A combination of the tight-binding theory, bond order-length-strength correlation and nonbonding-electron polarization notion, photoelectron spectrometrics, and density functional theory calculations has enabled us to examine the effect of atomic undercoordination on the local bond-electron-energy relaxation pertaining to Mo(100, 110) skins and atomic clusters. This exercise has led to the following quantitative information: (i) the atomic Mo 3d5/2 energy level located at 224.862 ± 0.004 eV shifts 2.707 eV deeper upon bulk formation; (ii) skin local bond is subject to 9.80% contraction; (iii) 5.952 e charge transfers from the inner to the outermost skin layer. Furthermore, the E4s level shifts from 61.229 eV for the Mo59 to 61.620 eV for the Mo15 cluster and the valence band undergoes a 1.057 eV upward shift. The globally positive core-level shift arises from the local quantum entrapment due to bond contraction and strength gain. The densely entrapped core electrons polarize the valence electrons and hence raise the valence band energy.