(a) Low- and (b) high- limits of the IXS spectrum correspond to photoabsorption (PA) spectrum and the energy loss spectrum within impulse approximation (IA), respectively. The IXS calculations were carried out with TPM using -vector along the -axis and the PA spectrum corresponds to . The polarizability tensor was calculated using OCTOPUS(Refs. 40 and 41) with the same grid as for IXS calculation, and the IA calculation was carried out using a method and computer codes described in Ref. 43.
Dynamic structure factor of gaseous benzene from (a) TPM calculation and (b) EELS experiment. The momentum transfers of the calculated spectra are (solid red curve) and (dashed blue curve). The experimental EELS spectra (from Ref. 44) are gathered at scattering angles of 2.0° (solid red curve) and 4.0° (dashed blue curve) that approximately correspond to the momentum transfers used in the calculation. The arrows indicate two spectral features whose -dependency is correctly reproduced by the calculation.
Separation of the directionally averaged dynamic structure factor of gaseous benzene into different transition channels at momentum transfers of (a) and (b) . At low momentum transfer the dipole selection rule dominates but when the momentum transfer increases, also nondipole transitions give a significant contribution.
Calculated IXS spectrum (left) of demonstrates the momentum transfer dependency of and in particular the enhancing of the dipole-forbidden quadrupole-allowed transition at 7.6 eV as increases. The generalized oscillator strengths (right) calculated with CM for the 7.6 eV transition are shown with experimental (Ref. 55) result.
IXS spectrum of (a) benzene at (directionally averaged) and (b) at (parallel to the C–F bond) calculated using TPM (solid red curves) and CM (dashed blue curves).
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