Vibrational effects on electron-impact valence excitations of $\mathrm{S}{\mathrm{F}}_6$

We report an angle-resolved electron-energy-loss spectroscopy study on the valence excitations of $\mathrm{S}{\mathrm{F}}_6$. Momentum-transfer-dependent generalized oscillator strengths (GOSs) or GOS profiles of the low-lying valence excitations have been derived from electron-energy-loss spectra measured at an incident electron energy of 3 keV. We have also performed theoretical calculations of the GOS profiles involving the influence of molecular vibration. Comparisons between experiment and theory have revealed that coupling between electronic states through molecular vibration plays a significant role in the $1{}^{1}T_{1g}$ dipole-forbidden transition.

Figure 1

Angle-resolved electron-energy-loss spectra of $\mathrm{S}{\mathrm{F}}_6$, which are presented in the form of the GOS distributions.

Figure 2

Expanded view of the low-E region of the electron-energy-loss spectra at $\theta =\left(\mathrm{a}\right)1.7^{\circ }$, (b) 3.7°, and (c) 6.2°. The dotted curves are the deconvolution functions and the solid curve is their sum.

Figure 3

Comparison between the experimental and theoretical GOS profiles of the $1{}^{1}T_{1g}$ transition. The solid and dashed lines represent the vibrational effects and equilibrium geometry calculations, respectively.

Figure 4

Comparison between the experimental and theoretical {$1{}^{1}T_{2u}+1{}^{1}T_{1u}$} GOS profiles. The solid and dashed lines represent the vibrational effects and equilibrium geometry calculations, respectively. Also depicted in the figure is the experimental result by Rocco et al. [21]. For ease of comparison all data are multiplied by a factor of 10 above $K^2=0.7$ a.u. The right-hand-side panels separately present the theoretical GOS profiles of the $1{}^{1}T_{2u}$ and $1{}^{1}T_{1u}$ transitions.

Figure 5

Theoretical GOS profiles of the $2{}^{1}T_{1g}$ transition. The solid and dashed lines represent the vibrational effects and equilibrium geometry calculations, respectively.

Figure 6

(a) Equilibrium geometry calculations of the GOS profiles for the transitions associated with the 13.3-eV band and (b) a comparison of their sum with the experiment by Rocco et al. [21]. The results for the $1{}^{1}E_u$ and $1A_{1u}$ transitions are not presented here, because of their negligibly small intensities.

Figure 7

Contributions of the individual vibrational modes to the GOS profiles of the (a) $1{}^{1}T_{1g}$ and (b) $2{}^{1}T_{1g}$ transitions. Inset in the figure is the pictorial representation of the $v_3$ mode. Since the contributions of the $v_1$, $v_2$, $v_4$, and $v_5$ modes to the $1{}^{1}T_{1g}$ transition are quite small, they are presented in the form of their sum. Similarly, the sum of the contributions of the $v_1$, $v_2$, and $v_5$ modes is depicted for the $2{}^{1}T_{1g}$ transition.