The First Femtosecond in the Life of a Chemical Reaction

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Science  21 Apr 2006:
Vol. 312, Issue 5772, pp. 373-374
DOI: 10.1126/science.1125514

When light initiates chemical change—such as photosynthesis in plants, or vision in an eye, or the formation of vitamin D in your skin—the first stages happen with breathtaking rapidity. Electrons in molecules can absorb a photon and rearrange in only femtoseconds (a femtosecond is 10−15 s). A bedrock of chemical theory known as the Franck-Condon principle assumes that such short times are so infinitesimal that for all practical chemical purposes they are instantaneous: All the atoms in a molecule remain frozen during the critical instant of electron transition. Yet quantum mechanics requires that the atoms in molecules are never truly at rest, and the removal or repositioning of electron charge initiates motion that eventually leads to chemical transformation. These earliest atomic movements have never been observed directly, because they are far too fast and too slight to detect. But this is just what the report by Baker and co-workers shows on page 424 of this issue (1). This research comes from the rapidly growing field of attoscience. An attosecond (10−18 s) is even shorter than the events that initiate photochemistry, but the name has been taken over to include physical observations on time scales shorter than a single cycle of visible light, or shorter than about two femtoseconds. The specific technique used here is high-harmonic generation (HHG) in molecules illuminated by intense femtosecond pulses of focused laser light.

The report by Baker et al. describes and then demonstrates a new method to convert the spectrum of high harmonics into an image of the motion of molecules (such as hydrogen or methane) in the first stages of chemistry. The HHG process, in which visible or infrared laser light is converted to vacuum ultraviolet radiation, has been known for nearly two decades (2). The light takes the form of odd harmonics—that is, odd multiples of the driving laser frequency. Harmonic frequencies greater than 100 times the laser frequency have been observed in a single spectrum. This extreme phenomenon was not predicted before its initial observation, and it seems to lie outside the reach of conventional nonlinear optics, the theory that predicts parametric processes such as second- or third-harmonic generation in light interacting with atoms and molecules. Yet HHG has an elegant and simple physical explanation, based in part on classical physics (3). HHG occurs when an intense laser field pulls an electron away from the molecule in a fraction of one optical cycle, and then sends the electron crashing back into the molecule when the field reverses on the next half-cycle (see the figure). The energy dissipated in the crash of each electron is converted into a single photon of radiation. The HHG spectrum is the forward-directed portion of this light collected from all of the molecules illuminated by the laser.

Tracking molecular motion.

(Top) A laser field (black arrow) pulls an electron quantum wave (blue) away from the molecule, causing the two atoms (black dots) to separate. (Center) When the laser field reverses, the quantum wave smashes back into the molecule. Color represents the wave energy, with blue for fast high-energy waves and red for slow low-energy waves. (Bottom) The electron wave is absorbed, creating photons with energy corresponding to the wave energy. In this way, each color of light shows the molecule at a different time as the atoms move apart. Total time elapsed is about ½ of an optical cycle, or one femtosecond.


The research reported by Baker et al. takes these ideas one step further. The authors note that according to this classical model, the energy of the photon must be tied to the kinetic energy of the electron that made it, which depends in turn on the precise time that the electron was pulled away from the molecule and the time that it returned. For example, electrons that leave the molecule at the very peak of the oscillating laser electric field take the longest time to return, and the field has slowed them nearly to a stop when they do. Electrons that leave the atoms a bit later will not go as far before turning back, and they return with some excess energy that can be put into a high-harmonic photon. The later an electron leaves in a field cycle, the shorter the duration of its journey, and the higher its energy upon return.

An electron that leaves the molecule about 1/20th of a cycle after the peak (18 degrees of phase) has the highest energy possible when it returns—about three times the average wiggle energy of an electron in the laser field. Electrons that leave still later in the cycle have even shorter total trajectories but return with less than the maximum energy. These “short-trajectory” harmonics were the ones used by the authors to view the just-ionized molecule. The lowest energy part of the spectrum shows the condition of the molecule at the earliest times after the ionization event, and the highest energy part shows longer times. But the total time interval covered by the entire spectral record is extremely short—about a femtosecond.

How should one interpret this spectrum to get any meaningful information, let alone a snapshot image of the molecule? Here the research team deftly switches back to quantum theory for a clue. The returning electron doesn't have to convert its energy to a photon when it crashes back into its home port. It could just as easily scatter from the molecule and careen into another direction from which it never returns. The odds of producing an HHG photon depend on whether the shape of the quantum wave function of the target molecular ion matches the space the neutral molecule needs to occupy when the electron comes back to rest. If the shapes don't match, the electron is likely to just bounce off. This quantum correlation between the ion and the neutral molecule is therefore reflected in the amplitude of the HHG spectrum. More HHG signal at a particular photon energy means a better match at that time. This is not much information, to be sure, but it is just enough to provide important clues used to reconstruct the motion of the molecule in the first femtosecond after ionization. Baker et al. report measurements of this motion in hydrogen molecules and in methane ionized by a laser pulse consisting of only a few optical cycles.

Competing effects influence HHG, such as the spatial arrangement of the atoms in the molecule, or the tendency of the molecule to distort under the influence of the laser field even before the moment of electron release. These phenomena also alter the HHG spectrum and could confuse the analysis (4). The most important limitation of the new technique is the very short time interval involved. Only the lightest atoms in a molecule move far enough to detect motion over one femtosecond. But hydrogen, the lightest atom, is the critical actor in much photochemistry, and its motion is considerable even over these short times. Furthermore, the continued improvement of ultrafast lasers is leading to infrared sources with longer wavelength and longer cycle periods, and this technique could be extended to longer times in this way.


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