Magari avvisaci Massimo quando possiamo andare. Secondo ancora sta perdendo YouTube ora? Sì, sì, vai, vai. Quando volete siamo pronti. So, what am I supposed to do now? Start or wait? Ok, can we start Massimo? Yes, ok. Ok, so, good morning everyone. So, today we have Paulo Giannozzi who will speak about charge densities and potentials, systems in 0, 1, 2, 3 dimensions, metals insulators, non magnetic versus magnetic systems. So, before starting the living room to Paulo, just let me say a few things regarding the organization of this meeting. So, from yesterday experience, we saw, we learned that the Zoom chat is quite an effective for posting questions because especially if you post questions during the meeting, during the talk, it is very, very difficult for us to keep track of all the questions. So, for today we would like to try in this way. Please, I will ask you to not write anything in the chat while Paulo is speaking. So, let's keep the chat clean. Then, at the end of Paulo's talk, I will ask, if someone of you want to do a few questions on speaking, I can enable the microphone for one or two questions on voice. So, if you have anything to ask, just keep it in mind. And then, at the end of the talk, raise your hand. You have the option in the bottom bar of Zoom. Just raise hand and I will let one or two people to do the question. And then, in general, at the end of the talk, you can write all questions in the Zoom chat. So, please, let's wait. Don't write anything from Zoom until Paulo finishes his talk. And then, when Paulo finishes, write the questions in the chat so that it is easier for us to manage the questions and keep track of all the questions. And so, yes, this is all. So, good morning everybody. And I leave room to Paulo. Please, Paulo. Okay, good morning to everybody. And there is somebody who has entered the waiting room and is waiting to be admitted. Yes, I'm meeting him, but there are some issues, but you can continue. Okay, so, we'll ignore the message. So, as Ivan, while Ivan was reading the title of my talk, was realizing that I have just collected a bunch of mostly technical issues. So, my talk, today's talk, doesn't have a real well-defined focus. I hope you won't be more confused at the end than at the beginning. Let me show if I manage to my screen. So, the first topic I would like to talk about a little bit is free transform. You may have heard yesterday, you may have seen yesterday in the hands-on that there is this mysterious fast-form grid that typically is automatically computed by the code, but maybe it's better if you have an idea of what it is and what it is used for. So, the basic point is that when you have a periodic function and we basically always have periodic functions in quantum espresso, in a way or another, the Fourier components of the periodic function here, it's a simple one-dimensional example. The Fourier components are a discrete set, discrete but infinite set of values. Now, we truncate this discrete set and we make it finite set. So, how can we deal with these functions in a truncato, with a truncato number of, with finite number of Fourier components? Now, what happens is that you can discretize the problem both in real space and in reciprocal space and you may associate to the functions in real space a grid of the function and a grid of finite grid of points and the same in reciprocal space and you have then a finite set of points both in real space and in reciprocal space and a mathematical operation called discrete Fourier transform which is actually the real Fourier transform specialized to the case of discrete functions. It can be written as I have written here in the slides below. It's a sum of exponential with those numbers here, those factors, the integer index here in both case runs from zero to some capital N. Capital N must be large enough to accommodate all the available Fourier transform Fourier components in reciprocal space. Notice that by construction both functions both in real space and reciprocal space are periodic. So you have a sort of fictitious periodicity in reciprocal space as well. You may, you actually exploit this fictitious periodicity to refold negative values of factors of Fourier components. So here you see there are in the definition of the Fourier components there are no negative values, but the negative values are to speak at the end of the other side of the box. So you have a box in real space, it's your unit cell that is subdivided into points that span the entire, on a uniform grid that span your entire unit cell and the same in G space and in reciprocal space and the components, the negative components are actually refolded on the side of large values of the index. That's because this function is actually periodic, exactly function in Q is periodic exactly as the function in R.   Basis vectors are defined reciprocal lattice, so-called reciprocal lattice. And the same for in real space you have a uniform grid that spans the unit cell defined as shown here below. So these are the grid points on which we know our wave function, our charge density on which we define our functions. So this discrete Fourier transform so that the relation between the discrete Fourier transform the variables in the discrete Fourier transform and the variables in the original Fourier transform is written here. So from the function in real space continuous function in real space to three dimensional grid and from the discrete Fourier component into a discrete grid of Fourier components. So those numbers N1, N2, N3, N1, N2, N3 those numbers must be large enough to accommodate all the available Fourier components. So those Fourier components you have a sphere of G vectors, you have Fourier components in a sphere of G vectors and you must be able to accommodate all those components. How many components do we have? Well, for the expansion of quantum orbitals we have plane waves up to the famous or infamous kinetic energy cut-off that we decide on the basis of our system the system we have. We choose it on the basis of the pseudo-potential. It's a pseudo-potential that typically the harder pseudo-potential determines which cut-off you should use for the plane wave expansion, for the plane wave set. But remember that we have also we are using this technology, this machinery of the discrete Fourier transform in order to compute charge densities and to compute product of the potential time the charge, the quantum orbital. This is an important piece in the calculation, an important part of the calculation. So if you look at how the charge density is defined in the simple gas space the straight forward definition of coefficient of the expansion of quantum orbital so this would be the sum of size squared written in a reciprocal space has this form, which is not very practical but we use it, it's not actually used but what you do, you look at you notice that here in this expansion there are g vectors up to two times the maximum g vectors that is present here in the expansion of quantum orbitals and the same also for the product of the potential times quantum orbital you need the potential up to the maximum g vector g vector of maximum length is twice the maximum length of the g vector you have in the plane wave basis set that you use to expand the quantum orbital. So finally, this means that if you want to use the same Fourier transform, discrete Fourier transform grid we need to use a grid that includes Fourier transform g vectors up to a cutoff that is four times the cutoff needed for just the expansion of plane waves of quantum orbital into plane waves ok, that's maybe you have already already heard so I'm maybe repeating notice however I'm going to talk a little bit about this later that for the specific case of so-called ultra-soft pseudo-potential and PAW pseudo-potential as well you may need an additional grid an additional Fourier transform grid in order to account for so-called augmentation terms in the charge density also notice that this grid sort of cube in the space of indices so n1, n2, n3 n3 ok, these are the refolded one and prime and prime are the refolded ones and n are those that run from 0 to n minus 1 actually from 1 to n, capital N in the code because for historical reasons actually once upon a time FORTRAN FORTRAN arrays started from 1 and ended some number so I was saying in this grid this sort of cube you will have also some empty space so you will waste some space so this graphical representation I think I stole this picture from Parlo Cavazzoni's slides sometimes I go in case you don't know I have a difficult relationship with graphics and with slides in general so from time to time I steal slides from other people anyway so this is the box the Fourier transform box and in the case of of quantum states only let's say 1 eighth approximately a cube 1 eighth the volume of the total is actually used while in the case of charge densities or potential you feel with a sphere of g vectors as much as you can of the cube of the Fourier transform grid this is relatively straight forward it becomes less straight forward when you start to consider how to to execute in parallel and the parallel algorithm is quite sophisticated and has to take into account this difference between the number of the space field in this case in this case the