 Okay, so thank you very much Mike and I'm very grateful for the invitation. It's very nice to be here It's the first time I'm triester, but of course I know about his workshop. So it's very interesting to be here so I'm interested with solid-liquid interfaces in the context of electrochemistry and This is some of the examples where electrochemistry is important It's certainly a very small portion of the places where solid-liquid interfaces are important And if we want to kind of tune or enhance the functionality of any of these kind of processes or even try to maybe suppress corrosion, then we need of course to understand the underlying mechanism starting from the atomistic scale and really knowing what's going on Density functional theory has been extremely helpful in providing insight with complement to experiment in many kind of materials materials problems and so the question is can we also use apinitio calculations in order to address problems in electrochemistry Now the problem that is close to my heart is corrosion since I'm working in an Institute for Iron and Steel Research So obviously corrosion is an issue. We have to deal with When we are thinking about these electrochemical systems, we are facing a lot of challenges Let me start with the example of a galvanized steel sheet which corrodes So the base material is steel which in itself is extremely complicated And what is done is to coat it with zinc kind of as a first layer against protecting it against corrosion Then of course the metals are not the thermodynamically stable state when When it comes into contact with an aqueous environment. So what happens is that we form some kind of Oxide hydroxide which hopefully has protective properties and therefore doesn't allow for further degradation of the material Now if you want to describe something like this, obviously we have to think of how to kind of Make it into smaller pieces So we need to translate somehow this materials complexity into representative structures that maybe we can treat it under to mystic level density functional theory and then try to see what we can learn about the overall problem of electrochemistry and The way we go about it is very often by combining density functional theory calculations with thermodynamic concept Which allows us to use the kind of divide and conquer strategy and look at representative parts or structures may be Molecule here or the interface or defects in the this oxide layer and so on and then connect everything via chemical potentials accounting for local equilibria which may occur in this systems and We have worked on different parts of this interface today I would like to talk about really the interface between water and the liquid However, if we think about is we have really also very different classes of materials and this imposes different Challenges to density functional theory calculations. We do have metals We do have semiconductors or insulators, and we do have water now. Let's start with water Which is probably the most obvious thing? When we are thinking about an aqueous environment, we just can't do just a t equals zero Calculation and just the total just the ground state search We have to use molecular dynamics because we need free energies And this of course bring us to some limitations regarding the time scales that we can address in density functional theory And really something in the order of a hundred picoseconds. It's a long trajectory for us When you think about water and density functional theory, probably people think okay We need to include van der Waals interactions. There are ways in which we can do this now A days something that is less frequently discussed that that we actually have a problem regarding the electronic structure of water Now here I've sketch kind of aligned on With respect to the vacuum level on absolute scale what the band gap of water is from experiment What we get out of PBE and what we get if we use hybrid functionals and you can see that Sometimes depending on the question we need to we want to address We actually have to use hybrid functionals and doing an MD with a hybrid functional is really a pain It also is a problem if we have a metallic system in contact with water because they are the hybrid Functionals are actually not something which you would like to use for the metallic system and Therefore we do have sometimes to we have really to worry about also level alignment Because if we have an alignment that is this way This electron transfer may not happen if it is this way it will happen and then this will describe very different physics or chemistry So we may totally miss kind of a point So we need to be very critical of the calculations that we are doing Typical DFT codes also use periodic boundary conditions and in some cases this is a problem And I will show a case where this is a little bit challenging to deal with periodic boundary conditions But let's come later to this and of course if you think about electrochemistry the observables that are kind of Which govern the processes and what is also controlled by experiment are pH and electrode potential So kind of our first objective was to try to understand from a microscopic point of view What is how can we understand pH and electrode potential and this was based on idea of semiconductor physics Where we think of ions in water are from a formal point of view very similar to defects in semiconductor So we use methodology from semiconductor physics in order to Make a connection to pH and electrode potential based information energies of ions and the concentrations Now this is a point I won't discuss we have here a paper where we discuss it in detail and if you have questions I'll be happy to answer them later But now I would like to talk about some more recent work and address two questions What is the role of the solvent actually in stabilizing surfaces? So can we just do calculation with neglecting water or are we making error there and the second is How do we treat the electrode potential in DFT? We would we know that there is a double there So there is an electric field at the interface and this will influence of course what happens at the surface And this is also what experiment controls, but how do we get an up in its your potential start in DFT calculations? So let's start with the first question and this is work, which was done by Suhyun you who is a PhD student in my group and The way we can model water in DFT is either, you