Grochala, Albrecht, and Hoffmann have recently observed that, for many organic and inorganic molecules, the bond lengths in the cation (R+), neutral system (R-gs), first tripler excited state (R-es), and anion (R-) approximately satisfy R+ + R- - R-gs - R-es approximate to 0. This paper shows how the Fukui function, a concept from the density functional theory of chemical reactivity, can be used to rationalize the Grochala-Albrecht-Hoffmann rule. The treatment also suggests which types of chemical systems will be best described by the Grochala-Albrecht-Hoffmann rule.