Symmetry-selective resonant inelastic x-ray scattering of C60.

Abstract

The resonantly excited x-ray emission spectra of the ${\mathrm{C}}_{60}$ molecule are presented and analyzed in terms of symmetry- and polarization-selective resonant inelastic scattering processes (RIXS). The theoretical analysis implements recently derived formalisms for symmetry-selective x-ray scattering. Isolated properties of the RIXS spectra are simulated and their cooperative action for the buildup of various features in RIXS of ${\mathrm{C}}_{60}$ are analyzed. Apart from symmetry and polarization dependences, the role of Stokes shifts, tail excitation, vibrational excitation, and interference effects are simulated in detail. Other relevant aspects are discussed in a more brief manner, such as influence of vibronic coupling and nonresonant anomalous contributions. Several conclusions about the nature of RIXS from ${\mathrm{C}}_{60}$ have been derived. The symmetry- and parity-selective character of the RIXS spectra is clearly visualized by excitation in the band gap. The symmetry selectivity leads to a strong correlation between the shape of the RIXS spectrum and the shape of the spectral function describing the incoming excitation photons. It also implies that the RIXS spectra become sparse in the limits of long core hole state lifetime and narrow-band excitation. Spectra pertaining to higher resonant energies involving a higher density of core-excited states are less symmetry selective and turn progressively into their broadband excitation and nonresonant analogues.Tail excitation and Stokes shifts have strong influence on the appearance of the RIXS spectra, both depending crucially on frequency and form of the spectral functions of the incoming photons and on the vibrational progressions of the core-excited states. The band-gap generated spectra emerge as consequences of Stokes shifts when the absorption energies are detuned from the lowest unoccupied molecular orbital resonance. The polarization and angular dependences of RIXS in ${\mathrm{C}}_{60}$ are found to be comparatively weak, something which is rationalized by the highly degenerate electronic structure and the spherical shape of the molecule. The computer simulations in this work rest on transition moments and energies obtained by ab initio Hartree-Fock calculations in the full ${\mathit{I}}_{\mathit{h}}$ point-group symmetry.