 Hello, everyone. My name is Willa. I'm a fourth year PhD student at Gilson Web at UCSD. Today I wanted to talk to you about a simple polarizable electrostatic model that we developed for molecular dynamic simulations. So today I want to quickly talk about the current polarizable models because this is not a new concept. We already know there are a lot of polarizable force field out there. And every time we have a bad simulation result, especially for protein ligand, we plan that our force field is not polarizable. There must be some errors happening there. Next up, I want to talk about this polarizable and why do we want to develop it for the use of this open force field. And finally, I would like to talk about a little bit benchmarking results that showed using our polarizable force field. So for the electrostatic part, why do we care about the polarizabilities? That's because in the molecular mechanics we use the Coulomb's law to calculate electrostatic interactions. And in the Coulomb's law, we have the dielectric constant as a contribution to the potential energies. And in the vacuum, the dielectric constant is really 1.1, and in non-polar solvent is really 2.1, not 2.0. When we do have solvents involved, that's for water, that's really around 80. And using explicit solvent, we simulate this part explicitly. So if we do not have a good force field to represent the dielectric constant, we will not have a good electrostatic potential energies. So that's why we care about it. And to talk a little bit more about how it is involved, so when we do have solvent involved in the simulations, there will be an electric field around the system. And when there are electric fields, and every atom has polarizabilities, they will induce a polarization effect. And those are not involved, they are not included explicitly in non-polarizable force field. So with a non-polarizable force field, we're not able to get a correct or relatively correct dielectric constant, which leads to the not very correct potential energies for electrostatics. And in the non-polarizable force field, we really have the rotational polarizability involved. However, if we do have a non-polar environment, there will not be much of the rotational polarizability involved. So we will not be able to have a good representation. And also we're missing a big part of the electronic polarizabilities. So for the current model, we already have, we have three models, induced dipole model that's widely used in amoeba, or this figure is taken from i-amoeba water model. The induced electronic polarization is included using the induced dipole. And another popular polarizable force field is drewed polarizable force field. That includes dummy addons next to the parent addons to include induced dipole and includes electronic polarization. And another one is the fluctuating charges that's based on the electronic activities. The problem with fluctuating charges is there's no auto-plane polarizabilities involved. So in this polarizable force field we developed, we wanted to be fast compared to amoeba because we used direct polarize, direct approximation of the polarizability or polarization, which means we only taken the first order of the polarization. And that means for all the electric field that's involved in inducing the dipole moment are all generated by the permanent electrostatics. So there will be no induced dipole-induced dipole interaction. And that's why it's fast because there is no self-consistent solving involved. And in order to use the polarizabilities in molecular dynamic simulations, we need permanent electrostatics to work with that. So in this work we introduced two charge models to work with polarizabilities. And we also implemented a Smerna plug-in to handle the polarizabilities induced dipole in our charge model so we can use our induced dipole model with open force field. And that will be applications used to ways open force field and open mm for the benchmarking. So as we talked about earlier, the direct polarization is introduced by induced dipole and the polarizabilities will only fail the permanent electrostatics. And so in that case, it will be a better representation for the electrostatics compared to the fixed charge model because the fixed charge model will not fail any of the external electric field and not respond to that. And it will be faster to compare to the self-consistent polarizations, which is used in Amoeba, where you have the induced dipole, where it interacts with the permanent charges, and the induced dipole. So if you could see that, it will be the red arrows interacting with the black arrows, and they have to be self-consistently at every time step. So that's very expensive, and it's hard to parameterize. In our model, the middle one, we only have the permanent electrostatics to induce the induced dipole. And we type the polarizabilities, so every time you just need to look at the force field file and you will have everything to induce the polarization effect. Now, since talking about looking at the force field file and look for the polarizabilities, where do we get the polarizabilities? The good thing about having polarizable force field is that you can train polarizabilities on gas phase data, but it can still reproduce pretty well condensed phase data, and training on gas phase data save a lot of time for us. So we train our polarizabilities on gas phase QM ESP, and what we do is we impose some electric field on one of the molecules, and we calculate the electrostatic potential around them, and we take the differences. And you'll see induced dipole to reproduce the differences in electrostatic potentials, and that will be our polarizabilities. And another thing is we train the polarizabilities without any permanent electrostatics. So in that case, our polarizabilities will be independent of charge model, and that gave us some freedom to find the best charges to reproduce the baseline electrostatics. And that two charge model I'm talking about. The first one is the REST style charge partial charges. That means the charges are also fitted to the electrostatic potentials. But for this one, it has the induced dipole when we're fitting to the electrostatics. Another one is a faster model that's a 1 BCC depot model. And that works similarly to the a 1 BCC in the