Density functional theory calculations confirmed the bond-order-length-strength (BOLS) predictions regarding the local bond length, bond energy and electron binding energy (BE) of Na atomic clusters and shell-resolved monolayer skins. A reproduction of the photoelectron spectroscopic measurements leads to the following observations:(i) local lattice maximal strain of 14.51%, (ii) BE density of 71.92%, (iii) atomic cohesive energy of 62.31% and (iv) the 2p core-level shifts by 2.749 eV for under-coordinated Na atoms.This information helps in understanding the unusual behaviour of the under-coordinated Na solid skins and atomic clusters.