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. , While a large number of course and tutorials already exists, they are mainly focused on audiences with strong background on solid state physics, and usually devoted to some particular electronic structure code. Far more unusual 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. This school is primarily targeted to PhD students and post docs who are interested or are starting to learning about the application theory methods and techniques to the study of the physics and chemistry of the solid state.

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, structure and reactivity at solid surfaces, including layered systems and highly correlated oxides, and magnetic properties. The afternoons will be dedicated to practical hand-on tutorials. Several 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.

- Summary of basic concepts. Space groups. Tensor quantities. Crystal strain. Bloch theorem. The symmetry of the wavefunction under periodic boundary conditions. Reciprocal space. Mean field solution of the electronic problem in solids and electron-correlation methods.

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

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

- Topologies of scalar fields in crystals. Electron density, electron localization function and reduced density gradient chemical functions. Chemical origin of compressibility. Chemical bonding reconstruction along a phase transition.

- 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.

- 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.

- 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.

- Methods for the calculations of magnetic and optical properties and polarons.

- Structure and reactivity at oxide surfaces.