number of g vectors in this case and in this case in order to to have a uniform distribution of uniform distribution and a good balance low balance of everything one has to resort to rather sophisticated algorithms so there is computational advantage in using when using this grid Fourier transform there wouldn't be such big computational advantage but the point is that you can perform the discrete Fourier transform with an algorithm known since many years by now is fast Fourier transform which is much faster than the plain simple algorithm one can imagine and so the plane algorithm would require order of n points squared so if you have a Fourier transform on a grid of n points three dimensional grid containing n points capital n points then you the ordinary Fourier transform would require n squared the fast Fourier transform require order of n log n and that's enormous and the especially in the so called dual space technique so in the dual space technique what you do what you need actually in most cases are things like most of the calculation is spent in computing products like Hamiltonian time prior wave function minus an energy but here the difficult part is the Hamiltonian times the trial wave function this is the basic ingredient of all calculations using iterative techniques be it carbonyl molecular dynamics or conventional molecular dynamics or iterative diagonalization self-consistency plus iterative diagonalization the basic ingredient is invariably this object here h minus epsilon times the a trial wave function now this can be done quite easily by looking at the various terms containing the Hamiltonian so you have a term here that is the kinetic energy and the kinetic energy is simple in g space let's say you compute the g space components plane waves component you have plane wave components so the kinetic part is simple this part here the local part of the pseudo potential plus the Hartree potential plus the exchange correlation potentials are potentials are v over r potentials in real space in real space so you bring the quantum orbit to real space you make the calculation on the grid you make the calculation it's just a calculation multiplication it's just a multiplication on the grid it's a local potential times the psi of r and then you go back the final term here the non-local term can be written can be manipulated in such a way that the non-local pseudo potential term can be written as some projectors and it's fast to compute either in g space or in reciprocal space so that's how it works everywhere you can use this trick of going to real to reciprocal space wherever it is more convenient execute the what you need in the most convenient space and go back to the other space that's done that's something that is invariably done everywhere in the quantum express and in similar code space on a plane wave basis set ok let's move to a different slightly different aspect so you may have seen yesterday that in order to compute the charges you have to perform a sum a finite sum on some set of key points and these key points are not actually typically given to cover that they are a uniform grid but typically they are not given as a uniform grid on the entire preview and so on but they are given they may be given only what is computed actually it's only the part of those key points that are symmetry in equivalence so you have those symmetry operations that of a crystal and you apply the symmetry operation given key point you obtain what is called the star of the key point the star of the vector so all the symmetry equivalent vectors and you keep one representative per key point per star with a weight that is proportional to the number of points in the star of course if you sum the charge density if you compute this quantity it may not have the correct symmetry generally it hasn't the correct symmetry so what you do is you symmetrize this quantity so you apply this operation you apply the symmetry operation to the unsymmetrized charge density you sum over symmetry operation the symmetry operation applied to the charge density gives the charge density in the rotated position with all arm rotated with all vectors rotated and you sum those so this is called the symmetrizization it is the reason why we can make all calculations only on the subset of key points notice a problem that may not be evident the way the way the algorithm current works is that you can either provide ask for in automatic grid and the code will compute the weights and the respective points automatically for you or you may provide a list of key points if you do that remember the code assumes that what you are providing is the list of key points that are inequivalent by symmetry with respect of the symmetry of the lattice of the brave lattice not of the crystal and the code will compute additional with add additional points the symmetry is not is lower than the symmetry of the brave lattice this is sometimes a source of confusion source of confusion and of problems in case your list of key points is not even for the correct lattice symmetry so if you in case of trouble use the automatic grid that the code computes there is a small utility that computes anyway list of key points it's called key points in fact but it does exactly the same the same calculation that's exactly the same calculation so just two more remarks there are symmetry groups that are non-symmorphic so symmetry operations are not only rotations but also fractional translation fractional with respect to the lattice translation there may be 1.5, 1.3, 1.4, 1.6 of a lattice translation in that case you have to just to generalize the symmetrizization formula and this was a source of trouble for a long time because and this fractional translation being fractional doesn't guarantee that the translated grid FFT grid overlaps the original FFT grids so it was a source of problem and occasionally still because this kind of symmetrizization in real space is still performed for some specific calculations in otherwise what is done symmetrizization is done in G space it's more it's less transparent more more complex less simple but it doesn't have any problem with fractional translations and also notice a detail the charge density as I have defined here and as it's used in the code is a dimensional so it's a charge density containing that integrates if you make the integral of the unit cell of the charge density you get the number of electrons you don't get the number of electrons times the charge again I have mentioned before that in the case of ultra-sosiductentiasis also in the projector augmented wave there is an augmentation term the charge density is simply the square of the conciam orbit it's the square of the conciam orbit plus a term that has this form in which the beta and q lm these objects that appear here beta and q are part of the definition of the pseudo-potential they are localized functions localizzate around the atomic position the ionic position and the short range and give this additional term this additional term may be somewhat harder on the point of view of the Fourier transform than this term so this term can be easily computed on the Fourier transform read as I have introduced before but this term very often almost invariably actually requires a cutoff requires a grid of g vectors because more slowly in g space than this one so it requires grid of g vectors that is larger than the grid of g vectors needed for this part here what is conventionally called the smooth part of the chart density so the ordinary cycle square so you have to take into account this part by introducing a second grid that in g space is larger so you need in addition to this grid you need another grid that can fit a sphere in which this radius here instead of being four times the radius here is not four times it's two times so this maximum length is up to times and anyway the sphere of g vectors that is needed is larger so you have another grid corresponding to larger sphere and larger cube of course there is a problem so in real space those grids are not necessarily commensurate so you may have in general you have different real space grids that may not have points in common so when you need to bring the things from one grid to another of course here you sooner or later you need it because you have this on one grid and this on a different one what you do is you work in g space so in g space you have a small a small sphere for size for air for instance and the largest sphere the largest sphere for augmentation of air so you can the largest sphere of course includes the small sphere so you bring your g vectors from here to here and they feed and you add what is missing and then you work with the denser real space grid sorry it's a little bit technical but maybe it's better if you have an idea of what is going on and why also as well again charge densities you may have heard yesterday you should have heard yesterday that in case of metals in case in which you have you don't have a clear distinction between occupied and empty bands and you have to and sometimes even if you have you have to resort to some method to deal with a firm surface and to deal with occupancy that change from 1 to 0 in the middle of a band now this is done typically the most straight follow way in that it's not the only