Theory of chemical exchange in zero field NMR : Two - site flips

With conventional NMR of polycrystalline solids, broad and often featureless spectra are frequently obtained and the effects of some molecular motions are not readily observed. 1 The resolution and sensitivity of nuclear quadrupole resonance (NQR) and broadline NMR is often so low that only the rigid and rapid motional regimes can be studied. In the intermediate region, where the exchange rate is comparable to the quadrupole interaction, the lines broaden appreciably and cannot be detected. Zero field NMR represents an attractive approach to overcome these difficulties. 3 In this paper, a theory is presented which deals with two-site motions of single deuterons, or pairs of dipolar coupled spin-l/2 nuclei. In previous work, Hennel et al. have developed analytical expressions for axially symmetric tensors.4 The work described here differs in that a spherical tensor basis set is used and there is no assumption of axial symmetry. Two-site exchange forms a good model for illustrating the effects of motion on zero field NMR spectra. It features in a number of chemical systems including: crystalline water; twofold flips of aromatic rings in liquid crystals, polymers, and proteins; chain motions in polymers and solids. There are several assumptions made in this calculation: ( 1) the motional model is a stationary Markov process; (2) the duration of the jump is negligible; (3) there are no couplings between the sites; and (4) only the spatial part of the Hamiltonian changes when a jump occurs. Assumption (3) may not always be satisfied in zero field NMR since dipolar coupling between deuterons is often observed. However, this interaction is small compared to the quadrupole couplings and can be further reduced by using partially deuterated samples. The effects of multisite exchange, as well as coupling between sites, will be examined in the following paper.