Atomic undercoordination refers to atoms associated with grain boundaries, homogeneous adatoms, point defects, solid or liquid skins, terrace edges, and nanostructures of various shapes and dimensionalities. Atomic heterocoordination means those associated with alloys, compounds, chemisorbed skins, dopants, impurities, and interfaces. One can create a new substance with desired functionalities by breaking the old bonds and forming new bonds between atoms. Harnessing the known properties of a substance by relaxing the bond and the associated energetics and dynamics of electrons in localization, densification, polarization, and transportation becomes therefore increasingly important.8 For instance, materials at sites surrounding irregularly coordinated atoms perform differently from themselves in the bulk interior. Although they are traditionally unwanted, such irregularly coordinated atoms are of key importance to the advancement of condensed matter physics, solid-state chemistry, materials sciences, and device technologies, in particular, at the nanometer scale.