Vibration-dependent photoelectron angular distributions and branching ratios observed across the Cooper-minimum region of bromobenzene

Vibrational state-resolved photoelectron anisotropy parameters, $\beta$, for the $\tilde{X}{}^2{B}_1$, $\tilde{B}{}^2{B}_2$, and $\tilde{C}{}^2{B}_1$ state ionizations of bromobenzene have been recorded at photon energies ranging from 20.5 to 94 eV, thus spanning the region of the expected bromine Cooper minimum (CM). The $\tilde{X}$ state displays no CM and its $\beta$ value is also independent of vibrational level, in accord with the Franck-Condon approximation. The $\tilde{B}$ and $\tilde{C}$ state $\beta$ values display the CM to differing degrees, but both show a vibrational dependence that extends to energies well below the obvious CM dip. Calculations are presented that replicate these observations. We thus demonstrate a wide-ranging Franck-Condon approximation breakdown detected in the $\beta$ anisotropy parameter in the absence of any resonance. Measured and calculated vibrational branching ratios for these states are also presented. Although the $\tilde{B}$ state branching ratios remain constant, in accord with Franck-Condon expectations, the $\tilde{X}$ and (especially) the $\tilde{C}$ state ratios display weak, quasilinear variations across the studied range of photon energy, but with no apparent correlation with the CM position.

Figure 1

Overview of the $h\nu =40$ eV data. The “magic angle” photoelectron spectrum is reconstructed by combining scans recorded with parallel and perpendicular linearly polarized light, and the $\beta$ parameter trace is similarly constructed from these recordings. Note the break in the vertical axis to truncate the intense origin of the $\tilde{B}$ band. A Franck-Condon simulation [9] is also shown with a small vertical offset for the vibrationally well-resolved $\tilde{X}$, $\tilde{B}$, and $\tilde{C}$ bands. Features assigned as vibrational hot bands are starred.

Figure 2

Bromobenzene $\tilde{X}\mathrm{band}\beta \left(v\right)$. Top: experiment. Bottom: calculations for the C-Br stretch, ${\nu }_{11}$.

Figure 3

Vibrational peak branching ratios for the bromobenzene $\tilde{X}$ band. Linear best fit lines are drawn through each of the data sets. The inset shows calculated branching ratios for the $v_{11}=0$–3 transitions. Note that because of the different normalization over 4 transitions rather than 6 peaks the absolute magnitudes are not comparable with experiment.

Figure 4

$\tilde{B}$ state vibrationally resolved $\beta$ parameters. On the left we show experiment, on the right calculation. Two insets (top right panel) show expanded views of the maxima and minima regions of the calculated curves. For the (unresolved) ${10}^2$ and $6^1$ excitations a simple average of the individual ${10}^2$ and $6^1$ calculated $\beta$ is plotted. The lower panels show corresponding residuals, $\mathrm{\Delta }\beta$ (see text).

Figure 5

$\tilde{B}\mathrm{state}$ vibrational branching ratios. (a) Experimental values. The straight lines drawn through the vibrational data sets are linear best fits; (b) calculated ratios.

Figure 6

$\tilde{C}$ state $\beta$ parameters and vibrational peak branching ratios. For the latter, linear best fit straight lines are drawn through each vibrational data set.

Figure 7

(a) Experimental $\tilde{C}$ state residuals $\mathrm{\Delta }\beta$ from the experimental mean $\beta$; (b), (c) residuals $\mathrm{\Delta }\beta$ for calculated excitations of ${\nu }_{11}$ and ${\nu }_{10}$ levels (referenced from the $\beta$ curve computed at a fixed equilibrium geometry).