Visualization of Electron Paramagnetic Resonance Hyperfine Structure Coupling Pathways.

The close relation between the EPR hyperfine coupling constant and NMR indirect spin spin coupling constant is well-known. For example, the Karplus-type dependence of hyperfine constants on the dihedral angle, originally proposed for NMR spin spin coupling, is widely used in pNMR studies. In the present work we propose a new tool for visualization of hyperfine coupling pathways based on our experience with visualization of NMR indirect spin spin couplings. The plotted 3D-function is the difference between the total electron densities when the magnetic moment of the nucleus of interest changes its sign and as such is an observable from the physical point of view. It has been shown that it is proportional to the linear response of the spin density to, the nuclear spin (i.e., magnetic moment). In contrast to the widely used visualization of spin density, our new approach depicts only the part of the electron cloud of a molecule that is affected by the interaction of the unpaired electron(s) with the desired nuclear magnetic moment. Because visualization of NMR spin spin couplings and hyperfine interaction is based on the same ideas and done using similar techniques, it allows a direct comparison of the corresponding pathways for the two phenomena so as to analyze their resemblance and/or dissimilarity.