Theory of the proton-proton spin-spin coupling surface of the methane molecule

The form of the proton-proton spin-spin coupling surface of the methane molecule is studied. The four first-order and seventeen second-order independent symmetry-coordinate coefficients required to determine the six distinct coupling constants for small but otherwise arbitrary displacements from equilibrium are identified. The coefficients needed to determine the dependence of the coupling on any selected combination of (small) bond length and bond angle changes are given. The results will be of help in understanding the effects of temperature and isotopic substitution on the coupling and in simplifying ab initio calculations of the surface for methane and for 2J(Y, Y) in other XY4 compounds of Td symmetry.