An advanced approach to the evaluation of the spin-rotational term for a nitronyl nitroxide in fluid solution

In this work we focus on the spin-rotational contribution to transverse relaxation rate 1/T_2 for a nitronyl nitroxide radical (PTIO) in fluid solution of toluene. We recorded the X-band continuous-wave electron paramagnetic resonance spectra of the radical in a wide temperature range and compared them with the calculated spectra. The calculation was afforded in two steps: first, we calculated the spectral profiles in the same range of temperatures taking into account the hyperfine interaction with the two ^14 N nuclei, by integration of the stochastic Liouville equation with the E-SpiReS package in the presence of the tumbling motion of the molecule, which modulates the hyperfine and the g-tensors. In the second step, we included the proton hyperfine structure by convoluting the spectrum with the pattern due to the 17 PTIO-coupled protons. A further Lorentzian broadening was added by a best fitting procedure to reproduce the experimental linewidths. The additional broadening is associated with a relaxation rate, Wγ, which varies linearly on k_B T/η; this trend is expected for the spin-rotational relaxation term modelled by the well-known Atkins–Kivelson expression. We found a discrepancy between thetwo parameters associated with the radii of the radical, obtained either from the rotational diffusion tensor in the framework of the Debye–Stokes–Einstein model or from the spin-rotational contribution. We discuss this issue in relation to the intrinsic approximations of the spin-rotational model and, in particular, the isotropic Brownian rotation.