 Can you see my slide? Yes, I can. Okay, great. So thank you Ravi for a nice introduction and of course many thanks to the organizers for giving me opportunity to present a part of my work on this meeting and I wish a good day to all of you. So I will briefly present you actually quite recent work from our group on Rudjer Boszkowicz Institute. It's actually a part of my PhD research conducted under supervision of Nadja Doshlic and with our collaborators, Professor Piero De Cleva, Professor Wolfgang Donke and Maxim Gelin. Okay, so the idea of a work was, so to say, to formulate a theoretical framework for simulation and assignment of time-resolved photoelectron spectra or shortly called Terpes or PRPES, but I will pronounce it in a Slavic form, so to say, so Terpes, it's a little bit shorter. And of course later we want to apply this framework to simulate some realistic Terpes spectra of some realistic photochemical processes. Here I will present you only one molecule, which we studied in this way. It's a pyrozin molecule, which you can see here. I believe many of you are quite familiar with photochemistry of PyPystar excited pyrozin, although it's not strictly speaking biological molecule, but it's a prototypical molecule for many other photoinduced processes in biological system. So its photochemistry is well-studied in the literature, and it has been monitored experimentally by Terpes method, by Professor Suzuki and his co-workers, which I will show you later. And here you can see the Terpes spectrum of PyPystar excited pyrozin, and later I will show you our simulation of, and designation of, sorry, of this Terpes spectrum. As you can see, usually in the Terpes you don't get fully vibrationally resolved spectrum due to the relatively poor resolution, so you basically basically just see the shape of each electronic band. But however, it's usually sufficient to understand the photochemistry of a molecule, which you are studying it. So we actually don't want to formulate a fully quantum mechanical approach for simulating these spectra, but rather a mixed quantum classical approach, which will be much easier to apply and to evaluate the expressions, which will arise. But it will still maintain the most important features of our time-resolved spectrum. Okay, before that, just briefly about the Terpes method in general. So it is usually performed to study photoinduced processes as a pump probe technique. So you initiate your process by excitation by the first pulse, which is called pump, and then you let your process evolve for some time, and then with some delay time with respect to the pump, you ionize your system with a second laser pulse called probe. And what you measure here is the relative amount of ionized electrons having different kinetic energies. Of course, kinetic energies are directly related to ionization energies of your molecule, which on the other hand depend of of an initially populated state of your molecule in that time during your reaction. And so in this way, you can obtain the information about the mechanism of your photochemical process. Okay, so how to simulate these kinds of spectra? You can derive the expression for pump probe signal in quantum mechanical manner from many different approaches. But as I said here, we want to go to the classical limit of this expression. So we want to formulate mixed quantum classical approach. And the most convenient quantum approach for taking classical limit is so-called doorway window formalism, which was introduced quite some years ago. But relatively recently, this year, it was for the first time being applied in a classical limit, taking account of all important sources of a signal in the pump probe experiment by Gelin and Donke and others. And it was actually applied on the transient absorption pump probe spectroscopy. So here, we just extend this formalism for the terpes as a pump probe technique. It's not strictly speaking the same formalism because in terpes, you don't measure the transmitted probe radiation as you do in transient absorption spectroscopy, but rather pot electrons. But I will not go into details. All in all, the final expression looks like this. Actually, this is only one term corresponding to excited state absorption contribution to the pump probe signal. Here we lack ground state bleach signal, which can be accounted also, but here for the sake of simplicity, we neglected it. Okay, so the excited state absorption is calculated as a product of two functions. So it's a doorway and window function. And we have to average this product along all nuclear phase space and all excited states, which can be reached by our pump pulse. Okay, so this expression is in practice, of course, evaluated by important sampling technique. So the first step to evaluate the terpesi density is to perform doorway sampling. So this is doorway function. It describes the interaction with the pump pulse. Actually, it gives you the probability that pump pulse will excite some certain classical points from nuclear phase space QP to some excited state I. So we have ground state regular distribution, oscillator strength of that excited state. And here we have a pump spectrum, pump intensity evaluated at the excitation energy. So in this approach, we actually account for specific shapes of our pump, and as you will see later, probe pulses in the in the pump probe experiment. Okay, then after you sampled your classical points, you need to propagate them in the