Long-lived states in solution NMR: Selection rules for intramolecular dipolar relaxation in low magnetic fields

Recent work has shown that singlet states of two-spin systems in low magnetic fields can have lifetimes up to an order of magnitude longer than the usual spin-lattice relaxation time. This result may enable new applications of NMR, and in particular hyperpolarized NMR via parahydrogen-induced polarization, to the study of slow processes that take place over previously inaccessible timescales. At present it is unclear whether similar results apply to multi-spin systems, or if these long lifetimes are a peculiarity of the two-spin case. Moderately long-lived states have been observed in systems containing more than two spins, although the mechanisms that prolong their lifetimes are not well understood. Here we present formalism for the study of relaxation in multi-spin systems in low magnetic fields. This approach is used to derive a family of quantum-mechanical selection rules governing intramolecular dipolar relaxation at low field that may account for the extended lifetimes observed in multi-spin systems.