Calculation of NMR Relaxation Times for Quadrupolar Nuclei in the Presence of Chemical Exchange

The correlation function for a quadrupolar nucleus which may exchange its environment between two kinds of sites in solution has been calculated from an appropriate joint conditional probability for changes in site and in electric field gradient direction with time. In the extreme narrowing limit, the resultant NMR linewidth depends both on the exchange lifetimes and also on the correlation times for rotation at each site; the NMR linewidth may thus be used to obtain information about any of these quantities. The results bear directly on the use of quadrupolar nuclei in the presence of chemical exchange of nuclei between suitable sites to obtain motional information about macromolecules in dilute solution. In particular, the proposed correlation function may account for anaomalously small calculated rotational-correlation times for large molecules previously obtained from such studies. A precise criterion for applicability of McConnell-modified Bloch equations is proposed. Other applications of the correlation function derived in this paper are discussed.