Origin of the pH Dependency of EPR Parameters: The Case of a Protonatable Nitroxide in Aqueous Solution

Protonatable nitroxides are electron paramagnetic resonance (EPR) molecular probes employed for pH measurements in bulk aqueous media. The change in the protonation state of the molecule induces a measurable change in the <i>g</i>- and hyperfine (<i>A</i>) parameters used as pH indicators. The quantitative understanding of the origin of the change of the EPR parameters in terms of electronic structure and different solvation patterns is still lacking. Here, we delve into the origins of the changes in the <i>g</i>- and hyperfine (<i>A</i>) parameters of ¹⁴N upon protonation of the heterocyclic nitrogen of the pH-sensitive nitroxide probe HMI (2,2,3,4,5,5-hexamethylimidazolidin-1-oxyl, C₉H₁₉N₂O) by means of combined experimental and theoretical techniques that have been developed and extensively validated in previous works. To establish a molecular-level understanding of the dependency of EPR parameters on the pH of the medium, we considered two limiting cases of deprotonated (pH ≫ p<i>K</i>_a) and protonated (pH ≪ p<i>K</i>_a) states of HMI. We found that, upon protonation of the heterocyclic nitrogen, the change in the electronic structure dominates the pH dependency of isotropic <i>g</i> and <i>A</i> values. Supporting this prominent role of electronic structure modulation, the average shift of EPR observables between the corresponding hydrogen-bonding states of the protonated and unprotonated forms remains constant. Furthermore, the results establish that the hydrogen bonding network structures around the nucleus of interest only marginally change upon protonation, although the populations of corresponding states with given H-bond numbers strongly do. This feature entails an additional, smaller contribution to the relative pH dependency of <i>g</i>^iso and <i>A</i>^iso values over electronic structure modulation upon protonation in a given H-bond state. The findings of this study pave the way to investigating HMI-based labels in peptides and other pH-sensitive EPR probes in protic polar solvents.