Core-level binding-energy shifts for the metallic elements

A general treatment of core-level binding-energy shifts in metals relative to the free atom is introduced and applied to all elemental metals in the Periodic Table. The crucial ingredients of the theoretical description are (a) the assumption of a fully screened final state in the metallic case and (b) the ($Z+1$) approximation for the screening valence charge distribution around the core-ionized site. This core-ionized site is, furthermore, treated as an impurity in an otherwise perfect metal. The combination of the complete screening picture and the ($Z+1$) approximation makes it possible to introduce a Born-Haber cycle which connects the initial state with the final state of the core-ionization process. From this cycle it becomes evident that the main contributions to the core-level shift are the cohesive energy difference between the ($Z+1$) and $Z$ metal and an appropriate ionization energy of the ($Z+1$) atom (usually the first ionization potential). The appearance of the ionization potential in the shift originates from the assumption of a charge-neutral final state, while the contribution from the cohesive energies essentially describes the change of bonding properties between the initial and final state of the site. The calculated shifts show very good agreement with available experimental values (at present, for 19 elements). For the other elements we have made an effort to combine experimental ionization potentials with theoretical calculations in order to obtain accurate estimates of some of the atomic-core-level binding energies. Such energies together with measured metallic binding energies give "pseudoexperimental" shifts for many elements. Our calculated core-level shifts agree exceedingly well also with these data. For some of the transition elements the core-level shift shows a deviating behavior in comparison with that of neighboring elements. This is shown to be due to a difference in the atomic ground-state configuration, such as, for example, ${d}^{5}s$ in chromium relative to the ${d}^{n}{s}^{2}$ configuration in vanadium and manganese. When the core-level shift is referred to, the ${d}^{n}{s}^{2}$ (or ${d}^{n+1}s$) atomic configuration for all the elements in a transition series, a quite regular behavior of the shift is found. However, some structure can still be observed originating from a change of screening within the $d$ band from a bonding to an antibonding type as one proceeds through the series. For elements beyond the coin metals the screening of a core hole is performed by $p$ electrons, which provide a less effective screening mechanism than the $d$ electrons for the transition metals. The coin metals are intermediate cases, partly due to a dominating $s$-electron screening and partly due to $d$-electron bonding in the initial state. The effect of the electron-density redistribution between the free atom and the solid on the core-level shift is particularly striking in the case of the rare-earth elements Pr-Sm and Tb-Tm. Here the remarkable situation is that a deep core electron is less bound in the atom than in the solid. Also for the actinides the electronic redistribution upon condensation gives rise to pronounced effects on the core-level shifts. Further, it is shown that the measured $6{p}_{\frac{3}{2}}$ binding energy in metallic uranium provides a clear demonstration of the occupation of the $5f$ level in this metal. The present treatment of the core-level shift for bulk metallic atoms can easily be generalized to surface atoms. From an empirical relation for the surface energy a simple expression for the shift of the surface core-level relative to the bulk can be derived. For the earlier transition metals, it is found that the core electrons are more bound at the surface than in the bulk, while for the heavier ones the opposite situation exists. This change of sign of the surface shift depends on the bonding-antibonding division of the $d$ band. To illustrate how the present approach can be applied to alloy systems, a treatment of core-level shifts for rare-gas atoms implanted in noble metals is undertaken.