 And we move to the breakout rooms. So the last talk we have, and not least, it's Claudia. So please share your screen and introduce yourself. Thank you. Thank you. So you have 20 minutes for the presentation. Is it OK now you see? Yeah. OK, so good afternoon, everybody. I am Crude Lecombe, worker at Lorraine University in France. And as chairman of the IUCR UNESCO Africa Initiative for Developing Crystallography and All-Connected Science. What I will discuss with you today is electron density and how we can get electron density and spin density from accurate x-ray and polarized neutron diffraction experiments. First, why we want to study electron density? In fact, electron density is very important. If you remember Hoenn-Betkoen theorem, the total energy of a system is a functional of the density. Therefore, density governs all interaction in a system and emerges as a bridge between structure and properties. Furthermore, molecular structure is determined by the associated electron density distribution because there is a system mapping between the structure and the electron density, which we can observe by x-ray diffraction, which can be calculated by DFT, the theoretical calculation. The Helman-Pheneman theorem also says that for a given arrangement of nuclei, the electron density uniquely determines the force acting on the nuclei, which are, in fact, classical electrostatic forces. Why do we want to do experimental electron density? It is because they permit to study difficult systems, which are sometimes not available with DFT calculation. This also would validate theoretical calculation and their related properties. Our ultimate goal is to make, to construct experimentally, a common model of the one electron-reduced electron density matrix using x-rays, some sort of magnetic scattering, neutron polarized and non-polarized diffraction and Compton scattering. For that, if you want to see what here is one electron-reduced density matrix, and we will use neutron diffraction to see the nuclei, x-ray diffraction to see the electron density, x-ray magnetic diffraction also to have the spin density and polarized neutron to have the spin density. Compton scattering and magnetic Compton scattering will give us the momentum of the electrons and the interatomic terms. Very important for looking to the very delocalized electrons. So we will have many experiments, x-ray diffraction, polarized neutron diffraction, Compton scattering, for example. And we will, from x-ray diffraction, we get structure factor, magnetic structure factor for polarizing, excuse me, and Compton profiles for Compton scattering. We will mix all these experiments together to get our one electron density matrix by this square. And we will minimize this function, which is all these chi-square that you see here. We can also add some other experiments like NMR, NQR, or x-ray magnetic diffraction. So first x-ray diffraction, everybody knows the intensity that we are measuring is, in fact, this product of the square of the interference function times the square of the scattering of the structure factor. The structure factor is a Fourier transform of the electron density. But what else we are measuring at a certain temperature, what we analyze is a dynamic electron density, which is, in fact, the static electron density, which we would calculate with DFT calculation, convoluted by the atomic probability density function due to the temperature. Due to the convolution theorem, in fact, this structure factor is the static structure factor times the Debye-Roller factor. And it is a static structure factor, which is very important for me, in which you see Fj which is a scattering or form factor, which is a Fourier transform of the electron density of atom G. That is, in fact, the curve that you see of the scattering factor as a function of the resolution. You see that mostly the core electrons are seen by x-ray. And the valence electron are seen only at low resolution. And that shows the electrons that I want to model. When people do what we call a crystal structure, they use a very simple model, which is called the IAM model, independent atom model. The electron density in the unit cell is the sum of all atoms of the spherical, non-perturbed, free electron density. It means that we can go very structurally every time and very short time. It is simple, but accurate enough for crystal structure. You can get good coordinates, but only for non-hydrogen atom. And as you see, you have almost 1 million already published crystal structure. The problem is that with this simple model, you cannot see the interatomic bonding. You can't difficult to see the hydrogen atom. And the anisotropic displacement parameters due to temperature are not accurate. And we have now better, very good detectors, which enable us to go much further than that. So the historical model of electron density that I will show here. In fact, for each atom, we see that each atom is electron density of the core electrons of the independent or the independent atom density plus a term, which is a deformation density. This deformation density is expressed as a function of radial function times an angular function, which are centered on the center of all atoms. And that's this term that we want to measure with our eyes. The most important model is so-called the Hansen and Coppens model, which we have coded in this software, Mopro. And for each atom, the electron density is shared between the core electron density, the valence electron density supposed to be spherical, but populated with PV electrons. You see a value here, which is the extension, contraction parameter of the electron density plus this non-spherical term times of a radial function, very often