Abstract: Consistency between density functional theory calculations and X-ray photoelectron spectroscopy measurements confirms our predications on the undercoordination-induced local bond relaxation and core level shift of alkali metal, which determine the surface, size and thermal properties of materials. Zone-resolved photoelectron spectroscopy analysis method and bond order-length-strength theory can be utilized to quantify the physical parameters regarding bonding identities and electronic property of metal surfaces, which allows for the study of the core-electron binding-energy shifts in alkali metals. By employing these methods and first principle calculation in this work, we can obtain the information of bond and atomic cohesive energy of under-coordinated atoms at the alkali metal surface. In addition, the effect of size and temperature towards the binding-energy in the surface region can be seen from the view point of Hamiltonian perturbation by atomic relaxation with atomic bonding.