Complex dynamic NMR spectra in the fast exchange limit

Symmetries in Liouville space are used to construct analytical relaxation equations for the density matrix of chemically exchanging systems in the fast exchange limit. The method is particularly useful when a symmetry group for the exchange superoperator can be found. The method is applied to the proton NMR of molecules which are dissolved in liquid crystals, and which undergo isomerization reactions, such as ring inversion and bond shift rearrangement. The results are compared with exact calculations in order to check the range of validity of the fast exchange approximation. For completeness the slow exchange approximation equations are also compared with the exact procedure. It is found that the approximate equation in both limits can faithfully reproduce the NMR spectra over most of the dynamic range and often without a gap. The approximate equations significantly shorten the computation time, making it possible to simulate dynamic line shape for as big a molecule as cyclohexane.