a slider type function, multiplied by spherical homonyx. For example, this here, as you see, if you want to modelize this sp2 carbon residual density after spherical atom refinement, you see that it is very easy to model it with octapolar real spherical homonyx 3 plus 3. So a multiple analysis gives you an analytical form of the experimental electron density. We can then calculate properties, the orbital population charge electrostatic potential or electrostatic interaction energy. It's very important for doing, for example, bio-population using molecular experimental force field for molecular dynamics. Here is, for example, one example of a static map, electron density map that we got on sodium nitrocosite, where you see very well here the depletion of electron in the dx squared, x squared minus y squared direction, and the buildup of electron in dx y direction. That is the electrostatic potential of a biological monique. First example, if you look to this crystal, which is mostly made by the association of two cobalt atoms linked by organic ligands here. Calculation in this crystal have shown that the anisotropy of the magnetic properties is explained by the 40 degree tilt of the cobalt 1 and cobalt 2 orbitals. The question was, can we measure it experimentally? What is the angle between cobalt 1 and cobalt 2 orbitals? Here is first, we met x-ray diffraction experiment at very low temperature, 80 k, with a high resolution. And that is what we got when you make a refinement after an independent atom model. So you see here the anisotropy of the D electron here. Very well known, the depletion around the ligand and buildup of electron density in between. After the multipolar refinement, the map is much clearer. It means that we have taken into account all the D electron density. And the result is static electron density map shows really very well the D electron orbitals, the electron density. And also you see the interaction of oxygen at this D x-ray measures y squared. This calculation enables us to look to the projection of the D electron density along the two-fold axis. And as you see, the angle between the orbitals, cobalt 1 and cobalt 2, is 39 degrees, which can be compared to 40 degrees. So you see, this model works very well for explaining the electron density. If you want now to look to magnetic to spin density, then you have to do with neutron diffraction. In neutron diffraction, you have two interactions, the nuclear scattering, which will give you the position of the nuclei. Here is the nuclear structure factor and the magnetic scattering, which will give you the spin density. This magnetic scattering can be written like that, where Bm is a magnetic form factor, which is the Fourier transform of the magnetic density of the electron j here. Multiply here by, if you lose this quantity, in this quantity, you see that you have M perpendicular, which is, in fact, the projection of the magnetic moment onto the scattering plane. So you can get the magnetic moment from this kind of experiments, which is very interesting is that bragg intensity of magnetic and nuclear scattering are of the same order of magnitude. So one will not hide the other. For unpolarized neutrons, we have an incoherent superposition of magnetic and nuclear, which means that we have this formula for the intensity. And for polarized neutrons, you have a coherent superposition of magnetic and nuclear contribution. This important formula for us, because this will give you the possibility of measuring the spin density. Here is what is an experiment. You come here, your neutrons are arriving here. They are polarized. Flip either up or down. And you count in the detectors, i plus or minus. And you measure what we call the flipping ratio, which is this, fn plus fm divided by fn minus fm squared. This is our data to the spin density. Here is the experiment. Here is a neutron half coming here. The polarizing monochromator, the cryo-fipper is here. The sample is here. You see the detector here. Here is one of the instrument at the LLB in France. The spin density that we want to calculate, in fact, is the Fourier transform of the magnetic structure factor. And mu is the magnetic model. S, it can be modelled the same way like the multiple model by modelling with multiples, as you see here. But contrary to X-ray, we have a very, very few limited multipolar development, very few fm's, and very limited multipolar development. So how to get a spin-reserve multipolar model? What we want to do is combine X-ray, neutron, polarizing electron in one single calculation to give our spin-reserve electron length. The electron density, as you know, is the sum over all density of each pseudo-atom. The spin density is the sum of the spin-up minus spin-down atomic electron. So our model is the following one. With split, the charge density is two components, up and down, the charge density is given by this formula. Or plus up valence density, plus down valence density, plus up as pericol electron density, plus down as pericol density. And for the spin density, it is a different between up and down electron density. And you have this formula. And all these formulas have been coded in a program, which we call MOLANX, which enables you to get the spin and charge density, which we call the spin-resolve electron density, under some constraints, the charge, the electron neutrality. And in other words, all the sum of spin is equal to the maximum. This is very interesting because it allows you to estimate some properties, the orbital population, net charge, electrostatic potential, some magnetization, electrostatic interaction energy. Other properties like energy and infrared optics can be obtained only if you use wave