Double perturbation calculations of spin-spin coupling constants using localized orbitals

The Fermi contact contribution to N.M.R. spin-spin coupling constants has been calculated to the fourth order by a double perturbation development starting from a fully localized determinant, according to the assumptions of the PCILO-CNDO method. The use of diagrammatic techniques greatly simplifies the evaluation. There is a cancellation of certain types of diagram. The coupling constant between bonded atoms appears in the second order through a contribution which only depends on the appropriate bond orbital. The next orders involve the other bonds and correlation effects. For nonbonded atoms, the first contribution appears in the fourth order and results from direct delocalization through space, involving only the bonds on the two atoms.

An analytical and numerical comparison with previous calculations is performed for H-H and C-H coupling constants on small organic molecules. The relative importance of the various processes is discussed for the J _HH vicinal coupling constants of ethylene.