Can you start the broadcasting? Okay. Okay. So hello everyone, welcome to this workshop on the physics and chemistry of solid-liquid interfaces for energy conversion and storage. My name is Ralf Gebauer. I'm from the ICDP in Trieste and I'm one of the organizers of this conference. I would first start by presenting to the other organizers. Perhaps I start with the Laura Sulpizzi. Laura, do you want to say some welcome? Oh, yes. I don't know. I will continue. I'll let you finish the introduction. Okay. So the other organizer is Simone Piccinini from C&R. Hello, everybody. I'm Simone Piccinini from C&R here in Trieste. Yes. And last but not least is Nicola. Hello. Welcome, everybody. Right. Okay. That was fast. Okay. So to start the workshop, before we come to the scientific part, I would like to say some words about ICDP and the organization, in fact, which is making this event possible. Let me share my screen. So I hope everyone can see this slide now. So this is a workshop which was originally planned to take place last year, also in May. And it was planned as a usual workshop as we have your ICDP with people traveling to ICDP, everyone being in the same lecture room and drinking espressos in the breaks and so on. But as we all know, the pandemic has made events like this completely impossible. So we moved to one year ahead. So instead of 2020, it's this year and the two days that this workshop starts and we start in Zoom instead of our main lecture room. So this workshop is planned to cover a very, on one technical, but at the same time, important topic, which is the interfaces between solids and electrolytes, which is a topic which is very important for many applications, as you will hear during the whole week. And this workshop, like many others, goes into the idea which ICDP, our institution, has the International Center for Theoretical Physics, which is to disseminate science, fundamental science, and to bring together people from all over the world. So what you see here is a picture of the main building, the main, the building effect from which I'm speaking right now. And you see that in front of the building there is a flag of the United Nations. So this is because formally we are a United Nations organization, so we are staff of UNESCO, which is the United Nations Science, Cultural, and Educational Organization. And so we function under an agreement between UNESCO, the International Atomic Energy Agency, and Italy. And so, as I said, our goal is to bring together scientists from every corner of the world to talk about science and to exchange about science and possibly to collaborate on scientific thoughts. Trieste, for those who have never been here, is located at the Adriatic Sea, the north-eastern part of Italy. And in fact, about six years ago when ICDP was founded by the Nobel laureate Abdu Salam, Trieste was, in fact, you see here on this map, there is the border to Slovenia, right behind ICDP and right behind Trieste. And at the time, that was one of the reasons for choosing Trieste because six years ago in the middle of the Cold War, one wanted ICDP to be not seen as an organization of the West or the East, but kind of really as one world organization. So this is why it was found, in fact, if you want directly on top of the iron curtain at the time. And today, obviously this iron curtain is gone and we are here very happily, scientifically collaborating with the scientists, also from all our neighboring countries, Slovenia, Croatia, Austria, and obviously Italy, so on. So our mission is to do, on one hand, advanced research ourselves here. We need to do research ourselves in order to, in fact, know what is important in order to be able to teach our students, but mainly to provide a forum of exchange, information and scientific idea and also to have these facilities for welcoming visitors and so on. And I hope that very soon when the pandemic will be more under control, that we can resume welcoming people from all over the world here in Trieste. I'm sure that many of the participants who are now in Zoom have already in the past been here and joined us in ICDP. So let me just give you some words about this workshop, which is about to start. We have in total about 300 participants. Most of them, so two thirds of them are junior scientists. About one third of them are female, two thirds are male, which is kind of probably corresponding, probably even a bit better than the average in hard sciences. And we are very happy to have a huge part of the community from Asia, which is joining this workshop, especially we have many Indians who are listening to us today in this workshop. So we are very happy to be able to reach thanks to this electronic broadcasting out to everyone. The disadvantage obviously of doing things interactively on Zoom rather than in person is that interactivity is limited in an event like this. But nevertheless, I would encourage every one of you to ask questions nevertheless. The way to ask questions is that you use the Q and A tab in the bottom of the screen. And in the end of the talks, we will either read some of the questions to the speaker or we will open your microphones so that you can ask the question yourself to the speaker. Okay, so this is how we plan to do everything. Let me stop sharing here. So here I take again. I think if the others do not have any other general words of introduction to say, then we can directly without any break come to our first talk. So our first speaker is Karen Chan. We are very happy to have her here. She is a professor at the Technical University of Denmark and she is a big expert on everything electro catalysis. So she and her group, in fact, they are working on understanding of electrochemical processes, wherever it's important for sustainable energy, but also for things like fuel and fertilizer production. So for storing energy in chemical bonds, if you want, I'm sure she will say much more about this in a minute. Before being in Denmark, Karen earned her PhD at the Simon Fraser University in Canada. Then she went to Stanford University and to the Slag Accelerator there. And now, as I said, she is in Denmark as a professor working on electrochemistry. Okay, Karen, the floor is yours and we are happy to have your talk on the impact of the electric double layer on electrochemical CO2. Okay, so thank you, Raoul, for that introduction and to the rest of the organizers for having me at this wonderful symposium with such a great diversity of topics and speakers. And so the general theme that I'm going to address here is the impact of the electric double layer on electrochemical processes. And in particular, I will draw examples from electrochemical CO2 reduction. I will first talk a bit about the challenges we face in obtaining activation energy barriers in electrochemistry. And then talk about the application of these methods towards a mechanistic understanding of electrochemical CO2 reduction, in particular focusing on the impact of dipole field interactions and then also solution phase reactions, which is a rather new topic, but it shows to have an important impact on the overall activity and selectivity towards desirable high value products. And so first of all, I would like to acknowledge all the people who did the work shown here are the first and co-first authors of the work that I will cover. I also want to acknowledge all of these co-authors who also really contribute it significantly, as well as all of the drivers, the PIs behind a lot of the efforts in our collaborations. And so very briefly, this is the vision that motivates all of our work, harnessing renewable electricity in order to electrochemically reduce, for example, CO2, back to fuels and industrially relevant chemicals. And so illustrated here are the processes at play, CO2 reduction to a variety of possible products, always in competition with hydrogen evolution, which very often has comparable or competing over potentials. And that the anode, we have water splitting to form oxygen, although more and more, we are looking at alternatives in order to take advantage of paired electrolysis. And so from a computational electrochemist perspective, our goal here is to achieve a good enough mechanistic understanding towards activity descriptors that can ultimately be used to design more efficient, more selective electrocatalysts. Okay, so first off, here is a schematic of the model system that we would like to understand. And as we all know, it's extremely complex with many elements, there is charge separation, the presence of solvents, ion effects, the need to apply a potential interfacial fields at the interface. All of these, which together are very challenging for us to treat from an ab initio, in particular perspective. And probably that is the reason why many of us are here at this workshop today. But amongst all of these challenges, there is probably one theme that we would, most of us would agree that we can treat, and this is the reaction thermal dynamics, in particular in cases where the vacuum approximation is okay. And shown here is just the example for say a free energy diagram of hydrogen evolution, calculate using this approach, and it really allows us to trivially relate our surface science simulations to electric chemistry for proton electron, as well as ion electron transfers in general. However, when it comes to activation energies, the impact of solvation, the impact of ions, the corresponding field effects, and the coupling of the kinetics to mass transports phenomena and the resultant impact on the activity and selectivity that we can obtain, these are open challenges and there's not one method that we all use and that gives us all consistent results. And so when we are attempting to understand the complex electrochemical processes, we are interested in persisting energy conversion. I am here making some big assumptions and the first one is that's when it comes to activation energies. We are approximating this with static water structures and sometimes an implicit electrolytes on top of that in order to charge the surface to the desirable driving force. When it comes to ions and field and mass transport phenomena, what I'm going to focus on in this presentation, all accounts for this with continuum mean field models. And so in what I am about to present, we are neglecting completely dynamics as well as any specific interactions with ions which is currently being studied by many groups today. And I'm sure we will hear a lot more about this as this week progresses. Okay, and so what I'm going to cover then in this talk are three topics. The first is how we determine activation energies today. And the one takeaway that I would like you to have in this talk is the idea that the surface charge density could be a good descriptor of the potential drop in the driving force at the interface in contrast to the commonly used work function of the metal solution interface. And I'm going to show why that is. And then I'll talk about the application of these methods towards a mechanistic understanding of electrochemical CO2 reduction. Okay, so starting with activation energies. So one of the major challenges in determining activation energies is how we can do so under constant driving force. In a fully explicit of an issue of simulation we are operating with a constant number of electrons whereas in experiments we are operating under constant potential. And this issue is illustrated here for a typical simulation of a Hey-Rovsky barrier on platinum where we can see along the reaction pathway there is a significant evolution in the surface charge density shown and these charge density isosurfaces here. And so we can see this issue if we look at say the work function of the metal solution interface where we see there is two to three electron volts change along the reaction pathway which is well beyond the range in the potential of any process that we might be interested in. And so how do we mitigate this issue? I would say of all the work that's been done in the past 10 years or so there's basically two classes of approaches. The first would be what I call extrapolation approaches and it goes along the idea that when we go to an infinite sized unit cell then we are operating under a constant driving force. And this is illustrated schematically here where we can see that the change in charge density along the reaction pathway becomes smaller as we go to larger cells. And originally in the Rosmeizel and Nerskopf group this was done explicitly where one would calculate the same reaction with the static water layer at larger and larger and larger unit cell sizes until one can extrapolate to the infinite cell size. And so this is computationally very expensive and one can approximate this process using a capacitor model for the electrostatics at the interface. The alternative which has really, really proliferated in the past few years are grand canonical implicit explicit hybrids. And there's a wide variety of possibilities when it comes to the implicit continuum approximations to the distribution of charge in the electrolyte. But the main idea behind this is as follows. And that if we have a process that leads to a large change in interfacial dipole for example, CO2 adsorption leading to a dipole as follows at the interface this is compensated for by the application of some continuum charge distribution. And this can be planar, it can be a Poisson Boltzmann and so forth. And just as an example here this is a charge density isosurface that is calculated using a linearized Poisson Boltzmann approach using the code that's been developed in Richard Hennick's group. And as you can see there's this kind of continuum counter charge applied in response to the CO2 adsorption which then keeps the work function constant. And so with all of these approaches out there to describe the process under constant driving force this begs the question of when they might be equivalent. And so to answer this question what we have developed very recently is what I'll call a multi-capacitor approach which is a general framework for us to deal with hybrid implicit and explicit method. And pictorially what this really does is it considers the various charging components of the interface whether it is say an explicit charge say a proton or a co adsorbate charge say corresponding to a very negatively charged adsorbates which also changes the driving force at the interface or some distribution of continuum charge whether it's a planar distribution or a Poisson Boltzmann distribution or a modified Poisson Boltzmann distribution and so forth. Each of these charging components we consider to in general have their own capacitance. There's no reason they should all be equivalent. And the main takeaway that we have from this approach is that when we have multiple charging components the interfacial potential drop from the charge distribution is not unique to some applied bulk potential. And so for say a given bulk potential or a given work function that can correspond to a very different potential drop at the interface which is driving the processes we are interested in. And what I would suggest is that this interfacial drop is really better captured by a surface charge density. And this idea that the electric double layer can affect the driving force and our kinetics is not new. It's a page from the playbook of Frumkin who proposed what he called the Frumkin double layer correction to Butler-Volmer kinetics. And this is essentially that idea here and it applies in our simulations and it applies experimentally as well as I will discuss later. Okay, and so to illustrate this let us start with some examples and let us first to go into the idea of the capacitor viewpoints of the electrochemical interface. Let us consider model systems that only have a single charging component. So this is fully explicit