Theoretical terahertz spectroscopy of free radical solutes in solution: an EPR spin probe in water

Free radical species are used as spin labels in electron paramagnetic resonance (EPR) spectroscopy of biomolecular systems in water, for instance in the frame of Overhauser dynamic nuclear polarization (ODNP) relaxometry to probe the local hydration water dynamics close to protein surfaces in aqueous environments. Widely used in this context are nitroxide spin probes such as TEMPO, PROXYL or MTSL derivatives. Here, we study the THz spectroscopy of HMI (2,2,3,4,5,5-HexaMethylImidazolidin-1-oxyl) in water at ambient conditions which has been recently investigated as to how its EPR properties depend on its solvation pattern in water. To enable theoretical THz spectroscopy of molecular radicals in solution, we have generalized well-established methodologies for THz spectral decomposition of closed-shell systems, namely the supermolecular solvation complex (SSC) and cross-correlation analysis (CCA) techniques, to open-shell polyatomic solute species in water. Based on this methodological advance, we have decomposed and assigned the THz response of HMI including its solvation shell by employing the generalized SSC and CCA methods to cope with the open-shell character of this free radical solute, in particular its unpaired electron localized at the nitroxy group. We reveal that the main modulations of the far-IR spectrum of HMI are dominated by the low-frequency intramolecular modes of the spin probe molecule itself while the solvation of its two hydrogen bonding sites contribute much less intensely in this spectral window. Finally, we have computed THz spectra of HMI with its local solvation water with an aim to provide a theoretical analogue of experimental THz difference spectroscopy. Beyond the specific case, our decomposition methodology that now is able to include open shells can be applied in future work to analyze the low-frequency vibrational response of the solvation shell of other free radicals in solution.