OK, let’s get physical organic here for a little while. For those outside the field, physical organic chemistry is the branch that studies how and why the reactions of organic chemistry happen – the details of which bonds break and form, in what order, in what arrangement, where the atoms and electrons are moving and why they should be doing that and not going down some other path. I have never had much patience for actually doing these kinds of experiments (it is necessarily very picky work), but I’m glad that other people do, because I’ve always found them interesting to read about. I’m going to go into a recent paper by Yexenia Nieves-Quinones and Prof. Dan Singleton at Texas A&M, and I have to say up front that this post has the potential to get fairly long and fairly geeky. But I’m going to take on the challenge of explaining what’s going on to non-chemists who want to follow along as well. The (non-indented) sections below that break into italics are the backgrounders for those outside the field; the indented italic parts are, as usual, quotes from the paper under discussion.
Everyone knows TNT, trinitrotoluene. You make it, unsurprisingly enough, by attaching nitro groups to toluene, a common solvent you can get at hardware stores. Most people don’t have the reagents and equipment sitting around to do nitration reactions, though, which is not such a bad state of affairs. The nitros go on one at a time, and they get successively harder to bring in, which does not make polynitration a very enjoyable process. But today we’re talking about just the first nitro group, the formation of the rather plain-vanilla nitrotoluene.
There are actually three nitrotoluenes, and that’s where all the trouble starts. Toluene itself is a six-membered benzene ring with one methyl group attached, and a moment’s thought (or a thought back to distant memories of organic chemistry) will show that you can attach the new nitro next to the methyl (ortho), one carbon down from that (meta), or across from the methyl (para). All of these are new compounds with slightly different shapes, polarities, boiling points, etc.
It’s been noted for a long time that if you nitrate a mixture of benzene and toluene that you get nitration on both molecules (less than twofold selectivity between them), but nitrating toluene alone is actually quite selective. You get hardly any of the meta isomer, but why should those meta-toluene carbons be much less reactive than plain benzene? A single methyl group added to a benzene ring shouldn’t change things that much. The same reasoning applies if you try to assume that toluene’s other two carbons have just gotten more reactive – if they’re so reactive, how come they don’t react much more readily than benzene itself when they’re in the same flask?
Now we get to one of the key concepts in physical organic chemistry: the “transition state”. In every reaction, there’s got to be a point where some bonds are partway broken and some new ones are partway formed, and this awkward instant is actually the highest-energy moment of the whole process – basically, it’s the hill that any reaction has to get over in order to make it down to a lower-energy product (if the product isn’t lower-energy than the starting material (what’s called an exothermic reaction), the reaction is very unlikely to go in the first place). There are actually plenty of reactions whose products are way lower in energy than the starting material, so you might just predict they’d happen spontaneously in a mighty blast of flame. But they don’t, because the transition state is so much higher in energy that unless they’re given a huge energetic kick to start things off, they can’t make it over. Aluminum is the perfect example: everyone has aluminum foil in their kitchen, it’s perfectly safe at any reasonable temperature. But with a really hot starting fuse, you can set off a mixture of aluminum powder and rust (iron oxide) in the thermite reaction, where the aluminum burns with enough release of heat to give you spitting white-hot iron as a by-product.
To make things worse, this mono-nitration is actually a pretty exothermic reaction. It has an early transition state, so it shouldn’t be very selective. It doesn’t even seem to matter how reactive the nitrating reagent is; they all give you mixtures of ortho/para with very little meta. That means that the transition state must be getting easier and easier to attain, but the reaction still gives you high selectivity, which really doesn’t make much sense. That’s where, in the 1960s George Olah (later a Nobel winner) came up with an ingenious proposal to explain all this. The rate-limiting step, he theorized, wasn’t the bond formation/bond breaking part, it was the formation of a pi-complex of some sort between the incoming positive nitro species and the aromatic ring. That’s why benzene and toluene react at close to the same rate – this complex forms at about the same rate for both. The positional selectivity come later, when the pi-complex breaks down to the various sigma-complexes after the carbon-nitro bond has formed. There was also talk of an “encounter complex” between the nitrating agent and the toluene, although whether this was the same as that pi-complex depending on who you talked to and what you meant by those terms.
That’s how I learned it in school, but there have always been objections to this way of looking at things. You can find proof for this mechanism with very polar benzene derivatives that are much more likely to form that initial pi-complex intermediate, that seems to be settled. But plain old toluene is harder to fit into this framework, and it’s only been in the last year or two that anyone has claimed to be able to see the complex and get any spectroscopic data on it. This is the situation in a lot of these mechanistic studies: reaction mechanisms change under different conditions, and you have to be ready to deal with the fact that your explanation is going to break down at some point. The problem is that if it breaks down on the simplest example possible (benzene versus toluene, in this case) then some fundamental misunderstanding is at work.