one there is also tetra-guidra I'm not going to talk about that about this the typical typical way to deal with metals is to introduce some broadening of levels so you have a set of discrete conchiam levels and you broaden them and you compute weights or occupancies that are fractional objects so run from 0 to 1 of course they are 0 close to 0 far from above the fermi surface and the fermi energy and close to 1 just below and they look like an integral of some broadening function with the condition that the sum of our fractional weights which gives a number of electrons as a function of the fermi energy is equal to the number of electrons in my system one in principle might use the fermi dirac fermi dirac protein fermi dirac is physical it has this form so why not use that just use set some finite temperature 300 Kelvin for instance now the problem is that in order to it's not very practical it's not very practical because you need a very high temperature in order to to be able to use a reasonably small set of key points so the electron gas is frozen it's well known so you add that finite room temperature very little happens to electrons so they don't differ that much from the zero temperature distribution so you have to set a very high temperature and with that very high temperature this distribution is quite long tails so in the case slowly so you have to include many bands above the fermi energy it's not something very practical so one use some other broadening functions chosen with with the criterion I am going to explain now now there is an important point you may should be aware of so in the calculation of the total energy you may introduce you may take advantage of the sum of one electron one electron states so you may write the total energy at the sum over one electron states over con some levels one electron levels minus the exchange the heart energy minus because it's counted twice in the sum of of con some energies plus some other terms we'll see it later plus or minus some other terms now how do you compute this term this con some energy the typical one would think okay we have weights here for the charge density then we sum the weights times the one electron the one electron energies well no what you have to compute is actually the integral of the energy over the broadening functions which is almost equal to these the sum of weights times con some orbitals con some energies but there is a small difference a small correction small correction that code prints out in the smaring contribution and if you do if you do the math so if you look at if you do the calculation of the functional derivative of this energy and this energy and you have no other terms of course you will find that the functional derivative of this energy is the correct one is the one that gives a minimized by this charge density and the forces are derivatives of this energy not of this energy so that's why this contribution is actually important now broadening functions can be chosen there is a various theories on how to what the optimal choice of broadening function the simplest one is a Gaussian like this one normalize Gaussian it's not very convenient actually what happens is that ideally you should you should compute you should use a broadening delta the sigma sigma is the object that is called the Gauss in the code and you have to provide it in Rieberg and you should define exactly this way it's a sort of fictitious temperature you may think that this broadening introduces fictitious temperature t equal to sigma divided by the Boltzmann constant and you may think that the energy that you get is a sort of free energy fictitious free energy functional the function of sigma so I was saying in principle one should use a sigma as small as possible and as few as few key points as possible of course the two things don't go go in different direction so the smallest the broadening the more key points you will need and vice versa so your interest is to use as large as possible sigma broadening assume that you have a given budget for computation that's what you have to do if you can afford that many key points then you have to choose sigma broadening that makes your calculation convergent with those key points you can afford now the problem is that this fictitious energy grows as with sigma as sigma squared so the difference, the error that it introduces in the energy in the forces everywhere is not that small for large broadening or a large error as well so there are these two these two kind of smart broadening so called metfessel Paxton and marzari van der wil Nicola marzari is a good friend of us so I'm morally obliged to advise for marzari van der wil co-smaring and those smart smearing are advised to reduce the dependency of the energy of the fictitious free energy which of course corresponds to the two energy at sigma equal to zero they have these smart smearing techniques have a weak dependence upon sigma so they allow to use larger larger values of the problem you may find in this page some detailed explanation by Nicola marzari something that something that was always known but was recently remarked and finally fixed is that under some conditions those smart smart smearing smart broadening functions may lead to a bad choice of the fermi of the fermi energy problem is that those smart broadening are not smart enough to avoid that occupancy may have un physical values so physical values are from zero to one my test may have negative occupancies or larger than one and marzari bandio is not negative but maybe larger than one which means that if you look at the number of electrons as a function of the energy that is the function I have introduced before somewhere this function as a this number of electrons as a function of the position of the fermi energy is not a modern function which means that you may under some unfortunate circumstances get a wrong fermi energy so there can be more than two more than one fermi energies that's the point in marzari by collaborator Nicola marzari ok, again for charge density what happens in the non magnetic magnetic and collina magnetic case in the non collin in the non magnetic case you have all orbitals occupied by two electrons up and down so you simply have the total charge density as twice the sum over the square of the orbitals times the occupances of course in case of ultrasonic potential here you have also the documentation I haven't written it explicitly because it's for simplicity it doesn't change anything in the case of collin polarizations so this is called LSDA Locaspin density approximation which is not necessarily local it's an old name but anyway what is important here is not L but the S so in that case which is the most common case of magnetization you have orbitals that have either spin up or spin down so in that case you define a charge density, a total charge density that is the sum of the total charge density coming from spin up orbitals plus charge density coming from spin down orbitals and you have magnetization which is a scalar it's a difference between the two n plus minus n minus notice also that there is a spin index in quantum express it's not used well in carparinello it is used actually in quantum express in the in the self-consistent code what we do actually is to hide this spin polarization index into key points so we have our set of key points we double it the first set of key points has conciamorbitas we spin up the second set of key points has conciamorbitas we spin down so un polarize case one charge density one array of charge density spin polarize case lsda two charge density and magnetization non collinea magnetic case in the non collinea magnetic case in the non collinea magnetic case we have a plane wave basis set that is composed of plane waves times spin on so up and down so basis set is doubled so you have vector of components for each orbital that have a spin index so vector for spin up and vector for spin down and and so in addition to the the total charge density which is simply the sum of all the components there is also a magnetization a vector of magnetization I have written here explicitly the are wrote to make it clear the vector magnetization in which the magnetization is computed from the the matrix elements of polymetricism so this sigma here vector of matrices are the three polymetrics and about potentials something that one has to be aware of is that we are dealing with an infinite system within infinite system so some potential terms are divergent in particular the g equals zero component of the potential of the electrostatic potential generated by the electron so the heart return is by construction infinite in fact if you look at its form in g space you see that the heart potential is the charge density in g space divided by g square times some four pi omega something but of course for g equals zero this diverges and the local part of the electron ion pseudo ion interaction also diverges so the minus z times charge square divided by r term, the Coulomb term give rise to the interaction that again it has a form of one over g square over z valence, the number of valence later divided by g square and so it diverges as well but for neutral system there are not diverges the potential does not diverge other terms instead of short range term