undercoordination, the X:R-Y systems show high chemical reactivity and catalytic capability because of the local strong electric field of the enhanced dipoles that gather electrons from the H + to O 2-of the surface H2O molecules. The surface dipoles make the "on-water catalyst" that accelerates substantially reaction rate and the hydro-voltaicity for electricity harvesting. On the second occasion, FIG. , a dipole M P replaces the X: to form the M P :R + -Y -bond (one can omit the valence sign subsequently for convenience). Atomic or molecular undercoordination results in bond contraction and nonbonding electron polarization , making the atom at the topological apex an protruding dipole pointing outwardly . The M P can point outward or inward of the solid, which determines the subsequent R-Y dipolar orientation. Furthermore, one can replace the M P with an atomic vacancy V 0 as the vacant edge atoms show stronger resultant effect of polarization with apparent protrusions and the Dirac-Fermon resonant of energy states associated with the core band entrapment and nonbonding polarization for graphite instance .