  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.
