Reimagining the geometry of transition states (in PRL!)

I'm excited to report that my former graduate student, Dr. Galen Craven, and I just published an article in Physical Review Letters (PRL). The critical question in determining the rate between chemical reactants and products relies on knowing when exactly the reactants become products. This is like asking yourself when did you get sick? You might remember when you were healthy and you know when you definitely have a cold, but do you know when you transitioned from being healthy to sick? Presumably, if you could know when this transition happens, then you would know when to take medicine or when not to. For example, if you start feeling a little off but you haven't hit the transition to being sick, you might still not get sick at all and so there would be no need to take a pre-emptive medication. In the same way, chemists need to know when molecular reactions really take place and when exactly they did so. Transition state theory then provides a way to use that transition to obtain the rate of a reaction. And that's also useful because then we know if it will take place in the same time scale as other events such as being fast enough to finish while you are on a quick break or so slow that it won't happen before the universe has ended.

Specifically, we discovered a new way for obtaining the structure of the transition state between reactants and products when the reaction is in a complex solvent. All of the previous methods had obtained this surface by optimization (using variational transition state theory) or through successive approximations (using perturbation theory).The key is a mathematical tool, called the Lagrangian descriptor, that had been developed earlier by Wiggins and his colleagues in the area of fluid mechanics.We were able to use the Lagrangian descriptor to obtain the transition state geometry directly without either optimizing the rate or employing perturbation theory. And this means that we now have a new tool for obtaining reaction rates in nonequilibrium systems.

As with most articles in PRL, it was a tortuous path through the reviewing process. We were pleased that nearly all of the reviewers (and we had 6 in the end!) saw the work as novel and potentially game-changing. The full reference of the article is: G. T. Craven and R. Hernandez, "Lagrangian descriptors of thermalized transition states on time-varying energy surfaces," Phys. Rev. Lett. 115, 148301 (2015). (doi:10.1103/PhysRevLett.115.148301) I'm happy to acknowledge the support from the Air Force Office of Scientific Research (AFOSR).

When the buffalo roam, do they go over the pass or across the plain?

In one of our papers from last year (recapped in an earlier post), we found that in at least one chemical reaction (the ketene isomerization), the reaction could involve rather distinct pathways. On the one hand, the system could go across the break between the two energetic mountains separating the reactant and product. On the other hand, it could find a flat plain in which it could meander slowly across. The first of these two cases involves a narrow pass that is difficult for it to get through. The other is a wide plain but it costs a lot of energy to get up to it. Chemical reaction rate theory is built on the notion that the reaction always goes across the narrow passage as long as it’s the easiest one to get over. However, in the last decade there has been a lot of work observing that roaming over the flat plain has its privileges.

My postdoctoral student, Inga Ulusoy, and I wondered whether the ketene reaction gave rise to both possible classes of paths. It did! We also wondered the degree to which each path affected the rate in which the molecule reacted. We found earlier that the traditional pathway (over the break between the barriers) was the most important one in a model of the reaction with only two degrees of freedom. This led us and others to question whether our result was an accident of the simplicity of our model. In our recent paper, we extended the model to a larger number of degrees of freedom. Interestingly, the main result was the same. Namely, the reacting partners still have the possibility of roaming, but the direct path over the break between the barriers is still the most important one.

The article, "Revisiting roaming trajectories in ketene isomerization at higher dimensionality,” was recently published at Theoretical Chemistry Accounts 133, 1528 (2014). (doi:10.1007/s00214-014-1528-z) The work was supported by the AFOSR. Equally, importantly, it was a real treat to include our work in an issue published in honor of Greg Ezra's 60th birthday. I have followed his work since I was a graduate student, and have learned much from it. While science is immutable, it’s the fact that people are involved in the discovery that makes it humane. And for this reason, it’s particularly fun to be able to contribute to issues that honor the people involved in advancing science.