In this paper we use the energy, the electronic chemical potential, and the molecular hardness together with a similarity index and a thermodynamic index to rationalize the behavior of various intramolecular rearrangement reactions in terms of the Hammond postulate (HP) and the principle of maximum hardness (PMH). The following results have been obtained: (a) in general, Hammond and anti-Hammond reactions satisfy the PMH in the sense that they present an opposite behavior for the energy and hardness profile along the reaction coordinate; (b) in Hammond reactions the hardest species among reactants and products corresponds to the most stable one; and finally, (c) in anti-Hammond reactions the less stable species among reactants and products is the hardest one.