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## EMTCCM School on Theoretical Solid State Chemistry

#### Location: Zaragoza, Spain

#### Organisers

The traditional quantum chemistry and condensed matter communities are rapidly converging by sharing methodologies and common interests, particularly in the field of theoretical simulation of materials. A large number of course and tutorials already exists, mainly focused on audiences with strong background on solid state physics, and usually devoted to some particular electronic structure code. Far more rare are the courses designed to teach the solid state techniques to chemists, thus contributing to eliminate the cultural barriers that still exist between both groups.

A large number of computational codes are actively being developed, capable of simulating molecules, pure and defective crystals, surface and transport properties, and reactive processes in the bulk and interfaces. Getting familiar with the different codes and their possibilities requires an adequate training that merges theory and practice in substantial amounts.

This tutorial on "Theoretical solid state chemistry" (TSSC), already celebrated in 2012 (Zaragoza, June 11—15) and 2013 (Zaragoza, May 13—17), is designed as part of the Erasmus Mundus Master in Theoretical Chemistry and Computational Modelling (EM-TCCM, <www.emtccm.org>), but it will be open to participants not involved in the master: in fact, they have been majority between those attending the 2013 course.

The level of TSSC corresponds to master or doctorate students in areas of physics and chemistry. For students of the EM-TCCM, this TSSC and the school on "Excited States" that already celebrated two editions at ZCAM, is a part of the master and we expect some 15 students from them. The TSSC tutorial is proposed to accept up to 25 participants, taking into account the facilities at ZCAM, the partial sponsor provided by the EM-TCCM, and the actual enrollment of 16 students at the 2013 edition.

The tutorial will cover the fundamentals and the practical use of state-of-the-art codes for the calculation of the electronic structure of bulk solids, surfaces, and defects and impurities in solids. This include applications in thermodynamical properties, phase transitions, temperature and pressure effects, magnetic and spectroscopic properties, and surface properties including reactivity on and at surfaces. Ab initio molecular dynamics is also discussed briefly. That is the content of the main theoretical and practical sessions, grouped into 6 and 4 subjects, respectively.

Theoretical Sessions (22:30 hours)

(Theo-1) Ab initio calculation of the electronic structure of solids. (Víctor Luaña)

Comparison between wavefunction and density functional methods. Hohenberg-Kohn theorems. Kohn-Sham equations and implementation differences. Exchange and correlation functionals. Jacob's ladder. Strong correlation treatment. Functionals and van der Waals interactions. Plane waves and pseudopotentials (pw-ps). Band structure and density of states. Brilloiun zone sampling. Introduction to Quantum Espresso. Converging a pw-ps calculation. From crystallographic data bases to the electronic structure calculation. Optimization of the crystal geometry. Post processing. Bonding and topology. LDA/GGA+u calculations and treatment of magnetic crystals.

(Theo-2) Thermodynamic properties of solids: pressure and temperature effects. Equations of state, phase transitions and symmetry aspects. (Miriam Marqués)

Thermodynamics of bulk solids. The E(V) curve and the static model. Vibrations in crystals. Equations of state for solids. Elastic constants. Phase transitions. Mechanisms and kinetics of phase transitions. Ab initio phonon structure calculation. Phonons at the gamma point. Phonons at a generic q point. Static and dynamic polarizability. Phonons in polar materials.

(Theo-3) Ab initio simulation of magnetic and optical properties, and structural instabilities of solids. (Miguel Moreno)

Introduction: Role of impurities in crystalline solids. Impurities in insulators. Localization. What are the calculations useful for? Substitutional Transition Metal Impurities in insulators: Description of states. Study of Model Systems: interatomic distances and colour. The colour of gemstones containing Cr3+. Static Jahn-Teller effect: description. Static Jahn-Teller effect: experimental evidence. Insight into the Jahn-Teller effect. Off centre motion of impurities: evidence and characteristics. Origin of the off centre distortion. Softening around impurities.

(Theo-4) Ab initio simulation of the structure, thermodynamic properties and reactivity in surfaces. (Antonio Márquez)

Computational models in Surface Science: cluster models and periodic models. Structure of surfaces: Tasker's classification of ionic surfaces. Relaxation, rumpling, and reconstruction of surfaces. Surface energies. Surface defects: O vacancies in metal oxides. Adsorption at surfaces: organic molecules and transition metal atoms on oxide surfaces. Reactivity at surfaces: organic molecules at simple surfaces. Role of point defects. Case study: CO oxidation on oxide supported metal catalyst.

(Theo-5) Ab initio molecular dynamics (Car-Parrinello). (Víctor Luaña)

Statistical mechanics. Classical formulations of Molecular Dynamics. Sources of potential energy. Designing a MD simulation. Solving the equations of motion. Steps in a MD simulation. Ensemble constraints: thermostats and barostats. Ab initio MD: the Car-Parrinello formulation. CPMD calculations in quantum espresso. Selected applications.

(Theo-6) Elements of molecular and crystal magnetism, (Francesc Illas Riera)

Model and Effective Hamiltonians: model Hamiltonians for magnetic interactions; effective parameters from material models ; obtaining the relevant energy differences in molecules and solids. Effective parameters for High-Tc cuprates: news in HTCs (LaO1-xFeAsFx); new compounds, old problems, which EXC?; electronic & magnetic structure of cuprates from DFT calculations; electronic structure of LaOFeAs; magnetic coupling in LaOFeAs: spin frustration. Modeling doped cuprates; the case of Ca2-xNaxCuO2Cl2.

Practical Sessions (16 hours): The responsible is the same person in charge of the theory, except when indicated.

(Prac-1) Electronic calculations with quantum espresso. Practical session for Theo-1.

(Prac-2) Crystallographic and symmetry tools. Practical session for Theo-2.

(Prac-3) Practical session for Theo-3 and Theo-6. Cluster model and supercell methods. (Pablo García Fernández).

(Prac-4) Practical session for Theo-4.

Tutorial final test (1 hour)

## References

**Spain**

Teresa Barriuso (University of Cantabria) - Organiser

Víctor Luaña Cabal (University of Oviedo) - Organiser

Antonio M. Márquez (Universidad de Sevilla) - Organiser

Antonio M. Márquez (Universidad de Sevilla) - Organiser

Wilson Rodríguez (Universidad Autónoma de Madrid) - Organiser