Experimental and theoretical study of valence electronic structure of tetrabromomethane by $(e,2e)$ electron momentum spectroscopy

We report a measurement of the valence orbital momentum profiles of tetrabromomethane (${\mathrm{CBr}}_4$) using symmetric noncoplanar $(e,2e)$ experiments at the impact energies of about 600 and 1200 eV. The experimental momentum profiles for the individual orbitals $5t_1, 13t_2, 5e, 12t_2$, and $9a_1$ and the branching ratio of $5t_1$ to $13t_2$ and $5e$ to $13t_2$ are obtained and compared with two kinds of calculations under the plane-wave impulse approximation. One is theoretical momentum profiles that have been calculated at the equilibrium geometry, the other is those that involve vibrational effects using a thermal sampling molecular dynamics method. The calculations considering molecular vibrations are in better agreement with experiment than the equilibrium geometry calculations, indicating the important role of nuclear motions on the valence orbital electronic structures of ${\mathrm{CBr}}_4$. The distorted-wave effects are observed in the experimental momentum profiles of $5t_1, 5e$, and $12t_2$ which display dynamic dependencies on the impact energies. A multicenter interference or bond oscillation effect has been observed from the momentum profile ratios of $5t_1$ to $13t_2$ and $5e$ to $13t_2$ which has direct information about the bond length of a molecule.

Figure 1

Symmetric noncoplanar geometry for the present high-energy binary $(e,2e)$ reaction.

Figure 2

Maps of the outer-valence molecular orbitals of ${\mathrm{CBr}}_4$.

Figure 3

(a) Experimental momentum-energy density map of ${\mathrm{CBr}}_4$ and (b) binding-energy spectrum summed over all azimuthal angles $\varphi$ obtained at the impact energy of 1200 eV plus binding energies. The dashed lines represent Gaussian fits to the individual peaks and the solid curve is the summed fit. The labels are the outer-valence orbital assignments.

Figure 4

Measured and calculated momentum profiles for the sum of $5t_1+13t_2+5e+12t_2+9a_1$ orbitals of ${\mathrm{CBr}}_4$ at the impact energies of 600 and 1200 eV. The dashed curve is the calculations with DFT-B3LYP/aug-cc-pVTZ method at the equilibrium geometry of ${\mathrm{CBr}}_4$.

Figure 5

Measured and calculated electron momentum profiles for the outer valence orbitals of ${\mathrm{CBr}}_4$ at the impact energies of 600 and 1200 eV. The dashed curves are calculations at the equilibrium geometry of ${\mathrm{CBr}}_4$. The molecule vibrational calculations are shown by the solid curves.

Figure 6

The momentum profiles for $5t_1, 13t_2$, and $5e$ orbitals in logarithmic scale (a), and the momentum profile ratios for $5t_1/13t_2$ (b) and $5e/13t_2$ (c).