 Well, thank you so much for having me and for giving me a chance to give this talk in front of such a distinguished audience. I'm really happy to be able to give this talk. And I'm just sorry. I wasn't able to be there in person. So today, I'm going to talk about how our group propagates maximally localized one year functions in real time. I'll talk a little bit about how we develop that. Propagation method and then I'll talk about kind of what we've done with it, how that inspired us to formulate and use these money functions to accelerate hybrid functionals and what we've done so far with the acceleration method and some results from that. So, for our group, we do all our work in the cue ball code. So our implementation of maximally localized one year functions is based on the work done by Francois and collaborators in the cue box code. Where they use the sign cosine method to maximally localized the cone sham single particle orbitals. And in their work, they had only done this for real wave functions, but they had discussed being able to extend it for complex wave functions, which is what we have done. And so in the cue ball code, we now propagate these complex wave functions and it's a two step process where we essentially propagate the wave function every step, and then localize it at every step. And this method of localization is found to be very robust as for a 64 Adam cell of crystal and silicon. We essentially see no drop off in the energy drift switching from the time dependent cone sham equations to the time dependent one a function equations. And also, I think very importantly, we see going to the maximum localized one a function only increases the cost of our calculations by about two times and that's for a 512 Adam crystal and silicon cell. So, originally, we implemented one a function to be able to apply a spatially homogeneous electric field to our calculations under periodic boundary conditions. And I will say, although this is not formally allowed in the theory, it has been shown that real time PDT can give very accurate results. When you apply the spatially homogeneous electric field to study different physical properties. So, there are essentially two ways to do this. One is to use the velocity gauge and effective potential. But since our code is a plain wave pseudo potential based code, implementing the external potential, which is non local is very difficult. Instead, we use the length gauge, and then using the one a function to be able to implement a scalar potential, where we can essentially apply a identical electric field to every one a function in the simulation cell, since the tails decay very rapidly, as long as they're highly localized. And that way we can simulate the spatially homogeneous electric field. And so I know, I'm sure everyone here knows all of these equations, but the idea was to be able to get the dynamic polarization essentially based on the monetary of polarization from the one a centers. And with the dynamic polarization to be able to calculate the conductivity, and then in turn the dielectric function or the dipole strength function to be able to get absorption factor for different systems. And most of the work I'll talk about here and results will be absorption spectra using this method. So, one of the first kind of molecular systems we looked at was Benzene. So, comparing it to experiment, we are able to capture nearly exactly the main peak around six and a half EV for Benzene. So the results initially were very promising using the LDA exchange correlation functional. And since we had the implementation of one a functions, we decided to look at this more complex system. Here, a Benzene in water in two different orientations for the pie electrons. And by using one a functions were able to decompose the spectra into the contributions from Benzene versus the contributions from water. So here I'm showing the absorption spectra contributions from Benzene only. And here we're able to observe changes in the low energy region in water versus vacuum. So these are some small scale systems, but our implementation is highly parallel and it's been shown to be very efficient. So we decided to study solvated DNA with about 12,000 electrons. And for a system like this, the only way we can get really any insight is to be able to use one year functions where here I've shown the essentially the DNA one a functions are in blue and magenta and the water functions are in science. And so here, the blue path is going straight through a projectile moving straight through the DNA, and the red path is the projectile moving along the side path of DNA. This way we can understand the effect of proton irradiation on solvated DNA. And so here I just have a little movie showing the changes in spread and displacement of the one a centers as a proton moves through the center. So size changes course and color changes correspond to changes in spread and any movement corresponds to displacement. And so why use one year functions here at all. Well, using one year functions, we can essentially break down the contributions from water and DNA and doing this and looking at one of the key properties here electronic stopping power or the change in energy. With respect to change in position of the projectile. We can separate out contributions to the stopping power from the DNA strand, or the red path, first the DNA base, the blue path and compare that to the stopping power for proton and liquid water, which is what's commonly used for cancer research. So our results have shown that when the projectiles moving along the side path. There's a significantly larger energy transfer to the DNA, as opposed to when it's moving to the center. And so, even beyond that we explored exactly what is taking place at the molecular level using one year functions so looking at the