Quadrupole-Central-Transition ²³Na, ³⁹K, ⁸⁷Rb NMR Studies of Alkali Metal Ions under Different Molecular Tumbling Conditions: A Simple Model to Treat Chemical Exchange Involving Quadrupolar Nuclei

We report a new NMR method for treating two-site chemical exchange involving half-integer quadrupolar nuclei in a solution. The new method was experimentally verified with extensive ²³Na (<i>I</i> = 3/2), ³⁹K (<i>I</i> = 3/2), and ⁸⁷Rb (<i>I</i> = 3/2) NMR results from alkali metal ions (Na⁺, K⁺, and Rb⁺) in a solution over a wide range of molecular tumbling conditions. In the fast-motion limit, all allowed single-quantum NMR transitions for a particular quadrupolar nucleus are degenerate giving rise to one Lorentzian signal. In the slow-motion regime, although the NMR signal from quadrupolar nuclei should in principle exhibit a multi-Lorentzian line shape, only the quadrupole central transition (QCT) is often detectable in practice. In all the cases studied in this work, we found that alkali metal ions undergo fast exchange between free and bound states. Using the new theoretical method, we were able to interpret the experimental transverse relaxation data (i.e., line widths) obtained for ²³Na, ³⁹K, and ⁸⁷Rb NMR signals including QCT signals over a large temperature range and extract information about ion-binding dynamics in different chemical environments. This work fills a gap in the literature where a unified approach for treating NMR transverse relaxation data for quadrupolar nuclei over the entire range of motion has been lacking. Our results suggest that the new approach is applicable in the study of alkali metal ion binding to biological macromolecules.