context of REST and a 1 BCC. It is the faster model, but it is also retrained the BCC parameters are retrained to consider the induced dipole effect. So that's the true electrostatics model we're trying to introduce here. So in a little bit more detail, details into the charge model. This is a standard REST fitting objective function. And what is different in the charge fitting part is we have induced the electrostatic potential from the induced dipole. That circle here. And what is there is the induced polarization we included. So what's also the polarizabilities at the center where we interact or respond to the local electric field. And since we're using in direct polarization, the electric field E is generated by the permanent charges and there is no self consistent solving involved. So even if it looks a little bit complicated, but it's a very simple. It's an easier process to solve for the REST style charges with in the context of polarization. And so that is the REST dipole style. And what is with a 1 BCC dipole. So, as I mentioned earlier, we retrain the BCC parameters to include the induced polarization effect. And we change the objective function of the BCC is to also include the we induce part. And the we induce part is generated similarly to the previous REST part. But the bigger one is the newly trained BCC parameters. And there were only between once against QM electrostatics. And after that training we'll be able to use the A1 BCC dipole model just like A1 BCCs. There's no other QM calculation involved. You can use open FF toolkit to generate that. That part is done by Simon's open FF recharge package. And so that is the two charge model we introduce for work, working with polarizabilities. And what is involved in the training process in the polarizabilities is QM ESP data, and it will have the polarizability library. And the libraries used to train another library BCCs. So overall, all we need to use this polarizable model is the already trained polarizability library here and another already trained BCC dipole library there. So no actual additional QM calculation needed if you want to use this model. So that is about the model. And how are we doing with gas phase dipole moment calculation, because we want our polarizable model to be able to reproduce both gas phase data and condense phase data. So how are we doing with molecular polarizabilities? That's experimental data. Since our polarizabilities are purely derived from QM calculations, we wanted to be able to reproduce experimental data. And finally, how are we doing with molecular dynamic simulations? We're looking at dielectric constant to check that part. And this is a little details into how are we going to use our force field with open mm and Smirno plug in. And also this is the infrastructure we need to introduce a new polarizable water model that's used to ways direct polarization and our permanent electrostatics. And we introduced two pendulars here. One is called the multiples. That is our permanent electrostatics. And another one is polarizabilities that's already defined polarizabilities. And so for the benchmarking and the training of polarizabilities, we did train two sets of polarizabilities. One is based on elements that only have carbon. Hydrogen, oxygen, nitrogen to make sure that the direct polarization model actually works. And another one is trained on the sage and the drones type that has 17 types in the force field. So we also trained based on those. And that is for us to explore this having more types actually help with the electronic polarization. Now, looking at the gas phase dipole moment reproduced by a one PCC depot we say that we choose the QM reference data at MP2 level because based on benchmarking results, that is the best affordable and QM dipole moment references. So, using both typed polarizabilities we're able to reproduce this quantity very, very well. There is no much significant improvement from using more types. And that opens the question do we actually need more types for polarizabilities. And that is about the gas phase, that's about the gas phase polarizabilities gas phase dipole moment for the electrostatics, how are we doing with the liquid phase experimental molecular polarizabilities. So in this case we also measure the molecular polarizabilities, you're saying the two types of atomic polarizabilities, the way to measure that is to sum up the atomic polarizabilities and our returns the molecular polarizabilities and as we can see, there is a very good agreement with experimental polarizabilities, and we can really tell if having more types help with in terms of the polarizabilities. And so finally we did, we did molecular dynamic simulations using the polarizable model, and we compared the dielectric constant calculations with non-polarizable SAGE model. And there are 17 polar and non-polar organic liquids that's included in the benchmarking data set. For the non-polarizable SAGE model, what we can say is there's not a very good agreement. And that's kind of to be expected, because for all those values that's sitting there around 1.0, those are non-polar organic liquids. And there are no much fluctuations in the dipole moment when they're in the liquid phase. So there will be no much contribution from there. And all that's coming from is the one, a constant one that's used in the formula to calculate the electric constant. And we also plot inverse dielectric constant here because the Coulomb's potential energies is inversely proportional to the dielectric constant. And using switching to use polarizable force field, we're able to improve the agreement with experimental dielectric constant. And using element type and SAGE type polarizabilities are all able to give us the better agreement. And that is the desirable result we want with a polarizable force field. So finally, the experiments with A1, B6, Cd-Pole charge model and the direct polarization is able to improve the accuracies in both gas phase and condense phase calculations. And since we have type polarizabilities and the fast charge model, everything is very fast to come to parameterize and the system will be ready to go with open FF interchart, interchange toolkit. And that is all I have for the polarizable model. And I think I'm right on time. Thank you all for your attention.