Paramagnetic systems have a wide range of applications ranging from energy storage or conversion to catalytic processes, metalloproteins and light-emitting materials. Over the recent years nuclear magnetic resonance (NMR) spectroscopy has become an established tool for studying the structural and electronic properties of these systems, largely because it can provide a link between the structure and the bulk properties. This progress was only possible due to improved probe technology and better radiofrequency irradiation schemes, since the hyperfine interaction between nuclei and the unpaired electrons generally hampers both the acquisition and interpretation of the spectra and, therefore, techniques that are standard for diamagnetic systems often perform poorly when applied to paramagnetic systems.

The aim of the present thesis is to continue the development of solid-state paramagnetic NMR and address some of the remaining limitations and bottlenecks in the acquisition and spectral interpretation. One specific area for which great improvements have been seen is the development of new broadband excitation and inversion sequences for systems under Magic-Angle Spinning (MAS) which employ adiabatic pulses. In this work, we provide a more rigorous understanding of the adiabatic pulses in solid-state MAS NMR applicable to both the design of new and improved pulse schemes, and their application in studies of an increased variety of systems, whilst avoiding potential implementation pitfalls.

We also demonstrate how a thorough understanding of the hyperfine interaction combined with quantum chemistry calculations can link bulk magnetic properties and magnetic resonance signatures both in solid-state NMR and Electron Paramagnetic Resonance (EPR), thus providing an accurate description of the geometry and electronic configuration of an organoytterbium complex with applications in heterogeneous catalysis.

Lastly, we explore the development of methods suitable for quadrupolar nuclei (spin I>1/2) in paramagnetic systems which have, so far, lagged behind their spin 1/2 counterparts. We focus more specifically on half-integer quadrupoles for which we propose a new method of processing Multiple-Quantum and Satellite-Transition MAS spectra which permits the separation of shift and quadrupolar interactions into orthogonal dimensions and evaluate the performance and limitations of the state-of-the-art methods for extraction of both quadrupolar and shift anisotropy tensor parameters on structurally complex systems.

We anticipate that the work developed throughout this thesis can help extend the fields of application of solid-state paramagnetic NMR.