Mode- and Enantiomer-Selective Catalysus with Polaritonics)

Let's get started. So if you think about chemistry and physics and one concept that pops up at some point are resonances, that you find where you absorb energy, where you emit energy, but also how you transfer energy within the system. So if you think of a donor-acceptor system, first a resonant energy transfer depends, as the name suggests, strongly on the involved resonances inside the system. So one natural way to interact with resonances and potentially also control them is then light. And if you typically take a molecule or whatever system you have and you place it in free space, then we talk mostly about the kind of inelastic scattering process, as it's a very weak interaction between light and matter. You have a material excitation, it has a certain line width, it comes from basically the photonic continuum in which it is embedded, and then you have fluorescence for instance. You can change this to some extent by confining the optical fields. So we talk often here about a cavity and not SKME, but really it's the cavity that confines the modes by basically enforcing certain sort of boundary conditions to those modes. And that means nothing else than carving specific discrete eigenmodes out of this photonic continuum. So you only allow certain eigenmodes to exist. And those can now interact more coherently, more strongly with the molecules that you place inside the system. The interaction strength depends on the number of molecules that you place into the volume. So you can see that either by decreasing the volume of the cavity, going for instance to small plasmonic cavities, or by putting a lot of molecules inside with a very strong dipole moment, you can reach a very strong interaction. And if it's sufficiently strong that you really see a hybridization between light and matter excitation, then you talk about polaritons. And those polaritons can be used in various different platforms for different applications. One is for instance, polytonic chemistry. So here in this experiment that will reappear during this talk a couple of times, the idea is that you have this deprotection reaction of this PTA complex here, it usually breaks the silicon carbon bond. And now I take the infrared cavity, I tune it in resonance to the silicon carbon vibration of the molecule. So one of the vibrations here, I get my polytonic states, my strong coupling between light and matter. And precisely under this configuration, I can see that my reactant is available for a much longer time. So the reaction, so to say, is slowed down, inhibited under vibration and strong coupling. There are also other possible platforms that are very interesting, for instance, plasmonic systems. And here it's really a mass of different possible processes that play a role. We have very strong optical fields in the vicinity of those plasmonic systems that are commonly used for sensing, but you can also use them for strong coupling to nearby molecules. You can also leverage the electrons, so the charged carriers that you generate after exciting those plasmonic particles and use them for catalysis. So you really have like a very broad tool set that you can apply to control chemistry with both of those systems. And what they have in common is that they're pretty challenging to describe if you aim for chemical accuracy in quotation marks here. So we have a really multi-scale, multi-time scale problem at hand where we have to describe the molecules, the chemical reaction of those molecules, potentially charge transfer happens over femtoseconds, and then also those big systems that are, so to say, giving rise to those more microscopic features that are affecting chemistry. And what we try to do is develop up initial QED to tackle this. The basic current state of the community or kind of where we are heading is very simple. We take quantum chemistry methods that are first principles, and we basically add photons to it. So, for example, we extend density function theory by the quantum electron density, by the quantum electron micro degrees of freedom. So that's what it's called in the end, QDFT, quantum electron micro density function theory. But you can do the same for coupled cluster or other approaches. Bottom line is really that you try to be as up initial as possible, and you add the photons on top to understand better how the photons can control the chemistry, for instance. So I want to focus on a bit more on one special aspect here that plays a role, vibration-strong coupling. And as said earlier in the introduction slides, the idea is that you have a chemical reaction that undergoes as usual, and then you confine it into an optical cavity, infrared cavity, to be more precise, coupled to one of the vibrational modes inside the system. And this way you can control the speed of the reaction or potentially also the product that comes out of this reaction. And we have this nice experiment. It was really one of the first ones. By now there's plenty of others as well that show, for instance, also a catalyzing effect or a steering effect inside the cavity. But this one was really the first one and probably also the most repeated one, most well done one. And we clearly see this inhibition under the vibration-strong coupling. Now the beauty of our initial theory is that we can really try to one-to-one simulate this. So you expect this kind of potential landscape where we have initial state, we have some intermediate, and then some transition state that we have to overcome for the chemical reaction to appear. And we really start with this initial configuration of a PTA molecule and then being attacked by a fluoride anion from the solvent. So basically it should go on a