Computation of DNP coupling factors of a nitroxide radical in toluene: seamless combination of MD simulations and analytical calculations

Dynamic nuclear polarization (DNP) employs paramagnetic species to increase the NMR signal of nuclear spins. In liquids, the efficiency of the effect depends on the strength of the interaction between the electron and nuclear spins and the time scales on which this interaction is modulated by the physical motion of the spin-bearing molecules. An approach to quantitatively predict the contribution of molecular motions to the DNP enhancement using molecular dynamics (MD) simulations is developed and illustrated for the nitroxide radical TEMPOL in liquid toluene. A multi-resolution strategy that combines explicit treatment of the solvent at short distances from the free radical with implicit description at large intermolecular distances is adopted. Novel analytical expressions are obtained to correct for the finite spatial extent of the MD simulations. The atomistic and analytical descriptions are sewn seamlessly together by ensuring that for molecular trajectories that start in the near (explicit) region and end in the distant (implicit) region the analytical dipolar spectral densities reproduce the MD estimates. The spectral densities obtained from the developed approach are used to calculate DNP coupling factors separately for the ring and methyl protons of toluene. The agreement with previously reported experimental DNP data at a magnetic field of 3.4 T is noteworthy and encouraging. Maximum obtainable DNP enhancements at other magnetic fields are predicted.