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The thesis is centred on the theory of experimental methods in solid-stateNuclear Magnetic Resonance (ssNMR) spectroscopy, which deals with theinteraction of electromagnetic radiation with nuclei in a magnetic field andpossessing a fundamental quantum mechanical property called spin.Orientation-dependent interactions in ssNMR, while offering a wealth ofinformation, lead to broad indistinct signal and therefore are averaged out,predominantly by Magic-Angle Spinning (MAS). Reintroduction of the couplinginteractions 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 averageHamiltonian theory (AHT) or the Floquet theory, the former is the popularapproach. The two theories yield the same effective Hamiltonian, valid forstroboscopic observations. Generalised expressions, for the effectiveHamiltonian using AHT, are derived in the frequency domain in this dissertationto allow for appreciation of the equivalence with Floquet theory-mediatedeffective Hamiltonian. The derivation relies on the ability to express the timedependency of the interactions with a finite set of fundamental frequencies,which has long been sought and the lack of which has, at times, beenmisunderstood as limitations of AHT. A formalism to represent any periodictime-dependent interaction in the Fourier space with no more than twofundamental frequencies for every involved spin, presented here, which allowsfor the computation of effective Hamiltonian for any pulsed experiment. Theformalism has been applied to understand established dipolar recoupling pulsesequences. Limitations of the pulse sequences are addressed by designing novelvariants of the pulse sequences, aided by insights gained through the effectiveHamiltonian description.

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