where then the only way that we would be able to modify the driving force is by changing the concentration of the charge species. So for instance, going to different cell sizes. And so this let us consider this for say the Volmer reaction. So a proton electron transfer to the surface as well as a CO2 absorption as I showed earlier which leads to a surface dipole. And in these cases, we can consider the electrostatics using a capacitor model and what this at least thus far assumes is that we are dealing with a constant capacitance and a reaction geometry that doesn't vary with potential. And so what we have found more recently is that this is in general not the case. However, for simple proton electron transfers in particular from hydronium, this is a valid assumption. And so one can determine the electrostatics by Taylor expanding about the charge Q. And so this is quite a standard approach. And I believe the first person I saw to write about this is Jean-Sebastian Filot in a paper from, I don't know, 15 years ago, perhaps looking at homogeneous background chart. And so by doing so, one can substitute in a couple of quantities for these first and second order derivatives. The first here, the change in energy with respect to charge at zero charge. This is the work function of the interface under zero charge. And the second term here is inversely proportional to the capacitance. And so then with that, we have this expression for the energy associated with charging this interface. And then for any given elementary step between two states, for instance, between a transition and an initial state, one can determine the variation of energy with respect to charge and converting this using the definition of capacitance. We can obtain the energy as a function of the average or the mean potential. Where in general, in a finite cell size, we do not have equivalent potentials between the first and the second states that we're considering because of this finite cell size effect. So then we have this linear relationship with respect to the charge of the different images we're considering. But if we are to take this to infinite potential, then the two potentials then approach one another, such that we get this relationship. And so this would be the infinite cell size result. And what this limit shows us is that all of our computations under the assumptions here, we would be able to obtain the constant potential limits by simply looking at the energy with respect to the mean potential. So our raw energies give us the constant potential limit at the mean potential between the states that we are interested in. And so considering this, then for the two examples, the Rormor reaction and CO2 absorption, we indeed as a function of mean potential obtain these linear relationships that we would expect if a capacitor model were valid. Okay, so this then is how we could describe model systems with just a single charging component. Now the question would be, what happens if we had more than one charging components like we have an implicit systems? What if we were to, instead of going to many different cell sizes, modify the driving force at the interface with the application of an implicit charge as illustrated here. Now what we find is that when we do so, the results depends very much on the system size or it in fact depends very much on the proportion of implicit and explicit charge. And so in general, a given work function doesn't uniquely determine the energetics when we are including multiple charging components. And so this is not something that we can do straight out of the box, take an implicit, explicit hybrid, set a work function and then obtain an activation energy because it depends very much on how we set the system up. And this, we can put some math on this again with this Taylor expansion approach where in principle, if we expand now about our explicit simulations, adding an implicit charge, then we can see where this comes from. So what we do here is we have this explicit result and the impact of the implicit charge is to add this contribution here. And so starting with an explicit value, we have an implicit contribution now with a slope that depends on the relative capacitances between the implicit and explicit contributions. And in general then, this is not a single valued function if the explicit and implicit capacitances are not equivalent since in general, we're adding an implicit charge above our explicit layers. And so there's no reason that we would expect a consistent capacitance. And so this is illustrated here, some charge density iso-surfaces of implicit charge on top of our explicit result. And it goes back to this idea that with different charging components, we can get multiple interfacial potentials depending on how we set up our systems. And so here I've shown everything with respect to mean work function, but we get exactly the same issue when we're doing grand canonical constant potential simulations with these approaches because the idea is the same, depending on the proportion implicit and explicit charge, we're changing the interfacial potential drop that is driving the processes that we are trying to probe. So how do we mitigate this issue then? This is a pretty significant issue considering the wide range of energies that one might be able to get when we're charging the surface. And we do want to be able to charge a surface with implicit charge because we wanna circumvent the need to go to different cell sizes. And so this is the strategy. If we were to take all the calculated data on the previous slide and we plot it as a function of the surface charge density, the average surface charge density along our reaction pathway, we actually get a consistent result. And we can actually see that from our simple capacitor models where if we are to consider then the energy as a function of surface charge density, then we obtain a single valid function. And the physical meaning behind this is really the surface charge density at a conductor is proportional to the electric field. And the electric field is a good proxy for the potential drop at the interface that is driving the processes that we are interested in. And I just wanna note one corollary to this and that with this understanding of the interface then our results are insensitive to the counter ion places. And so there's many different ways to put the counter charge under with current methods whether it's a planar or a Poisson Boltzmann or so forth. And if we were to say, look at the energy for COCO coupling as a function of the mean work function, we get slight variations depending on where we put the charge. And this is exactly the same effect that I was showing before. But if we were to consider everything as a function of surface charge density, then we get consistent results. And so the main takeaway here then is that we should determine our energies as a function of the average surface charge density. And with that, we can relate that to the energetics as a function of work function using known properties of the charging of the metal solution interface. So double layer capacitance and potential of zero charge. And essentially what this does is it corrects for any unphysical capacitances that might arise depending on where we're putting the implicit charge in our simulations. Okay, so then with that, I would like to move on to some applications towards a mechanistic understanding of electrochemical CO2 reduction. I will be focusing on two phenomena, adsorbate dipole field interactions and then solution phase reactions and the impact of mass transport. And what I would like to note here is that both of these effects manifest themselves as what I will call pH effects. And that is deviations from the reversible hydrogen electrode scale. And so these are not effects that we can treat with a computational hydrogen electrode since they involve the electrolytes. And so starting then with adsorbate dipole field interactions, these are really already known to us from thermal catalysis. And they have been quite thoroughly studied in relation to the role of promoters in thermal catalysis where the adsorption energy of some very polar polarizable adsorbates can be stabilized with respect to field through this Taylor expansion that we show here where we have the dipole moments and the polarizability of the adsorbate. And CO2 reduction in contrast to say oxygen, the oxygen redox reactions or hydrogen redox reactions has some critical intermediates that are very sensitive to the electric field. And shown here are the adsorption energies as a function of the electric field. And what we find here is that they're quite decisive when it comes to critical intermediates such as CO2 as well as OCCO, which are the intermediates towards CO production as well as the production of C2 products. And this effect actually has significant impact on the effect of pH and the identity of electrolytes on CO2 reduction. And so before I delve into the actual data, I just want to explain the general principle behind how dipole field interactions give rise to what we see as a very significant impact of pH on electrochemical CO2 reduction activity. And so shown in these cartoons here are the decisive steps towards CO production and C2 products, the adsorption of CO2 and COCO coupling. And so when these processes are limiting the rates of our process, they interact very strongly with the electric field here. And the electric field is a function of the absolute potential that our interface. That is the potential on an SHE scale. And so, I mean, this here is just a very simple picture of how field varies with potential. It's just a cartoon and one can imagine more complex relationships. But in general, we have this monotonic function as a function of potential. And so here, when we are at potentials, negative of the potential of zero charge, we have an increasing stabilization of these very polar intermediates. But when we're considering the RHE potential scale, which determines the efficiency for proton electron transfer processes, a given stabilization corresponds to a very different potential depending or over potential depending on what pH we're working with. So the difference between pH seven and pH 13 would be 0.36 volts. And so this is a very, very large number. It's well beyond improvements in activity that I know of through electronic structure, through optimizing our catalyst. So this is a really big effect. And this manifests in the dramatic pH effects that we see experimentally. And so the way to think about this is the pH effects that we see in electrochemical CO2 reduction, think of them as the Nernstian shift in our RHE reference with pH. And OH minus, the chemical potential of OH minus or protons, they really play no role in promoting these particular steps. It's really a potential and a field effect and not to do with the actual concentrations of OH minus, for instance. Since there's some controversy about whether or not having more OH minus in the electrolytes environments can be promoting these steps. It's a field effect. And this I will talk about in terms of pH dependence experiments and what follows. Okay, so this is the central idea. So let us look at what the experiments and the simulations say. And let us look at gold and copper which are the best transition metal catalyst towards the production of CO and CO2 products. Okay, so shown here is the experimental data taken by our collaborators in the Haramio and Han group back at Stanford University. And what is shown here is the activity towards hydrogen and the activity towards CO. And there is a stark difference here amongst the two sets of data in the sense that hydrogen evolution is very sensitive to pH. And we would expect that since hydrogen evolution is limited by proton electron transfers. And so its activity would depend on the proton donor that's at play. Whereas in the case of CO production there is no such pH dependence, not even when we're going to acidic conditions where we know we have a change in proton donor. And what this suggests is that proton electron transfers are not involved in the rate limiting step in the production of CO. And that it's on field driven chemical step that is limiting the rates of our process. And this is consistent with what we would expect theoretically as well. And so what we have done here is we have determined the energetics of this process to proton electron transfers as illustrated here using implicit planar counter charge and coupled the corresponding kinetics to a transport model that accounts for the diffusion and migration and the buffer equilibria of the various species at play. And this is the result compared against a large variety of experimental data that has been normalized to surface area as an approximation of the turnover frequency. And there's a lot going on here. We would expect a transition in rate limiting step at very, very low over potentials but that region is very, very difficult for us to probe experimentally. But what is suggested by the theory is that as well CO2 absorption under a large potential range prior to the onset of mass transport limitations as illustrated by this leveling off here, we have CO2 absorption as the rate limiting step. And what this implies then is that in addition to the binding energies of the various intermediates that's so often used in electro catalyst screening, the dipole moment of the CO2 as well as the double air capacitance here would potentially affect the activity through its impact on the taffle slope. And what this suggests to us is that we can perhaps tune these quantities towards higher activity that these are also critical descriptors of activity towards CO production. And another thing that I would like to note here is that there's no reason for us to see cardinal slopes of 60 or 120. The taffle slope here depends on the dipole moments and in fact, it depends on the dipole moments even in proton electron transfer steps. And so there's a lot of importance placed on what a 60 millivolts per decade slope means or what 120 mean and what this means about the mechanism. But in general, there's no fundamental reason that it should be those values and we shouldn't be concluding mechanisms on the basis of that. And in fact, the pH dependence can be a lot more instructive for us in terms of what is rate limiting. Okay, I just wanna note then that's actually the same analysis applies to copper. And what I illustrates here is this experimentally determined again, pH dependent data on copper now towards C2 products. And like CO2 reduction to CO on gold this does not depend significantly on pH even when we're going to acidic conditions. And this is consistent with what we see theoretically at large over potentials. And I show here the free energy diagrams that have been calculated for the initial steps for C2 production on copper and shown here is the lowest energy pathway corresponding to COCO coupling and then a proton electron transfer to OCCO in order to form OCCOH. And what we can see here is that at high potentials or low over potentials here we are limited by this proton electron transfer to OCCO but that as we go to lower and lower over potentials we are limited by COCO dimerization. And this is shown here in the simulations where we at first are limited by OCCOH formation and therefore there is a pH dependence but that at high over potentials we are then limited by COCO formation. And I wanna note here that these shaded areas correspond to uncertainty estimates just associated with the uncertainties in the GGA level functionals that we are using. And that's in general when we're trying to simulate kinetics it is expected that we have orders of magnitude uncertainties in the turnover frequencies and that shifts in onsets potential between experiments and theory of say you know, several hundred million electron volts is an inherent uncertainty in our simulation. But what theory and experiment together will suggest is that at high over potentials we are limited by COCO dimerization as the rate limiting step. And this is not a very new idea. I think it was first proposed by Mark Koper many years ago although there's alternatives to this being the rate limiting step that has been proposed. But I think the important parts here is to what we propose as the rate limiting step it needs to check out against a pH dependence. This is something that's really accessible experimentally and it really tells us a lot about the mechanism. If it's not consistent with the pH dependence and experiments then it's not likely to be the rate limiting step. Okay. And so now having shown the decisive influence of these adsorbate dipole interactions on electrochemical CO2 reduction the question is can we optimize the energetics of these? And at least theoretically, I would suggest that the answer is yes. And in terms of the adsorbate dipole this is what we hypothesized to be happening with supported single atom catalyst.  