these, the students continued with a large set of advanced exercise within the fields of e.g. Catalysis, Molecular electronics, Electrochemistry, GW calculations, magnetic structures, correlation energies from the Random Phase Approximation etc.

The previous summer schools in this series in 2008, 2010, 2012, 2014, and 2016 were very successful and the positive feedback and large number of applications received showed the need for a summer school in this area. The five previous schools had around 110 participants (70 external graduate students, 20 local graduate students and 20 lecturers). At the 2018 Summer School we had more than 100 graduate students from other groups, 15 graduate students from the Technical University of Denmark, 15 invited speakers and 5 organizers/teachers from the organizing institution. Compared to previous summer schools we included new subjects that are gaining territory in the field such as topological insulators and machine learning.

**School program:
**

For the first time ever the summer school was held outside DTU. The venue for the school was Marienlyst Strandhotel. The hotel is located by the sea in Helsingør in the beautiful North Zealand, overlooking Sweden and Kronborg Castle. It is organized by the section for Computational Atomic-scale Materials Design, Department of Physics, Technical University of Denmark. The summer school is running for six days.

The program for the summer school can be downloaded here.

Each day was divided into morning lectures, afternoon lectures, and computer exercises. The morning lectures were primarily tutorial, whereas the afternoon lectures presented applications of basic theory. On Monday evening there was a poster session, and on Wednesday afternoon/evening there was an excursion and conference dinner.

**Invited Lecturers:
**Hardy Gross, Max Planck Institute of Microstructure Physics, Germany

Jens Nørskov, Stanford University, USA

*"Computational Design in Catalysis"*

Hannes Jonsson, University of Iceland

*"Rate Theory"*

Bjørk Hammer, Aarhus University, Denmark

*"Structures and Reactions at Surfaces" and "Machine Learning and Structural Search"*

Jan Rossmeisl, University of Copenhagen, Denmark

*"Electrochemistry"*

Georg Kresse, University of Vienna, Austria

*"Many-Body Perturbation Theory"*

Claudia Draxl, Humboldt-Universität Berlin, Germany

*"Theoretical Spectroscopy"*

Nicola Marzari, EPFL, Switzerland

*"2D materials"*

Christopher Wolverton, Northwestern University, USA

*"Machine Learning and Materials Science"*

Anatole von Lilienfeld, University of Basel, Switzerland

*"Machine Learning and Chemistry"*

Thomas Bligaard, SLAC National Accelerator Laboratory, USA

*"Materials Informatics"*

Yan Sun, Max-Planck-Gesellschaft, Germany

*"Topological States of Matter" *

Stefano Curtarolo, Duke University, USA

*"Discovery of Novel Electronic Materials"*

Aron Walsh, Imperial College London, UK

*"Materials Modelling for Solar Cells: Perovskites and Beyond"*

Kieron Burke, University of California, USA

*"The Future of DFT"*

**Lecturers by organizers: **

Jakob Schiøtz, DTU

*"Electronic structure tools: ASE and GPAW"*

Kristian S. Thygesen, DTU

*"Excitations in 2D materials"*

Karsten W. Jacobsen, DTU

*"Machine Learning Basics"*

Thomas Olsen, DTU

*"Spin-orbit physics"*

Tejs Vegge, DTU

"Batteries"

**Credits:**

A diploma which certifies that the students have participated and earned 2,5 ECTS points will be issued to the participants upon completion of the summer school.

**Scientific Organizing Committee**:

Kristian S. Thygesen, Technical University of Denmark

Karsten W. Jacobsen, Technical University of Denmark

Jakob Schiøtz, Technical University of Denmark

Thomas Olsen, Technical University of Denmark

Tejs Vegge, Technical University of Denmark

**Administrative Organizing Committee:**

Marianne Ærsøe, Technical University of Denmark