displacement. We see that for the side path there's a slightly larger change in displacement for one representative velocity. And we're shaded regions correspond to sugar phosphate side chain one year function centers. And as expected, since the projectile as it moves along the side path or the strand path is much closer to those we see a much larger contribution to the displacement from those side chain one year centers. And we did the same similar breakdown for spread change to get a measure of electron the localization and the same story. So, that was a lot of our original work, but everything I've shown so far is based on using a GGA or an LDA exchange correlation potential. And in real time PDDFT, there is a very large dependence on the results on which exchange correlation potential we use. So, just to give an example, crystal and silicon with 512 electrons 128 Adam. If you use LDA or GGA get the absorption spectra. You get one story. If we go up one wrong on the Jacob's ladder for DFT, and we use a meta GGA and incorporate the kinetic energy density. We get a different picture of the absorption spectra. And if we go beyond that using hybrid functionals. We get a different picture again. However, using hybrid functionals in real time PDDFT is very costly due to this exchange integral electron at the top here where we need to calculate the this exchange for every electron pair within the system. And so even for a 512 128 Adam system of silicon. This is very costly. However, the simulation cell is not still not converged with respect to cell size. So, to use hybrid at the gamble point, and to get a converged simulation cell, just using LDA, we have to go all the way to 8,000 electrons before we see an agreement with respect to K point for the silicon system. So, one thing we've done is use one year functions to essentially improve this hybrid efficiency. At each step in the propagation, whenever you're calling a hybrid functional. We define a distance function, which says if our. Pairs or essentially our money functions centers are certain distance apart. Say 20 a you. If they're farther apart than 20 a you don't calculate the exchange ignore that pair. If there was in 20 a you calculate the exchange for that pair. And for the crystalline silicon cell. We've been able to go all the way down to 15 a you or only. 15% of pairs and still get an identical absorption spectra for that. So, and this is based on work done that's been done in FPMD. As another way to improve hybrid. And so, beyond being able to do that for the 512 items. So, we looked at this for a 2000 electron cell. And in that case, we've seen even more and even larger improvement in the efficiency. As at 25 a year, we only using 7% of pairs. And we're still essentially able to capture the same behavior where the relative iteration time is now on the order PV is much closer to PBE than the typical PBE zero time. So, significant cost savings. And at the moment, we're looking to do the same absorption spectra for the 8,000 electron cell and then move beyond just fully crystalline silicon and use this to study properties like defects where. The gamma point and the large simulation cell is key to actually understanding what's going on. And so, just in summary, we use real time PDFT and the 1 a function to get molecular level details and study absorption spectra of different system. And then we found that utilizing the 1 a functions centers and using them as a pair distance function, we can significantly reduce the cost of hybrid functional. However, our implementation is limited at the moment as it's gamma point only, which is part of the reason why we have the need for this cost savings and these large, very large simulation cells. So in the future, we'd like to move beyond this gamma point only and extend it to multiple K point. Thank you very much for a nice talk. Any questions from the audience. Thank you for. Thank you. Can you repeat that. Do you update your functions when you do the time pollution or do you just update the parameters. We update the 1 a function every step we do the time evolution. Any other questions, but you can hear us when I speak on this. Can you hear me now better. Thanks for the talk in the previous slide of your topic you show the DNA structure in water my question is, is one year function able to simulate the hybrid man water. So, for our solvated DNA, we only looked at it this with PD. Where am I miss hearing your question. So the question is whether you can simulate. No, not, no, we, we cannot see the hydrogen bonding with the one year functions we've, we only have used them to essentially separate out the contributions from water versus the DNA. Okay, any other questions. Yes, so I think it's maybe better to come here and use this microphone, just speaking to this thing. Hi. Yes, sorry. Do you hear me. Yeah. Okay, so concerning the time evolution of the venue functions, I understand that you've been your rise and then you evolve your states. So, in doing that the localization gauge of the many functions is it evolving under time and if you want the related question is, is the shape of the many functions or some more defined because of the different block components move at a different with a different energy in a different phase. So do you serve for instance, a broadening of the many functions over time or do you re optimize. So could you comment on that. So do you optimize the gate at every step and okay here to make sure. Yeah, we take care to make sure the electric field applied is in essentially the linear response regime so it needs to be small enough essentially that you don't change the character of the one year functions during application. Thanks, thanks very nice thanks. Any other questions. Okay, if not let's thank Christopher again. Thank you so much for having me. Thank you.