Consistency between density func-tional theory calculations and X-ray photoelectron spectroscopy measure-ments 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.