minimum and then at some point break out. In order to simulate this, we have to, of course, perform some approximations. And so up initial does not mean that you don't perform any approximation, it just means that you try to be not too scrutin in the perspective that you apply those approximations. We describe the electrons with QDFT, so this extension of DFT. Nuclei are classical following the first equation of motions and the cavity are Maxwell's equation of motions, so also classical fields here. And probably the most severe approximation is that we only describe a single molecule in single cavity mode. So this is really a severe limitation of our descriptions. And I will go later about methods that we would like to apply in the future, trying to circumvent this limitation. But let's focus on the simple model first here. And this is what we get. So we simulate three different trajectories, and they're illustrated here on the potentiometer surface. So it's not MD, I said it's aerodynamics for the nuclei, but it's just for visualization on the potentiometer surface here. And you can nicely see that all three trajectories, they're entering the slope minimum, so this PTF minus pentameter complex here, basically acetylene chloride, distance just reduced. And then at some point, the outside cavity and off-resonant configurations, they cross the transition state and breaking the acetylene carbon bond, which is the reactive bonds in this case. However, if you're on a resonance with the cavity, then you see that you stay trapped in the slope minimum. So something is the cavity doing here to kind of inhibit crossing this transition state. And when I say resonant, that should probably be a sphere and tell you what resonance means. So in the experiment, they looked at like 860 centimeters. So this resonance here, which is this vibration excitation, you can see the vibration spectrum down here. And here on the top, you see the average silicon chloride, silicon carbon distance. So it's something like a primer, a figure of merit for the reactivity of the system. And you can see that outside the cavity, you have kind of this baseline, and then everything is inhibiting. But there are certain features appearing here that clearly show that for given frequencies of the cavity, you can imagine that you can change the frequency of the cavity, but it's changing distance between the mirrors, you can kind of more selectively inhibit the process for the reactivity. And the strongest effect always appears where you have a strong interactive mode with a strong contribution of the silicon carbon bond. Makes a lot of sense, right? So you want to have a strong coupling between light and matter. But you also want to have that the mode that you couple to is really relevant for the reaction. So that's why you have this combination that seems to be very dominant here in the effect. So you can try to understand this a bit more in detail of what's potentially the mechanism is here. And what you what I've shown you here is the difference in mode occupation between the resonant cavity and the off resonant cavity. So basically, you can see that a lot of vibration energy is kind of redistributed during the chemical reaction inside the system. And some modes are more strongly affected than others. Those modes that are more strongly affected than others are the ones that have a strong silicon carbon character. Again, makes a lot of sense, right? Because it's involved in the chemical reaction. And you can see that between certain modes between 850 for instance and 540, you have a somewhat coherent exchange of energy actually via the cavity over a certain time frame. But most of the energy is kind of loosely getting distributed inside the system. So what's the running idea of the mechanism so far is that if you think of what the chemical reaction should process like, you thermally excite the system in some way like the fluoride is bunching the system kind of in a scattering process, you deposit a lot of energy and now the normal mode start to reorganize this energy. So that means that at some point when you attempt to break this bond, you need certain superposition of those modes that really want to elongate the axis. This means that you have a strong current inside your system. The strong current, think of Maxwell current and uses an optical field. The current can interact very effectively with cavity. So you have a very strong light meter interaction at this moment, which means that the cavity can very effectively absorb energy out of the molecule and really takes energy out. And in this way effectively reduces the temperature for the reactive molecule. So it kind of cools it down. And in the end, it's kind of a Robin Hood effect where reactive molecules, the hottest molecules are getting cooled down by the cavity. And this energy is redistributed in a more equal fashion. It might just be stored for a short time in the cavity. It might get lost to the environment. It might be redistributed to other molecules or simply to other vibrational modes in the energetic vicinity. So I think this was a very important first step trying to understand this, but we have a couple of limitations in this method. One really severe one is that the statistics is very limited. So we've only had like 30 trajectories here, which basically gives us more like a taste, but not very reliable as to what would happen. So the next step, we try to approach this problem by combining machining potentials that we train for energies, forces, and dipole moments for those molecules. And now combine this with molecular dynamics, including the cavity that is also propagated again with maximum. So it's basically now molecular dynamics plus the cavity and