And this site motif really takes inspiration from molecular porphyrins. But in principle, there are other sites motifs that can also be stable. And I show some examples of transition metals doped into single or double vacancies at a variety of nitrogen coordination. And our hypothesis here is that supported single atom catalyst have tunable adsorbate dipoles and therefore more tunable activity towards electrochemical CO2 reduction to CO. And so what is interesting about these catalysts is that depending on the identity and coordination of the metal either COOH or CO2 formation can be rate limiting. And this is illustrated here for iron and nickel site motifs. In the case of iron for the more coordinated iron which is more suggested to be more stable it is CO2 adsorption that is rate limiting as shown in this free energy diagram. Whereas in the case of nickel for all of the site motifs that we consider it is usually the COOH formation, which is rate limiting. And so we would expect since one of these is a proton electron transfer and the other not there would be different pH dependencies. And this is what was shown experimentally by the stressor group where they show that for iron there is no pH dependence suggesting that CO2 is rate limiting. Whereas in the case of nickel they do observe a pH dependence corresponding to a proton coupled electron transfer being rates limiting. And so we can take these insights and put them together into an overall activity volcano. These are computed turnover frequencies from a corresponding kinetic model as a function of these critical intermediates CO2 and COOH. And as with usual catalytic volcanoes a moderate binding energy is the most favorable for activity since at very weak binding energies we'd be limited by the formation of all the various intermediates and at very strong binding energies we would be poisoned with CO as shown in the corresponding coverage plot. So what is interesting about this here is that there is a transition metal scaling line here corresponding to stepped transition metal surface and that the single atom catalyst tend to be shifted downwards from those and sometimes in favor of higher activity. And the reason for this as I will show arises from the large dipoles that are stabilized here for the critical CO2 intermediates. And this is shown more explicitly here the computed dipole for a variety of transition metals as well as iron and nickel doped graphene. As we can see here in general for the decisive CO2 intermediate it has a larger dipole in general. And we associate these with the differences in electronic structure on these materials. As you can see here the D states associated with the single atom catalyst are very, very narrow and they're more molecular like relative to the transition metals as illustrated here. And the dipole moments that results depends on the occupancy of the adsorbate induced states. And when it comes to more narrow D states it changes the occupancy in favor of stabilizing higher dipoles. And the main takeaway here is this principle something that we can exploit also in other processes where dipole field interactions are decisive. For instance in COCO coupling or the OCCO where the OCCO dimers dipole is decisive for activity. And so then also comes the question of whether or not we can tune the double layer capacitance in favor of higher activity. And this we hypothesize through the reason behind the sensitivity of CO2 reduction to the identity of the cation. And so our hypothesis here is that it's a site it's simply a size effect. So when it comes to different sized ions and we're dealing with the hydrated ion size here lithium for instance has a larger radius than cesium. And this means it can be at the interface at a larger packing density. And so what this results in going back to this double layer picture is that lithium has a slightly smaller field than cesium such that we have slightly different electric fields and the slightly larger field of cesium would stabilize the polar intermediates in CO2 reduction. And this is an echo again of the from can double layer correction to electrochemical kinetics. And so this effect here is something that we can account for using continuum models in conjunction with our ab initio simulations. And so again we have determined the energetics of the critical intermediates using a planar counter charge model and then coupled the results to a modified Poisson-Boltzmann model where we have this volume exclusion term here corresponding to the ion diameter. And then the limit that this goes to zero then we simply recover the Poisson-Boltzmann equation and recover Gouy-Chapman theory. We also relate the surface charging to the charging properties of the interface using these Robin-type boundary conditions that depend on this gap or Helmholtz capacitance and the potential of zero charge. And so with that we can determine the relative activities as a function of the ion size. And so shown here is the activity where the relative activity towards C2 products normalized by the activity on lithium and the activity towards CO on silver normalized again by the activity on lithium. And what we can see here is a correspondence between the theory and the experimental relative activities. So note here it's the relative activities because again we don't expect to be able to get our turnover frequencies quantitatively with our simulations. We have also compared this with experimentally determined stark shifts using available data from experiments of CO on platinum as well as CO on copper. And in general this correspondence between experiments and theory suggests to us that our hypothesis about ion size to be valid. And this model would then suggest is that in general small hydrated cation radius and in fact we also believe large charges would be advantageous for tuning C2 and CO production. Although in the case of large charges we have not been able to observe this experimentally and there are some practical challenges to do with precipitation and solubility when it comes to going to divalent cations for example. But that is in principle a prediction from the approach that some larger cations would also be advantageous. And the way cations would do this is that they slightly increase the surface charge density and the effective double layer capacitance thereby tuning the dipole field interactions. And so then to summarize this part then is the main takeaway would be that in CO2 reduction the combination of model and experiment would presently suggest that there are rate limiting steps with strong adsorbate dipoles that give rise to the dramatic dependencies on pH that is observed experimentally. And that we can furthermore potentially tune this effect through single atom catalyst tuning the dipole and cations which tune the interfacial electric field and the corresponding overall capacitance. Okay, and so in the last few minutes of this talk then I'm going to switch gears and talk a little bit about solution phase reactions and how these are impacted by mass transport phenomena focusing on CO reduction towards acetate. Okay, and so when it comes to CO or CO2 reduction towards C2 products, generally we think of ethylene and ethanol, although when we're going to increasingly alkaline conditions and say CO reduction acetate is also observed as a major products as illustrated here. And so what is interesting about acetate is that in contrast to the other C2 products what we see is an increase in activity even on an SAG scale when we're going to high pH. And in addition to that the selectivity towards acetate has this U shaped dependence on potential as well as on the type of copper that we are working with whether it's copper nano sheets, oxidized copper and so forth. And so a hypothesis for why this might be would naturally be that we might have different active sites on different types of copper that are selected towards different products. But this is not a hypothesis that holds up when we look at the experiments. And what Georg and Hendrik here have done is they have painstakingly collected all of the available experimental data on copper and normalize them with respect to surface area such that we get an estimate of intrinsic activity. And when taken collectively what we can see here is that there's really not so much of a shift amongst different types of copper. The spread in the values that we see when we exclude the bending over, the data that bend over as a result of say mass transport limitations when we're looking at the linear region it is a very, very small effect. And so when we have a change in active sites we know from the Arrhenius law that we would expect orders of magnitude change and we've just not seen orders of magnitude when it comes to transition metal catalyst for CO2 reduction in general. And so our suggestion here is that we likely have the same or extremely similar active sites on all forms of copper investigated and perhaps different populations of these but we don't think from the area normalized data that it's possible we have different active sites. And so our hypothesis is that the spread in the data and it's a little bit larger in the case of acetates is that we have the presence of a solution phase reaction with hydroxide and it is minor shifts in the reaction environments that is influencing the activity towards C2 and selectivity. And so this we have explored again with a combination of ab initio simulations and kinetic transport modeling. And so based on previous work we have assumed the same rate limiting step towards C2 products followed by a series of proton electron transfer towards this CCO intermediates followed by proton electron transfers towards this critical key team intermediate that is desorbed since it's very saturated when it comes to all the bonds. And this can either be followed by a solution phase reaction with OH-2 form acetate or it can read sort of undergo further proton electron transfers to other C2 products. And I just wanna note here that it is these three steps here past the rate limiting step that is determining the overall selectivity and that this proton electron transfer step here is sensitive to potential and that it can be rate limiting at lower over potentials at higher over potentials it becomes overall downhill. This solution phase reaction then would be sensitive to the pH now at the interface the concentration of the OH- and it becomes increasingly important with increasing current density and an increasing buildup of OH- mines. And so we have explored the energetics of these with ab initio simulations and what we find here is that in general the barriers are surmountable under the potentials we're interested in with the exception of the 111 facet. And so we can't on the basis of the accuracy assign an active site but it is feasible on different forms of copper. And so then the ab initio reaction energetics and the corresponding kinetics we have coupled to a very simple one-dimensional model of transports where the impact of nanostructuring at the interface is only accounted for using just a roughness parameter in our kinetics. And we have formulated effective diffusion for the various inter for the various species at play CO OH-minus and this ketene intermediates and included a source term here for the solution phase reaction. And so the corresponding coupled kinetic model coupled kinetic transport model is solved under a steady state. And this is the corresponding computed selectivity which shows the qualitative features that we see experimentally with respect to pH roughness and potential. And we can understand where that comes from by inspecting our proposed mechanism here. So first of all, I mean, when it comes to pH that's kind of trivial because we are here looking at a solution phase reaction involving OH-minus and so a higher pH would favor this reaction and favor acetate selectivity. When it comes to the impact of roughness now this has to do with the competition between kinetics and transports. And so when we have a higher roughness for instance transports is relatively slower relative to the kinetics. When we have a lower roughness on the other hand the relative rates of transport is faster. And so when we have say a faster relative rates of transport we have a lower double layer concentration of this ketene intermediate thereby leading to a lower coverage and a lower selectivity towards the other C2 products. We can also rationalize the potential dependence in the selectivity. At low over potentials this proton coupled electron transfer is limiting. And so the driving force towards the C2 products would be increasing as a function of potential such that we get a decrease in the selectivity towards the competing acetate pathway. And this then leads to this overall minimum in the selectivity. However, as we go to higher and higher potentials we get a buildup of the OH-minus at the interface such that we start to favor acetates again such that we get this overall U shape in the selectivity. And Karen, about five minutes or so. Ah, okay, thanks. So I think then I just finish up here. So main takeaways from this model then is that the acetate selectivity arises from this complex interplay of mass transport and kinetics. It's not just a matter of changing the active sites on copper. It's really a matter of the competition between roughness and mass transport. And that one can increase the selectivity towards the acetates within increasing pH or decreasing catalyst roughness. And so this here summarized the different topics that I have touched upon. Main takeaway from the first part is to consider using the surface charge as a proxy for the interfacial potential since the work function does not map one-to-one to the corresponding potential drop right at the interface. And that I hope I've shown that electrolytes solution phase reactions and mass transport in addition to the electronic structure of the electric catalyst can be decisive for activity and selectivity. And so just some then design rules coming from the mechanistic analysis. More alkaline is good, but not always for the same reason. Sometimes it's a dipole field interaction effect and sometimes it's a solution phase reaction effect. And that's with the adsorbate dipole field interactions we can think of some strategies in terms of stabilizing larger dipoles and tuning the double layer capacitance in favor of higher activity. And so I will just end with acknowledgements towards those who did the work here. Thank you very, very much, Kern, for this very nice overview of a lot of work which you have shown us a lot of insight. So unfortunately, people cannot clap. So I clap the name of everyone. Thank you. Yes. So we have a couple of questions. I