Pulse Design in Solid-State Nuclear Magnetic Resonance: Study and Design of Dipolar Recoupling Experiments in Spin-1/2 Nuclei

The thesis is centred on the theory of experimental methods in solid-state Nuclear Magnetic Resonance (ssNMR) spectroscopy, which deals with the interaction of electromagnetic radiation with nuclei in a magnetic field and possessing a fundamental quantum mechanical property called spin. Orientation-dependent interactions in ssNMR, while offering a wealth of information, lead to broad indistinct signal and therefore are averaged out, predominantly by Magic-Angle Spinning (MAS). Reintroduction of the coupling interactions is achieved through radio frequency recoupling pulse sequences. NMR experiments are in general understood by finding the effective Hamiltonian, which best approximates the spin dynamics and is found using average Hamiltonian theory (AHT) or the Floquet theory, the former is the popular approach. The two theories yield the same effective Hamiltonian, valid for stroboscopic observations. Generalised expressions, for the effective Hamiltonian using AHT, are derived in the frequency domain in this dissertation to allow for appreciation of the equivalence with Floquet theory-mediated effective Hamiltonian. The derivation relies on the ability to express the time dependency of the interactions with a finite set of fundamental frequencies, which has long been sought and the lack of which has, at times, been misunderstood as limitations of AHT. A formalism to represent any periodic time-dependent interaction in the Fourier space with no more than two fundamental frequencies for every involved spin, presented here, which allows for the computation of effective Hamiltonian for any pulsed experiment. The formalism has been applied to understand established dipolar recoupling pulse sequences. Limitations of the pulse sequences are addressed by designing novel variants of the pulse sequences, aided by insights gained through the effective Hamiltonian description.