On the dependence with bond lengths of the observed energies of NEXAFS resonances of diatomic molecules

Abstract

An analytical theory is developed for the position of the resonances in near-edge X-ray absorption fine structure (NEXAFS) which yields extremely good agreement with experiment and allows a universal curve to be calculated for the resonance energies. The analytical calculations indicates that, if scattering events are taken as purely atomic, the product kϱ = constant , where k is the wavevector of the outgoing electron at resonance and ϱ the internuclear distance. This is in accord with a rule previously proposed by Natoli. It is found, however, that both the constant and the muffin-tin zero energy in the NEXAFS region depend on internuclear distance. Their variation as a function of bond length is determined and reveals a more appropriate form of the dependence of sigma resonance energy Δ (measured relative to the ionization potential) with bond length should be: Δ = A + B ϱ + C ϱ 2 . This equation shows good agreement with the experimentally observed variation in resonance position with bond lengths for series of molecules with constant values of ( Z 1 + Z 2) where Z 1 and Z 2 are the atomic numbers of the scattering nuclei. In fact, this function is rather linear over the bond length range commonly encountered in organic molecules. Finally, the observation that empirical rules for the variation in resonance energy versus geometry are obeyed for molecules with constant ( Z 1 + Z 2) is also rationalized.