I'm Corin, CEO and co-founder of Rowan, and in this video we're going to talk about calculating Fukui indices. Fukui indices are named after Kenichi Fukui, the 1981 Nobel laureate in chemistry, along with Roald Hoffman, and really a leader in the field of applying molecular orbital analysis techniques to predict sites of reactivity, which at a high level is what Fukui indices are all about.
Now, if we think about trying to predict where a reaction will occur on a complex molecule with many potentially reactive sites, we can imagine doing things the old-fashioned way, using a tool like Rowan or any other computational chemistry package. We could find a transition state for a reaction with each individual site. We could run optimizations of these transition states to do them at a high level of theory, and then sort of predict the difference in energy between all of the competing transition states to predict which sites will react quickly and which sites will react slowly.
Now, this is a rigorous method and one which will almost certainly work if the transition states can be found. But there's something about this that feels a little bit wrong. In many cases, a trained organic chemist can look at just a substrate—if you say this is going to react with an electrophile, they can predict where a reaction is most likely to happen without actually needing to know the structure of the electrophile. In some sense, it seems like it's a little overkill to have to run a different transition state search for each different electrophile when often what we care about is just, where is electron density stable or unstable on this molecule? You know, where are there electron-withdrawing and electron-donating groups?
And this, at a high level, is what Fukui index calculations are all about. When we're calculating Fukui indices, we're essentially adding or removing electrons to a system and then seeing where this extra positive or negative charge flows. And by looking at this, we can tell where on a molecule the positive or negative charge is going to be stabilized and predict where reactions will happen.
Let's see what this looks like in practice. So from the homepage of Rowan, we can click on “New Fukui index calculation” here, which takes us to this submission screen. And I'll quickly input a SMILES string for a simple but relatively non-trivial molecule. So we'll look at this sort of extended conjugated alkyne here. Sorry, not an alkyne: we have a double bond, a carbonyl, and then we have a diene here, and then we have a methyl group on the end. So this has potentially a lot of different sites of reaction. Let me go in here and just rotate around this dihedral to sort of align a little bit better with our chemical intuition on what this will probably look like, maybe go to a little bit of an s-trans conformation here. And obviously, you know we can imagine looking at the system that you could see 1,2-addition, 1,4-addition, or 1,6-addition if you were to add in a nucleophile and so we might actually care about where this is likely to happen or you know what the relative proclivities are going to be.
Here we can see the output of our Fukui index calculation. We have three different Fukui functions: these are called in the literature f(+) or Fukui positive, f(0), and f(-). So f(+) represents reactivity towards nucleophiles, f(0) represents reactivity towards radicals, and f(-) represents reactivity towards electrophiles. Let's sort of go through these one by one. We can see here that, you know, the exact value of the function is broken down a little bit by atom. And we can actually see the values here, but we can also see a lovely visual highlight just by which sites are more red. And we can see here that you know the most red carbon on this molecule is actually C6, so the 1,6-conjugate addition site. And so what this is telling us is that you know 1,4-conjugate addition and 1,2-conjugate addition are definitely possible, but if we're adding a nucleophile to this system we can probably expect a reaction to occur here at this carbon. If we look at f(0) which represents reactivity towards radicals again, we can see that carbon 6 is predicted to be the most likely site for radical attack. And now if we look at the negative Fukui function (reactivity towards electrophiles) here we can see that now C2, this alpha carbon is the most likely site of reactivity towards electrophiles as opposed to the other carbons which are slightly different in color, although C6 still sort of looks okay here as well, which is interesting.
Now, these values are obviously a little bit imprecise. This is just a function of where charge ends up going—and so a lot of atoms often end up having large changes in charge no matter what, like these oxygens. Carbonyl oxygens almost always have some value for the Fukui index, as do heavy atoms, like halides, so it's not a perfect metric. It needs to be sort of filtered through your own chemical intuition as to what's reasonable or not. But nevertheless, Fukui indices are a great way to quickly try to build up an intuition for reactivity, and they can be used for a lot of other downstream processes too, where the identity of the reactive partner is complex or might not even be known.