Determination of molecular orientations on surfaces from the angular dependence of near-edge x-ray-absorption fine-structure spectra

A model is presented which allows the determination of molecular orientations on surfaces from analysis of the angle-dependent resonance intensities in K-shell near-edge x-ray-absorption fine-structure (NEXAFS) spectra. In particular, we discuss the origin and angular dependence of so-called σ and π resonances which, in a molecular-orbital picture, correspond to transitions from 1s initial to empty ${\pi }^{\mathrm{*}}$ and ${\sigma }^{\mathrm{*}}$ molecular-orbital final states. All molecules are classified into two general groups, depending on whether the final-state molecular orbital points into a specific direction (‘‘vector’’ case) or whether energetically degenerate orbitals span a plane (‘‘plane’’ case). General equations are derived for these cases which describe the dependence of the resonance intensities on the π and σ symmetry of the final state, the substrate symmetry, the molecular orientation on the surface, and the incidence angle of the elliptically polarized synchrotron radiation with respect to the surface. Model calculations are presented to elucidate the sensitivity of the resonance intensities to the molecular orientation on the surface and the degree of linear x-ray polarization. The capability of NEXAFS to accurately determine molecular orientations on surfaces is illustrated by two examples. Molecular ${\mathrm{O}}_2$ on Ag(110) is shown to lie down on the surface with the O-O axis along the [11¯0] azimuth, and the plane of the aromatic ring in benzenethiol (${\mathrm{C}}_6$${\mathrm{H}}_5$SH) on Mo(110) is tilted by 23° from the surface normal.