An equation for the prediction of the vicinal coupling constants aJHn in substituted HCCH fragments is formulated as a truncated Fourier series in the torsion angle q9 between the coupling hydrogens with coefficients expanded as a Taylor series in a substituent parameter 2. The different terms in this series have definite meanings: (1) the independent terms k. give the angular dependence of 3JHH in ethane, (2) the linear terms kni2i represent the effects upon 3Jan of the individual substituents, and (3) the cross terms k.ij 2i 2~ 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 aJnn couplings under reflections and rotations of the nuclear coordinates enabled us to derive some relations between the 3Jnn couplings with different orientations of the substituents with respect to the coupled protons. Equivalent relations may also be established between the coefficients kni or k,i j with the consequent reduction in the number of terms to be included in the equations.

The dependence of spin–spin nuclear magnetic resonance (NMR) coupling constants on the basis set and electron correlation has been investigated in methane using Hartree–Fock and multiconfigurational self-consistent field wave functions (HF-SCF and MCSCF). The effect of the size, contraction, and tight s functions of the basis sets is analyzed. Some suggestions about the contraction scheme are indicated. MCSCF wave functions with different numbers of active orbitals and different numbers of excited electrons were used. An approximation to determine spin–spin coupling constants at a high level of electron correlation from three calculations with a smaller level of correlation and reduced computational cost is investigated. The best calculated JCH1 and JHH2 couplings are 120.63 and −13.23 Hz, respectively, which are 0.24 and 1.24 Hz smaller than those experimentally obtained for the equilibrium geometry. The remaining error in these coupling constants can be attributed mainly to correlation and not to basis set effects.

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