# Electronic structure theory

In general, solid state materials can be quite well described by their crystal structure. An ideal crystal can be characterized by a periodic arrangement of atoms in space, where the ration of the atoms is given by the composition of the material. A long standing goal of solid state research is the derivation or even prediction of basic physical properties of a material based solely on its crystal structure. In the past, these so called structure-properties-relations rely mostly on empirical rules, which have been derived and tested in a large number of systematic studies and the respective vast data base. However, in the last two decades, ab-initio calculations for solid state compounds, mostly based on density functional theory (DFT), became more and more feasible, reliable and accurate, in particular supported by the swift development of computational power. Nowadays, complex systems with more than 100 atoms per crystallographic unit cell can be treated in reasonable time and high accuracy on a standard computer. From such an electronic structure calculation, many properties of the material can be derived, e.g. its metallic or insulating nature, electronic density of states and band structure, lattice vibrations and thermal expansion or its magnetic properties. Although we are able to describe many compounds with good accuracy by this method, several compound families cause major problems: Materials, which are composed by transition metals and/or rare earth elements often exhibit so called "strong electronic correlations". The origin of these correlations is a large Coulomb repulsion of the rather localized transition metal *d* or rare earth *f* electrons. Unfortunately, present day density functionals can describe such correlated electronic states only poorly. Therefore, DFT calculations for such systems need some improved treatment of the correlations, which can be achieved by additional orbital specific terms for the relevant *d *or *f *electrons. Alternatively, on can isolate the most relevant sub-system and its parameters for a specific compound by an uncorrelated calculation and treat the correlations explicitly in a subsequent model approach. Numerical simulations of the resulting physical properties allow for a direct comparison with experimental data. Such close combination of ab-initio calculations, subsequent modeling and numerical simulations with state of the art experiments is a very powerful tool to get deep insights into the physics of complex materials.

*Based on the experimental crystal structure, density functional calculations yield information about the electronic band structure and density of states. They allow for the extraction of relevant subsystems and coupling parameters, like magnetic exchange integrals. These parameters can be used as a realistic starting point for the numerical simulation of thermodynamic and magnetic properties which in turn are compared with experimental data from single crystal or powder measurements.*