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## Theoretical Solid-State Chemistry: theory, modelling, and simulation

#### CECAM-ES

#### Organisers

From the theoretical side, the course briefly covers the basics of electronic structure methods in solids, with a focus on DFT, and provides some insight on perturbation theory to quickly move to applications. This includes an overview of bulk thermodynamical properties, the relationship between bonding and electronic structure in solids, phase transitions, temperature and pressure effects, magnetic and spectroscopic properties. Solid surfaces’ structures (relaxation, rumpling and reconstruction), electronic properties, influence structural vacancies and their relationships to chemical reactivity will be examined in two of the morning sessions. The school will cover the fundamentals and the practical use of a state-of-the-art codes for the calculation of the electronic structure of bulk solids, surfaces, and defects and impurities in solids. At the end of the course, the students will have acquired the basic knowledge on which Solid State Chemistry is founded. They will be able to apply this knowledge understand and analysis more complex concepts and phenomena in the field. And, finally they will be able to perform computational simulations on structural, electronic and magnetic properties of periodic and semi-periodic systems choosing with critical thinking the one that best suits the nature of the system or phenomenon to be studied.

Symmetry. 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.

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.

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.

Multiscale methods. Current difficulties in solid-state calculations. Scaling in the construction of the Hamiltonian of different methods. Scaling in diagonalization. Construction of sparse Hamiltonian matrix. Linear scaling techniques. Metals, insulators and the Fermi energy. Force fields in solid state. QM/MM and combination of force-fields and electronic structure codes. Applications: Excitons and polarons.

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.

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 compressibility. Chemical bonding reconstruction along a phase transition

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.

## References

**Spain**

Cristina Díaz ( Universidad Autónoma de Madrid ) - Organiser & speaker

Pablo García Fernández ( Universidad de Cantabria ) - Organiser & speaker

Antonio M. Márquez ( Universidad de Sevilla ) - Organiser & speaker