will just try to switch on the microphone. So the first one comes from Deepak Kumar. Can you say something? So switch on your microphone. Deepak. Yeah. Am I audible? Yeah, hello. Can you perhaps please first say your name and affiliation and then ask your question? Am I audible? Yes, yes. Yeah. Yeah. This is Deepak Kumar from India. So hi, Tenna. This is a nice presentation. So basically I'm interested to know is there a method you use experimentally to observe and confirm the involved mechanism in the processes through dipole excitation or some by some other ways. So I want to know how can we check experimentally this thing about the mechanism? Yeah. So maybe if I first talk about the experiments that I had shown on my slides. So it's not a direct probe that it's a dipole field interaction. But it is a pH dependence measurement, right? And so if your pH dependent measurements where you have different proton donors shows no effect of the proton donor, then it would suggest that there's some other potential dependent process. And this I'm attributing to the dipole field interaction. And we know that it's something that is there from thermal catalysis as well. The dipole field interaction can be probed with stark effects spectroscopically, but it's not just the field that affects it. So it's not straightforwardly that that's the effect because there can also be coverage effects there. But in principle, you can probe the dipole through IR spectroscopy as well. But it's getting a direct evidence that it definitely is dipole field. I think it would be quite challenging, but you can see that indirectly if you were to simply change the pH of your activity measurements. And I would say that that's such a, well, I wouldn't say it's trivial, but it's something that can be done quite readily and that should be done in order to evaluate the nature of the rate limiting step. Okay, so thank you very much. The next question comes from Suorendra Kumar. Can you try to say something to see if you unmute your microphone? Do I have to unmute your microphone? Still muted. Okay, so then perhaps I can simply ask a question in half a half. So the question is, is there any effect of temperature on the dipole field interaction and how is this happening? Well, I can imagine that temperature can certainly have an impact on the field through its impact on, say, the structure of the electrolytes, although it's not something that I've explored. So I don't know the magnitude of this effect, but that's an interesting question. Okay, and a very quick technical question. Which code did you use for the app initial simulations? Good question. We have used VASP. So the VASP Sol package, which uses a linearized Poisson-Boltzmann approximation of the electrolytes. And we have recently started using a implicit explicit G-POL code called SJM, which uses a Jellium model of the counter charge. And so beyond the usual differences you might expect when changing pseudo-potentials in code, there is also a difference in the implicit electrolyte model. But as I said, if we account for the surface charge, then it doesn't matter where you put the counter charge. So for this particular application, the actual counter charge model in an implicit explicit treatment would not depend on that, yeah. Okay, another question has been asked in the chat, in fact, by Fatima... What's the name Fatima Shalena? Can you say something? I've allowed you to speak. Yes. Yes, can you perp state your affiliation and then ask your question? I'm from Sri Lanka, from the United States of America. So I would like to ask from you, is there any significant effect on effort as it did electrolytes on surface charge? Rather than maybe compared to other electrolytes? Aqueous? Electrolite? Rob, sorry, can you say that again? Or can you speak a little bit more into your microphone? Sorry. I want to know, is there any effect on aqueous electrolytes on surface charge rather than maybe compared to other electrolytes? Is there? You were talking about acetate? So acetate is a product. And so, I mean, it does have a certain charge, but so it is, sorry, what's significant effect? Let me try to read of aqueous rather than other. So are you asking whether the acetate itself could have a cation effect or an anion effect there? I'm not entirely sure what the question is here. Well, in my understanding of the question, but is that she asked about aqueous electrolytes with respect to other forms of electrolytes? Oh, okay, I see. I mean, I would imagine that for instance, dielectric properties could be different. Charge densities could also be very, very different. And so that could have a significant impact on the double layer and non-aqueous electrolytes could also have much less availability of proton donors. And that's known to change the selectivity. And so, I mean, at some point, one needs some sort of proton donor. And if they're in very, very low concentration, you could tune the selectivity towards the products for sure. Does that answer your question? Oh, yes, that's right. Thank you very much for that. Okay. Thank you very much, Karin. Okay, so thank you very much, Karin. I think at this point, we should stop the questions because we are running too far behind schedule. Perhaps people can also reach out to you by email and ask further questions if they should be. So thank you very much again, Karin, for this nice talk. All right, thank you. Okay. And with this, we move on to the next speaker, who is Mikael Spriek. Mikael Spriek is a Manitou's professor at the University of Cape Bridge in the UK. And Mikael is really a pioneer of Appinicio molecular dynamics and molecular dynamics being applied to watery system and everything water. And so for me, even when I first joined the community of density function theory and Appinicio calculations, Mikael was always one of the people who made part of the Carparinello and the CP community and of simulations of water and so on. And one of his big scientific interests has been in recent years and interfaces and electrolytes. And I still remember that many years ago, he was in a talk of his the first time that I saw a proton appearing during a simulation and disappearing again during a simulation, which I remember as something very impressive. And so Mikael has told me that in recent years or not in recent years that because he was forced to retire, he kind of gave up a domestic simulation and is now working on more analytical models of the same kind of systems. And I'm sure he will tell us much more about this now in a second. So Mikael, the floor is yours. Thank you very much for this slightly introduction. Can you see my screen? Yes, yes, you can see it. Well, thank you for inviting me. This is going to be rather different from the previous talk. It's not about the electrical analysis. It's also not even about structure. And I want the organizers about this, but they get me on the list. So I'm of course very grateful for this. It's about the number of elementary questions about electrical statics in electrolytes. I'll come to interfaces, but the picture you see here is an homogeneous electrolyte. And the question is what happens if you treat mobile charge as polarization? Ions in electrolytes are usually considered external charge and then the divergence of the dielectric displacement is the ionic charge. Now we're going to represent these ionic charges by their own polarization. That means then that the divergence of the dielectric displacement becomes zero. This is a kind of preview or a graphic contents. So I will all explain this later. So the divergence of the dielectric displacement is zero. But of course it still appears in the Lorentz equation. And that will open new possibilities of manipulating the electrostatics in an electrolyte. So that is the talk I will be about. No electronic structure calculation, all simulations are classical SPC. Now this is a collaboration between a number of people. Stephen Cox and Zhao Zhang who were in Cambridge. Now Stephen is still is. Zhao is now in Uppsala and the people in Paris. Rothenberg and Matjesalan. This thing over here is the new logo of the Sorbonne Aclomerate. All right, so what could this be using the dielectric displacement as a handle on the system? Here is an example. So here is my electrolyte, these red lines dash lines can always be the periodic boundary conditions. And you know if you put a finite field on this and you can do this, I will explain this later, you get a current, a current J proportional to the electric field to apply and the proportionality constant will be the conductivity. Of course, if you want to define polarization of ions in this case, you would simply be tempted to integrate the current. That would be a continuum definition, but of course that will be not stable. It will increase this time. You integrate the current and the current is constant. Now what will happen if you do constant D? It is possible to apply constant D as we'll see later. Then surprisingly, you'll get a stable polarization. Why? Well, suppose this is a perfect screening, the electric field E is really is, I shouldn't do that, it's really zero. And then D equals P times four pi. So the D you have under control, so that will tell you that the polarization is stable and finite. So that is a big difference. And this is what we're gonna test or investigate first in a homogeneous solution. So here is a slide I want to rush through. It is the way of applying a finite electric field to a periodic sample. The reference in electronic structure calculation is that of the famous Stengels, spelled in Thunderbilt nature physics paper. And so, but I'm doing this entirely classical. So there is, that's my, yeah. Oh, yeah. There is a standard SPC type Hamiltonian. There's a short range part and there is a long range part, the A-Wald sum, which I just represent by a reciprocal space summation. And then as you hopefully know, the electric field, the average electric field is set to zero by the A-Wald sum. And you really would have to add it to take account of it. And this happens in this second term, the term, oh, I shouldn't do that. Here is the applied electric field and this is the polarization. So this is an extended term. Now, what from the built and Stengels show that provided the, oh, I have to turn in this, provided you use the itinerant polarization as polarization that is the integral of the current, then this E that you have here is already the screened microscopic field. That is not the applied field, it is the screened field. So I will have to leave it at this, but I will first give you an example that you already know that you should use the integral of the current and not simply the cell polarization. Here is a famous example. It is hidden in most textbook. Here you have just SPC water. This water over here is moving from dashed to solid and it stays nicely in the periodic box inside the red lines. But the other molecule is moving out. In the end, it sticks out one proton and what you shouldn't do then is put the proton back in the box. That is the cell polarization. That's the wrong polarization. What you should do is you should keep proton too as the magenta one as the one you count, the one you follow out of the box. And the difference is really dramatic. Here is the green line is the itinerant polarization what you already would be doing anyway and the black line is if you put the proton back and you see you get nothing while the green line is nicely polarizing and is even saturating at a high field. So the field power is there at the bottom. All right, so people have tried it to test their program. Now we're doing the same thing with the ions. This is a slightly more complicated picture. Now I've put in an electrode, gray, water, blue. There are two, everything is periodic. I'm not doing anything outside a full periodic boundary condition. So the green line is one way of drawing the cell and the red line is another way. In one ways, the electrolyte is in the middle. In the other case, the electrode is in the middle. Now look at iron one, it moves from dash to solid. It stays within the green cell. It stays within the red cell, same iron. Now iron two stays within the green cell and stays within the red cell. However, you should take a different image. So it's in a different box, but iron three is actually moving out and you should follow it and not put it back just as we did with the protons. All right, so now as I said, if this works and you integrate this attendant polarization you should see it go up linear in time if you apply a finite field and this is done here. You see these lines are nicely here increasing in time. This law becomes bigger and bigger with the field that is the conductivity. All right, so if you don't look at the water polarization which is the standard to SPC type polarization now you see that it increases also with the field in beginning it is linear and then it becomes slightly non-linear, fine. All right, now we're going to change if we don't apply a microscopic E field but a microscopic D field on the built and Stengel has also explained to do that. You change the extended term, you put D, D with the bar means that's the one we impose. It's not a variable, the system can change and then the P is again this itinerant polarization. So if E and D would be zero then E equals zero would correspond to a short circuit. The charges on the boundary electrons at infinity nicely fully compensate for the polarization charge. Well, if it is D equals zero there is no charge on the electrodes, boundary electrodes and the polarization has to fight its own self polarization and you get a big difference. So then we're gonna test this, we put our D and remember what I said in the beginning if the electrolyte is a proper electrolyte and set the E to zero we would get a stable ionic polarization and indeed we do, it's very nicely linear in this D and surprisingly the water polarization is almost zero, that is the green line. So that is rather different. So summarizing if we put the E then we have conduction the ion polarization would go up linear in time the ions carry the current. If we put D we have stable polarization water is hardly polarizing at all and the ions in fact screen the water from the field. And this is called on saga screening as opposed to the barrier screen. All right, so that worked rather nicely. Stephen was working in on this wanted to do also something useful. So we looked at the dielectric decrement which is the decrease in the dielectric constant with increasing fields. This now again is at constant E and you see that if I at zero you start out with the water SPC dielectric constant which is the normalizing constant here. And then if you are at one more you are almost half less for dielectric constant. This is well known but we could check it. We also looked at conductivity. We have now two ways of measuring the current we can look at this polarization and divide by time or we can directly measure the current and that is much more noisy. That's sort of pink lines but it should in the end give the same thing. The slopes are more or less the same. And then Stephen checked the core rational which is conductivity as a function of concentration. You see that it is the Polar's Law says it's a limiting constant. I have difficulty with this pointer. I'm doing something wrong there. Labder zero and the concentration depends this square root that is not bad in this plot and we even get for the limiting value quite well the experimental value of one of 0.1. Okay, so this is the homogeneous electrolyte. Now an interface. So this is a schematic picture. So what is this is? Again, the red lines are the what do I do about this pointer? The red lines are the periodic boundary conditions and everything is on the full periodic boundary condition. So here we have put the electrolyte blue in the middle and in the bottom, we have put the metal electrode in the middle and you see it should give you the same thing. And if you put then the field across you get the potential across the cell. Potential across the cell is seemingly incompatible with periodic boundary conditions. But what you do is you measure the field and multiply with the length of the cell. All right, so we prefer to use the bottom line, the middle, the central, the electrode in the center and Chao test many, many times whether this is actually the same. He did this for an insulator, not for a metal, but it was quite well verified. All right, so here is a more detailed picture. What is the idea? We have an electrode in the metal. It's polarized by the field. The field is a zero inside the metal because it's a conductor. And then in the electrolyte also conductor will also be zero. And then only we have a field in the dial in the double layers. Of course the charges induced on both sides are the same, but the double layers may have a different width. So the capacitance may be different. But this is our scheme. Mikael, may I ask you a question? Yes. For me it is not clear kind of how you're simulating this. So the electrode I imagine is Elena Jones or something with the charges on top of it? And the metal, how are you? That is in the next slide. Ah, okay, sorry. This was very, very general. As I said, I'm not doing an electronic circuit. I'm not doing an electronic circuit. I'm not doing an electronic circuit. In general, as I said, I'm not doing an electronic structure calculation. So this is a very good question. All right. So what we do is we're using the program of the people in Paris. It's called metal walls. And it's a very cheap and cheating way. I hope he's not listening to, to simulate a metal. You don't have a Fermi level. You only have a piece of material in which the cost, the potential is kept constant by a trick. And what you do is you have fluctuating charges on these metal atoms, these black dots that you see there. And you force the potential, the static potential to be a constant everywhere inside this metal.  