The chemistry and physics of under-coordination at a surface, which determines the process of catalytic reactions and growth nucleation, is indeed fascinating. However, extracting quantitative information regarding the coordination-resolved surface relaxation, binding energy, and the energetic behavior of electrons localized in the surface skin from photoelectron emission has long been a great challenge, although the surface-induced core level shifts of materials have been intensively investigated. Here we show that a combination of the theories of tight binding and bond order-length-strength (BOLS) correlation [C. Q. Sun, Prog. Solid State Chem., 2007, 35, 1-159], and X-ray photoelectron spectroscopy (XPS) has enabled us to derive quantitative information, by analyzing the Be 1s energy shift of Be(0001), (1010), and (1120) surfaces, for demonstration, regarding: (i) the 1s energy level of an isolated Be atom (106.416 ± 0.004 eV) and its bulk shift (4.694 eV); (ii) the layer- and orientation-resolved effective atomic coordination (3.5, 3.1, 2.98 for the first layer of the three respective orientations), local bond strain (up to 19%), charge density (133%), quantum trap depth (110%), binding energy density (230%), and atomic cohesive energy (70%) of Be surface skins up to four atomic layers in depth. It is affirmed that the shorter and stronger bonds between under-coordinated atoms perturb the Hamiltonian and hence the fascinating localization and densification of surface electrons. The developed approach can be applied to other low-dimensional systems containing a high fraction of under-coordinated atoms such as adatoms, atomic defects, terrace edges, and nanostructures to gain quantitative information and deeper insight into their properties and processes due to the effect of coordination imperfection.