Theory of carbon-13 proton spin-spin coupling and the proton shielding surfaces of the methane molecule

The form of the carbon-13 proton spin-spin coupling surface of the methane molecule is investigated. The three first-order and twelve second-order independent symmetry coordinate coefficients required to determine the four distinct coupling constants for small but otherwise arbitary displacements from equilibrium are identified. Valence coordinate coefficients for the surface are also determined. The results will be of help in understanding the effects of temperature and of primary and secondary isotopic substitution on the observed coupling and also in simplifying ab initio calculations of the surface for methane and for 1J(X, Y) in other XY4 compounds of Td symmetry. The results are also applicable to the proton shielding surface of methane and the Y nuclear shielding surfaces in other XY4 compounds of Td symmetry.