the forces that drive the dynamic of the molecule are now combined force of the standard forces from the planetary surface and the cavity forces that are basically nothing else than driving with the cavity the gradient of the dipole moment. And then we get this result here. So it's a lot of information. Let me guide you through it. On the top left, you have the infrared spectrum, and you can see nicely that for higher temperatures, you have more oscillations and broader peaks, also slight red and blue shifts, but that's not too relevant here. And then you can go over to figure B here, where the difference in silicon carbon power spectrum is plotted. So this basically just means that if I look at the silicon carbon bond, it will oscillate at a certain frequency. And depending on which mode it contributes to, it will have a different frequency. And you can nicely see that inside the cavity, you decrease it at certain resonances where the cavity agrees in frequency with the vibrational mode. And it will kind of shift this intensity, the silicon carbon intensity, to, sorry, to the hybrid, to the platonic states in the vicinity. So you see those nice avoided crossings appearing here, where you also have, because there are different contributions of the carbon bond, they're differently in intensity. What really stands out is that you have those low energy features. And kind of intuitively, if something is very slowly modifying in the reactive bond, it should have an impact on the chemical activity. This is indeed what you can see here. If you look at the rate for the system for the different cavity frequencies, you can nicely see that you have certain domains that are now catalyzing, others that are inhibiting. And it's not as clear as before in the previous study, where we used the Ehrenfest plus DFT plus Maxwell in our studies. You can look at certain frequencies, we would like to understand better, like what is the change in entropy and entropy, and perform an erroring plot. And this is basically the result here. The experimental relevant domain is again at 856 inverse centimeters, so the green line here. And if you look at those results, it's really for the first time in qualitative agreement with the experiment, not quantitative, but qualitatively it's for the first time in agreement. So we see an increase in entropy and entropy as an experiment. Now the question is, of course, how does it come that it's not purely inhibiting anymore? The only thing that we changed was that we went from, so to say, full up initial Ehrenfest plus QDFT to MLPs plus MD. And if you do rerun with exact same initial conditions as we have used in the previous study, now with our MLP plus MD approach, you can see that the overall trend for the change in reactivity compared to a different metric, but I mean, they are somewhat comparable, is somewhat consistent. But we have this massive offset. And that is something that we don't really understand yet, that we still have to explore more in the future. One possible reason of what could happen here is that we're not really accounting for the effect that the cavity has on the electronic release of freedom of the molecule. You can imagine if you have a very strong field in your cavity, it basically acts like a static polarizing field on the electrons. The electrons moving much faster than nuclei, right? So if you have a certain configuration of cavity plus nuclei, this will be almost static for the electrons. And that's really not something that we're accounting for. So this kind of polarization correction that we need to account for is not included yet. This might be one reason, and it might be connected to this artifact that we're using the single molecule to simulate the chemical reactivity here. While in practice, it's of course many molecules that kind of collectively interact with this cavity. What we definitely need is more experimental data, because at the moment we only have data like 860 inverse centimeters, and both of our descriptions give us here an inhibiting effect. And as I said, it's consistent with the experiment, but it would be extremely helpful to have also more data outside this domain. So the take-home for the first part is that we have this inhibition under vibration-strong coupling, which is in qualitative agreement with the experiment. We have this change in enthalpy or increase in enthalpy and entropy for the inhibition, inhibiting reaction in this case here. And we have a decent understanding of the possible mechanism, which basically is that we change how vibrational energy is redistributed inside the system, effectively cooling the molecule. So this kind of Robin Hood type effect. But we definitely need more, especially overcoming this distinction between the current theory, single molecule, to the experimental conditions, to really understand it in detail. With this, I would like to basically keep the idea in mind. So we can control the spectrum of the molecule with strong coupling. We control how energy is flowing inside the molecule or between different molecules, and this way control the reactivity. Keep this idea, and now we can transfer it to a different setup. We want to make it enantiomer selective. So what do you need to transfer this idea to enantiomer selective processes, to make it enantiomer selective? First, we need a cavity that is now confining only one handedness of the field. So if you take a normal gold mirror, for instance, then I come in with a certain circular polarization, I reflect at the surface, I invert the propagation direction, but the circular polarization is retained, which means that the handedness of the field is inverted. So this is a basic principle of reflection symmetry on the surfaces. So