OK, why does anyone care? The short explanation is that we’d like to be able to predict what reactions are going to do before we even run them. Pat that, if we had a complete picture of how all these things work, we’d be able to discover new chemistry just by letting the simulations rip and coming back later to see what they’d found. We are a long way from that as things stand, of course, but to get there we need to really understand every nut and bolt of simple reactions. And this is actually a pretty simple one – the products aren’t weird and the starting materials are common industrial chemical. Aromatic nitration shows up in every sophomore organic chemistry class, and the fact that we can’t seem to get a handle on why some of the absolutely simplest cases behave the way they do is proof that we’re missing something important.
This new paper offers a different explanation. Nieves-Quinones and Singleton have done a lot of computational modeling of the reaction, and are coming at the question from a different angle. Even though this is not a particularly complicated reaction, going after it from the ground up, computationally, is still not straightforward. All the various methods have their own biases – they overvalue some sorts of interactions compared to experiment and undervalue others, they over- and underestimate the energies of particular chemical species (again, compared to experimental evidence) and so on. A further complication is the addition of solvent molecules, and if you’re going to explain a real-world reaction, you have to account for the fact that it’s surrounded by solvent and not taking place out in an intergalactic vacuum. Picking the least biased calculation technique under all these constraints is not easy, but this paper does an admirable job of explaining the complexities and showing why they used what they used.
Computational chemistry can be absolutely bewildering even for other chemists, so don’t worry if all this sounds complex to you if you’re coming from outside the field. The problem is that quantum mechanics does an absolutely terrifyingly great job at explaining the behavior of electrons and other subatomic particles, but it’s too much to handle for whole molecules. As far as physics goes, quantum mechanics and relativity (dealing at the other end of the scale as far as physical objects go) are the gigantic undefeated badass champions of theory. They stand at the plate in front of the entire stadium, point out exactly where they’re going to hit the next pitch, and swat it over the fence time after time. It’s even more impressive than that: they do the equivalent of pointing out how the next one is going to bounce off the tomato slice on that sandwich ad next to the scoreboard and land in the beer cup of that guy with the bad haircut in Section ZY, and then do just that. Over and over. Which is why it’s deeply unnerving that the two theories seem to be fundamentally incompatible when it comes to gravity, and are probably going to end up being parts of some bigger and even more terrifying understanding, but that’s another story.
At any rate, you can calculate exactly for very simple quantum systems, but not for more complex ones. If you’re talking about whole molecules reacting and moving around, you’re going to have to introduce approximations and fudge factors to get anywhere at all, and that’s where the complications and the arguments start. There are a lot of different ways to model the behavior of whole molecules computationally, and they all have their advantages and their disadvantages. A method that looks wonderful on one aspect of molecular structure or behavior may well be turn into a stumbling wreck if you push it onto another task. Knowing these things and dealing with these limitations is the domain of the computational folks.
Fitting the current understanding of toluene nitration to computational methods has not been easy – there’s a long trail of papers over the years doing just that, none of them wildly successful. In this latest work, too, trying to explain the nitration reaction via study of the pi-complex and the various possible transition states did not lead to anything that matches experiment:
Overall, the attempts above to understand the selectivity of toluene nitration based on transition states failed on multiple levels. Predictions of the product ratios from the energies of TSs fail entirely to account for the selectivity. On a higher level, the pervasive implicit assumption in such a calculation, that transition states lead to a single product, fails. Finally, even when the TS studies are augmented by trajectory studies to allow for the mixture of products obtained from the various TSs, the calculations are still unable to provide a reasonable prediction of experimental observations.
That’s not so good. As the paper notes, when this happens, it’s tempting to think, well, OK, we’re getting the energies wrong here – the theory would work fine if we had the whole energy surface (hills, valleys) lumped around the right way. One problem with that is, though, that the solvent in a reaction can be part of these energy calculations, and when that’s the case, things can get very hard to evaluate. That’s especially true if you’re moving between a less organized cloud of solvent molecules to a more organized one, or vice versa – these entropic effects can be decisive, but very hard to take into account.
What Nieves-Quinones and Singleton found, though, was that they could, in fact, predict the reaction’s outcome if they went back and included solvent molecules and calculated the trajectories and dynamics of each individual species. They had the nitration taking place inside a sphere of one hundred and one explicitly calculated dichloromethane molecules, which must have burned up a pretty good amount of processing time.
