Determination of Zero- and Double-Quantum Relaxation Transition Probabilities by Multiple-Selective Irradiation Methods

Any multispin system can be reasonably approximated by a sum of pairwise spin-spin interactions. As a consequence spin-lattice relaxation of any spin i coupled to a group of spins j can be approximated by summing the relaxation effects of all the spin pairs, yielding (1): $$d /dt = -{R_i}\left( { -{I_{0i}}} \right) - \sum\limits_{i \ne j} {{\sigma _{ij}}} \left( { - {I_{0j}}} \right)$$ (1) where $${R_i} = \sum\limits_{i \ne j} {{\rho _{ij}} + {\rho _i} * }$$ (2) Ioi is the equilibrium value of which represents the expectation value of the nuclear spin operator and it is proportional to the total integrated intensity of the NMR signal. σij is the cross relaxation term which is usually contributed by dipole-dipole interactions only. ϱij is the dipole-dipole direct relaxation term, while ϱi* accounts for direct relaxation of spin i due to mechanisms other than the dipole-dipole.