Chapter 12: Magnetic Resonance

The foundation rests on understanding how nuclei with spin angular momentum function as magnetic dipoles whose energy levels split in the presence of an applied external field, a phenomenon quantified by the Larmor frequency that describes the precession rate of the magnetic moment around the field direction. Nuclear Magnetic Resonance spectroscopy probes transitions between these nuclear spin states and reveals detailed information about molecular environments through two primary spectral features: chemical shift, which indicates the electronic shielding surrounding a nucleus and varies predictably with local electronic density, and fine structure or spin-spin coupling, which arises from indirect magnetic interactions between neighboring nuclei and provides constraints on molecular connectivity and three-dimensional conformation through relationships like the Karplus equation. Modern NMR experiments employ radiofrequency pulse sequences that excite spins away from equilibrium, generating a time-domain free-induction decay signal that contains the complete spectroscopic information; mathematical Fourier transformation converts this temporal data into the conventional frequency-domain spectrum. The chapter addresses essential relaxation phenomena that govern how excited spins return to equilibrium: longitudinal relaxation describes the recovery of magnetization along the field direction and depends on molecular tumbling rates, while transverse relaxation characterizes the decay of magnetization perpendicular to the field and reflects local magnetic field inhomogeneities. Advanced applications include the Nuclear Overhauser Effect, which enhances signal intensity by exploiting dipolar coupling between nearby spins and enables distance measurements in complex molecules. The principles extend to Electron Paramagnetic Resonance spectroscopy, which detects microwave absorption by unpaired electrons and typically displays hyperfine structure from interactions between electron spins and surrounding nuclear spins, quantitatively described through relationships such as the McConnell equation.