Abstract: Can chemisorption bonding shifts be separated from relaxation‐energy shifts in photoelectron spectroscopy?

Abstract

Consider the surface‐molecule limit of chemisorption in which an adatom orbital with eigenvalue εa forms a bond with substrate orbitals of energy εs. The molecular orbital (MO) eigenvalues are (typeset math) where the hopping integral V causes a chemical bonding shift. In a photoemission experiment from such a MO, the electrons ejected from the bond are observed (upon subtraction of the photon energy) at the energy (typeset math) where δε±(rel) is the relaxation energy due to hole creation in the MO state.1 The problem to be addressed is how to determine a value of V, given ε (obs).Demuth and Eastman2 have analyzed photoemission spectra from CO chemisorbed on Ni under the assumption that the relaxation shift of the nonbonding σ orbitals on CO is identical to the relaxation shift of the bonding π orbitals and (implicitly) that the relaxation shifts of the Ni d orbitals are equal to the nonbonding (clean surface) value. In this approximation scheme, the neglect of the MO charge‐cloud distortion due to bonding‐charge pileup between the a and s centers is compensated for by allowing each molecular constituent to have its full uncoupled relaxation shift. To check out the independent atom relaxation energy approximation, the relaxation (or polarization) energy shift for hole creation in a diatomic hydrogen molecule embedded in an electron gas has been calculated3 and the results indicate that the relaxation energy differs by only 2%–9% (depending on electron‐gas density in the range 5≳rs≳2) from the uncoupled atom value. Assuming that this difference can be neglected, we can then replace ε±(obs) of Eq. (2) by ε± of Eq. (1) with εs→εs+ δεs(rel) =εs(obs) and εa→εa+δεa(rel) =εa(obs) where now δεa(rel) is the extra‐atomic or polarization self‐energy.1,4,5 Within this scheme, the observed MO energy is related to the known quantities εs(obs) (from clean surface experiments) and εa (from gas‐phase experiments) and the unknown quantities δεa(rel) and V by (typeset math) Rather than calculate V, we calculate the polarization energy δεa (rel) for a hole created in an atomic orbital state φa(r) on the adatom located a distance s from the effective image plane of the surface. Following Hedin4 and Hodges,5 the polarization energy is given by: (typeset math) with the nonlocal self‐energy (typeset math) the ω component of the potential induced at r′ by a charge at (typeset math) with εq(ω) the electron‐gas dielectric function, r∥ and q lying in the plane of the surface, and G0 the hole Green’s function.Taking εq(ω) ?1−ω2p/ω2 with ωp the bulk plasmon frequency and neglecting dynamic and van der Waals polarization, the system of Eqs.(4) can be reduced to (typeset math) For illustrative purposes take φ:da to be a single, optimal Gaussian, (typeset math) where now, the z origin is taken at the image plane, and the atom– surface separation is s. Equations (5) and (6) can be reduced6 to the single quadratture: (typeset math) with 0.5 ≲δεa(rel)/εim<1 for atomic scale values of s and with εim=e2/4s, the image potential shift.8 As a parenthetical check, we note that the relaxation shifts experienced ty the 5p levels of Xe physisorbed on W, as reported by Waclawski and Herbst,9 fall within this range.Since a well defined procedure for calculating the adatom relaxation energy shifts [Eqs. (4) – (7)] has been given, the only remaining unknown quantity in Eq. (3) is V and thus we can conclude that (within the approximation scheme discussed here) chemisorption bonding shifts can be separated from relaxation energy shifts in photoelectron spectroscopy.