Watching a Molecule Break Up Reveals How Quickly It Changes Shape

In papers that dissect the physics of chemical reactions, you’ll often find a cartoon. The molecules in the cartoon appear as colored blobs or stick figures. Simple arrows indicate key motions. More succinctly than words or Hamiltonians, the cartoon embodies and conveys what’s going on.

Getting to the point where one can draw such a cartoon is an arduous journey. Even for simple molecules whose structures are known, solving the quantum mechanical equations requires months of computer time. It’s just as hard in the lab. Between reactants and products lies a host of short-lived quasistable intermediaries whose existence—let alone properties—is difficult to pin down.

But now a team of researchers has taken a different, more direct route to distilling the essential physics of a reaction. Using an innovative spectroscopic method, Timur Osipov of Kansas State University, his thesis adviser Lew Cocke, and their collaborators in the US and Germany have succeeded in tracking and timing how an acetylene molecule changes into its structural isomer vinylidene. ¹

The transformation is simple—the hopping of a hydrogen atom from one carbon atom to another—and the molecule is small. But, says MIT’s Bob Field, “It’s really an extraordinary accomplishment.”

Hydrogen swapping

Acetylene has the chemical formula C₂H₂. Its four atoms are arranged in a straight line: two triply bonded carbons on the inside, two hydrogens on the outside. To make vinylidene, its free-radical isomer, remove a hydrogen atom from one of the carbons and attach it to the other.

Although hot-burning acetylene is industrially important, physicists and chemists are just as interested in its role as a model system. The acetylene-to-vinylidene isomerization involves what organic chemists call a 1,2 hydrogen shift. Many important reactions, especially in biology, include the shift. For measuring or modeling it, acetylene offers one of the simplest subjects.

But simple doesn’t mean easy. Vinylidene is so short-lived that its status as molecule has been controversial for 20 years. Just recently, after running their computer models of acetylene’s vibrational eigenstates for 10 months, Emory University’s Joel Bowman, Alex Brown, and Shengli Zou concluded that vinylidene is indeed a stable isomer. ²

Osipov’s thesis work on acetylene is one fruit of a decades-long collaboration between Cocke’s group at Kansas State and Hörst Schmidt-Böcking’s group at Frankfurt University. Other team members include Reinhardt Dörner, Thorsten Weber, Ottmar Jagutzki, and Lothar Schmidt of Frankfurt University, Allan Landers of Western Michigan University, and Mike Prior of Lawrence Berkeley National Laboratory (LBNL).

The team uses cold-target recoil-ion-momentum spectroscopy (COLTRIMS). Developed mostly in Frankfurt, COLTRIMS combines detector concepts from particle physics with cryogenic techniques from atomic physics. The union provides a complete picture of the momentum acquired by each molecular fragment in each fragmentation.

Different splitting

Studying isomerization requires a way to tell the two isomers apart. Acetylene and vinylidene weigh the same, but if you sever the bond between the two carbons, the two isomers fragment differently: Acetylene splits into two CH fragments, whereas vinylidene splits into CH₂ and C. Ionizing the fragments and applying an electric field, as in COLTRIMS, endows the fragments with different and distinguishing velocities.

But something is also needed to trigger the isomerization, and if you’re interested in time scales, you need a stopwatch, too. Nature obligingly furnishes the trigger. Using an x ray to knock out an inner-shell photoelectron from one of the carbons creates a “core-excited” acetylene cation that deexcites by emitting a second, Auger electron. Five years ago, Xavier Gadéa of Paul Sabatier University in Toulouse, France, suggested that a core-excited acetylene cation could form a vinylidene cation. ³ Because Osipov and company needed to ionize acetylene anyway to use COLTRIMS, x rays could act as both ionizer and trigger.

The x rays for photoionizing acetylene don’t have to be especially energetic; 290 eV suffices to reach the carbon K edge. But, to give fragments enough time to reach the detector before the next round of ionization, the x rays have to arrive in short, widely spaced bunches. To use such bunches, the COLTRIMS team took their experiment to the Advanced Light Source at LBNL, where, for four weeks a year, the delay between pulses is stretched from the normal 2 ns to 150 ns.

Figure 1 shows the COLTRIMS experiment. Cold acetylene molecules spout upward from a nozzle and cross a beam of linearly polarized x rays. Ionized by the x-ray broadside, the cations acquire a second positive charge when they emit an Auger electron. Holding two positive charges, one at each end, is too strenuous for a small molecular ion. Whether acetylene or vinylidene, the dication breaks apart into two singly charged cations. An electric field accelerates the cations, which fly off to strike a particle detector.

