An unexpected spin flip alters the course of a chemical reaction

The behavior of small molecules, alone and in reactions with one another, has been well studied. The basic physics is simple to describe: To a good approximation, it’s just nonrelativistic quantum mechanics with Coulomb interactions. Exact solutions to the Schrödinger equation are not feasible for any but the simplest systems; as a result, many quantitative details—reaction rates, cross sections, energy barriers, and the like—remain to be measured or numerically determined. And there’s plenty of room for innovative new computational and experimental techniques to illuminate those details (see, for example, Physics Today, October 2013, page 15 , and November 2013, page 15 ).

By and large, though, molecules’ dynamics are consistent with the patterns established by generations of experiments and calculations that have come before. It’s highly unusual for a pair of colliding molecules to behave in a way that’s qualitatively new and unexpected. But in an experiment by the University of Missouri’s Arthur Suits and colleagues, that’s just what happened. ¹

Suits and company were studying the gas-phase reaction of atomic oxygen with dimethylamine (DMA, CH₃NHCH₃) to produce a pair of charge-neutral radicals, OH and CH₃NHCH₂. In at least 90% of the reactions, they observed an intersystem crossing, or radiationless spin flip, from an overall spin-triplet state to a spin-singlet state. So far, that’s not so surprising: Intersystem crossings, facilitated by strong spin–orbit coupling, are common in molecular dynamics.

What makes the new result unusual is that the intersystem crossing occurred after the molecules had already reacted and the products were starting to move away from each other. That possibility had never before been observed or even considered. Intersystem crossings take time—typically between nanoseconds and milliseconds—and the products of a completed reaction can fly away from each other in just femtoseconds.

To help explain that so-called exit-channel intersystem crossing, Suits and his Missouri group called on Temple University theorist Spiridoula Matsika. Together they concluded that the explanation was twofold: The products separated more slowly than usual, and the system’s electronic configuration was just right for the intersystem crossing to be atypically fast. Neither the slow separation nor the fast spin flip is by itself especially unusual, so exit-channel intersystem crossings may turn up in other systems as well.

Long-lived complex

The discovery was serendipitous: “We were not looking for this at all,” says Suits. Rather, they were looking for suitable experiments to do with an O-atom source—a jet of gas-phase atoms introduced into a vacuum chamber—that postdoc Hongwei Li had just built. Li made the O atoms by breaking up sulfur dioxide molecules with a laser; that reaction has the advantage of producing O purely in its spin-triplet electronic ground state, with no contamination by the excited spin-singlet state. They chose DMA as the other reactant, also introduced into the chamber in a molecular beam, because they knew that the reaction products would be easy for them to detect.

As is typical for chemical dynamics experiments, the existence and timing of the intersystem crossing had to be inferred indirectly. The researchers didn’t monitor the reaction progress or molecular spin state in real time. Instead, they measured the speeds and directions of the product radicals, and from that information they deduced what must have happened during the reaction.

The crucial and surprising observation was that the reaction was almost perfectly isotropic: The product radicals were no more likely to emerge in one direction than any other. From that, the researchers inferred that the reactants had been bound to each other for tens to hundreds of picoseconds, long enough for the bound complex to tumble around many times before finally breaking up into products. Like the seeker in a game of blindman’s bluff, the products emerge with little memory of their original directions.

But there’s a problem: Such a long-lived complex must be energetically stable, and the triplet-state system doesn’t have access to any such structure. Suits and colleagues considered two ways the triplet reaction can happen: The O atom could approach one of the methyl groups and extract a hydrogen atom directly, or it could initially approach the nitrogen atom in the middle of the molecule, then migrate to one of the ends to extract an H atom. The first pathway, represented in green in figure 1, has no discernable energy peaks or valleys at all; the second, represented in red, has a few, but they’re not nearly deep enough to bind the complex for the requisite time.

Figure 1.

In the singlet state, shown in black, the situation is different. Rather than gently rolling hills, the energy landscape features two deep wells with a mountain in between. Each well is sufficiently deep to trap the complex for long enough to produce the observed angular distribution, but it was easy for the researchers to deduce that only the second well would do. The O and DMA beams were introduced into the vacuum chamber at known speeds that correspond to a total kinetic energy of 7.8 kcal/mol. If the complex had crossed to the singlet state early in the reaction process, it wouldn’t have had enough energy to surmount the 46.9 kcal/mol barrier to complete the reaction. It must, therefore, have undergone intersystem crossing late in the reaction and plunged into the second energy well, where it would have enough energy to get back out.

Spin–orbit coupling

Once Suits and his fellow experimenters had satisfied themselves that the reaction must involve an exit-channel intersystem crossing, they turned to Matsika to help them understand how it happens. Unfortunately, a theoretical smoking gun—a simulation of the full reaction in sufficient quantum detail to show the change in electronic state—is far too computationally costly. So Matsika focused on the part of the reaction trajectory in which the intersystem crossing is most likely to occur because the singlet and triplet states have nearly the same energy. First, she analyzed the electronic configuration to estimate the speed of the possible spin flip. Then she determined how long the complex spends in the near-degenerate geometry.