function. Therefore, there is a need to develop a new method to obtain experimental wave function, that is what we have done, which we call the new spin-resolve orbital model, and which has been applied for the systems to a yttrium-titanium pair of sky, which is republished at the end of the year. So it is a long story, in fact, because the charge density can be divided for its core density, balance density, plus some interaction terms between two terms, between A and B, electrons. You have four minutes. Yes, I think it will be fine. Thank you very much. So the electron density is for the core electron is given by this formula, where R is the radial function, which is the population of these radial orbitals for the core electrons. For the valence density, we developed a valence density as this formula here, where you see that our basis function are the product of a radial function times a spherical harmonic function. Therefore, the valence density will be the sum over all valence atomic orbitals, phi A, which is given by this formula, where N i here are the partial population. And what we want to do is to know from our history and neutron experiment, what is the value of N, the number, the partial population, and how are expanded the radial function. And we also can try to calculate an interaction term between two atoms, which is we hope here, which would be calculated that way. And N ij would be the population for this interaction term. So, if you look at this entity, in fact, it is the core, plus this part, which is the valence orbitals scan, that are orbitals, plus the interaction terms that you have here. What are our basic functions? And now sure, we have to normalize everything, which are of the wave function. For the radial slater type function, we have either slater or Gaussian type function. The Gaussian type function are mostly used for the interaction terms. And then the structure factor are calculated like F char or F core, plus F valence, plus down and up, and up, plus F interaction, down and up, whereas the spin is different between the two terms. And you can calculate from that the structure factor in all these terms and refine the structure factor against our data. We have to get the thermal motion and the population of the orbitals, as well as the expansion contraction of the orbitals. We have to have some constraints, the electron neutrality, electric magnetic moment also, and auto normalize atomic orbitals in order we can use them for some calculation. We apply that to the titanium perovskite, etriome titanium perovskite, which is here. Titanium is in the center of the centrosymmetric distorted oxygen, octane, and roll. And in the literature, it had been studied a long time ago, and they showed by calculation and X-ray magnetic scattering that there were orbital ordering for DXY and DZ, XZ orbitals. So that's the space group, the NMR of this one problem. The experiments have been made at synchrotron beam line at spring head of Japan at 20K to 1.67 angstrom minus one resolution in sinus data over on that. And the neutron experiment, polarize neutron as we made at octane, at electric. Yeah, you see when we collected a big, big number of X-ray diffraction data compared to the few number of splitting ratio of neutron diffraction. We made multiple refinement, as I showed before, an orbital model refinement, and you see that they give almost the same goodness of feed, both for X-ray diffraction and polarize neutron diffraction. We have very marginal differences when our interaction terms is identical. If you look to the statistic of the refinement, you see that all models, model one, orbital one, and orbital two with interaction terms are statistically equivalent for X-ray or for neutron. And the chi-square also is the same for all this experiment. Their whole model are statistically unexpected. If you look to now the electron density, calculate it either by the orbital model or the multiple model to see that that looks like very much the same. That's the most important difference that if you look to the orbital model, you see the depletion of the X-ray minus square orbitals and the population of X-ray here and the same for the other plane. You see also here the spin density of the related experiment. And the most important thing as a result is this one. Here are now the orbitals. What I show you here, you cannot see the title, it's the orbital on a titanium atom. We have defined six orbitals, phi one, phi two, phi three, phi four, and phi one is mostly a four S orbital. And we have refined all population of these orbitals as you see phi two is a linear combination of these five orbitals here. And you see that mostly this phi two is populated by this 0.62 electrons for XZ and 0.78 by for YZ. Therefore, phi one and phi two are the main of the titanium orbitals. One is a pure S for S and the second one shows the orbital order. The linear combination of these orbitals is populated by spin up electron as you see here, nothing for spin down. And it is also an excellent agreement with our previous work, which we publish in physical volume to yourself and for some other authors who did work 10 years ago. So the time is over, but if you have one minute to wrap up. Yes, I just have two slides. As you see that now we have trying to see if you have some interaction terms between titanium and oxygen, for example, it would confirm or not that we have some covalency. And as you see here, we have no interaction terms. Therefore, this compound, this peroxygen almost to be ionic. In conclusion, this orbital model has been coded in a new program which we call monance.orbitor. It works well and it is available for everybody. It was applied to the titanium peroxygen. Interaction terms