And, and on the other side, sorry, you do the same thing. And the, the constraint of this potential can be different. And in this way, you can introduce a potential difference across these metals. And the electrolyte in the middle will just have to respond. This is an SPC electrolyte. So this is all this has been used by these guys to simulate storage supercapacitors already for, for a number of years. This was a big success. And this program, if you are interested, is actually public, they tell me, and you can download it somewhere. All right. So here is this picture again. But what I didn't say is that this really is not 3D. What they have is 2D evals. They have periodic boundary conditions in the X and Y direction, but not in the Z direction. So in the, in the normal direction. And we're going to do this now. Our way fully 3D and we put this phony metal, this fluctuating charges for which the potential is kept constant in the middle. And then we apply the field rather than this constraint potential. And we're going to see if that's the same. Now here's the test. This is all work of the people in Paris. The gray bit in the middle is this phony metal. And indeed the potential is a constant. It is a constant also in the electrolyte, the white bit, because they're both conductors. And then you see a structure in the potential in the, in the interface. All right. So now comes the test. Is it really the same? If they do the 2D thing and apply a potential and we do the 3D thing and apply a field, is the induced charge on the service really the same? That means it's the capacitance of the double layer is the same. And it is remarkably similar. Only at very high field there seem to be a bit of a deviation. What really surprised me is that also the fluctuations are the same. They should be the same if the capacitance is the same, but still at this is really remarkably similar. So you see here the fluctuations of the charge induced on these phony metal surfaces for different fields. Again, in the 2D and in the 3D setup and this, this really is the same. All right. Then, then much ahead this idea that maybe we can use this D thing to, to, to do amperometry. So here, what is this? This is again my, my, my systematic scale. So the metal is in the middle. Unfortunately, it's now white. The, the double layer is gray and the electrolyte is blue. The magenta line is again a schematic potential flat in electrolytes changing in the double layer. And so the, the, the full potential over the cell will be the sum of the potentials across the double layer. So we can never separate this. Unfortunately, we always get the sum. All right. So now we're not going to apply constant E but constant D. So here's the Lorentz equation. And here if, if since we put all our charge in the, in the polarization, the D is really constant across the whole cell. It is the D that we have applied in the fundamental that is this bar. Now, if this thing in the electrode is again a perfect screening, then we can set E to zero. And what you'll find is that the charge induced on the surface is determined by the D you have imposed. So this is a way to control the charge of the surface by implying a D. And then since we know also the potential from the electric field, we can calculate the capacitance again. However, as I said, there is a, this is a test that you indeed, you get the same, whether you impose a field or a D or an E. So then this is the idea that you had. So now we can ramp the D and then the charge on the on the surface will, will, will change. And that is effectively a current running through the cell. Remember that my cell is periodic. And we can look at the response of the potential, which is the, is the, is the bottom panel. And if we do this very slowly, 150 nanoseconds. So clearly this must be classical. And you see the potential following in a zigzag, the, the, the, the, the sort of variation of the imposed charge. And if we do it a bit faster, 100 times faster, you see that the potential response becomes a bit non-linear. So this, this, from a theoretical point of view, you could see, compare this to a pyrometry, but remember, there is no further days coming on here. This is just the double layer and nothing, nothing catalysis of further day coming on. You could also do the other way. You could vary the potential by implying the E field, ramp it, look at the charge response with, with the current. So then we do photometry. Again, slow. It follows nicely fast. The response of the charge is a bit more irregular. We have not analyzed this further. Of course, we should do this. The guys did check the following that the capacitance, which we simply have the potential divided by the charge, is the same if you do forward for a pyrometry and photometry, if you do it slowly, but if you can do it faster, which would be the scan rate in photometry and the current density in pyrometry, then you see a difference. The capacitance goes down somewhat less drastic in the case of the imposed current in, as opposed to the imposed potential. So that looks encouraging. Of course, this is a very primitive model. And here I have to say we tried to implement this in an electronic structure model together with your Hooter, including the CP2K code. And there are some problems that I will not spell out. So we don't have this ready to do this in an electronic version, apart from the problem of time scale and system size. Okay. So I hope you didn't confuse you too much. And now I'm trying to give a bit of a theoretical background. Why can you do this? Why is it possible simply to put mobile charge in polarization, even though most textbooks tell you not to do this and treat mobile charge as an external charge? Now, a book that seems very encouraging to do the opposite is this book by Kovac. I discovered this rather late, and this is really a revelation. It was a revelation to me. It treats electronics strictly from a continuum point of view. It doesn't talk about dipole densities or charge densities. And at that level, in the electrostatics, you don't have to make a difference between dipole densities and charge densities only in the constitutive relations. That is, when you want to calculate the polarization as a function of the applied field. So this I can really encourage this book. And what it then suggests is to treat a dielectric, sorry, an electrolyte body as a dielectric body. So here I've tried to indicate this in the schematic picture. On the left is the textbook dielectric sphere. The electric field is inside, completely homogeneous. It is not the same as the applied field outside, of course, but it is, the difference is the dielectric concept. In fact, it is homogeneous. And the D, which is the musculoskeletal field plus the induced polarization, is if you take the divergence, you get zero. Why? Because there is no external charge. This divergent D equals zero is the hallmark of a pure dielectric. But now we're going to do the following. We're going to put the polarization of the ions in a polarization vector. And then again, there is no external charge. The external charge is now polarization. And if you don't apply a field, the dielectric sphere, a drop, if you want, responds not exactly like a dielectric because of the mobile charge will accumulate in a space charge at the boundaries. But it is stable. It can't go anywhere. In the end, it can't go out of the body. And again, and that's the main point, the divergence of the dielectric field is zero. Now we're going to use this. What use is this? I will show this. And this indeed will even give you some conceptual insight in screening that you wouldn't get too easily if you would treat ion charge as external charge. So forgive me, I will go now to a couple of equations. The first ones you should have seen. This is how you do a dielectric sphere. So you have the maximum, everything is now small e. That's tradition in this field. And moreover, I switched from the Gaussian to the standard international system. So no four pies, but epsilon zeros. So the crucial field is the cell field, the one with the little hatch on it. That is the field related to the induced polarization. And again, these are the Maxwell field equations. The cell field is a proper electric field. So it has zero rotation, zero curve. And D is a proper dielectric field that has zero divergence. All right, now we want to have a free energy function for this, a polarization energy function. And that consists out of a polarization cost. The microscopic cost of inducing the polarization and another static term, which is of course the full energy, the energy of the applied field, which is not depending on anything. And the energy due to the induced field, whether it is the interaction of the polarization with the applied field and the interaction of the cell field, that is the polarization with itself. To derive this for the sphere is actually not that easy. You have to include the stray field on the outside. That's why this says here, integrate over all space while for the polarization cost, you only have to integrate over the body because of course the polarization inside the body is finite, outside is zero. But the induced cell field and also the induced cell of the electric field is not zero outside the box. So you should keep it there. And this person, Eriksen, he's a continuum organics person, has worked this out in this paper. And this paper is in a journal that you usually don't look, but it is a crucial paper in the story to follow. All right, so what this Eriksen says, now we want to make a functional for the non-agribbable polarization and try to, sorry, try to minimize it in the polarization. So the first term, the polarization cost in continuum organics, this is called the stored energy is simple. p squared divided to chi is already a function of polarization. But what about the static energy? Now you can write this as integral over a electron energy density. The energy density is what I just showed you p in E and the cell of energy. And if we then substitute for the cell of energy, the Lorentz equation, then you have a function of polarization. But of course you introduce now the D, the cell of D. So you have now all of a sudden one extra degree of freedom. And the trick now is to, the purpose now is to minimize this functional, an AF under the constraint of the Maxwell equations. That is, a longitudinal electric field and transfers dielectric field. Now, if you are from a biological background, you know this is a very nasty problem. People have studied this forever. And what they tend to do in Poisson-Wolzmann and also in the electric theory in continuum theory is they try to replace the electric field by a gradient of the potential, which satisfies the first and then they get stuck in the second one. That is no longer a variational problem. Now, Eriksen says you have to do it all the way around. You have to impose the D by making it a curl of a vector potential and then hope that the variation of the potential and hope that the variational problem in A treated as an additional variable will recover your other Maxwell equation. So this constraint, the minimization problem is really not easy. Okay, so that we do. Now we have now already the curl, sorry, I put the curl of the vector potential for the D in my electrostatic field energy. And now I'm not going to go through it. I hope I'm going not too technical here, but the Eirel Lagrange equation, the minimum, the first-order change in this auxiliary vector potential looks like this. It will indeed recover the other Maxwell equation. Why? Because it says the curl of the curl of A minus P must be zero. So if we make, oh, sorry, if we make the curl of A minus P, again, D minus P is E, then indeed you find that the curl of E is zero. So you have recovered your first Maxwell equation, but the second one has been imposed by this trick of the curl. All right, I hope you're still with me. So now we do the variation in polarization. That's easier. This is quadratic function. This is also a quadratic function. We do now P, not E. We can keep A constant. And you have to balance the variation of the constitutive energy to the balance of the variation in the electrostatic energy. And if you then put back what you had before, that this is simply the E. You recover P is pi times E. The E zero comes from the first term and the self-field comes from the second term. Okay, this is very, very elegant. Again, I didn't think of it. And as far as I know, nobody in our community thought of it. This is something that comes from the electromechanics engineering community. I may be wrong here. All right. So now back to my sphere. Now we're going to do this. Yes, I still have time for the electrolyte. And this will be a bit of a surprise. So we put now, no, D is again zero because we have put the ionic charge in the D. So how are we going to make our functional now? We still have, of course, the Maxwell equations. But in the Lawrence equation, there is now two polarizations, one for the ions and one for the solvent. And still it is a transverse field. But now, of course, first we had an electrostatic field and an electrostatic field. And we had a stored field, which was pi over chi. But now we also need a constitutive energy for the ions. And we'll come back, which will depend on ion polarization. I'll do that in a minute. But here is the first surprise. I remember in continuum theory, it doesn't matter what the polarization is. The electrostatic energy is a function of the sum of the two polarizations. It does not separate them. So your energy density has D minus P, I minus P, S. It is additive in the polarization. And of course, people know this. The ion polarization screen, the solvent polarization, the solvent polarization screens the ion polarization. It is mutable. And this is made now explicit in this trick. And by representing ionic charge, not as charge, but as polarization. So this is rather neat. And the epsilon, by the way, the epsilon zero is, of course, here, epsilon zero, because the dielectric response is hiding in the stored energy. This is not epsilon, but epsilon zero. This is another advantage. OK, now we go through the same thing, but we start have to make a function for the configurational energy of the ions. And of course, what we do now is we write the cation, as the sum of the total density and the divergence of the ionic polarization. We do the same for the anions. This minus sign is always a convention. And if you take, oh, sorry, I shouldn't do that. Then the divergence of the polarization is really the excess charge. The excess charge can be zero, like in the middle of the sample, but the polarization can still be finite. And this, then, is going to be substituted in the ideal gas equation, right? The osmotic free energy of the ions. It's a complicated expression, which I will save you. Spare you. You just have to substitute for n plus and n minus this. And you get a function of n and p.  