Singlet–triplet near-degeneracy is achieved in geometries similar to the CH₃NHCH₂–OH structure in figure 1, and it’s intuitively easy to see why. Each fragment, the OH and the CH₃NHCH₂, carries one unpaired electron. The farther apart the fragments get, the less it matters to the overall energetics whether the unpaired spins are in a singlet or triplet configuration.

Just because the singlet and triplet states have nearly the same energy, though, doesn’t mean the system can easily move from one to the other. Spin–orbit coupling is a relativistic effect. It’s strong in the presence of heavy atoms, such as bromine or iodine, whose electrons orbit at a significant fraction of the speed of light. When the heaviest element present is O, the coupling is much weaker.

But not always. According to a principle laid out 50 years ago by Mostafa El-Sayed, spin–orbit coupling can be relatively strong, and intersystem crossing relatively fast, when the change in spin is accompanied by a change in orbital angular momentum. ² The O–DMA complex satisfies that criterion, as shown by the molecular orbitals in figure 2. The organic fragment’s unpaired electron occupies MO3 (which has some amplitude on the OH fragment because the fragments are not yet completely separate). The OH fragment’s unpaired electron can occupy either MO1 or MO2, which are nearly equal in energy but different in orientation. The electron can move from one orbital to the other in tandem with a spin flip.

Figure 2.

Furthermore, the electron density hardly has to change at all: Both MO1 and MO2 are localized on the O atom. A similar situation—a large change in orbital angular momentum with a small change in electron density—has been observed in isomers of nitronaphthalene, ³ which undergo intersystem crossing in mere hundreds of femtoseconds. From Matsika’s calculations, the researchers concluded that their system is likely to be similarly fast.

But even that’s generally too slow for an exit-channel intersystem crossing. By the time the OH and organic fragments have separated enough for the singlet and triplet states to be degenerate, they should be well on their way to separating for good.

Roam if you want to

The second half of the explanation lay in another counterintuitive molecular phenomenon, the roaming pathway, first described in 2004 by Suits and collaborators. ⁴ In some chemical reactions, those researchers found, the products don’t separate immediately but instead orbit each other for a while before parting.

To see how that happens, consider that a molecule or complex of N atoms has 3N − 6 internal degrees of freedom, most of which correspond to normal modes of vibration, and only one to the reaction coordinate (for example, the lengthening of the bond that ultimately breaks). In a highly vibrationally excited system, energy flows at random among the degrees of freedom, and only when enough energy builds up in a single bond does that bond break. “That’s unlikely, and it takes time,” says Suits. But it’s less unlikely for the bond to accumulate enough energy to stretch to a long distance—two or three times its resting length—without breaking. As the bond stretches, it becomes floppier; the emerging molecular fragments remain quasibound but behave almost like independent roaming entities. “Molecules are sticky at long range,” says Suits. “They are not billiard balls.” (For more on the physics of roaming pathways, see the article by Joel Bowman and Arthur Suits, Physics Today, November 2011, page 33 .)

Sure enough, a detailed simulation of the triplet-state reaction showed that the product radicals roam around each other for more than half a picosecond before ultimately separating. With that observation, all the pieces fell into place: During roaming, the molecular complex undergoes an ultrafast intersystem crossing, falls into the singlet-state energy well where it remains for tens to hundreds of picoseconds, and then dissociates with an isotropic angular distribution.

None of the key ingredients in that process are terribly rare. The same configuration of molecular orbitals that enables the subpicosecond spin flip is present in many other reactions involving O and N atoms. And roaming pathways, first recognized in photoinduced decomposition of formaldehyde molecules, ⁴ have since been observed in various other systems. Now that researchers know to look for it, the exit-channel intersystem crossing may prove to be similarly general.

If fast intersystem crossings are so common, why haven’t they been noticed before? Part of the reason is the indirect nature of the tools, both theoretical and experimental, that are used to probe chemical dynamics. To interpret their results, researchers often must already have a sophisticated understanding of how they expect a reaction to play out. If that understanding is wrong, the interpretation may be too, and if the difference is subtle enough, the error may go unnoticed. But Suits and colleagues happened upon a reaction in which the unexpected intersystem crossing, positioned on the precipice of a singlet-state energy well, completely changed the angular distribution of the reaction products. It was impossible to ignore.

“Our inner dialog is always how much we understand about things, rarely how much we don’t understand,” reflects Suits. “As our tools get sharper and we look more deeply, we see that extrapolation from simple models may overlook key features that force a change in our perspective. I am confident that many more surprises are in store.”