Hyperconjugation: The Electronic Mechanism That May Underlie the Karplus Curve of Vicinal NMR Indirect Spin Couplings

Abstract

The electronic origin of the Karplus-type behavior of vicinal NMR J couplings for H 3 X-C 2 H 4 -XH 3 , X = C, Sn model compound is analyzed within the framework of the polarization propagator formalism. It is shown that its whole pattern can be understood by generalizing previous hyperconjugative mechanisms, in such a way that the hyperconjugative delocalization effect from an excitation σ → σ* should be replaced by two simultaneous excitations according to a second-order electronic property. All and the main coupling pathway which involve, at the random phase level of approach, RPA, the two pairs of localized MOs closest to the coupled nuclei follows a Karplus-type dependence with dihedral X-C-C-X angle, θ. The specific two-electron integrals which include correlation at RPA level of approach are the main factors which define the total behavior of J. The Karplus-type dependence is also found at HF level for individual coupling pathways though that is not observed for the total J; the so-called nonlocal perturbators together with the inverse of the differences of energies define, at this level of approach, the functional dependence with θ.