An analytical perturbation extension of the Pople-Santry theory of the Fermi contact term in reduced spin-coupling constants 1K(E-L) has been developed for the substituted compounds ELm-kL'k (E is a transition metal, M, or main-group element, A) where the ligands L have a valence ns orbital. The difference in ligand σ-orbital energies, δα'=α(L')-α(L), was taken as a perturbation. It was found that changes in 1K(E-L) under substitution should typically follow changes in the s contributions to the E-L bond-overlap population, the latter having been determined earlier for the various polyhedra ELm-kL'k. The obtained results agree with experiment and permit the known regularities of 1K(E-L) to be explained and a number of predictions to be made. © 1979, American Chemical Society. All rights reserved.