know doing the explicit calculations Which is obviously the most accurate way we would go about it But of course the most painful way in in terms of computational time So very often what is done in the community is that we consider maybe one or Lately also more water layers, but then we still have a vacuum region In later years now now it has become also popular to use an implicit solvent and Nicola has done their work for a long time and This is kind of a compromise between this thing and this thing so what we do in an implicit solvent And we can we fill the vacuum with a dielectric continuum It is certainly an approximation But if we just want to look let's say a thermodynamic or stability at surfaces This may be a way which by which we can go and so The knowledge that we have actually most people study metals the predominant literature is on metals There is less literature on semiconductors and also there is kind of a generally accepted picture that the Impact of the solvent is rather small beyond specific adsorption But this is not really been proven and people kind of assume it so well So the question is this really true and do effects beyond let's say the specific adsorption play a role We also know that metals and semiconductors may behave in a very different way So what we have in metals surfaces is typically that we have relaxations, but on semiconducting surfaces We do have some reconstructions which are kind of you know very often driven by the Attempt of the surface to remove surface charts. So they're electrostatic arguments probably play a role and We know that well there is an easy availability of water Derivatives OH and hydrogen group. So this is typically considered as adsorbates on the surface But if we think about the bulk water continuum It will have if what about effects of polarization or electrostatic screening, which are important there And so we thought okay we won't do it now an explicit calculation we use an implicit solvent and we consider a set of surface structures for which we can Perform two sets of calculations one a calculation in which we have the structure embedded in an electric So in an implicit solvent and one in which we have the surface in contact with vacuum and The surfaces I'll be looking at our zinc oxide polar surfaces So I would very briefly like to tell you something about this material It's a semiconducting material which stabilizes in which has a word site structure And which means that each oxygen and each zinc atom within the structure is the trahidrally coordinated to its neighbor Which means that in the bulk the each zinc atom would contribute kind of half an electron to a bond and each oxygen atom would Contribute three half an electrons to the bond so each bond within the bulk has two electrons Which is the maximum number of electrons you can have in order to have a stable situation Now when we cleave the material perpendicular to the z direction to the c direction Then we end up with surfaces on one side which are purely zinc terminated and on the other with oxygen terminated surfaces And I'll be looking at the zinc terminated polar 001 surface this indicated here We do have each of these atoms has a dangling bond which is filled with half an electron So we do have a surface charge on the surface and because the sp3 hybrids are kind of high in energy oxygen hybrids a low in energy We usually there is a strive to transfer the zinc electron to the oxygen and thereby End up here with an empty and here with a filled dangling bond And this is what we also find the drive reconstructions at the surface now We've considered various surface models here some OH groups just saw in various coverage It's a soft on the cleave surface. There are large reconstructions which have kind of a triangular shape Then we have kind of a mixed surface termination. We do have vacancy or adsorbate structures and We perform for each of these structures a calculation DFT in vacuum DFT with implicit solvent And then use thermodynamic modeling is indicated here in order to evaluate the change in the Gibbs free energy Now within this system, we do have a few chemical potentials We have to consider the zinc oxide is characterized by a sink and an oxygen chemical potential while the equisystem is characterized by hydrogen and oxygen chemical potential so this means that we end up with From from Gibbs formation energy, which is kind of dependent on three potentials But because we have to account for the stability of both sink oxide and water in the end we end up We can see that both the hydrogen is depending on the oxygen chemical potential and that thing So we end up with a situation in which we have here just the dependence on the oxygen chemical potential and And We can well who use our derivations which where we show that the hydrogen chemical potential can be expressed as a function of the Electrode potential and the pH scale in order to make them a transformation and end up with the poor be diagram so poor be diagram is a electrochemical diagram in which What one sees is on one axis the electrode potential change with respect to the standard hydrogen Electrode, which is the reference used in experiments and on the other scale Axis we do have the pH scale in each of the Areas that you see here would correspond to the stability of one phase We built now such a poor be diagram once for the calculations without the solvent You don't have to understand all the details Just what I would like you to remember that this kind of blue phases are as cleaved surface is this various Coverages of OH group on the surface. Well, this red surface is kind of a triangular reconstruction We do have one experiment experiment, which is a disconditions and when we compare we see that they do have here Triangular constructions. So obviously we are not quite describing reality here when we look at the Surfaces in which we considered now the solvent We do see that the first the diagram changes So this kind of greenish and red colors are triangular reconstructions either with OH group with hydrogen groups or without any coverage and What we can see that now in the region where the experiment sees triangular Reconstructions at the surface we can also see within our phase diagram a triangular reconstruction at the surface So obviously salvation effects are important, but can you understand? What do they actually do why what's the underlying physics and for this we need to take a little bit closer look