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 includes applications in thermodynamical properties, phase transitions, temperature and pressure effects, magnetic and spectroscopic properties, and surface properties including reactivity of and at surfaces. The influence of structural vacancies both in bulk and at surfaces will be addressed as an important topic influencing in a significant way the properties of different materials. The chemical reactivity of surfaces will be the subject of one of the lectures of the course, with a full discussion of different aspects of the modelling of the CO oxidation in a Y-doped TiO2 supported gold nanoparticles catalyst. That is, in summary, the content of the main theoretical and practical sessions, grouped into 8 and 4 subjects, respectively.

(Theo-1) Symmetry (Pablo García Fernández)
Summary of basic concepts. Space groups. Tensor quantities. Crystal strain. Bloch theorem. The symmetry of the wavefunction under periodic boundary conditions.

(Theo-2) Electronic structure. (Cristina Díaz)
Cluster and periodic models. Atomistic models. Kohn-Sham equations and DFT methodologies. Electronic structure calculations. Phonons and crystal searching.

(Theo-3) Thermodynamic properties. (Cristina Díaz)
Static models. Equation of state of solids. Phase transitions. Mechanisms and kinetics of phase transitions. Thermal effects.

(Theo-4) Chemical bonding and microscopic approach. (Julia Contreras)
Topologies of scalar fields in crystals. Electron density, electron localization function and reduced density gradient chemical functions. Chemical origin of compresibility. Chemical bonding reconstruction along a phase transition.

(Theo-5) Ab initio simulation of the structure, thermodynamic properties and reactivity in surfaces. (Antonio Márquez)
Computational models in Surface Science. 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. Case studies: organic molecules and transition metal atoms at oxide surfaces. Reactivity at surfaces: organic molecules at simple surfaces. Role of point defects. Case study: CO oxidation on an oxide supported metal catalyst. Case study: highly correlated metal oxides: the case of ceria.

(Theo-6) 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-7) Magnetic interactions in Molecules and Solids: Basic concepts and Spin Hamiltonians (Coen de Graaf)
Spin Hamiltonians. Effective Hamiltonian theory. Magnetism in condensed matter. Spin waves for ferromagnets. Antiferromagnetic lattices. Electron transport. Quantum Chemical approach to solid state magnetism. Four center interactions in cuprates.

(Theo-8) Magnetic anisotropy, Double exchange and spin wave theory (Coen de Graaf)