that don't have this problem diverges and can be computed by straight forward way and again something that should be remarked is that those potentials are actually potential energies so in the code we use energies multiply the potentials by the charge density the electron charge density absolute value not to the sign and so they are their energies and they have the dimensions of energies with berger Hartree atomic units is how the potential look like in a specific case a silicon you see that the potential may variate quite a bit and the sum of the various terms that tend to compensate in particular electron, ion interaction potential the local part here in red is heavily compensated by the exchange correlation close to the nuclei in silicon I haven't mentioned how to ok how to about the exchange correlation potential in this case actually the non collinear magnetic case is quite tricky because you have basically there are no exchange correlation potential for this form here so function as of the charge density and of the magnetization vector so you have to choose a direction in each point you choose a direction of the magnetization you look at components of magnetization up and down you use exchange correlation functional of the local charge and the local magnetization the problem is with GGA in which you have a gradient and the gradient it's not necessarily in the same direction of the local magnetization so it's quite tricky ok and a more ok now after potential that move to two energies as I mentioned before total energy can be written as the sum of a cone of one electron energies and the term we have seen before and we have seen before how it can be must be computed for metals minus the heart energy the electrostatic energy repulsive energy between average repulsive energy between electrons this one of course is also divergent it has a G equals zero divergence so what you subtract out here is the term without is the energy, the heart energy out of that term then we subtract out the exchange correlation term here it is not the correct one and we add back the exchange correlation term which is which is the correct one this is not problematic at all then we have the energy electron electron ion-ion interaction energy of course again divergent we remove the divergence by considering the interactions of nuclei in a background in a neutralizing background now there are several several divergent terms here so one is here and it's removed another one is here another one is hidden here it's in the potential this also removed and so all these terms in a neutral system cancel out all this divergent term cancel out and the total energy is well defined now for a periodic system so what happens is that the energy per cell is well defined but you can't have a net charge it's well defined for neutral systems if the system is not neutral the charge in the cell the energy per cell diverges there is nothing one can do about that more exactly there is something one does about that it's just throwing away the divergence so you have you treat the charge cell as it were as if it were neutral for what concerns divergent term divergent term so as consequence of the periodicity net charge on a unit cell equal trouble second consequence well of course the potentials have to be periodic as well so they have a periodicity of the lattice which means that there can be no macroscopic electric field macroscopic electric field described by potential like this with e electric field and it sounds that cannot cannot be cannot be present in a periodic system so no macroscopic electronic electric field more exactly well there are techniques to there are techniques to to simulate the macroscopic electric field some are based on the modern theory of polarization some are slightly more tricky we will briefly describe one later especially for slabs in the so-called slab geometry so when you have supercell of alternating layers of material and empty and of a vacuum in like for a surface in that case you may simulate an electric field by adding a potential that has this form in the region you are interested in and then it goes back to periodic to the periodic form in the region where nothing interesting happened a more intriguing problem with periodicity is that the zero of the energy so the zero actually the zero of the potential the V the V potential at G equal zero is arbitrary so in particular it has no direct relation with the vacuum level so the energy the zero energy of an empty space there is no outside so the crystal extends periodically everywhere and so there is no outside a crystal so absolute values of eigenvalues for instance have no direct meaning they can be whatever it depends upon the arbitrary value of the potential of the zero of the potential finally also dipoles are not well defined in general so for a finite for a finite system you can easily find the electronic dipole from the charge density so you just compute R times charge density at the end of R well maybe here I should have added the charge the electron charge while the ionic potential the ionic dipole straight forward that's it but in a periodic system what you compute in this way depends upon what you choose for the periodicity so in this case we have a dipole here and the dipole here apparently here the dipole points towards the left from minus to plus but if you look at the different choice of a cell the dipole points in the opposite direction of course if you are dealing with a finite system with a super cell then the dipole may be well defined in that case you have the possibility to define a dipole by considering only cell that includes one finally one copy of your finite system so as long as you have a prescription to divide your crystal into units then the dipole of that unit is well defined problem is that a finite system you have a clear prescription in general in this case for instance you may assume these as your unit cell or these and they give different values of the dipole so as I was mentioning before it's not impossible to deal with charge system just the code does it automatically because automatically it sets the divergences as if the system were neutral but what you may find is that the actual value of the energy you get in this way depends upon the choice of the zero of the potential and you may notice that for instance in the self-consistent code pw.x you will get a system of some value you perform the same calculation of the carpanello code which uses a different choice of the zero of the potential you get a different number in addition to the factor 2 because the carpanello code prints results in Hartree and the self-consistent code prints the results in Reitbergen so you have to be very careful not to compare you can simply compare energies with different charge states you have to resort to some tricks you have to align the g-vectors in the g-pull zero potential and you have to in any way the result will always depend upon the energy you you may typically you have a reservoir of of charges given chemical potential and the result the stability will depend upon the energy the chemical potential of the reservoir of charges another fact that is not sure it's really relevant in practice but in principle due to this dependence upon the choice of that is dependent upon an arbitrary potential there is no guarantee that if you perform a structural optimization calculation in a charge system what you get is sensible in practice I have no evidence that this doesn't happen but there is no guarantee let's say now let's come back to finance systems so for instance to molecules treated with supercell in periodic boundary conditions of course having supercell approach as many advantages but it also has some disadvantages in particular you may have a spurious interaction between periodic replicas of your system you are interested in an isolated system in a molecule you have an array an infinite array of such systems what guarantees that what you get from this infinite array is valid also for a single one well nothing but if the isolated system have no dipole are not charged have no dipole the interaction between periodic replicas the spurious interaction between periodic replicas vanishes quite quickly sufficient to have a few hamstrong of empty spaces between periodic replicas and you get basically compared results but but it's not always possible and in particular in particular if you have a charged system it becomes really a problem in case of when you have a charged system or even if you have a dipole so the dipolar interaction between dipoles decays quite slowly and you may notice that just increasing the size of the supercell doesn't help that much it helps but it takes a very large supercell now there are several approaches the first two are implemented in quantum express of the service not the simplest one is a correction on the energy in which you use an electrostatic model to take the spurious interactions out from the results to correct just the energy which is in principle not completely correct because the presence of periodic images also affects the potential there is a way to correct the energy and the potential as well by cutting the coolant potential in reciprocal space so coolant potential is responsible for the long range of course of the