Sensitivity Analysis of Magnetic Resonance Spectra from Unoriented Samples

In a recent paper, Hyde et al. (1) explored the sensitivity of the EPR spectra of square-planar Cu*+ complexes to variations of the spin-Hamiltonian parameters by simulation of spectra both at the rigid limit and under a range of rotational correlation times. The purpose of this sensitivity analysis was to establish criteria for the optimum determination of the various parameters by simulation. The paper raised various questions, the central of which regards the conventional strategy of minimizing the sum of squares (or absolute value) of the deviation between the experimental and simulated spectra throughout the entire anisotropic lineshape. This difficulty arose because of the, at first surprising, result that the same region of the spectrum displayed maximum sensitivity to the parameters corresponding both to the parallel and to the perpendicular orientation of the magnetic field with respect to the principal axis. A somewhat analogous problem to that considered in Ref. ( 1) is the analysis of the sensitivity of STEPR spectra to anisotropic motion. This was addressed previously by determining those regions of the spectrum that displayed optimum discrimination between axial and off-axial motion (2). In the present paper the same approach is employed to sensitivity analysis in conventional EPR. A simple analytical axial model is considered, which contains the essential features of anisotropic powder patterns, and this is used to define the spectral regions with optimum discrimination between the different spin-Hamiltonian parameters. The general spectral intensity distribution for a sample with an orientational distribution, y( Q), is