Quantifying methyl tunneling induced (de)coherence of nitroxides in glassy ortho-terphenyl at low temperatures

The low-temperature Hahn echo decay signal of the pyrroline-based nitroxide H-mNOHex in ortho-terphenyl (OTP) shows two contributions on distinct time scales. Tunneling of the nitroxide's methyl groups cause electron spin echo envelope modulation (ESEEM) on a faster time scale compared to the slower matrix-induced decoherence contribution arising from nuclear pair ESEEM. Here we introduce the methyl quantum rotor (MQR) model that describes tunneling ESEEM originating from multiple methyl rotors coupled to the same electron spin. By formulating the MQR model based on a rotation barrier distribution P(V₃), we account for the different local environments in a glassy matrix. Using this framework, we determine the methyl groups' rotation barrier distribution from experimental Hahn echo decay/two-pulse ESEEM data by a non-linear fitting approach. The inferred distributions are in good agreement with density functional theory (DFT) calculations of the methyl groups' rotation barriers in the low-temperature regime where tunneling constitutes the dominant methyl proton exchange process. In addition to comparing our results with previous decoherence studies performed on the same spin system, we experimentally confirm the characteristic properties of methyl tunneling by demonstrating that P(V₃) is magnetic field independent and predominantly temperature independent between 10 and 50 K. This confirms the assignment of the fast Hahn echo decay contribution to methyl tunneling, showcasing how pulsed EPR sequences can coherently probe this quantum phenomenon for commonly employed nitroxide spin-labels.