interactions you may implicitly you may cut off the coolant potential and if you cut off the coolant potential what is beyond a given distance it's just invisible so this is what is actually done in the third cases in the so-called Hockney method you cut off the coolant potential but you do that only in the heart potential do that only in the heart potential because it's the only one that is long range so when you compute the potential by H you cut the coolant potential it can be done in a more simple way also in reciprocal space so you cut off the it's equivalent to cut off the real or reciprocal space it's more sort of equivalent it's called the Martina Tarkovana approach and this is actually implemented let's see the simple case it's a mark of pain correction in the mark of pain correction let's assume that you have a cell a cubic cell of side L a capital L so one can study the convergence of a system without dipole no charge and no dipole it converges as the fifth power of minus one over the fifth power of the unit cell of the cell side so quickly with a dipole it converges as one of the cube of the length of the side of the cube so more slowly and for the charge system it converges as one of L so it converges never basically and this is also difficult so one writes down correction that has this form it's sort of for charge there is a net charge one removes the material energy of the rail of net charges and one removes the dipolar equation and hope I have written it correctly no I haven't it's L cube of course because this one it's L cube and then one finds that the energy converges quite quite well to much better to expected result for for surfaces for surfaces one typically uses a slab approach so you have piece of surface piece of some empty space and it is periodically repeated of course you have to to make some serious convergence study with respect to both the dimension of the slab of the number of of layers that you consider for for your surface and the number of the amount of empty space to leave in order to reproduce an isolated surface so one side of the surface shouldn't see what happens on the other side or of the cell and inside the middle of this lab the material should behave sufficiently close to the real crystal ok that's one has to depends a lot upon the specific material specific problem one has to do some specific some convergence some careful convergence study this is an example the recent example I've taken from work I've been I've also contributed to this guy is postdoc in Udine he performed first calculation of gold surface so the black one this is the potential energy the local part of course you can't represent the non local part average in the plane so this is a function of the z components of the vertical components orthogonal the surface and the plane and it's average in x y the x y direction so here you have the gold and here you have those oscillations and outside you see the behavior of the potential it's flat notice the values here the electron volts and here outside we are at 8 9 EVs so the zero is 90 apparently is 8 8 EVs also but again it is not important because this zero is arbitrary but of course once you have a function a slide like that a slab like that then you may for instance compute the work function so the energy needed to to take an electron out from here to here you may find what the average of the potential is inside the material and then refer the one electron states to the average value here and then you have the energy that is needed to remove an electron from the metal and to bring it in the empty space now in addition to gold here there is after the first calculation in gold alone we have added molybdenum disulfide it is a very fashionable material posed by the bidimensional material and the interest was in starting contact with molybdenum disulfide on various metals people disulfided on this side of course now you see that what happens is that this polar material produces a dipole this dipole can be evaluated by looking at this called dipole correction something that the code can compute one adds a compensating dipole so if you don't do anything here the potential instead of being flat is curved you may add this compensating dipole here in the region of empty space where nothing happens that brings the potential that causes the potential to become flat again on this side and this side and this gives information on the actual dipole that is present on the surface ok i think i finished here um something more something i wanted to also to talk about what i haven't prepared slide is about application of electric fields you may in a case like that we'll see that for instance the black one the black lines how can you apply an electric field here on this material while you add a source of potential like that that in this region the region of empty space of course it has to be periodic so it goes down and then it repeats periodically so the potential simulates an electric field here in the region of the material and then simulates something that is completely un physical of course in the empty space what happens in the empty space of course the potential the overall potential is periodic and it's made periodic by reverting it in the region in a region far away from the material a frequent mistake is to misunderstand what where the empty space is and to give parameters that make the electric field to change direction in the middle of the materials instead of the middle of empty space so be careful when you do that ok, I think I've finished for now thank you very much Paolo so we have it's 10 to 10 so I think we have quite quite an amount of time for questions so if whoever wants to ask a question directly speaking voice you can raise your hand you have the the button in the lower ok here we have one so Daniel Torres please hello and thank you thank you professor Dianassi for such a beautiful calm and detailed talk and my question is the next I've read and watched a lot of videos on DFT and they talk about these correlation problems on DFT would you say this is more of a user or a cold problem sorry which what is exactly a correlation problem because choice of an exit correlation potential you mean because I've read papers where they say this is a correlation problem in DFT it's misrepresented correlation well it's true that when people don't find the correct results they say oh it's correlation and well depends a little bit about the materials for which the materials and the properties for which this correlation problem is invoked so there are some well known cases of DFT failures or maybe you heard more about that why tomorrow or when is the advanced functional stuff the day after tomorrow Thursday Thursday there is a day dedicated to advanced functional and of course when you when you talk about advanced functional you have to specify what backwards functional don't get right and there are a number of of known problems in DFT in plain simple DFT let's say and also of known known measures to known things that can be done to avoid those problems so it's you should have a look at the specific case I mean for instance the lack of under bus interactions in DFT in plain DFT let's say maybe missing electronic correlation actually missing known local non local correlations between distance between clouds of charge that are do not overlap or overlap in a marginal way that's more or less known and it's also more or less known what to do in that case use under bus aware functionals or add corrections of various kind of corrections whatsoever answer your question ok ok thank you thank you Daniel so of course now you can write all your questions in the zoom chat I see there is another raised hand Doria et cetera please hello good morning from Spain thank you for the invitation for this wonderful school I was thinking about the clear explanation you did about the charge density and I have seen in literature that often some of these effects are not introduced in the self consistent cycle I think for example in magnetism or in spin orbit coupling in the case of non collinear magnetic calculations these effects are introduced in a tie binding model at the end of the calculations and this of course allows to low expensive calculations and makes possible to converge some calculations that are really difficult to converge so is this a good practice or are we losing something important because I understand we would be using a charge density that is far away from the real physics it's a good practice but it works I haven't mentioned this but non collinear magnetization is a pain to converge it's hard to converge and also spin orbit when you have spin orbit because things are a little bit better non collinear magnetization without spin orbit is not that physically not very very sensible because magnetica isotropy comes from a spin orbit doesn't come from directly from the action correlation function and but I'm aware I don't know very very well what how spin orbit works in quantum espresso I think it's implemented the proper way in a complete way you start from pseudo potential with a spin orbit term you perform the self consistency with everything on everything on all terms that are there it's expensive and slow to converge it's true I remember that some guide years ago presenta in