Discriminating crystal binding from the atomic trapping of a core electron at energy levels shifted by surface relaxation or nanosolid formation

On the basis of the atomic-coordination-atomic-radius correlation (Feibelman, P. J. Phys. Rev. B 1996, 53, 13740. Goldschmidt, V. M. Ber. Dtsch. Chem. Ges. 1927, 60, 1270.) and its perturbation of the Hamiltonian of an extended solid, we have developed an effective yet straightforward method to determine the core-level energies of an isolated atom and the crystal-binding intensities of the core electrons at energy levels shifted by bulk formation, surface relaxation, or nanosolid formation. The developed method not only allows the predicted size dependence of core-level shift to match observations but also enables conventional X-ray photoelectron spectroscopy (XPS) to provide comprehensive information about the behavior of electrons in the deeper shells of an isolated atom and the influence of crystal formation.