Electron Coupling of Nuclear Spins. IV. Temperature Dependence in Substituted Ethanes

Abstract

The proton-proton coupling constant, AHH′, in H–C–C′–H′ groups is known to depend upon the dihedral angle, φ. Previous valence-bond calculations by Karplus have given the result that AHH′≅A0cos2φ+B.This relation is used to estimate the effects upon the average coupling constant of torsional vibrations and reorientations about the C–C′ bond. For substituted ethanes, it is found that torsional vibrations produce a modest temperature dependence, of opposite sign for the trans and gauche coupling. However, for molecules in which the potential function, V(φ), has threefold symmetry, rotational averaging leads to a cancellation of the vibrational effects, giving a temperature independent value, 〈AHH′〉, for the average coupling. This prediction has been verified in experiments on ethyl nitrate for which 〈AHH′〉 was found to have a constant value of 6.92 cps over a 100° temperature range. When there is an energy difference, ΔE, between trans and gauche forms, ΔE determines the sign and magnitude of the temperature dependence of 〈AHH′〉; however, corrections for the vibrational effects appear desirable if accurate values of ΔE are to be obtained from such experiments. The temperature dependence of 〈AHH′〉 could not be calculated analytically for any but the simplest potential functions and simplest approximations to the torsional motions. However, it was found that the detailed form of V(φ) has but a slight effect on the results. 〈AHH′〉 is, of course, more sensitive to the functional form of A(φ).