excited state manifolds. You can do it in many different ways. The most obvious way is surface hopping dynamics in which you propagate your classical points on adiabatic surfaces, but you allow your molecule to change the currently populated state in a time in each propagation time step. After you have your trajectory is done, you have to evaluate the window functions along each of trajectories. The window function actually describes the probability that the probe will detect your classical trajectory. So it's actually for the case of terpesses of pump probe spectroscopy, it's given by partial photo ionization cross section weighted again by the probe intensity on transition energy here. It's a little bit tricky how to calculate partial photo ionization cross sections. They can be extracted from the transition dipole moments between so called Dyson orbitals for certain ionization channel and so called continuum orbitals. Dyson orbitals are pretty much, I believe familiar quantities in photo electron spectroscopy, but the continuum orbitals are much, much higher, much complicated to calculate. They can be calculated again in many, many ways here we applied maybe one of the most accurate ways for treating the photo ionization continuum B-spline static exchange DFT approach. Okay, so basically this is this is the theoretical putting on which we are working. So the final expression is relatively simple I would say. So it resembles to the nuclear ensemble approach which is often used to simulate one-dimensional ordinary so to say absorption spectra, but it has to be applied on each time step along surface hopping trajectories while you account for specific pump and probe shapes in the frequency in the energy domain. And here we come to the main drawback of this approach. Due to the sum approximations we applied we actually lost the information about temporal shapes of our pump and probe pulses. But however it appears that this information can be reconstructed as shown by Bonacic Kutecki and Mitrich simply by convoluting your so to say pure doorway window signal with pump probe cross correlation function which looks like this if you assume if you assume the Gaussian shape of your pulses. Okay, so now we have everything and we just need to evaluate all of these expressions and for Pyrozin case it looks like this. So this is experimental terpes of Pyrozin as I said recorded by Professor Suzuki and these are our two simulations so we have pure doorway window simulation in which as you can see we don't get any signal for negative delay time because we don't have temporal shapes of our pump and probe pulses included and this is temporal convolution doorway window simulation as you can see now we have some non-zero intensity for negative delay time times the same as in the in the experiment. Okay so all in all as you can see the agreement is I would say pretty good so we have all bands properly simulated in the terms of energy position this we probably owe to the accurate treatment of bound neutral and cationic states here we employed Caspiti True treatment. We also have accurate description of dynamics of each band for example this decaying band we see that its dynamics is relatively accurately described so it's again due to the accurate treatment of non-adiabatic dynamics which surface hopping appears to be in this in this context. The intensities relative intensities are also relatively accurately described apart from this band here we don't get this bright signal here but as you can see this is extremely low photoelectron kinetic energy value so these photoelectrons are quite slow and they are continuum orbitals they are not easily calculated especially not by static exchange DFT approach which actually breaks for for such slow photoelectrons. I will not go into details here regarding the things which we learned about the pyrozin photochemistry from these simulations I would rather refer you to our publication regarding this work but what I want to share with you next is automatic way how to assign this spectrum so when you have a spectrum you want to assign it in the terms of electronic state to understand the photochemical process which you are which you are investigating. In the case of time result petroscopy it's it's inconvenient to do it by hand by examining your molecular orbitals and CI coefficients because you have quite a lot of trajectories and quite a lot of time steps so you have quite a lot of geometries in which you should visualize your orbitals and and examine CI coefficients so we tried to formulate so to say automatic assignment procedure which is based on diabetization so we'll calculate a component of TRPES arising from a single ionization channel in diabetic basis not adiabatic because we are usually interested in the assignment in the terms of diabetic states the states which maintain their their electronic character as the geometry of molecule changes and we obtain window function for this type of diabetic signal so to say simply by waiting the overall window function by the matrix element of adiabatic to diabetic transition matrices for neutral and cationic bound states. In practice it looks like this so this is the doorway window simulation of TRPES of a pyrazine which breaks down to the components arising from ionization of three different states of neutral pyrazine so we have B3U, AU and B2U states you we can also decompose it according to ket ionic to the character of final ket ionic state