Vicinal proton-proton coupling constants

Abstract

An equation for the prediction of the vicinal coupling constants ³ J _HH in substituted HCCH fragments is formulated as a truncated Fourier series in the torsion angle φ between the coupling hydrogens with coefficients expanded as a Taylor series in a substituent parameter λ. The different terms in this series have definite meanings: (1) the independent terms k _n give the angular dependence of ³ J _HH in ethane, (2) the linear terms k _niλ _i represent the effects upon ³ J _HH of the individual substituents, and (3) the cross terms k _nij λ _i λ _j account for the effects of interactions between pairs of substituents. This interpretation is based on a model for the effect of the substituents that explains the Fourier coefficients as a sum of contributions from ethane, from individual substituents and from interactions between pairs of substituents. The model reduces to the equation when several simplifying assumptions are made. Otherwise, some refinements can be introduced in the equation. The invariances of the ³ J _HH couplings under reflections and rotations of the nuclear coordinates enabled us to derive some relations between the ³ J _HH couplings with different orientations of the substituents with respect to the coupled protons. Equivalent relations may also be established between the coefficients k _ni or k _nij with the consequent reduction in the number of terms to be included in the equations.