Simulation of static and dynamic magnetic resonance parameters for solid mixed conductors

A detailed understanding of the atomistic processes within a lithium ion battery is expected to facilitate the progress of energy storage technology, which is a key element for the exit from nuclear and fossil--fuel energy. Nuclear magnetic resonance (NMR) spectroscopy can provide information about local electronic structure and dynamic properties of battery materials by addressing the nuclear spins of lithium (Li). Support by independent $\textit{ab initio}$ simulations is indispensable to meet the challenges presented by state--of--the--art electrode materials in NMR spectroscopy. In this thesis, the initial steps towards a novel, theoretical multi--scale method for retracing Li NMR experiments on battery materials are presented. First, the theoretical concepts of calculating NMR parameters are summarized. Then, the accuracy of NMR parameter simulations for Li and their dependence on different criteria are benchmarked. On the basis of the high--capacitance, disordered electrode material Li$_4$Ti$_5$O$_{12}$ (LTO), an approach for clustering the NMR quantities according to the local, crystallographic structure is established, reducing the number of $\textit{ab initio}$ NMR calculations. Theoretical sampling of the LTO configuration space demonstrates that the customary one--to--one assignment of experimental observables to crystallographic positions is inaccurate and misleading for complex materials. Finally, a kinetic Monte--Carlo (kMC) model, which simulates the atomistic dynamics, is combined with the NMR autocorrelation function (ACF), which provides the effective observables for spin--alignment echo (SAE) experiments. The simulated, static Li NMR parameters enter the kMC model together with atomic mobility parameters. The kMC sampling of the NMR ACF finally yields observables, which compared to experimental findings confirm the hypothesis of two domains of mobility on separate length and time scales in LTO. Additionally, a theoretical pre--screening approach for organic pH--marker molecules in aqueous solution is outlined. The pre--screening approach is demonstrated for biomedical applications, but might be transferred to energy research applications to study local reaction conditions of transient electrochemical processes. The various results demonstrate the synergy of combining theoretical simulations with NMR experiments. Together theory and experiment amplify the gained knowledge and make additional insights into the basic processes in a battery available