High-Resolution NMR Study of Relaxation Mechanisms in a Two-Spin System

A description of nuclear spin–spin and spin–lattice relaxation is presented for a system of two coupled nonequivalent spin−$\frac{1}{2}$ nuclei subject to mutual dipole–dipole interaction and interactions with external magnetic species. Expressions are derived for the six transition probabilities linking the four energy levels, in terms of an internal dipole–dipole relaxation parameter $T_D$ , external relaxation parameters $T_{\mathrm{XA}}$ for nucleus $A$ and $T_{\mathrm{XB}}$ for nucleus $B$ , and the degree of correlation $\mathrm{(C)}$ between the interactions of $A$ and $B$ with external magnetic species. These molecular relaxation parameters are related to the initial rates of recovery of the NMR signal intensities after a selective pulse has rotated the magnetization vector of a chosen line through $\pi$ radians in the rotating frame of reference. A small general‐purpose computer has been used to control these pulse experiments and to program a synthesizer to provide the required stable audiofrequency signals. Measurements have been made on the high‐resolution proton spectra of dilute degassed solutions of 2,3‐dibromothiophene and 3‐bromothiophene‐2‐aldehyde in carbon disulphide. Assuming an interproton distance equal to that in thiophene, the direct dipole–dipole contribution to relaxation has been used to estimate the rotational correlation times ${\tau }_C{\text{\hspace{0.17em}=\hspace{0.17em}4.4\hspace{0.17em}×\hspace{0.17em}10}}^{\text{−12}}$ sec for dibromothiophene and ${\tau }_C{\text{\hspace{0.17em}=\hspace{0.17em}5.2\hspace{0.17em}×\hspace{0.17em}10}}^{\text{−12}}$ sec for bromothiophenealdehyde. Evidence is found for a small but significant difference between the external relaxation parameters $T_{\mathrm{XA}}$ and $T_{\mathrm{XB}}$ , and the degree of correlation between the interactions of $A$ and $B$ with external spins is found to be 0.67 in both molecules. This can be related to the nominal distance of closest approach of the species responsible for external relaxation.