at the structure Now within the strangler reconstructions We do have edges which are decorated with oxygen atoms while the terraces have zinc atoms And if you remember the oxygen atoms have three half electrons per dangling bond Zinc atoms have one half electron to dangling bond So it would be easy if they are close by for an electron from the zinc dangling bond to go to the electron To the oxygen dangling bond thereby ending up with a situation where we don't have charge at the surface If we have the same number of zinc and oxygen dangling bonds now if we look at the Electrostatic energy associated with this and solvent The salvation energy that we gain we can see that there is a correlation Now what happens if I have a small triangle is that this Oxygen and zinc dangling bonds are close by so we don't have to pay a big electrostatic penalty to transfer an electron If we increase the triangular size then of course the bonds are further away and therefore This structure has become less favorable in vacuum from an electrostatic point of view And what the solvent does is to screen this unfavorable electrostatic interaction thereby stabilizing Structures which have a high electrostatic penalty in vacuum There is a second effect now We do have a few structures where we don't have the same number of dangling bonds of zinc and oxygen So therefore we still retain some electrons at the surface. So these are metallic states And what we can see so within this plot this are kind of metallic structure on this side We are structures which are structures which are semiconducting and as you can see as the structures become more Semiconducting there is also a strong gain and salvation energy, which means that in cases where So structures with not a non-metallic surfaces are really for favored by the solvent as compared to metallic surfaces And for this we can kind of draw some general conclusion regarding our modeling So in cases where we don't have metallic character and where Electrostatics are important to the surfaces Considering the solvent will be important and we are actually making a big error if we do not consider it in metallic systems Where electrostatic interactions may play a less Important role and where screening is also mediated by the substrate itself Just say if we neglect the solvent we are actually making a lesser error So for thermodynamic considerations, we are probably Kind of can't work if we just have one or two water layers though, of course, it will be better to do the full With us, I would like to go now beyond the thermodynamic model that I described here And to look also how we can actually describe reactions and for this We need to think about how to build a potential start in a DFT calculation Because how can we apply charge and this is work which is done by Söderchanzer in Drillau who is Another PhD student in my group Now let's look at what do we have in experiment. We typically have we have an anode on one side We do have a cathode on one side on the other side They have different charts so that we have a potential drop Due to this potential drop we may have dissociation So the anion would move to the anode the cathode cut iron would move to the cathode This will screen the charge on these electrodes and what we will have is a potential drop What is done in experiment is then is that there is some charge flow So their electrons are provided on one side removed from the other so that we restore the Potential drop that we have and this is something we would like to model The problem is if you look just at the separated so kind of just as a half cell Which is very often done in modeling. This is a grand canonical system Which means it's a system open to the exchange of both electrons and protons and in a standard DFT code This is not something that we can easily do. We need you know constant Chemical potential DFT code, which is not the standard that we have If we however look at the overall system, this is a canonical system with respect to the exchange of electrons and Protons because what is kind of lost on one side is added on the other side So if we were able to describe this kind of system then maybe we can do actually an Up in its you potential start now the difficulty comes that we typically have in our codes periodic boundary conditions and If we start with the situation where we do have two metals We do have different Fermi energy as we do our SCF cycles due to the periodic boundary conditions In the end we end up with kind of the same Fermi energy throughout the system and so our field is kind of gone So what do we do? We thought about it and sort of cave I mean can we use concept from semiconductor physics and semiconductor physics people do bandgap engineering So what if I kind of substitute my counter electrode the one that I'm not so interested in By a semiconductor, but this is kind of a computational Electrode which allows me to apply a field and By doing this we can for example apply here p-time doping which will mean that again We will have then electron transfer and what we end up it with a field Of course, it can't dip beyond here because then we will get field emission. So in the end we will have a field which Is going up to here That's nice. We need to kind of find a suitable semiconductor. That was a hard part Really because we thought okay, let's take something like let's say aluminum nitride or one of these Helites which are have big bandgaps The problem is of course when we are doing a periodic boundary condition We have the metal on one side. We are interested in we do have the other metal or the semiconductor on the other side They have to be Match with respect to the lattice constant which decreases the bandgap anyway in DFT We do have a problem with also the bandgap So we ended up for example for aluminum nitride with something that was too easy White bandgap, which is definitely doesn't give us much flexibility for the variation of the potential So we are kind of scratching our heads and really thought okay. What do we do? Let's look in Google What is the? Material which has a big bandgap and it turned out that neon is the material which has the largest bandgap in nature From an experimental point of view. This is of course not viable, but I don't care I mean if in computational this just in computational physics this neon would be just a trick in order to have something with a large bandgap In fact the bandgap of neon is 22 EV and even with PBE it