Symmetry assignments of occupied and unoccupied molecular orbitals through spectra of polarized resonance inelastic X-ray scattering

We derive symmetry selection rules for polarized resonance inelastic X-ray scattering (RIXS) in randomly oriented molecules belonging to any of the 32 crystallographic point groups or to the two groups of linear molecules. Compact formulae are derived for cross sections of RIXS processes in randomly oriented molecules for photons of arbitrary polarization; linear, circular or elliptical polarization. It is shown that a specification of polarization ratios of RIXS cross sections yields sufficient information to permit an unequivocal identification of the symmetry species of the occupied and unoccupied molecular orbitals (MOS). The given tabulation of RIXS symmetry selection rules can be used as a quick guide to assign symmetry properties of molecules of experimental interest.