Quadrupole-Central-Transition <sup>23</sup>Na, <sup>39</sup>K, <sup>87</sup>Rb NMR Studies of Alkali\nMetal Ions under\nDifferent Molecular Tumbling Conditions: A Simple Model to Treat Chemical\nExchange Involving

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