alternative way in particular to compute band structure before sort of perturbation and from what he showed it was much faster and results were quite good very good so it might good it might be a good alternative in cases in which you have really comparison is difficult ok thank you thank you for your answer thank you Dario so I don't see any other raising raise the hand ah yes there is another one but maybe let's read a few questions from streaming and then the question so from streaming I see there are two quite similar questions one is what materials will provide the cases where mp or mv smearing will provide a non unique Fermi energy ie when the materials is x, y, z and the other question I think it is quite related how should I decide when to choose fixed occupation fractional occupation and type of smearing for bad metals exitonic insulators with pseudo gap case of non unique Fermi energy I think the guy who who found the fix will publish it soon so if you look in github on the developers portal there is an issue that now is closed I am not sure I can I can find it now because it's quite old this was observed some time ago typically typical case in which some trouble could arise is when you have a single state what was the case this is for true metals it doesn't happen it might happen when you had very few states contributing to the Fermi energy to the densile state at the Fermi energy so when you have very few states in that case you may occasionally get the bad Fermi energy it's not a big problem but it was sometimes some failures have been tracked to a problem like that about the choice of fixed occupation fractional occupation but how should I decide to choose fixed occupation fractional occupation type of meeting I see it on the chat well typically even even for if it's for insulator sometimes you need to specify broadening because during the self-consistency you may have level crossing and so this will your system may become a metallic during self-consistency or you may have level crossing and so you run into trouble with convergence the self-consistency convergence so typically whatever problem if your system is problematic you may have fractional occupations for broadening so we have another question regarding exchange correlation potential are there some approximations for exchange correlation potential or hybrid functional to solve that term and the term is meant to be the exchange correlation potential in the conciame Hamiltonian so if there are approximations for exchange correlation potential or hybrid functional to solve the exchange to solve that term the term is the exchange correlation potential in the conciame Hamiltonian so maybe Cristian could you write it better maybe specifying better which term do you mean because it sounds are there approximations to solve exchange correlation potential are there approximations ok, so maybe let's try to write the questions a bit more specific and we have another question later I have two related questions regarding the corrections for finite systems with PBC could you possible comment on finite side scaling instead of such corrections well they both are good you can use both use correction and finite side scaling correction help finite side scaling finite side scaling with charged systems well try and you will realize that it doesn't work so you really require so large super sales but anyway it can be used yes how do I use the correction already implemented in quantum express while this one has to to look a little bit carefully to documentation and to examples if there are some not sure there are many examples but there must be some example here and there for each of these corrections of course you have to activate those corrections and look at with some flag in the input and you have to to look at parameters if there are any for instance for for the electric electric field you have to be very careful to where you put your electric field your reversal of electric field so we have time for other questions no in principle no because the code anyway will try to figure out what the correct symmetry in practice it may happen sometimes that system has trouble in finding the correct symmetry because what you have provided is almost symmetric is an old problem if you you have a real symmetric material with no symmetry you should provide the correct symmetry it makes life easier but in principle it should work anyway how can we examine effect of electrons holes is it just enough to add remove an electron no unfortunately no you have to take into account well it depends which effect you are looking at so effect on geometry with the caveat I have mentioned just add and remove an electron and let the system relax with the caveat that or effect on the electronic structure is something that you can easily you can easily see if you remove an electron where it comes from and if you add one where it goes from the consciousness we have the exchange correlation potential which approaches are used to solve it well the actually I have maybe I should have I should I should have say that the action for the action correlation potential action correlation potential is a functional of the charge density so what do you need you need a local a local density part which you have some function of the local of the local density so you compute the density in charge density and you have the you compute directly for the local part you compute directly the potential this will be a function in real space that you can transform back to reciprocal space if you need it for the GGA part you have a function of the local density and of the local gradient square gradient or some combinations anyway is something internal to action correlation potential so you have the charge density in real space for instance because your sum of a size square in real space because it's convenient then you go to reciprocal space and multiply by G and that's the gradient you go back to real space and that's the gradient in real space then you have the charge in real space the gradient in real space and the function that at each point using the charge density in that point produces the action correlation potential the more sophisticated the action correlation potential is the more the passage from charge density question correlation potential is complex so-called meta-GTA have an additional term in the Hamiltonian that again must be computed based on the charge density again with similar techniques hybrid functionals are much more complex because they have no local term it is completely different it must be computed with a different technique but plain action correlation functional GTA simply functions of local density charge density and gradient the charge density it's something that you have in input you compute the gradient using the FFTs that's it well the functions may be sometimes quite complex and sometimes also numerically noisy especially in empty space when you have the charge density that is small and the potential should go to zero it does for atoms analytically it doesn't for condensed matter system sorry that's it it's nothing especially complex yeah are we late? we have 2-3 minutes left maybe we can let Ignacio ask his question and then we close so please Ignacio thank you I would like to know what would be your approach to modeling paramagnetic phases in the FFT I know it's somewhat ill-defined and people usually resort to non-magnetic calculations from a paramagnetic material which I don't find very satisfactory so what would be your take on this what do you mean by paramagnetic materials? some examples a material beyond its critical temperature where the magnetism is not magnetically ordered anymore ah well something it has been said explicitly is that these calculations in principle are t equals 0 calculations yes yes of course so so you cannot directly account for the temperature so you may for instance you may consider supercells with some randomly oriented spin because this answer can be done actually with non collinear magnetism you can impose constraints on the magnetization typically you have to otherwise the system doesn't converge so you might in principle take a system and make a supercell with a random random spin or magnetic moments otherwise you don't know one can always typically non one tries to do with magnetism is to obtain parameters for an effective Hamiltonian and then use the effective Hamiltonian at high temperature for calculations of statistical mechanics statistical mechanical properties ok thank you very much so thank you very much Paolo and now we are really late and we have to close in front of your questions in the proper Slack channel of day 2 and we meet again at 10.30 for the answer session from a professor Anton so see you later bye Paolo thank you again we stay connected right we can stay connected the meeting is going until the end of the day so yes we actually if you share a screen I don't know if the people from my CDP are here connected exactly Paolo c'è il microfono aperto non sto dicendo nulla ok ok non è che poi uno se ne dimentica ehm sono paolo ci sono solo che qua ci sentono tutti magari ci sentiamo tanto non devo dire niente dimmi no niente in realtà no l'acqua cosa c'è ora? ora c'è il tutorial c'è la partenzone che fa a Tone cosa si chi farà