A quantitative comparison is made of the covalent bond indices recently introduced by Cioslowski and Mixon and the sharing indices introduced by Fulton. First, an inequality between the two sets of indices is proven. Then a numerical comparison of the indices for a number of molecules is made at the HF/6-31G* and HF/6-31++G** levels of approximation. The inequality, valid for single determinant wavefunctions, is that the sum of twice the values of the interbasin sharing indices is always less than or equal to the sum of the interbasin covalent bond indices. This has the implication that, for a two basin molecule, twice the sharing index has the same value as the covalent bond index. For most of the multibasin molecules considered, the two sets of indices are found to be remarkably close in value. For example, twice the sharing index for a carbon-hydrogen bond runs from 2 to 4% less than the corresponding covalent bond index, with a systematic variation in proceeding from a hydrogen attached to a saturated carbon to a hydrogen attached to a triply bonded carbon. The differences in the sets of indices are consistent across the two levels of calculation. Unlike most molecules, the indices for benzene show qualitative differences. The covalent bond indices break the symmetry of the molecule in such fashion as to correspond to a Kekule structure while the sharing indices retain the symmetry of the many electron wavefunction.
