Screening energies in photoelectron spectroscopy of localized electron levels

Screening or polarization energies (often called "extra-atomic relaxation energies") associated with localized-hole creation in photoelectron spectroscopy in or on metals have been calculated. Following the procedure of Hedin and Lundqvist, the screening energy is written in terms of an effective matrix element of a nonlocal random-phase-approximation self-energy between wave functions of the localized-hole state. The relevance of spatial extent of the hole, electron-gas dielectric properties, chemical-bonding effects, and surface effects are examined. Calculations for $1s$ core and bonding ${\mathrm{H}}_2$ orbital holes in atoms or molecules which are embedded in and adsorbed on electron-gas surfaces are presented. The interplay between orbital size and host interelectron spacing (as manifested in screening lengths) is emphasized. The relationship between screening energies and classical image potentials in photoelectron spectroscopy of adsorbed atoms and molecules is established. Finally, interpretations of observed photoelectron spectra are discussed in terms of binding energies and relaxation, chemical, and "dipole" potential shifts, and the problem of "proper" referencing is addressed.