Polycrystalline ENDOR patterns from centers with axial EPR spectra. General formulas and simple analytic expressions for deriving geometric information from dipolar couplings

Abstract

We present a formulation for rapid simulations of polycrystalline ENDOR patterns for systems whose EPR spectra exhibit axial-resolved magnetic interactions (g tensor and “central”-nucleus hyperfine couplings). The ENDOR response of interest is from a nucleus with nonaxial hyperfine couplings and unresolved splittings. The equations simplify when the hyperfine tensor of the nucleus being observed in ENDOR has axial symmetry in its principal axis frame, as would occur for an I = 1 2 nucleus ( 1H or 19F) interacting by a through-space, electron-nuclear dipolar interaction. In such cases the field dependence of the ENDOR frequencies can be described by simple analytic functions, well suited to least-squares determination of metrical parameters that define the nuclear position. Sample calculations are given for a proton interacting with a nitroxide radical.