Final-state screening of core holes in metals

Core-level photoemission is often employed to extract chemical information concerning the atomic site and this requires assumptions concerning the balance between initial-state chemical and final-state screening effects. With this in mind, we have calculated the binding energy of the $4f$ level in gold metal using local-density total-energy calculations. We find a binding energy of 83.7 eV in good agreement with the experimental value of 83.9 eV. We are thus able to test several less complete computational schemes. For example, confining the response to a single site yields 84.3 eV, an error of 0.6 eV, while limiting the screening to the atom and its near neighbors produces an error of 0.07 eV. In addition, we have calculated the heat of solution of mercury in gold. This may be related via a Born-Haber cycle to the core-level binding energy assuming local screening and the equivalent core approximation. This yields a binding-energy error of 0.15 eV which, while small, is of significance. Finally, we have explicitly decomposed the binding energy into initial- and final-state contributions and find a relaxation energy in gold of 17.7 eV compared to 13.1 eV for the isolated atom.