and we can decompose it according to both so we we get sort of sort of matrix of spectral components and now we immediately know that I don't know for example this this band here on approximately four electron volts of kinetic energy that in the early times it originates from the ionization of B2U by pi star state but in the later times it originates from ionization of these two and pi star states B3U and AU okay so I believe this is more or less all I wanted I wanted to share with you so I will just briefly summarize so here we formulated a simple mixed quantum classical approach to simulate TRPES spectra and it yielded quite accurate simulation of valence ionization TRPES for the pyrazine case however it has to be combined with accurate treatment of bound electronic states as I said here we employed multi-reference treatment a single reference would also here do the job but however it should it should be highly correlated single reference method like coupled blaster with with triplets and and and so on and you also need an accurate treatment of projections which you can obtain by static exchange DFT approach and also we formulate a simple automatic assignment procedure for these kinds of spectra which is based on diabetization all you have to do is perform diabetization along your surface hopping trajectories and you you get your time results electronic in this case photoelectron spectrum immediately assigned in the terms of of electronic diabetic states this can actually be applied on any other case of electronic time result spectroscopy like transient absorption or any any other okay for the end I would like to thank to the funding so creation science foundation and Isabella cluster and of course to to all of you for your kind attention thank you very much so thank you Thomas love so we have time for a few questions so far I do not see raised hands overall so I had a couple of questions actually with regards to your doorway window formalism so so how do you you know so how do you describe your uh pulse shifts here the epsilon squares that you have are the delta functions are the Gaussins okay here here we employed we assume the Gaussian shape of of the pulses as noted in the experimental work of Suzuki and in this in this work here actually the pulses the pump and probe pulses which were used in this work were generated and previously and there are two separate publications with the the details of temporal and frequency shapes of these passes so we we just took their parameters like forward half maxima which which you can which you can see here of course you can do Fourier transform and then get the forward half maxima in frequency domain yeah so I was it was interesting because you actually have zero time delays and negative time delays as well right so that indicates like an overlap of the pump and the probe exactly but but only but only if you only if you uh calculate this time convolution dory window so here we have we don't get any signal here so this is this is obtained by assumption that the pump and probe pulses are non-overlapping right so that that accounts for the probe arriving even before the pump is that right actually yes but uh this this simulation does but uh not in so to say in very accurate way uh not in the sense of so not not not from the first principles but rather like this so the convolution from yeah from this paper from this paper here this is also derived by quite several approximations but it's not it's not only that the probe comes before pump but rather that delay time is is is is not the time difference between the moment in which you detect by the probe your system and you're you're excited it's not that difference it's it's rather the time difference between maximum of pump and probe but the probe the probe can excite your molecule slightly before t equals zero and the probe uh for i don't know delay time 25 milliseconds it can ionize your molecule slightly after after it's maximum but you in the experiment you will prescribe all of the data to delay time equals 25 so this is this is mainly accounted for by this by the convolution yeah exactly okay that makes sense i had a very quick question about that plot that you just showed um you know so i noticed that the resolution in the regular doorway window before the time convolution right so the resolution is poorer i mean that's simply because of intrinsic resolution in the calculation or uh you mean the the temporal resolution or uh yeah the temporal resolution i mean in the sense in the sense not only is the black region missing right before the zero time delay but also the shapes appear to be slightly different little bit fuzzy yeah uh this temporal resolution it it glances a little bit obviously yes so so you're right you're you're right uh this is pretty more pretty much fuzzier than than than than this um however the the time step is the same maybe it's just an optical illusion here because this is this is much more glancer uh but as you can see in the experiment it's it's more or less glance right it's it's flat so this temporal convolution does the job here not only by generating a signal for negative delay time but also for for glancing your your bends as you will see in the experiment if you want to see that i hope thank you tomas yeah question no you did actually i it's it's fascinating but um anyways i think it's time now to thank tomas law and we move to the next talk um thank you so tomas law if you can unshare