what we need to do is to break the symmetry. Basically, we need to convert left handed into right handed circular polarization when you approach the surface. And you can do this by designing certain metamaterials that include, for instance, those kind of drilled ellipsoids into a certain gold surface. And given this configuration, you can really confine chiral eigenmolds in this metamaterial cavity here. And this is a simple simplified description. You can really see that you have this kind of corkscrew nature, cosine science here, and the relationship is left or right handed. So if your handedness of the field is left or right handed, basically depends on if this is included in the factor lambda here. And the beautiful thing is now that if I calculate just purely the vacuum chirality density, so how chirally polarizes my vacuum by the vacuum fluctuations of the field, then I will find that indeed, they're chiral. No big surprise, really, if you think about it, because we confine now mostly one handedness inside this cavity, while the other one is basically just going through. So there's no confinement or enhancement, so to say. But this means that if you now place molecules inside the system, and this is not fully up in issue, it's really simple. Assume just the simplest imagination for molecules, how many oscillators and two level systems. Important thing is that they have an electric and magnetic dipole moment. So if you now place them inside the system, you would expect again, strong coupling, right? And indeed, we find the same basic principles as before. So again, it scales with the amount of polarizing material that you place inside this cavity. But then you also have the second factor, one plus lambda chi. I said lambda is the handedness of the field. So it's plus or minus one for transversal fields. And then chi is the degree of chirality for the molecule. So basically, the proportionality between electric and magnetic dipole moment. So if they're now of opposite sign, so if the molecule is left handed, and the field is also left handed, well, then this will increase this one, you can see, right? I increase the interaction strength between light and matter. While if they're of opposite sign, so if they're mismatched, then I would decrease the interaction strength. So I can talk selectively to one enantiomer stronger than to the other one. And I can use this now in multiple different ways. One possible approach is to really control even just lifetimes. If you think of fluorescence, for instance, then the rate of fluorescence depends very much on the optical environment you can find in the molecule. So that means if I talk more strongly to one enantiomer, then this will have an enhanced fluorescence rate compared to the other one. If I reach strong coupling, so I create those polytonic states and we split them in energy, then I can, for instance, more selectively excite one of the two enantiomers. I can transfer those vibrations from coupling ideas that I've shown you before, now also to enantiomer selective reactions. Or you can look at really fundamental features like homochoreality, trying to understand better why is one chemical species, one enantiomer, more present in our body, for instance, than another one. Here we can really selectively and very controlled break the symmetry in the which would be extremely useful for understanding those processes. I think I'm running out of time. So last aspect. So there is still open challenges that we will fix in the future. And one is very much that the degree of correlity is for many molecules very small. So that means that this selectivity is also small. And one possible fix is to move away from only polytonics, transversal fields, to combine this with longitudinal fields. So mix chiral polytonics with chiral plasmonics, because this allows us to really boost this lap-factor lambda here, if you have longitudinal fields, and in this way be more selective. So I will skip the next part because I'm running out of time. Basically, the bottom line is that we can also control plasmonic catalysis by using vibrational strong coupling, sorry, vibrational strong coupling, electronic strong coupling. But I think I would like to come to the conclusion here. So I've demonstrated that vibrational strong coupling can control the chemistry. We have now a qualitative agreement with the experiment. We have a decent understanding of the mechanism that is controlling how vibrational energy is flowing within the system by using the optimal release of freedom. But there are still open questions, like how do we account properly for localization? Is this relevant? Is it important to treat many molecules? For sure, to get a quantitative agreement, but maybe the qualitative agreement that we find is already sufficient for a single molecule. So many open questions and a lot of method development that will be involved here. It's also interesting to mention or highlight that, of course, there is an interaction with the solvation shell around those molecules, right? So if I control the polarization, for instance, of those molecules by placing it inside the cavity, then this will have an effect on aggregation and solvation dynamics. So we have some studies on this here. I've also shown you that you can transfer this to chiral systems and make an enantiomer selective. And I have not shown you, but maybe you can believe me or read up on it, that we can, to some extent, also control plasmonic catalysis. In this case here, boosted by factors six to seven. And then there's a lot of method development that is still to be done here, just simply because this up in the QT topic is very fresh domains. Thank you for attention. I'm looking forward to your questions.