The reaction certainly looks different from this perspective. The “encounter complex” forms very readily by these calculations, with the nitrosonium species readily homing in on the ring every time it gets close. Along the way, a lot of the hills and valleys that were seen in the previous energy calculations just sort of disappear, and the pi-complex just doesn’t make an appearance at all. Sigma complexes do show up, but in an odd manner. These new calculations are dynamic, that is, they present a picture of the reaction over time. And the sigma complexes take a weirdly long time to form, about twenty times as long as you’d expect based on what we know about nitrations. As you run a bunch of simulations from different starting points, the nitrosonium often enough appears to be sort of hovering over a carbon that it could react with, but it just sits there looking at it for hundreds of femtoseconds, which really is a long time as these things go.
The nitrosonium also takes its time making up its mind, sort of roaming around the ring. It never crosses the middle of the toluene ring, interestingly, but moves around it while staying above the plane. And it “makes up its mind” about what carbon to react with quite late in the game. The way the paper describes the nitrosonium molecule’s movements reminds me of a hummingbird trying to figure out which flower to go for – it hovers, dips in, changes its mind, moves over a bit and thinks about it again. Finally, though, a sigma-complex does form, and what’s interesting is that these calculations end up reproducing the experimental ratio of products, which none of previous calculations (or textbook explanations) have ever managed to do.
So why is this different? Well, when chemists learn about transition state theory, the time involved in the various stages is just not part of the picture. We have a static picture rather than a dynamic one – we think about the energy levels of the different species and how the reaction can slide from one of these to the next, but not about how long it takes to do those things. It may be past time for us to revise our thinking. It’s not like molecular dynamics is some sort of neglected field, but it’s just quite hard to do well. We’d love to apply such timing insights to even more complex systems, but that can lead to even fuzzier results, and no one’s sure how much to trust the outputs in any given situation.
So where does the selectivity come from? It turns out, according to this approach, to have a lot to do with the solvent molecules around the reacting species. The positive charge on the nitrosonium molecule and the positive charge on the eventual sigma-complex that it forms with the toluene are different beasts with the charge in different places, and the reason for all the hummingbird behavior seem to be the solvent molecules needing time to orient themselves around these charges. If you’re trying to calculate this reaction in a vacuum (old-style), you’ll miss all of that completely, of course, but you also miss it if you try to use the easier approach to including solvent (implicit solvation), because that assumes that all the solvent molecules are always in equilibrium with the reacting molecules at every step. And the key thing is, they aren’t. They need time to sort things out.
So the classic way of thinking about reactions just doesn’t cut it here. In fact, the standard way to approach these things leads you off in the wrong direction. As the authors put it:
The implicit assumption that a thin mechanism, one only considering transition states and intermediates, was sufficient to understand experimental observations in nitrations forced a particular description of the mechanism. Because the intermolecular and intramolecular selectivities did not fit together, it was surmised that there had to be an intermediate followed by a series of separate transition states affording each of the products. The nature of the intermediate was debated, and no proposal comfortably fit all observations, but the view that there had to be an intermediate followed by productdetermining transition states was unquestioned. This view fails.
There aren’t any intermediates other than the sigma-complexes, and there aren’t any transition states other than the one leading to the initial encounter between the two reactants (and that one doesn’t amount to much). According to this work, all the extra intermediates and transition states that had been brought in are like the epicycles that Ptolemy and his successors added to the motions of the planets in an attempt to keep the Earth at the center of the scheme while explaining the increasingly annoying data from the actual skies.
These conclusions will not please everyone who reads them. Coming along and saying that classic transition state theory is inadequate to explain a reaction that’s taught in sophomore organic textbooks will get on some nerves, and I think that I speak accurately when I say that computational chemists are not shy about disputing each others’ conclusions. The authors throw down a glove near the end of the paper by saying, essentially, that this approach is the only one that actually predicts what you get out of the reaction, so if you have a better idea, come on down. And they maintain that since they’re the only ones who have actually gotten a correct prediction, after many and varied other approaches, that they feel that they have a good chance of being correct.
The last sentence of the paper also lays down a marker: “Our results suggest novel methods for the control of selectivity in these reactions, which we are pursuing.” Now, that’s the way to do it. If your new theory really is the right stuff, then you should be able to use to to predict things that the other schemes wouldn’t pick up on. I very much look forward to some further experimental backup, and I’m sure that Singleton and his group are cranking away right now trying to generate some.