Ab initio SCF/6-31G** calculations are performed on the 1,Zhydrogen shift reaction in some HAB molecules and HAB+ ions (AB = CN, SiN, BO, A10, BS, AlS, BeF, CO, SiO, CS, N2) in order to test the validity of the maximum hardness principle. The hardness is found to be a good indicator of the more stable isomer in most cases, as is the chemical potential. Profiles of these quantities, as a function of the reaction coordinate, do not exhibit extrema at the transition state, but other extrema are noted at unexpected points. While the total energy does not exhibit the same behavior as the hardness or the chemical potential, the individual electronic and nuclear repulsion energies are in close parallel with them.