Parameter estimation of saturated magnetic resonance spectra

We have shown in previous work that magnetic resonance spectra may be profitably analyzed by using concepts derived from information geometry. The systems that have been studied so far have been restricted to the linear response regime where constraints, in the form of sum rules for example, induced a geometry on the line shape function treated as a probability density function (PDF). Although careful analysis of the linear response line shape is a useful tool for quantifying important details of molecular structure and dynamics, complementary information is available from the non-linear response line shape which is often sensitive to processes on longer time scales than the transient coherences probed in the linear regime. The non-linear response of a system satisfies constraints that do not allow for a direct interpretation in terms of a PDF, as the non-linear response may have absorptive and emissive character and thus cannot be constrained to be non-negative in all circumstances. Nevertheless, entropic methods and concepts from information geometry may be used to compare simulated and measured non-linear spectra in order to infer appropriate model parameter values. We demonstrate how this can be achieved for a model system described by the Zeeman interaction of a magnetic moiety with an applied magnetic field modulated by stochastic processes such as rotational diffusion. For the case of Electron Paramagnetic Resonance (EPR), we will show how the methods presented here may be extended to include hyperfine interactions which arise due to couplings of the electron magnetic moment with nearby nuclei.