were negligible and this study confirms the orbital order. Next, we want to estimate the interaction term by studying ionic covalency like pyride. We want to test this method on small organic materials. And we want to improve the calculation of the interaction terms. And finally, if we have the wave function, we will try now to calculate derived wave function properties, which is in fact the aim of our work. And I would thank you for your time, sorry for being a little late. Thank you very much. Thank you for the interesting talk and now we can open for the questions and answer. Ali, you can go ahead. Yes, so thank you very much, Cloud, for your interesting talk. I have a partly scientific and maybe slightly philosophical question which is, so you talked about, can you hear me? Just a little. There was a problem at the beginning now. Okay. So you mentioned charge transfer in your talk. Yes. Do you have any way of measure this experiment? The charge transfer? The measure charge transfer experimentally. Yes, yes, yes. In fact... Yeah, experimentally. Experimentally. We have done that, for example, in very, very well-known organic materials such as TTFCA materials, for example, which undergo face transition at ATCA to a conducting state. And for all these materials, we have found that we have a 0.7, if I remember well, 0.7 electron transfer. We can do that, yes. So what if the electron transfer was much less than 0.7? It was 0.3 or 0.2. I have no example for that, but we could do that because, in fact, what we use is we use a theory which is atoms, we look to the topology of the electron density or the topology of the spin density which enables us to partition the atoms in a way we can calculate the charge transfer. Okay, thanks. Is there is any interesting or someone have a question? We have two minutes for a quick question. Okay, please. I have one question. Okay, please. Yeah, so also, please, I am interested on the population, transition of state for the population. So I wish to know if the experiment, this type of experiment can enable us to predict those transitions. Could you repeat the question, please? I am asking. My main focus is about population transfer. Yes. Yeah, so I wish to know if this experiment can enable us to predict such a transition. In fact, if you are able to get good crystal enough, we can predict after the experiment, we may modelize this charge transfer, yes. Okay, so now, if we have lattice vibration maybe in the system, how do you cope that within the experiment? We use, we model the lattice vibration is by the double or double wall of factor. And for example, in this Iterium titanate, we have also two unharmonic terms, but that is something we can do also. And we can model also the thermal vibration. And I think that using our new model of wave function now, we can find a way to calculate the high air vibration frequencies. But that is the future. Oh, okay, thank you. Okay, great. So thank you again for the interesting talk. And I would like to thank all the speaker of this session. And we can give about five to 10 minutes that each speaker can get maybe questions from one of the participants. I mean, if someone has any questions for any of the three speakers of the session, you can raise your hand or write down. Okay, so just speak a little bit loud so we can hear you. Yeah, please. Okay, please. I have a question. I have a question. Yes, please. Please. Okay, please. My question goes this way to the last speaker, please. I want some vibration in the density can affect the outcome of the neutron interactions. And can this vary with location? Please. What you want to know. Thank you. It's for me for closing the question. What you want to know is the role of the neutron. Yes, yes, all of the neutrons. Yeah, we use the neutrons either for having the structure, mostly the hydrogen atom, for example. But more importantly is to get the magnetic structure because the neutrons spin. So we make the spin, we diffract the new, the neutron are diffracted by the magnetic atoms. And then from that we can get the spin density. And to measure the spin density, as I showed before, you have to make a polarized neutron diffraction experiment. If you want to know more, do not hesitate to send me a mail and I will answer you today or tomorrow. Okay. Okay, thank you. So do we have others to question? We have a possibility for two questions. Amadou has a question, Amna. Okay. I would like to thank Claude for this very, very important talk and nice talk. And on behalf of the African Physical Society, so we would like to keep in touch with you for future collaborative action. Because I know that you are also in charge of UNESCO for crystallography in Africa. And I think that there is a possibility also to work with African Physical Society and to see what we can do together. So thank you very much. I thank you very much for this proposition. And you know, at the beginning it was a project between the International Union of Crystallography and UNESCO. But I'm sure that we can discuss that together before I go to UNESCO and discuss that. So no problem. I think it would be very important. That's why I wanted to have a talk also today. Yes, thank you. I am very interested by the physics. Yeah, it's a good opportunity for collaboration and establishing a new maybe way for being in touch and get a good research between Africa scientists and outside. I mean, a broad internet. Absolutely. Yes, thank you. OK, so do we have one question before we move on? If not, then I would like to thank the speaker and I would like to thank you for being around. And we can now move to discuss about what is the breakout room it is. So Ali, maybe you can say something or I just. Yeah.