The Summer School on Computational Materials Sciences aims at the identification and promotion of the common elements developed in theoretical and computational studies of materials properties across materials types, metals, ceramics, materials for new energy technologies, electronic materials and minerals. To accomplish this goal, the School brings together leading experts from a wide spectrum of materials simulations including theory, modeling, and computation, engaged in the study of a broad range of materials properties. Several lectures will be devoted to experimental challenges in the field, and will be conducted by outstanding experimentalists within Materials Sciences.

Therefore, this School provides a forum for exposing young researchers and students to most recent state-of-the-art theoretical and computational developments in studying, understanding, and predicting the properties of materials. Also, the School encourages interdisciplinary contributions, such as between the fields of condensed matter physics and applied materials sciences, chemistry, metallurgy, etc.

**Website**

http://dipc.ehu.es/ws_presentacion.php?id=53

## State of the art

Accelerated by the rapid progress in computer technologies, the electronic structure theory has become a mature field of modern condensed matter physics. Today it allows one to obtain reliable predictions for the thermodynamic, mechanical, electrical and magnetic properties of metals, semiconductors or insulators without any adjustable parameters fitted to experiments. There is a strong community of researchers in this field, known as Psi-k network. The theory is now employed not only by physicists, but also by materials scientists, chemists, geophysicists, biophysicists, metallurgist, and in other scientific fields. The basic research is often strongly motivated by practical applications, and many problems considered by condensed matter theoreticians nowadays originate from interdisciplinary contacts and directly from industry.

The past few years showed huge progress in the field of computational materials sciences, both with respect to the applications and the fundamental research. To show just a few examples, which illustrate a variety of problems where the theory is applied, one can mention a suggestion of a novel mechanism to enhance hardness in multilayer coatings by restricting dislocation movement in transition metal carbides via phase stability tuning [1], understanding of the kinetics of point defects produced by irradiation in Fe [2], an identification of cathode materials for lithium batteries guided by firstprinciples calculations [3], an optimization of ionic conductivity in doped ceria [4], understanding design principles of phase change materials [5], or an understanding of the Invar effect in Fe-Ni steels [6]. But there are also great challenges, which will be presented to School participants.

In particular, the corner stone for the electronic structure theory of solids is the Bloch's theorem. However, it is valid for systems with ideal three-dimensional periodicity. At the same time, almost all materials for technological applications have substantial deviations from this highly idealized model. The main goal of the School will be to introduce basic electronic structure theory for non-periodic solids, and present techniques to model their properties from the fundamental principles of quantum mechanics and statistical physics. We will emphasize the two principal issues: (i) competence development and (ii) competence transfer.

**Competence development.**

1. Complexity. There are increasing demands in theoretical understanding of more and more realistic materials (including materials for nano-science, amorphous phases, quasicrystals, non-commensurate structures, alloy surfaces, etc.) and materials phenomena (radiation damage, hydrogen storage, ion conductivity, brittleness, hardness). Increasing the length scale for the simulations requires a development of novel, more efficient techniques for solving the electronic structure problem within the local density - generalized gradient approximations of the density functional theory (DFT). The alloy theory at present relies on two main approaches: (i) the supercell technique and (ii) the effective medium theory [7,8]. New algorithms and new ideas will be presented, including the effective medium approaches that go beyond the mean-field description and efficient linear scaling methods, applicable for metals.

2. Temperature: From the total energy towards the free energy. A majority of applications still involve simulations at T=0K. For instance, the problem of structural and phase stabilities is most often solved by comparing total energies between different competing phases as obtained from DFT T=0K calculations. However, it is well known that at least some of the phases may be dynamically unstable, making such a comparison meaningless. Indeed, there are several studies which demonstrate that the various excitation mechanisms in a solid such as lattice vibrations and/or magnetic excitations may strongly influence the alloy phase stability. The School will therefore introduce to the participants reliable tools and discuss recent development how to include and compute finite temperature contributions using DFT. Specifically, the following aspects shall be covered:

• Efficient schemes for calculations of elastic constants, phonons, and magnons

• Efficient sampling strategies to compute thermodynamically averaged quantities such as ab initio molecular dynamics, thermodynamic integration, or umbrella sampling.

• Development of reliable quasi ab initio approaches (the so-called multiscale modeling) that connect DFT with mesoscopic macroscopic concepts such as thermodynamics, statistical mechanics, or continuum elastic theory.

3. Strong electron correlations. For many realistic materials of technological importance it is crucial to employ novel manybody techniques which are able to overcome deficiencies of the semi-local DFT functionals such as the infamous band gap problem. Recent progress shows that the availability and application of such techniques substantially enhances the capabilities and predictive power of theory and becomes important for e.g. electronic applications, semiconductor alloys, fuel cell, batteries materials, light emission and light detection processes, and transport. Fundamentals and recent developments of such novel many-body techniques will thus be covered by the School.

4. Complex magnetism. Many modern structural materials are Fe-based alloys. It has recently become clear that the complex magnetism of Fe substantially influences properties of these materials. Theoretical techniques, which allow for the simulations of materials with complex crystal and magnetic structures, will be presented. Combining alloy theory, first-principles calculations and/or statistical mechanics new schemes have been suggested [7].

5. Structure-property relations. A traditional paradigm for ab initio theory is to determine physical properties for a given material. This is done for the particular composition and structure with the latter determined via a minimization of the total energy for the system at hand. However, state-of-the-art experimental techniques allow the design and fabrication of kinetically rather than thermodynamically stabilized materials, with hitherto unprecedented quality and reliability. The possibility to reproducibly fabricate metastable materials widely opens the parameter field and space for materials design and consequently a new and exciting area for theoretical modeling. Consequently, we are currently witnessing a shift of the paradigm for the theoretical simulations: Rather than starting from a specific material and computing its properties one asks how should the material be composed to give rise to predefined properties [9]. Such a strategy can be easily extended to include not only materials specific but also economical criteria such as e.g. the price for the individual components. The availability of accurate theoretical predictions together with efficient inverse optimization strategies will lead to a rapid progress of this field.

**Competence transfer.**

A distribution of computer codes for the electronic structure calculations goes much faster than the transfer of the corresponding knowledge for the underlying theory. Unfortunately, though the codes have become really user friendly, the theory on its own has not. Therefore, using the codes is not completely fool proof, which is a real danger for the credibility of the entire field. In particular, errors produced by non-experienced users, as well as their unmotivated high expectations, may accumulate, and create an overall negative impression with respect to the reliability and the possibilities of electronic structure calculations. It is therefore crucial to educate highly qualified experts in the field, at a substantially higher rate than in the past. We firmly believe that a paradigm change is needed: a training of individuals (individual PhD students and Postdoctoral Fellows carrying out their projects with leading Professors) has to be complemented by a general training for the wide community of users of ab initio simulation tools. For this, the present Summer School is organized.