ora ora c'è il test di convergenza quindi punticappa check at off punticappa disney c'era una domanda si gli sta rispondendo Stefano ora guardo un attimo anche se è bo magari due minuti ok ok are we going to do some HPC test Tone, you are muted ok, can you hear me? yes I can maybe just show at the end of the hands on how tomorrow we will start using it ok cool ok perfect but then later in the afternoon I will test all the three machines so that it will be consider that the reservation of ICTP is open up to 4pm today everyday is open from 6am to 4pm ok ok, yeah anyway I am here I mean I am going to be here if you do anything so it's 10.30 maybe we can start so now Professor Anton Coccal will give the hands on session about SCF calculations and post processing before starting let me just say a few things regarding the organization so basically from yesterday we saw that Slack is very effective for the hands on session so please all the participants please write all your questions on the Slack channel and the tutors please check the Slack channel for questions because in that way there are more people who can monitor the questions so there are more chances that you get an answer and yes so use the Slack channel because we also have threads and here if you write here on zoom the chat will scroll down and we lose the questions other thing please remember to answer using reply in threads so the answer will stay bound to the question and it is easy even to understand the flow of the conversation so for both the participants and tutors and whoever reply in thread whenever possible and use the main chat only to open a new thread so for a new question another thing one last thing we have the breakout rooms as you see there are four rooms one per tutor so we have four official tutors for this session for the tutors if you read the questions on Slack and you feel that you can give close assistance to people who are asking questions on Slack feel free to write on Slack and you can join to my breakout room so when the participant reads this sentence you can find here on zoom the breakout room menu in the bottom bar and you just join the breakout room of the tutor who answered you on Slack so I say it again just for clarity the participants ask questions on Slack if the question is tricky your participant need a closer assistance from the tutors the tutor will read the question and answer please join to my breakout room so the participant can join the breakout room from the bottom bar here you see that the breakout rooms are named after the tutors so Malica tutor room Potsberg tutor rooms so if one of those tutor answered you join my breakout room you come back here on zoom and enter that breakout room where of course also the tutor will join the breakout room and you can chat there and solve whatever issue so let's try this way which seems to us to be the most effective so far sorry for these these words even just a very short a very short recommendation this is Stefano Baroni speaking concerning the usage of breakout rooms I would recommend all the tutors to use them as much as possible particularly for technical questions technical and seemingly trivial questions such as the location of buttons on the screen the simple simple setup stuff that is trivial to explain in words and may take several lines and trial and errors to explain on the chat so feel free please to use at your discretion of course but the chat rooms as much as possible I've seen that that some questions get multiple answers which is good of course but these kinds of penalizes the optimal allocation of the tutor's time here again if some of the questions can be discussed in breakout rooms these would probably save some of the tutors of the tutor's time thank you very much and have a profitable morning or afternoon whatever it is at your place, night thank you very much Stefano so please Tony let's begin the answer ok so thank you very much Ivan and thank you very much to Stefano for all the explanations now let me try to share the screen first ok so can you see my screen yes yes we can see fine ok so hello everybody my name is Anton Kokal known as Tonya to colleagues and friends I come from Joseph Stefan Institute from Riblana Slovenia and the subject of today hands on a session are convergence tests yesterday after the excellent presentation given by Ralph Gebauer there are a lot of questions on the slack how do I choose a proper set of coin points how do I choose the proper cut of energy and so on so there is no general answer to such questions the answer depends on the system and the answer depends on the context and so during today hands on session you will learn how to try to give an answer to such question for a given let's say particular system ok so here is the skin of today hands on session so first we will make some basic convergence tests for silicon bulk this is located I will show later in the directory example one silicon so here we will test we will test cut of energy we will test k points and so on then we will do one metallic system aluminum in particular and here we will see this smiting issue that Paolo described this morning and then we will go to example 3 which is iron and for iron which has a 3D states we will use ultra soft pseudo potential and it is also magnetic and so we will see this kind of how we need to increase the cut of energy for the charge density beyond 4 times that of the way function there is a lot of examples here so I'm not sure we will be able to do all I will be able to cover all in 2 hours but nevertheless these slides contain all the information and so now it depends you can follow me when I will do the examples or you can just listen to me and then you do these examples later on in order to know what she or he thinks is the best for her ok now this is something now comes the point where we will do this more or less every day we will update let's say these exercises and to do that I will show later how to do git pool should be sufficient but if you have changed some files ok then git pool may fail and if this is so then here at the bottom of the page you have the 3 commands that you need to do and then your exercises will be updated ok and now I will shift from the slides and I may be just one useful information for those of you who are not used to Linux do you see my mouse pointer this is a question which is important I think so you see here at the bottom you have these virtual workspaces and this sometimes is very useful for organizing if you have multiple open windows ok so now this was already described in Friday and yesterday here we have these exercises organized in per day basis so today is day 2 and so we can double click this day 2 and the file browser will open and now for each let's say for each day and for each exercises we have two different sources of information the first one which is in the top directory of a particular day there are hands on slides so these are the slides I just showed you before the first two pages but then there is another source of information which is a readme file and this readme file exists in every directory so I now jump into example 1 and you see a readme file here so the information contained in this hands on slide and the readme slide is a bit complimentary so these PDF these slides they contain let's say a more descriptive more explanatory description of the hands on exercises whereas these readme files are more like cooking recipes it goes like ok let me open it so if you double click it it will open in a firebox browser and so this readme file is more like a cooking recipe it says ok in this exercise you need to do a calculation A like that and a calculation B like that and a calculation C like that so these are these two information that you have in order to understand what each particular exercise is about now let us do this first thing of the day so we can right click on the file browser here I have open terminal and then I will do read pool 1 and if get pool face for me I am already upto date because I have done this before you can do get refresh get pull get splash apply on this is described on the 2nd page of the slides ok now let me go to slides and the first example is silicone and here you will see dell'esplosizione della struttura dell'input file, quindi potete ripetire questo per dirlo, invece, andrò ad esempio 1, così. E, ovviamente, se non lo fai, o se fai dietro di me, sempre puoi vedere il file rigui e l'esplosizione è quella che vuoi fare. E ora sono in esempio 1, ma magari prima di procedere, solo una domanda, sono questi fondi in questa strada sufficiente o dovete esplorare? Qualche informazioni? Per esempio, potete esplorare un po' più. Esplorare un po' più? Ok, proviamo. Se questo funziona, ok, ora è un po' più grande. Ok. E quindi qui, insieme, in questo esempio silicon, ho diversi subesami, un file rigui, e qui è il file d'esplosizione per il PWX. E ora si può esplorare l'esplosizione in Emax, o un altro modo è di usare il file d'esplosizione. E quindi qui possiamo vedere alcuni listi del nome, alcuni listi del nome, e in questi modi Emax, tutto che è in red significa commento. E anche questo hash qui, questo significa commento per le carte, ma non è in red in modi Emax. Ok, quindi questa è la struttura basica di il file d'esplosizione del