Although computer simulation of the electronic structure and properties of solids began decades ago, only recently the solid state methodologies have become sufficiently reliable that their application has resulted in an increasingly important impact on solid state chemistry and physics.

The level of this tutorial corresponds to master or doctorate students in areas of physics and chemistry. After two initial days where the fundamentals of theory of the treatment of the electronic structure of solids will be presented to the students, the remaining of the tutorial will be devoted to the examination of specific and hot areas like characterization of chemical bonding in solids and relationship to macroscopic properties, reactivity at solid surfaces, including layered systems and highly correlated oxides, and magnetic properties. The afternoons will be dedicated to practical hand-on tutorials. 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.

- Symmetry. Summary of basic concepts. Space groups. Tensor quantities. Crystal strain. Bloch theorem. The symmetry of the wavefunction under periodic boundary conditions. Reciprocal space.

- Electronic structure. Cluster and periodic models. Atomistic models. Kohn-Sham equations and DFT methodologies. Electronic structure calculations. Phonons and crystal searching.

- Thermodynamic properties. Static models. Equation of state of solids. Phase transitions. Mechanisms and kinetics of phase transitions. Thermal effects.

- Chemical bonding and microscopic approach. 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.

- Ab initio simulation of the structure, thermodynamic properties and reactivity in surfaces. 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.

- Optical properties of Solids. Macroscopic Maxwell equations: conductivity and dielectric tensors, polarization and currents. Microscopic interpretation. Simple models: metals and insulators. Multiband transitions. Examples. Hamiltonians for light-matter interaction. Time-dependent evolution of a periodic system under electric fields. Absorption and reflectivity. Excitons and polarons. Limitations of current theoretical methods.

- Magnetic interactions in Molecules and Solids: Basic concepts and Spin Hamiltonians 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.

- Magnetic anisotropy, Double exchange and spin wave theory.

Practical Sessions:

- Electronic structure calculations.

- Topology of chemical functions.

- Cluster model and supercell methods. Optical properties.

- Structure and reactivity at oxide surfaces.