Modeling of motional EPR spectra using hindered Brownian rotational diffusion and the stochastic Liouville equation

Electron paramagnetic resonance (EPR) spectra of molecular spin centers undergoing reorientational motion are commonly simulated using the stochastic Liouville equation (SLE) with a rigid-body hindered Brownian diffusion model. Current SLE theory applies to specific spin systems such as nitroxides and to high-symmetry orientational potentials. In this work, we extend the SLE theory to arbitrary spin systems with any number of spins and any type of spin Hamiltonian interaction term, as well as to arbitrarily complex orientational potentials. We also examine the limited accuracy of the frequency-to-field conversion used to obtain field-swept EPR spectra and present a more accurate approach. The extensions allow for the simulation of EPR spectra of all types of spin labels (nitroxides, copper²⁺, and gadolinium³⁺) attached to proteins in low-symmetry environments.