Electron Trapping by Molecular Vibration

In photoelectron spectroscopy experiments performed at the ALS, a group of researchers has found that electronic transitions normally thought to be forbidden can in fact be excited in conjunction with certain types of molecular vibrations. Specifically, they found that when the symmetry of a linear triatomic molecule is broken by asymmetric vibrational modes, photoelectrons can become temporarily trapped by the molecule before ultimately escaping, giving rise to a broad feature in the photoelectron spectrum known as a shape resonance. This process represents a novel type of symmetry-breaking phenomenon that has not been observed previously but appears to be widespread. Such coupling between electronic motion and nuclear motion becomes increasingly important as scientists learn more about the geometry and dynamics of novel chemical structures such as those found in nanodevices and transient chemical species, and the results have implications for studies that use photoelectron spectroscopy as a diagnostic tool.

Broken Symmetry, Forbidden Transitions

Philosopher of science Karl Popper once described science as "the art of systematic oversimplification." Indeed, many valuable insights can be gained by reducing a system to its bare essentials. For example, the basic description of atomic and molecular structure, in which electrons with specific energies inhabit "orbitals" around immobile nuclei, has resulted in remarkably useful explanations of spectroscopic data, complete with specific rules that predict which electronic motions (i.e., energy-level transitions) are allowed and which are forbidden. Popper believed that good scientific theories must include such predictions because they make the theories falsifiable. Then again, violations of predicted rules offer an excellent opportunity to explore more complex phenomena underlying the simplified theoretical picture. In the work described here, Rathbone et al. observe a nominally "forbidden" electronic transition that is activated by molecular vibrational modes that break the molecule's symmetry. Their observation and analysis of this unprecedented behavior provide valuable insight into the subtle interplay between electronic transitions and molecular vibration.

Vibrational modes of CS₂: Bending mode (top), symmetric stretching mode (middle), and antisymmetric stretching mode (bottom).

The researchers performed vibrationally resolved photoelectron spectroscopy studies of gas-phase carbon disulfide (CS₂), a simple molecule consisting of a central carbon atom with two sulfur atoms on each side, 180 degrees apart. This molecule has one "bending" vibrational mode and two "stretching" modes: one symmetric and one antisymmetric.

Photoelectron spectra with incident photons on-resonance at 40 eV (left) and off-resonance at 30 eV (right). The peaks for the bending and asymmetric stretching vibrational modes are greatly enhanced on-resonance. The peak representing the case with no vibration (red) is provided for reference.

Using the High-Resolution Atomic and Molecular Electron Spectrometer (HiRAMES) endstation at ALS Beamline 10.0.1, the group investigated how the vibrational structure in the photoelectron spectrum changes as the incident photon energy is varied. They found that when the incident photon energy is tuned to the shape resonance (about 40 eV), the peaks corresponding to the bending and asymmetric stretch modes are dramatically enhanced.

This is a new resonance phenomenon: the observed shape resonance is the result of coupling between vibrational modes and electronic transitions that are "forbidden" by selection rules. However, such rules are based on simplifying approximations, and nominally forbidden behavior can occur as the result of unanticipated processes. Thus, exceptions to the rules provide opportunities to gain deeper insight into how electronic motion and nuclear motion are intertwined. In the case of CS₂, the forbidden behavior is observed only when the photoelectrons are tuned to specific resonant energies and become trapped, or quasibound, when the molecule is distorted from its equilibrium geometry. This point is made dramatically clear in plots of the relative probabilities (branching ratios) of the various vibrational modes vs. incident photon energy. The resonance peak appears vividly for the two asymmetric vibrations but is absent in the plot for the symmetric vibrational mode.

Branching ratios as a function of energy for different vibrations.

In addition, the researchers note that the shape and width of the curves for the bending mode and the antisymmetric stretching mode are very similar; only their amplitudes are different. This indicates that the resonance trapping does not depend on the specific type of distortion in the molecular geometry, only on the fact that the motion breaks the molecule's symmetry. The researchers have found that this type of unprecedented behavior is exhibited for other molecules and is likely to be a general phenomenon. In addition to these experimental results, they have performed accurate electron-molecule scattering calculations, and these theoretical results were largely responsible for the qualitative explanations provided here.

The results demonstrate that there are resonances with little sensitivity to distortions in bond length. Because it is common to correlate shape resonance position with changes in bond length, this has implications for studies that use vacuum ultraviolet or x-ray probes for analyzing complex or exotic structures. More generally, the results provide a natural means of examining coupling between nuclear and electronic degrees of freedom and for developing tools based on the connections between them.

Research conducted by Jeff Rathbone and Erwin Poliakoff (Louisiana State University); John Bozek (ALS); and Robert Lucchese (Texas A&M University).

Research funding: U.S. Department of Energy, Office of Basic Energy Sciences (BES), Chemical Sciences, Geosciences, and Biosciences Division; the Robert A. Welch Foundation; and the Texas A&M University Supercomputing Facility. Operation of the ALS is supported by BES.

Publication about this research: G.J. Rathbone, E.D. Poliakoff, J.D. Bozek, and R.R. Lucchese, "Observation of the symmetry-forbidden 5σ_u→ kσ_u CS₂ transition: A vibrationally driven photoionization resonance," Phys. Rev. Lett. 92, 143002 (2004).