Meanwhile, the same field accelerates the photoelectrons in the opposite direction toward another detector. By itself, the electric field lacks the strength to steer the photoelectrons onto the detector, so a magnetic field is added to confine them. The Auger electrons, being more energetic, mostly miss the detector. Any that don’t are discounted by the detector’s electronics.

In principle, determining the momenta of each pair of cations boils down to applying the simple dynamics of accelerated ions. The ingredients are the two-dimensional positions of the cations on the detector and the cations’ time of flight, which is determined by subtracting the ionization time (supplied by the clock that synchronizes the x rays) from the arrival time (measured by the detector).

In practice, however, you need to discern differences in time of flight. Acetylene and vinylidene break up along the carbon—carbon bond, so the biggest differences in time of flight arise when a dication’s axis lines up with the electric field and, right after breakup, one fragment shoots forward and the other backward.

To boost the number of such events, the x-ray polarization is aligned with the electric field. This arrangement helps because acetylene’s electrons inhabit orbitals that follow the molecule’s linear shape. The closer the photon’s electric field parallels the molecular axis, the greater the ionization yield. Selecting events of modest transverse momenta also sharpens the distinction between acetylene and vinylidene.

Osipov found that about 30% of the photoionized acetylene dications isomerize to vinylidene before breaking up. But, given that the isomerization occurs before the fragments reach the detector, how could he and his collaborators determine isomerization time? Their answer is ingenious.

Once dislodged, an inner shell electron takes a mere 40 attoseconds to escape the molecule. Although there’s a modest probability that a photoelectron will flee in directions diagonal to the molecular axis, most of the time the photoelectron’s escape route runs parallel to the axis. In the molecular reference frame, the distribution of escape directions at photoionization, σ⁺(φ), looks like a cigar with a central, butterfly-shaped protuberance.

COLTRIMS can’t determine σ⁺(φ), but it can determine σ⁺⁺(φ), the distribution of escape directions measured with respect to the molecular axis at fragmentation. Cocke and Osipov realized that photoionization, being so prompt and directed, could act as a stopwatch. If a dication fragments right after photoionization, they reasoned, σ⁺⁺(φ) would look pretty much like the unmeasured but predictable σ⁺(φ). The top panel of figure 2 shows that for acetylene fragments σ⁺⁺(φ) does indeed share the same slim, butterfly-crossed shape of σ⁺(φ). Evidently, acetylene dications break up promptly.

But suppose—hypothetically—that an acetylene dication does have time to tumble about before it breaks up. In that case, σ⁺⁺(φ) would lose its resemblance to σ⁺(φ). Of course, acetylene’s lifetime can’t be artificially extended, but the effect can be mimicked by measuring escape directions in the lab frame rather than in the molecular frame. The bottom panel of figure 2 shows the resulting distribution.

Vinylidene’s σ⁺⁺(φ), which appears in the middle panel of figure 2, falls between the other two—as if the isomer’s birth and life last long enough for the dication to rotate a bit, but not enough to wash out the distribution.

To determine vinylidene’s rotation angle, Osipov took acetylene’s σ⁺⁺(φ) and then, in a computer program, added varying amounts of rotation-induced blur until it matched vinylidene’s σ⁺⁺(φ). That happened at a rotation angle of 20°.

In the acetylene-to-vinylidene isomerization, a hydrogen atom swings around its carbon until the other carbon captures it. At the same time, to conserve angular momentum, the rest of the molecule rotates in the opposite direction. A back-of-the-envelope calculation says that angle is also 20°. Apparently, vinylidene’s birth is so quick that the dication barely survives long enough to rotate much further.

To derive an upper limit to the isomerization time scale, Osipov determined how much additional rotation the data could accommodate. His conservative estimate was 10°. To convert the angle into a time, he assumed that a vinylidene dication is set spinning by the ejection of the Auger electron. Using the other side of his figurative envelope, he derived the momentum kick and, from it, an isomerization timescale of less than 60 femtoseconds.

Chemists would love to know how fast neutral acetylene isomerizes. Unfortunately, the relationship between the neutral’s and dication’s isomerization time scale is hard to quantify. Osipov’s upper limit is, however, suggestively similar to the bending period, inferred from spectra, of hydrogen on the end of acetylene.