is still 11 EV and it is properly aligned So I don't care It has other advantages So apart from the very large bandgap neon is van der Waals pound it So it has a very small deformation potential and in this way actually even by straining the Neon layer that we put as a counter electrode. We hardly have any deformation potential there So the bandgap stays still as big and it is inert to the reactions with the possible solvent molecule So it is turned out that neon is kind of the perfect counter electrode We also checked, you know again alignment here the system. I was interested in magnesium Then we looked at if we have just vacuum we have kind of the proper transfer of electrons and That we also get fields here, which are According to what we would expect What I didn't say is how we kind of introduced discharge and this is done by something which is called pseudo atoms People who are doing semiconductors are probably familiar with this because pseudo atoms is something which we use on a backside of the Slap in order to saturate dangling bonds So probably hydrogen three quarters or one half or something is familiar to you and we use here exactly the same trick So we have actually pseudo neon atoms This has the advantage that we are not bound to changing the charge just by integer numbers But we can change it also by fractional numbers and in this way. We are much closer to the experimental situation and The what we did is to use so the way we Implement it is is actually not to change anything in vast which we use but we have kind of a loop around Vast were basically by a Python script, which was done in our Serial master model Pyron and we then check for the You know whether the potential drops had changed Compared to what we would like to have and then we supply charge depending You know such that we keep a constant potential drop Now with this I would like to show you one application where we have used this approach to show you that This is extremely useful and we can really solve problems with this and this is looking at magnesium corrosion Atonautic conditions now magnesium is interesting Because it is a very light metal and so we're in all kind of lightweight application It is an alloying element that people would like to use However, if one looks at the corrosion property of magnesium, it's kind of almost off the scale It's extremely bad, and this is a problem It also skip is a very strange corrosion behavior now at a nodic condition, which means that magnesium is positively polarized There is observed apart from a very high corrosion rate also the evolution of hydrogen Which is something which is completely counter-intuitive and has puzzled people for more than a hundred and sixty years so We thought okay now we can maybe perform our calculation at a nodic condition Look what's happening, and we can really look at the electronic structure at the atomic structure Maybe we can understand what's going on. So these are some details of the setup and First we did just the calculation without applying any voltage I hear so what is left here is kind of the trajectories of some of the interesting atoms Water molecules trajectories are kind of blended out and also the magnesium trajectories that are not interesting But what you can see here is that almost immediately we have kind of the dissociation of water and forming of OH group and hydrogen groups and for the time of our trajectories we And it up with the coverage of one quarter one-third to monolayer of hydrogen of OH on the surface Which is also consistent with DFT calculations and other calculation, which just look kind of at as ground state properties Now what happens when we make and magnesium more anodic? So basically we make the material more positive and this is you can see this is kind of our targeted voltage the instantaneous voltage and the average voltage One can see that we really nicely follow our targeted voltage and this is the charge that we need to supply Now this is the same picture like the one I showed you before but now really under anodic polarization Anodically polarized magnesium and you can see that much more is going on So again, we have here dissociation of water in and OH coverage. However, this time it reaches one monolayer What we see also that we form here Hydronium ion which as expected would move to the neon side and kind of screen to charge the charts here And what we were very excited to see is that we really see reaction and the formation of hydrogen molecules within this system now we looked at the Kind of geometries that are associated with the formation of these hydrogen molecules and here are a few snapshots from the MD So what you can see here is a hydrogen Atomate soft on the surface which is otherwise hydroxylated and there is a water molecule approaching the water molecule binds hydrogen in a kind of an Expected geometry for people who are doing quarter because they usually don't expect that the hydrogen will bind to a hydrogen and then there is a Dissaciation the hydrogen molecules is formed which then eventually leaves the surface while they await the source Now this is a kind of reaction that has so this kind of reaction. This is what is written is known however for Situation where we do have cathodic conditions where there are There is a surplus of electrons at the surface now here We are at electron deficient conditions because the magnesium is positive So where does this electron come from? What we did is to look at the difference density of a surface Without hydrogen with the neutral Hydrogen and just the overall and what we find is that hydrogen on this magnesium surface is negatively charged So we don't have an additional electron that is coming somehow from the substrate But actually the absorbed hydrogen is slightly negatively charged and the reaction we have is this one here and This kind of goes hand-in-hand with Observation that we make this magnesium Behaves also in other cases a little bit weird because it has a very High spill out at the surface and it's very polarizable As we discussed in this work So with this I think I'm at the end and would I hope I was able to show you that we were able to implement An up in its your potential thought which allows us to do Calculations for surfaces at applied potential and this kind of opens really roots to look at Questions which are difficult to address by experiment and really Compliment and get some understanding and thank you for your attention