You introduce this vector field to take care of the transverse character of the dielectric displacement. We get, again, that our Maxwell declaration for e is satisfied. We have now a constitutive relation for p s, which was as before. And just p is chi times e. And we get another one now for the polarization for the ions. And I have worked this back in terms of concentrations. And what this basically tells you is that the Nernst potential, sorry, is constant across the sample. The osmotic part plus the electric part does not change. I have not worked it out, but here is a gradient. It looks kind of reasonable. And if you then do the minimization in the total density, you get the mean activity. Fine. And now the point is, what a big deal is this in the end? It is just Boltzmann, Poisson Boltzmann with the added detail that we can now account for transverse polarization. So you don't have to have only flat services. You can also have round services, spherical ones. I worked this out in a recent PRE paper. So the message is that I'm not claiming that this is going to have any computational advantages, although it may have so. You can account for transverse polarization, but in particular, it gives you some further insight in screening, which can become important if the double layers are no longer simple, flat, but start showing structure and so on. All right. I think I'm getting there. So what is this all good for? What does this have to do with this meeting? So what I want to do now is I want to look at the electromeganics of an interface. In the previous talk and in the talks that we'll follow, people always talk about charge distributions and structure and GeoVars. I could rather frustrated with GeoVars because they don't seem to tell you very much about double layers. But there is this issue of the pressure. The forces in double layers must be huge. Just imagine at high concentration or in ionic liquids. So this solvent is going to be compressed and the ions are going to be squeezed together, changing the stress. And this stress enters in the equation of state. So capacitance in the end should also depend on the electromeganics. So here is again my double layer schematic picture. It's an open systems, ions come and go, electrons come and go. And if I treat this now my way, putting all the ions in the polarization, then I can again apply a field D that is transverse. And what the thermodynamics tells you then that the electric field should also relate it to the excess free energy, which of course is the ground potential, because it is an open system. And here comes the inclusive equation. The ground potential in fact is, this is all very schematic. There is an integral of the off diagonal part, sorry, of the anisotropic part of the pressure. And the pressure in double layers is no longer hydrostatic. It is as a component along the surface and perpendicular surface are different. And I think these pressures will be really quite high. And I want to see if I can understand the capacitance, the differential capacitance, the behavior of capacitance with this charge and field that Karen has talked about in the previous talk. If I can understand this relating it to the pressure. So if you want, this is a glorified form of the Liebmann equation. I'm clearly not there. I'm just beginning to think about this and this way of treating polarization, ionic model charge as polarization is really helpful in calculating the stress, but I'm not there yet. So this is going to be a promise. So last but not least, oh, sorry, some literature for the applications. I mentioned the homogeneous electrolyte, the metal wall electrolytes. And here is a review paper about this finite field techniques. This is Steve. This is Majer Salan. I'm not sure if he actually is watching, but here he is. And this is Ciao. As I said, he's in Uppsala. So here I think I'll finish. Thank you. Thank you very much. Also to you, the virtual clap, which comes only from Nicolaas. Also there, clapping his hands. Very nice. So I invite everyone to type questions in the Q&A. In the meantime, I would like to start with the kind of the key question of this is, so you have shown in this last slide, I think it's 39 if I see it right. The link, as you said, of your continuum theory with this interface, double layer physics. So what I would like to know is how would these results come out of really an atomistic treatment? Would you also be able to get this pressure? Yeah. You can still hear me. Yes. Yes. So here you're touching on a very important question. People calculate stress tensors in atomistic simulation. In classical simulation, this is called the urban corporate equation. However, there is a large controversy about it, because they derived this as an integral of the force density and they're missing then exactly this important bit, the transverse part. So I'm really very annoyed about this. The way this is usually treated in the statistical mechanic community is to deny that this quantity is even important, but you can calculate it in electronic structure theory. The one who was calculated, this is of course, is Richard Martin. He did this already 30 years ago with an under periodic boundary conditions. He calculated the Maxwell stress tensor. And this is my next step. I want to calculate the Maxwell electronic stress tensor. But yes, in principle, you should be able to calculate it in an atomistic simulation, even in an electronic structure calculation, as you can believe. Richard Martin, he has something about it in appendix F in his book. You can look it up. Okay. So I see that Laura has raised her hand. I do have a question on the nature of the electrolyte. So is there any limitation on or assumption, let's say on, on the electrolyte, meaning all these results are going to be valid for dilute, as well as concentrated electrolyte. Well, the test calculations here, this is a concentrated aqueous electrolyte. However, the calculations of this a parametry use I showed, I didn't say a word about that. But they are actually an ionic liquid, much as a lands favorite ionic liquid. So I have not analyzed the results, but clearly this, this, this time dependence will be crucially dependent on the electrolyte. This is all what people are interested in. But I have not, we have not looked, I have not looked into this. This is not an easy theory. Okay. Another, maybe another question is, what happens if you have a net charge in your electrolyte, you can also treat such a system? Yeah, sure, you can do this. Of course, you would be interested in the end in electron transfer in a, in a faraday process, right? But you can put an electric net charge there. And then of course the electrodes should have the, the counter charge, right? This is, this is possible. Okay. Thank you. Okay. Okay. Okay. Thank you very much for this very interesting talk as usual.  I mean, in principle, I want to, to kind of join Ralf with the question about how to make contact with a domestic simulations. Because if you have your simple double layer model, you can use it as a, you know, you can use it as a, you know, you can use it as a, you know, if you have your simple double layer model, the, the crucial thing is as far as I understand the, the potential drop, but if you have your simple model, you can change the potential drop by either changing the distance of the capacitor planes or by changing the charges. Does it play a role and, or what is the consequences? Well, the, the distance. So this came up also in, in a cancel. You must make, you know this better than me. You must make a difference between potential and fields, right? Yes. You changed the, the distance between capacitor plates. You changed the potential, but not the field. Yeah, but if you change then the charge, you can also, you can end up with the same potential drop. Yeah, sure. So you have infinitely many models to model, to model this, this potential drop. Yes. Is this, is this a question? The question is how much matters it if in your, in your model, whether I just use it, so to say describe the potential drop by, by just slightly changing some of the parameters. Do they enter the charge density? Of course the, the, the, all the numbers I calculate are crucially dependent on, on the model, right? So here, this capacitance, for instance, I, this is also maybe, but here, this, this capacitance is miserably small, right? I mean, this all depends on the model, right? Okay. Yeah, yeah. No, I'm, I'm only looking at the, the theory, not at the application. Okay. Yeah. No, no. I mean, if you want to look at the structure of the double layer, you, this all comes in, maybe you and Cheng will say something about that in his, his talk later. Okay. Thank you very much. Okay. We have also a question from the participants. In fact, Deepak Kumar, who we have already had before. Can you say something, please? You have to unmute yourself Deepak. Hi. Am I audible? Yes. We hear you. Yes. Yeah. So my question is like the calculations, which you are shown, they are restricted strictly to double layer system or can be extendable to a high layer scenario as well. Well, again, I, I, I'm, I've talked about Maxwell's theory in a periodic system. It doesn't matter what the periodic system is or what the model is. Of course the interpretation of, will very much depend on the model, but you can have triple layers, whatever, right? Even for the day, reactions, but I don't know how to, how to do this. So what exactly is your question? Yeah. The slide, which you are showing like 39. So you have mentioned there this, when the, the scenario in the double layer. So I, I got curious if there is some constraint on that or it is a general scenario, like in electromagnetic theory, we apply. Well, as Axel was saying, I mean the model will be critical as soon as you really want to learn about the real system, such as it's very complicated. So what I understand, for instance, of current stock is that the absorption on for absorbed species, the field is really important. This from correction is really for outer sphere for reactions, but where the potential is important, but the field is important. I understand that for the surface. And that's of course is not there in my model. I just have something very silly. There's no electronics, no absorption of any, any physical sense. So all of that is not in there. You have to put it there. Another question comes from the, the panelists. I see you and I think. Please. Okay. Hi, I'm here. Thank you. For the very stimulating talk. So I have to say, I really need to catch up the theory, particularly behind the electronics. But, but these days, I really basically forced a, a lot of like experimental colleagues to think of complex interfaces like. Yeah. I know. Sorry. Like SCI, for instance. Yeah. Sorry. That's a good example. Yeah. Yeah. And also the, I say in fuel cells, people using this polymer, right? That's polymer electrolyte. So, well, I'm thinking of the, the, this implication. For instance, you charge out the double layer, you charge out the double layer, you charge out the double layer, you charge out the double layer, you charge out the double layer. Particularly if you have a nano particle of certain size. So the double layer charging will cause a huge, like stress. Yeah. Yeah. Yeah. Yeah. So the ACI or electrolyte interface with that push really, I mean, that's that can really break things, right? If there's a huge pressure. Yeah. So the, the, the, the mechanical continuum people have all kinds of models for damage for fraction and, and dislocations, right? And, and if you do that on, on, on a lithium, on the lithium anode, right? It's an enormous effect. Not, sorry, of a lithium battery. So there are models, continuum models for this, but these are not atomistic models, which is what you are, you are obviously interested in, but the, yeah, I mean the, the, I would be a good, a good point to start, right? Yeah. We should talk about this. The, there are all kinds of continuum models that might be useful. And flag Ray is working on this with somebody. Fleming, Fletcher, one of the two. So it is, it is, it is, is something about it. Okay. Thanks. So, another question. There is a question by. The question is about the. Software you're using for these. Dynamics. Can you show that slide perhaps again? So this is an, you said this is open source available for anyone somewhere or something or. Yeah. So, yeah, sure. So this is. These two people here are software engineers, right? This is material. And this is. Oh, Madden who started this, right? But they tell me you can download it from somewhere. So you just have to look for this name. But also there must even be a manual. I mean, they're working hard on it. Okay. Good. And then I think the last question, which has also been around you have already answered. If this you can affect this effect also on, I mean, like the. Helmholtz and the other layers and so on, but I think that is the same question as we've already had. Yeah. Okay. Yeah. Yes. I should say again. I maybe I'm over over emphasizing this point, right? But this, this whole world is. It's a very old story. Atomistic models can, sorry, I'm trying to find my page. Atomistic models can really hide some important features that you don't so easily see at the level of a G of R, right? And again, this book was opening my eyes to this. So I really can recommend it. Okay. Okay, so I just see that also Tanya Cook is a quick question. Can you? Yes, I just have a quick question. It popped in my head when I heard the last one, which is that you're treating this all as polarization, not as free charges. Can you think of the protons in the same way that way as the ions? Well, in my last bit, there was a limitation to a one-to-one electrolyte. So in principle, yes. In practice, I have not worked it out, right? But in principle, yes, of course. Okay, thank you. But there would be quantum, of course. So in the end, I can't because protons are no classical, right? But in principle, yeah. Okay, thank you. Okay, so thank you very much again, Mikkel, for this nice non-automistic view on this layer. Thank you very much. What can you do if you no longer have a computer, huh? All right. Okay. So anyway, thank you very much, Mikkel, and looking to one screen. Sorry. No, to Unshare. But you have a lot of time to find the right button because if I look at the program, we now have a coffee break, a virtual coffee break. Oh, yes. So those of you who are in Italy can now get a really good espresso and those who are in the rest of the world have to get something else to drink. And