Revisiting the Spin–Lattice Relaxation of Homonuclear In-Phase and Antiphase NMR Magnetization

Hyperpolarization techniques such as dynamic nuclear polarization (DNP), chemically-induced dynamic nuclear polarization (CIDNP), and parahydrogen-induced polarization (PHIP) enhance the sensitivity of NMR spectroscopy and MRI, but the associated antiphase magnetization patterns often relax faster than those of conventional in-phase signals. This study analyzes the spin-lattice relaxation matrix for single-quantum transitions in an isolated, weakly coupled two-spin AX system to identify eigenvectors and eigenvalues that govern the time evolution of in-phase and antiphase longitudinal magnetization. The analysis predicts that AX antiphase magnetization, such as that generated by PHIP hydrogenations in high magnetic field, can relax up to twice as fast as the in-phase magnetization of traditional inversion-recovery or saturation-recovery experiments. To validate these predictions, a dedicated NMR pulse sequence was used to selectively generate and monitor antiphase magnetization. <i>trans</i>-Cinnamic acid in deuterated DMSO served as a model compound, with the hydrogen atoms on its central conjugated double bond forming a weakly coupled AX spin system with a large scalar coupling (>16 Hz). The large scalar coupling allowed for the separate integration of the two lines in each doublet. Experimental results confirm an accelerated relaxation of antiphase magnetization but also reveal that in-phase relaxation is influenced by double-quantum transitions, which do not contribute to the relaxation of antiphase magnetization. The findings of this study highlight the importance of distinguishing in-phase from antiphase relaxation, providing a basis for optimizing hyperpolarization experiments with explicit consideration of antiphase signal dynamics.