AbstractVicinal proton‐proton coupling constants depend on a variety of stereochemical parameters such as bond angle, bond length, substituent electronegativity and orientation, and — most importantly — on the torsion angle between the coupling protons. The sensitivity of vicinal proton‐proton coupling constants3JHH′, to variations of dihedral angle ϕwas first rationalized in valence bond terms by Karplus, who showed that the coupling constants could be approximately fitted to a cos2ϕ function. The Karplus equation3JHH′= Acos2ϕ + Bcosϕ + C (or variants thereof) has been a major tool of the structural chemist for 35 years. Karplus started with the Ramsey formula for Fermi contact contribution, expressed by ground‐state wave functions and a mean excitation energy. More sophisticated molecular orbital (MO) treatments have afforded analogous expressions that may be used to predict trends correctly but are rarely useful for accurate estimations of dihedral angles. Numerous attempts have been made to account for the effect of substituents, bond angles, and lengths — either empirically by the choice ofA,B, andC(with different values for each type of compound) or semiempirically, starting with theoretically more sophisticated expressions with statistically adjustable parameters. Theoretical and empirical approaches are re