we meet here again, so in a bit less than half an hour for the talk by James Turans, okay? So stay in the same channel and in half an hour or so we meet again. See you and thanks again to the speakers of the first part. But James, is everything right on your side? Everything set for starting in some minutes? Yes. Perfect. Just wait some more minutes, for more instance, and then... Have you already seen Francesca for the next talk or not? No, no, no, I haven't seen her. But my hope is that this is the California effect because very early in California, so I imagine she will connect in the last minute. Okay, yeah, that's cool. Perhaps someone can shoot an email to her, reminding me. Oh, it's gonna be... It's nine hours, right? Yes. Rest of time. Nicola Simone, can one of you send an email to her just to remind her? Sure, I'll do it right away. Okay, so in the meantime it is 4.30 so we can start with our next session. So we stay with the speakers wise in the United Kingdom and we move from Cambridge now to London to the Imperial College. Our next speaker is James Duran. So he's professor of photochemistry at the Department of Chemistry at Imperial. James, he studied at the University of Cambridge and at Imperial College in London. And got there his PhD for research which already was kind of related to light because it's on the photosystem too, which is important for photosynthesis of course. And he's a big expert on everything solar, solar cells, solar fuels, photo catalysis and all these very nice applications which are the heart of this conference. James has been awarded a series of very prestigious prizes and medals like for example in 2002, the Tilden Prize, the Yooks Medal in 2018 and the Environment Prize by the Royal Society of Chemistry. He's also fellow of the Royal Society. So we are very happy to have James here now to give us the next talk. And can you try to share your screen to see if everything works? If everything works. Okay, so screen sharing seems to work and we will now hear from him about operandospectrochemical analysis of water exhalation kinetics at metal oxide and water interfaces. Okay, so James, the floor is yours. Thank you very much, Ralph, for that kind introduction and also inviting me to this really interesting workshop. I have some confessions at the start. I'm not a theorist, which is a little daunting. Talking to an audience which I'm aware is primarily theoretical. And also, even worse, I'm not an electrochemist. I'm a photochemist by training. And most of my work has been looking, as Ralph said, around soda-driven reactions. But over the last few years, we started to become more interested in catalysis. Initially, photoelectric catalysis and now more recently, electric catalysis, where we're trying to apply some of our spectroscopic tools to measure kinetics. And that's what I want to talk about with you this afternoon. And I hope it is useful. And I hope I don't make too many fundamental errors in my understanding of theory and electric chemistry. So what I thought I'd do is just very briefly introduce the area of photoelectric catalytic waterspitting as I've become the first speaker really to talk about that. And particularly, I'm going to be focusing on water orchestration. We've already heard a lovely talk by Karen on the reduction side, looking at CO2 reduction. But of course, on the oxidation side, when you're reducing CO2 very often, you're oxidizing water. And indeed, if you try to make hydrogen from water, also very typically, it's water oxidation, which is the key reaction you need to try to understand. I'm going to be talking about it mainly in photoelectric chemical systems where we're driving reaction primarily by light. But I'll be making parallels towards the end. I'll be talking explicitly about electric catalytic water oxidation on a range of metal oxides. All the work I'm going to be talking about is based upon using operandospidoscopy. So this is the idea that we have some sort of electrode, which we put into a photoelectric chemical cell. And we apply a potential, and maybe we apply some light as well, and we drive water oxidation. I've got the one point I'll talk about proton reduction. But the key thing is that we can measure the flux of water oxidation or proton reduction, or if we wanted to study it, CO2 reduction, by the current measured by the potential stat. But at the same time, we can use optical spectroscopy to measure the absorbance of charges in those electrodes and by the Behr-Lambert law, we can turn that measurement of an optical signal into a concentration. And so essentially what this whole talk is about is using UV-Vis absorption spectroscopy to measure the population of charges in electrodes under the conditions of water oxidation in a photoelectric chemical or electrochemical cell. And I'll be applying these to a range of questions. Karen talked in her talk about activation energies for water oxidation. I'll give you examples of where we're measuring activation energies for water oxidation on a hematite surface as a function of surface-hole density. I think this is quite related to what Karen was talking about. But in this case, both the activation energy and the surface-hole density are measured experimentally. In terms of electric catalytic systems, one of the classic ways people like to think about electric catalysis is volcano plots where you have some indicator of reaction rate versus some energetic factor on the x-axis. Where typically this energetic factor is measured, it's calculated theoretically, and the vertical axis is a current density. In this case, this is an all-experimental plot of a turn of a frequency versus the energetics, the reaction measured electrochemically. And then as quite a recurring thing in the talk, very often when people talk about electric catalytic genetics, where people apply a Butler-Volmer model. And I'll be talking how, for some of the systems we're looking at, it seems more appropriate not to apply Butler-Volmer, but to apply a population model, essentially the idea the reaction gets faster because you have a higher concentration of species of the surface driving the reaction. So take a step back, first of all, and just thinking about what the overall purpose is. But of course, where the driver here is to try to move towards a more sustainable synthesis of fuels and chemicals. And there's many pathways and many elements to this. But the particular area I'm going to be focusing on is the challenge of how we can use either light or electrons to drive the synthesis, the splitting of water into hydrogen and oxygen. And of course then the hydrogen becomes a key energy vector for many aspects of our future energy system. From a viewpoint of certain fuels of artificial photosynthesis, this is all about the idea of learning from Mother Nature and thinking about how we can harness sunlight to drive the synthesis of either hydrogen or hydrocarbon-based fuel. And this of course has many potential benefits in the idea of sustainability, but also in the idea of storing solar energy on many of the long time scales, for example, for inter-seasonal storage and also the idea of trying to provide a market for CO2 utilization. When you think about pathways for converting sunlight to fuel, then there are multiple pathways. And you can see an illustration here of how we can go from sunlight and water and CO2 down either to green hydrogen as an output or carbon-based fuels. But in all of these pathways, catalysis is key, particularly electric catalysis is key. And I'm going to focus just on two elements of this, the photo-electrochemical spitting of water or the electrochemical spitting of water and focusing particularly on the idea of a water oxidation. Now, in terms of water oxidation catalysis, my own group has studied a range of systems. Years ago, as a PhD student, I studied plant photosynthesis and I've got one slide on some of the lessons we can learn from how plants oxidize water. We also are studying molecular catalysts, in this case, for water oxidation. Most of my talk, or pretty much all my talk, is going to be around metal oxides. I'm going to start off talking about wide bandgap metal oxides, interesting as photo electrodes for water oxidation and in particular, hematite, a particularly stable and cheap and low-efficient system for oxidizing water under solar radiation. For particular materials I'll be talking about Michael Gratzel, the DPFL, these nano-collic lars. Then in the last part of my talk, I'll talk about electric catalysts. In particular, I'll be talking about ion-nickel oxyhydroxides and their kinetics of water oxidation. And as you can see from the idea here, from the axis of these plots, I'm going to focus very much on how the reaction kinetics measured typically as a turn of the frequency change as a function of the density of charge accumulated over the surface of those electrodes. When we think about lessons from nature, from plant photosynthesis, then of course the key challenge plants have or one of the key challenges they have is the idea that chlorophyll photoestotations are short-lived, typically their lifetimes are nanoseconds, while the time scales of catalysis, and in this case the time scale of water oxidation catalyst, this is the option involving complex photosystem two, are typically on time scales of milliseconds and so plants spend lots of their energy and much of the key design features of very active centres are there to achieve the separation of charge to drive that catalysis. And we see that same challenge of the gain of lifetime to drive catalysis in pretty much all the photoelectric chemical systems we use, we're interested in studying for water spitting. I'm not going to talk about the lifetime gain and the challenges of separating charges in these materials today. I want to focus just on the time scales of a catalysis. And then in photosystem two, water oxidation occurs on this manganese cluster. So there's a cluster of four manganese ions which are oxidised sequentially by separate photons in this photosystem. And they go through a series of molecular redox states progressively up to four manganese four. Once you achieve four manganese four, we can have some arguments of really where the oxidations are, whether there's some of the amino acids are oxidised at the same time, but certainly we generate four oxidised equivalents which then go on to oxidise two molecules of water to make one molecule of molecular oxygen. There's obvious features here, but we're accumulating multiple oxidisants, multiple highly oxidising states to drive this challenging chemistry. There's also notable that there's redox levelling, that many of these electron transfer steps are coupled to proton release. Such that whilst we have four sequential oxidations of a single cluster, each of those oxidation steps occurs essentially of the same redox potential. So it's no harder to go from the zero to the first oxidation state is to go from a third to the fourth oxidation state. They all occur with the same potential and the main reason they occur with the same potential is because these oxidation steps are coupled to proton release so that they will charge neutral. I'll come back to these concepts when we talk about heterogeneous catalysis during my talk. If we switch gears away from molecular systems, we're then very often when people talk about water oxidation on a metal oxide electrode, we're then they focus much more on the idea of the oxidation of single metal sites, very often sometimes multi sites, but often single sites. And the focus particularly on the issues of the binding strengths of oxygen to the surface, in particular the binding of O groups and OH groups to the surface. And for example, there have been extensive studies looking at how understanding the kinetics of oxygen binding to the surface allows us to calculate the sort of volcano plots plotting a measure of experimental activity in this case no potential for one milliamp of current density versus a calculated thermodynamic predictor of water oxidation rate based upon the oxygen and the OH binding strengths on the surface of that metal oxide. What I'm interested in is thinking about whether but sort of more molecular viewpoint which you might get from thinking about from that manganese cluster implants, has any lessons for how we should think about or could think about oxidations on a metal oxide surface. And so thinking about the idea of but if you are generating holes by applying a bias and driving those to the surface or indeed if you are shining light and separating the electrons and holes and driving the holes to the surface, you end up accumulating positive charges surface holes if you like, or oxidized states on the surface of your electrode. And then those oxidized species have to come together to oxidize water. And in general, we're gonna need four oxidations to come together to drive two molecules of water to make one molecule of oxygen. And so one of the questions we're interested in is how do the kinetics of water oxidation change with surface molecular viewpoint of water oxidation on these surfaces? So to think about in terms of localized states coming together forming specific redox states that drive that chemistry. Do the states need to move to an active site? Are all the holes on the surface equivalent and capable of driving water oxidation anywhere on that surface? As we accumulate these states on the surface, what happens to activation energies for reactions? Does the activation energy change with reaction rate? There's obviously a lot of interest in this and carry measure effects. So things like redox leveling and proton management, such as we see and can think about in photosystem too. And so we're interested in trying to understand whether the sort of pictures we have in PS2 have some parallels of how we can think about heterogeneous catalysis on a metal oxide surface. Another way of thinking about it is the chemical, is the overall rates of reaction, the electrochemical rates of reaction that we use controlled by chemical or electrochemical steps that we control primarily by the rate of formation of the relevant oxidizing species or are they controlled by the chemistry of bond formation? I'll talk about all of those points as I go on through the course. The other point which we're gonna discuss is the potential of Fermi-level dependence, the reaction rate. The well-known Butler-Rommer model for a metal, for electrochemistry at a metallic surface has the idea that as you apply a potential to a metal when you drive a Fermi-level deca, and the primary effect of this is to reduce the activation barrier for the reaction. The enthalpy of the charters on the surface goes up, the entropy doesn't change particularly. An alternative viewpoint is not that as you drive a Fermi-level deca, that you change the enthalpy of the reacting species, but then as you change, if you have a semiconductor, as you change the Fermi-level of a system, you change the population of species at the vanence band edge. And in this case, the primary thing the Fermi-level change does is not so much to change the energetics, the enthalpy of these states, but to increase the density of these states. So if you like thermodynamics to change that, to reduce their entropy, so to increase their free energy. This we can most simply call a population model. It's been proposed many times, literally before, but has been less widely applied to both photo-electrochemical and electrochemical water oxidation. And it's most likely to be relevant in systems where you can store many equivalent oxidizing species on a surface. And so most applicable to systems where the charges are quite localized compared to the dimensions of the surface. I'll talk about this more during this talk. And so the first example I'm going to give is water oxidation