Electron-Coupled Proton Spin-Spin Interaction in Saturated Hydrocarbon Molecule. I

Abstract

Electron coupled proton spin-spin interactions in saturated hydrocarbon molecules. J HH' , are investigated theoretically. The general formula for J HH' is derived by double perturbation method, in which \(\mathfrak{H}_{F}\) (the Fermi interactions between electrons and proton-spins) and \(\mathfrak{H}_{1}\) (correlations between electrons) are taken as perturbations. The calculation is performed up to first order in \(\mathfrak{H}_{1}\). It is shown that the zeroth order term in \(\mathfrak{H}_{1}\) becomes nearly equal to zero under the approximation, in which energy differences between the ground state and the excited states are replaced by a suitable mean. Therefore, J HH' calculated by the molecular orbital method without configuration interactions is a part of J HH' , which is different from the one calculated by the valence bond method with the above approximation. The order of magnitudes of the zeroth and the first order term in \(\mathfrak{H}_{1}\) are compared in the case of methane molecule.