Revisiting dipolar relaxation of a homonuclear spin pair in the presence of a radio frequency field: A tutorial

Abstract

NMR studies exploit spin relaxation in a multitude of different ways, providing information on molecular structure and dynamics. Calculating the relaxation rates of NMR active nuclei in multi-spin systems is often a prerequisite for the proper analysis of experimental data. For many researchers the calculations appear complex, often involving different basis sets or expressions describing relaxation in different frames. In this tutorial paper we derive expressions for dipolar relaxation of an I-S two spin spin-system in the presence of a B₁ radio frequency field, where spins I and S can be either like or unlike. We consider two different approaches for the derivation of relaxation elements that have been used in the literature, including one where a series of transformations are carried out to the interaction representation of the effective field, comprising B₁ and Zeeman components. A second procedure is based on the well-known Solomon equations. We show that both approaches lead to identical results, in the process presenting a pedagogical description of relaxation theory.