Intramolecular surfaces for vicinal proton-proton coupling constants 3JHH

Equations for the intramolecular surfaces of the (3)J(HH) coupling constants in ethane, ethylene, and acetylene are formulated, and the corresponding coefficients are estimated from calculations at the DFT/B3LYP level. The chosen variables are changes in bond lengths, in the torsion angle phi between the coupled protons H-a and H-b, in bond angles, and in dihedral angles. The (3)J(HH) surface of ethane is formulated as an extended Karplus equation with the coefficients of a truncated Fourier series on the torsion angle phi expanded as second-order Taylor series in the chosen variables taking into account the invariance of (3)J(HH) under reflections and rotations of nuclear coordinates. Partial vibrational contributions from linear and square terms corresponding to changes in the geometry of the H-a-C-a-C-b-H-b fragment are important while those from cross terms are small with a few exceptions. The (3)J(HH) surface of ethane is useful to predict contributions to (3)J(HH) from changes in local geometry of derivatives but vibrational contributions are predicted less satisfactorily. The predicted values at the B3LYP/BS2 level of the (3)J(HH) couplings (vibrational contributions at 300 K) from equilibrium geometries are 9.79 (-0.17) for acetylene, and 17.08 (1.93) and 10.73(0.93) for the trans and cis couplings of ethylene.