Fast electron paramagnetic resonance magic angle spinning simulations using analytical powder averaging techniques.

Simulations describing the spin physics underpinning nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) spectroscopy play an important role in the design of new experiments. When experiments are performed in the solid state, samples are commonly composed of powders or glasses, with molecules oriented at a large number of angles with respect to the laboratory frame. These powder angles must be represented in simulations to account for anisotropic interactions. Numerical techniques are typically used to accurately compute such powder averages. A large number of Euler angles are usually required, leading to lengthy simulation times. This is particularly true in broad spectra, such as those observed in EPR. The combination of the traditionally separate techniques of EPR and magic angle spinning (MAS) NMR could play an important role in future electron detected experiments, combined with dynamic nuclear polarization, which will allow for exceptional detection sensitivity of NMR spin coherences. Here, we present a method of reducing the required number of Euler angles in magnetic resonance simulations by analytically performing the powder average over one of the Euler angles in the static and MAS cases for the TEMPO nitroxide radical in a 7 T field. In the static case, this leads to a 97.5% reduction in simulation time over the fully numerical case and reproduces the expected spinning sideband manifold when simulated with a MAS frequency of 150 kHz. This technique is applicable to more traditional NMR experiments as well, such as those involving quadrupolar nuclei or multiple dimensions.