on a hematite surface. And the idea here is that we take a hematite system, we apply a strong and constant and noted potential to create band bending to separate the charges, and to mean that we can accumulate long-lived charges of the surface. We then shine light on the system and we vary the light intensity to vary the density of holes at the surface. And we measure the current density by simply the flow of the current in our photo-electrochemical cell. And we measure the surface density of holes at the surface by measuring their optical absorbance. And then we most simply undertake a rate analysis to understand how the current changes with that density of charge of the surface. Here's an example of data on this hematite where at the bottom we have the current measured in response to a five second light pulse of varying intensity. You can see the current goes up, it stabilizes and then it becomes constant. The top shows the corresponding optical absorbance change of holes accumulating at the surface. And so this is a measurement of our hole density, this is measurement of our current density. These holes are probably aimed for oxo species. When we plot the current versus the optical density, we see something quite striking where we observe that, so this is a log, log plot of a surface hole density measured per square nanometer after applying the real Lambert law with the distinct coefficient of those holes which we can measure versus the density of current. At low charge densities, we typically see first order behavior. So if you double the amount of charge at the surface, the current doubles. But at higher hole densities, or one suns about here is in the middle of this trend, we observe that if you double the density of charge at the surface, the current goes up as the cube of that charge density of the surface. And that we found quite striking and interesting. Another way to put that is that the reaction order changes as we increase the surface hole density and we measured that reaction order by arranging different techniques, the details don't really matter. But what's maybe interesting is that this change of reaction order which implies a change in mechanism happens more or less when we start to have nearest neighbor hole oxylations. And so in this case, at around about one hole per square nanometer corresponds to where you start to generate nearest neighbor ion centers getting oxidized. And this suggests that when you start to have nearest neighbor interactions, then you start to change the mechanism of reaction. The first order reaction is probably quite trivial. Hematite's got a deep brain and span. And so it's quite likely the first order reaction is surface holes reaction of OH minus to make OH radicals. The third order reaction was a little more surprising. We'd actually expected to see something fourth order because we knew that we needed four holes to oxidize water to make molecular oxygen. But we never saw four holes for an order reaction of four. We only see an order reaction of three on a hematite. How do we think about this? So what we're observing, now I'm four oxoes. So we're not observing the higher oxidation catalytic intermediates of a water oxidation. So what we imagine is that as we accumulate more and more holes at the surface, then we shift the equilibrium towards the short lived catalytic intermediates with determining steps. And so the idea here is that we're accumulating singly oxidized species on the surface. In order to oxidize water, these have to come together in some way to access a highly oxidized state or site which then can drive the exciting chemistry of our bond formation. And the implication of our third order behavior is that the rate determining step happens when three holes come together. Now you've seen similar sorts of behavior for a range of oxides. And so the data you can see here are surface hole densities versus turnover frequencies calculated per surface holes. So not per surface site or surface metal, but per surface oxidized state we can measure at the surface. And we can see that in all cases, at low surface hole densities, we have potential independent or surface hole density independent kinetics. So that's first order kinetics. So single holes reacting to give water oxidation. But at higher hole densities, we get the kinetics accelerate. We have a cooperative effect which we imagine is associated with three holes coming together to generate for a determining step. We can see that the deeper the balance band, the faster the kinetics are, which suggests that we are shifting in the kinetics equilibrium more towards this rate determining step. Now, one of the interesting things that we have here is that because we are measuring a turnover frequency, we can turn, we can do an rate law, we can calculate rate constants. And so because we have a population and we have an order of reaction, we can calculate the rate constant for that reaction as a function of surface hole density. As a function of reaction condition. And maybe one of the most interesting things to measure is how the rate constant for reaction changes with temperature because of course that allows you to calculate the activation energy, the reaction. And so these are typical data where we observed that whilst the current changes quite a lot with temperature, if you don't measure just the current but actually measure the current not versus potential or versus light intensity but versus the actual density of surface holes, we observe that in the high light intensity regime that essentially the reaction becomes independent of temperature, almost independent of temperature whilst at lower hole densities, we see a significant slow down of the reaction as we cool the system down. We can calculate activation energies for the first order reaction is around 300 millivolts or seven kilocalts per mole. But for the third order reaction is almost activation-less. It's not much more than KT. So this suggests that accessing this third order reaction allows us to access to catalyze water oxidation with a lower energy of activation. Another way of this idea that the activation energy may change with surface hole coverage is not unique to our own studies. This is our experimental measurement of the activation energy versus surface hole density and it changes due to a change in reaction mechanism. This is analogous to a recent report by Nong et al where they were calculating the activation energy for water oxidation on an iridium surface the origin of this activation energy change is rather different.  But both analyses suggest with understanding how the activation energy changes to surface hole density is interesting. And of course, this is also something which Karen talked about earlier. We can go on and not just measure the temperature dependence, we can measure the rate constant as a function of pH or as a function of kinetic isotope. And you can see, for example here that the rate constant for water oxidation is rather insensitive to pH until we hit pretty much the PZC of hematite. This suggests that there's something around how the pH dependence impacts is primarily determined by the degree of protonation of the hematite of the surface. This is analogous to think, you think to how people think about how in photosystem two there are proton relays which allow the movement of protons away from the reactive site and probably surface OH groups serve a similar function on metal oxide surface helping to move protons away from the oxidised species in order to facilitate the accumulation of oxidised states on the surface of an oxide. We can also see the nest isotope effects quite small, suggesting that OH bonds are not being broken directly in the rate determining step. We can put these sorts of numbers. It's helping us to think about what might be an appropriate model for describing water oxidation on a hematite surface. And in particular, we talked to one of our colleagues who spent a long time trying to understand water oxidation in photosystem two and he applied the same model he's been using to analyze water oxidation in that manganese cluster to try to understand water oxidation on a hematite surface and particularly just taking a very simple cluster of two ion centres on the 110 surface of hematite and thinking about how he could model the data in a way which was consistent with our experimental data. And so in particular, the idea that we have a very small activation energy for the rate determining step and that we're observing, if we have an equilibrium between this rate determining step and these surface holes, then the idea that these surface holes are most obviously operating at similar oxidation potentials for each of the three steps. You can see actually the calculations here suggest that the accumulation of three holes at the surface does not involve a large increase in enthalpy because each of those three steps is associated with proton release. Now the full details of this mechanism I'm not going to go into, I'm not an experiment, I'm not a theorist and indeed it's rather a complex transition state which Victor calculated. I would want to suggest this is the only possible mechanism for water oxidation which would be consistent with our data. But it does suggest that thinking about water oxidation on oxide surface with no particular active site simply just the surface of the oxide and thinking about the accumulation of oxidizing of a multiple oxidized state on this hematite surface can allow us to think about mechanisms of water oxidation which would be consistent with our experimental observations. And so the idea is that under conditions of oxidation of the surface, we start to accumulate oxidizing species on the surface of our hematite. These oxidizing species, these iron four states can be in equilibrium with the rate determining catalytic state. As we increase the density of these iron four oxos then we shift the equilibrium towards the intermediate and this accelerates the reaction. Another way to think about that is that what's driving the reaction is that we're going from states with a relatively high entropy these holes moving around on the surface to a state with a lower entropy which of course is the intermediate state and that's one of the challenges and that's why we have to really drive a high identity of these states to drive the chemistry. The downward steps after the rate determining step all downhill. This sort of model was consistent with our pH and glycemic defect data and indeed this sort of model is also consistent with some previous literature mechanisms such as Heinz-Franes who is also discussed the idea that water oxidation may require surface diffusion of charged carriers to accumulate to drive the relevant kinetics. And so this is the idea that if you want to think about water oxidation on these metal oxide surfaces then maybe it's interesting indeed to think about the idea of oxidized states coming together to generate higher oxidation states which are rate determining states for water oxidation but understanding this equilibrium is critical to understanding the kinetics. It's also interesting to think about that the model we have doesn't require any particular cathodic sites for oxidation. It's simply the idea that the surface of hematite if you accumulate multiple states of that surface it's possible to drive water oxidation by pathways which are essentially activation-less. Now the picture we have here is based upon this population model that I talked about earlier not the Butler-Volmer model which is more widely used to consider reaction kinetics. This analysis we have here it's just some indication that model seems to work quite well. And so for example, what we've got here are calculations of a water oxidation rate constant at different applied potentials both for water oxidation indeed here for methanol oxidation. And the key point here is that we're changing the reaction potential which under Butler-Volmer you might be expected to change the rate constant but the rate constant doesn't change the rate constant only changes when we change the surface cell density which is really supporting the idea that the kinetics we observe and dependencies we observe are not so much caused by changes in the enthalpy of the states as you apply a higher potential but by changes in their density. Now, it is a little surprising but that's what we observe. So this is essentially the idea but as we drive if you increase the density of states of the surface then the only thing which is changing is their population. We don't see any effects for example of what's often called band-aid jump inning the idea as you accumulate more charge at a surface then the energy of those states will change. Maybe that's because the charges we're accumulating are primarily charged neutral because every time we drive in oxidation that tends to result in release of a proton from the surface. It may also be associated with the idea the water oxidation is probably an inner sphere reaction rather than an outer sphere reaction and so maybe this is less associated with some of the fields in that Helmholtz layer but of course these are topics which we are still puzzling over and indeed are rather controversial at present. So that was water oxidation on a metal oxide photoanode I also briefly touched on observations of methanol oxidation on the same sort of surfaces. What I thought I'd finish my talk is it's moving on to talking about the difference between photoelectric chemical and electrochemical water oxidation. I'll first of all talk about a study we did on proton reduction on ruthenium oxide and then I'll go on to talk about water oxidation on nickel ion oxides and at the end I'll mention something about iridium oxide. So if we first of all talk about ruthenium oxide proton reduction when we got into this, we actually hadn't planned to measure the genetics of catalysis at all. We were actually studying photo electrodes from Michael Gratzel based on Cooper's oxide as a light absorber as photocathodes for proton reduction. But he was using a ruthenium oxide co-catalyst on these photo electrodes. And we thought we ought to study the control of just the ruthenium oxide alone to study the comparison of the kinetics of the ruthenium oxide as an electrocatalyst and as a photoelectric, photoelectric catalyst. Now, when we think about electrochemical kinetics then very often these are analyzed by tarp analysis. And you can see a tarp analysis for these data here plotting a log of the current versus applied potential. And whilst of course, these are very useful and give us some insight into reactive genetics. It's often quite challenging even for electrochemical systems to determine our reaction mechanisms from the tarp slopes. So there's many potential ways these tarp slopes can shift and when you come to photo reactions that understanding is even harder. So what we wanted to try to do, or what we ended up doing was try to understand how the rate of reaction here depended not upon the applied potential but upon the degree of oxidation of the ruthenium oxide. The first thing we had to realize and was challenging was that of course, ruthenium oxide has at least two oxidation states. We haven't gone into the detail nature of these states. We're simply here calling them the first reduction and then the second reduction. But by measuring the spectrum, the UVV spectrum of our electrode in the UVV spectrometer as a function of applied potential, we're able to observe two different spectroscopic features. A wave which corresponded to rather broad absorption of broad bleaching of absorbance across the UVV spectrum. And then beyond a certain potential, the appearance of a new feature, a positive absorption, a positive, an increasing absorbance, primarily towards the near IR. And we observe this both with electri