Tuning out vibrational levels in molecular electron energy-loss spectra

The phenomenon whereby features associated with certain vibrational levels in molecular states of mixed electronic character disappear under specific scattering conditions in electron energy-loss spectra is investigated. In particular, using a combination of experimental measurements and coupled-channel calculations, anomalous vibrational intensities in the mixed valence-Rydberg ${}^1{\Pi }_u\leftarrow X{}^1{\Sigma }_g^{+}$ transition of N${}_2$ are explained. A single parameter, i.e., the ratio of the generalized electronic transition moments to the diabatic valence and Rydberg components of the mixed states, dependent on the experimental scattering conditions, is found to be essentially capable of describing all observed relative vibrational intensities, including the near disappearance of the $b{}^1{\Pi }_u(v=5)$ feature for momentum-transfer-squared values $K^2\approx 0.3$ a.u. This result highlights the interesting possibility of experimental control of molecular quantum-interference effects in electron energy-loss spectra, something that is not possible in optical spectra.

Figure 1

Diabatic potential-energy curves used in the CC model, referred to the $v=0,J=0$ level of the $X{}^1{\Sigma }_g^{+}$ ground state (not shown). Solid curves: ${}^1{\Pi }_u$ states. Dashed curves: ${}^3{\Pi }_u$ states. The lowest singlet levels are indicated, associated with the nominal diabatic potential-energy curve, and emphasizing the perturbation resulting from the $b\sim c$ crossing.

Figure 2

Diabatic optical electronic transition moments used in the CC model (see text).

Figure 3

Comparison of experimental GVOSs for $b-X(5,0)$ and $b-X(2,0)$ bands of N${}_2$ (solid and open symbols, respectively). Circles: $E_0=100$ eV. Squares: $E_0=50$ eV. Triangles: $E_0=30$ eV. The optical oscillator strengths of Stark et al. [47], adjusted to room temperature [48], are also shown (large circles, plotted on the GVOS-axis for convenience).

Figure 4

Comparison between experimental ($E_0=100$ eV) and coupled-channel GVOSs for the ${}^1{\Pi }_u-X{}^1{\Sigma }_g^{+}$ bands of N${}_2$, with all quantities plotted relative to the modeled GVOS for $b-X(2,0)$. Error bars: Experimental values from present energy-loss spectra. Solid lines: Values computed using optimized CC model. Dashed lines: Optical oscillator strengths of Ref. [47] ($K^2=0$). Dotted lines: Near-optical GVOSs from Ref. [12]. Graphs are labeled according to the excited-state vibrational level, ignoring any overlapping triplet levels which are not expected to contribute significantly (see Sec. 2).

Figure 5

Calculated GVOSs of selected ${}^1{\Pi }_u\leftarrow X$ bands, relative to $b-X(2,0)$, labeled according to the excited-state vibrational level. The independent variable $r$ is scanned by modifying the GETMs of the Rydberg $c$ and $o$ states by a common factor. The vertical line ($r=1$) corresponds to optical conditions.

Figure 6

Scaling of optical transition moments necessary to reproduce the observed GVOSs of $b-X(2,0)$ and $b-X(5,0)$ bands. For the three cases, $E_0=100$, 50, and 30 eV, the scaling of $M_{bX}$ relative to the optical case is plotted in black, and the common scaling of $M_{cX}$ and $M_{oX}$ is plotted in gray.

Figure 7

Relationship between $1-r$ and $K^2$ for the scattering of $E_0=100$, 50, and 30 eV electrons. Here, $r$, defined by Eq. (6), is the ratio of Rydberg- to valence-state GETMs, relative to optical conditions.