PWX. E quindi, se siete solo interessati in il nome, quindi cosa è il file d'esplosizione del PWX? Il file d'esplosizione significa che puoi andare qui per FireFox, ora perché il zoom è riuscito, è un po' più spesso, e poi puoi andare a questo «How to» e tu hai qui il file d'esplosizione, e puoi riuscire al logico di come il file è riuscito. Ok, fine. E quindi, suppone che non siano saputi che il variabile è giusto, quindi abbiamo preparato per te. Abbiamo preparato per te. Questo FireFox con i bottoni e qui se cliccate il PWX, poi, ovviamente, per ogni variabile particolare hai l'explanazione. Per esempio, se andiamo alla calcolazione, potrei vedere diversi tipi di calcolazioni che possono essere imparate nel PWX. Ora, ovviamente, in una machine virtuale, tutto questo è arrangito per te, ma magari dopo, quando non usate la machine virtuale più, suppone che vuoi questa informazione e quindi come possiamo fare questo. Well, we google it and let's say that I'm interested in the NEP description, so in the Google I would say inputNEP.html and so the Google is smart and the first hit is the description about the NEP program. Otherwise, this information is also contained on the quantum express of web page. So why I did this NEP example is because here you see a lot of buttons, but because there are so many of them, we did not notice that NEP is missing, NEP will be used next day and so we can just add a NEP button. So this can be done very simple I just drag this somewhere here but I've done this yesterday for myself and then maybe I can just make a shorter description like that. Now I have two NEP buttons because I've done yesterday this. So I will remove this one. Okay, this is just, if you would like to know what a given variable is, go to today we will use PW, we will use pp, we will use bands, we will use dos and so on and so on. You go here and then you find the information. Now it is time to go on and I go back to slides and so one of the first thing so one of the important thing when we try to model a given system is to input the structure. To input the structure and so silicon is crystallizes in a diamond structure and so now how do I visualize? So here I have this input file or even here of silicon so it is ebrav equal 2 so if you will go to this PWRX description of the input file you will click ebrav you will notice that ebrav equal 2 means FCC lattice. Okay, in order to visualize this structure and then you can see we have two atoms in the unit cell and this is not means number of atoms and number of type of atoms is just silicon and two atoms. Okay, and I can visualize it like that x k is then minus minus PW i the name of the input file. Okay, so this is the reduction so if I have a crystal is a 3D system I do not reduce, if I have a surface I can reduce to two dimension if I have a molecule I can reduce to zero dimension now we have silicon bulk so no reduction of dimensionality and now this is a silicon structure I can even display atomic symbols and now I don't see any bonds and this is sometime annoying I just show how you can display bonds you go here to atomic radius and you enlarge the chemical connectivity factor I need press update and now I have the bonds. Okay, but now very important buttons are here on the bottom this is kind of nicely tessellated unit cell this would be just a translational asymmetric unit but now is a problem here we can see that there are four eight atoms one, two, three, four, five one, two, three, four, five, six, seven, eight but here in this input I just specified two atoms so how is this possible it is because we are looking at the conventional cell if I want and the code is smart the code is smart because the conventional cell is four times smaller now I have just two atoms and this is basically what code calculates this is why we just specify here two atoms okay and now to really verify to really verify that this silicon structure is composed of two FCC lattices let us play a bit so I will say number of atoms one and then I will comment one of the silicon atom and then I so I modify the input file and I will press reload and I obtain something like this and here you can really see that this is the FCC structure so silicon basically we have two units two atoms per unit cell and so basically we have two FCC lattices displayed one with respect to the other so now I will undo these changes so this was a bit of explanation how we visualize the structure how the FCC structure of this conventional this interplay between conventional and primitive structure but now it's time that we do the first convergence test now let me go back let me go back to slides okay so basically what is here I now did kind of a real demo oops okay and then here is also some explanation of the key points and okay but maybe we can just do the first calculation before we do the convergence test and yesterday on the slide there was some confusion about this usage so this flag means minus input it can be minus i minus in whatever instead of that we can also use this what is this smaller than redirection operator but we cannot use both just this or that but notice that this is not recommended on parallel machines because it cannot work so this minus in is more secure because it always work in a sense so I can copy maybe this let me see and I do a simple SCF calculation and this will be super fast because even with one processor because this is a really very simple system so we see less than one second now okay this was a simple simple calculation and in this virtual machine so if we would look here we have this out there and pseudo there commented and there was some discussion yesterday on the slack and it means that we are using in virtual machine express of pseudo and express of TMP the environmental variables so most of the exercises for today will not explicitly set out variables and then of course you can also do something like that to see in the temporary directory ok uh we didn't copy well ok but now you can see this is the temporary these are not quantum espresso files but here these are quantum espresso let's say scratch files that quantum espresso has written out the directory now you see doing where single SCF calculation is very important and then we can also grab the total energy from the output file we can write the output file directly for example if I want to so I can create the output file like that and then I can read it but of course I can instead of that and then we can do something like that and this is described here on this page but now let us go to convergence tests and so the first so this the logic of this first exercise is the power let us do the convergence convergence tests with respect to basis that is with respect to kinetic energy this is the variable i punti K, questo è il punto K, e poi con la potenza di energia e i punti K, lasciamo calcolare il parametro latino di Silicon bulk, e poi il bonus è che, una volta determinato a questi parametri conversati, possiamo calcolare la struttura di Silicon. Ora, come uno tipico fa i test di converso? Questo significa che se voglio fare una testa di converso con la struttura di energia, bisogna piccare una struttura di energia, diciamo la struttura 16, calcolare la struttura e poi coltare la struttura di energia. Poi, cambiare l'input fila, trattare la struttura a 20, e ripetere il processo coltato di energia, e così e così. E quindi questo è molto utile per fare manualmente, e quindi nessuno fa questo manualmente. E quindi per questo motivo usiamo le strutture, che otteneranno il processo. E quali sono i strutturati? Vorrei dire tradizionalmente, le strutture di Unix sono usate all'inizio, e qui è così, spero che questi caratteri, che sono molto piccoli, si potessi vedere, se non potessi vedere quei caratteri qui, che sono piccoli, allora, ok, guardate i strutturi, e si potessi vedere. Quindi questo è una struttura di Unix Shell Script, quindi è una struttura di struttura, diversi strutturi di struttura, 12, 16, 20, 24, 28, 32, e poi qui vedete questa struttura E-CUT, la funzione web è uguale alla struttura E-CUT. E quindi facciamo la calcolazione e poi coltiamo la struttura di energia in un file. Quindi questo, mi ricordo quando ero bianco, quando ho iniziato a fare le calcolazioni, questa struttura di Unix Shell Script è stata molto semplice per me, quindi non ho capito come questo è inizio. C'è un'altra possibilità, e questo è i script PwTk, e sono più piccoli, in un senso, e sono più piccoli. E oggi, avremo usato i script PwTk. E quindi il logico di questo script PwTk è il seguito. Qui abbiamo questo logico di PwTk, che significa logico di PwTk input. Veload il file d'input. Ok, qui avremo l'open-sum file dove i risultati saranno scritti. Abbiamo fatto una struttura sulla struttura di valori. E poi abbiamo messo questa struttura di variabile e la calcolazione. Poi avremo la struttura di valori con questa struttura di valori, l'energia del totale, e questo è tutto. E questo è tutto. E quindi penso che questo è, in un senso, molto più piccolo e più più piccolo che i script PwTk. E oggi avremo usato i script PwTk. Ora, se andisco, posso andare ad esempio. Una struttura di valori, se andisco all'interno, andrò all'interno del classico. Se andisco all'interno, vedo la struttura di la struttura di valori che hai visto prima. Sto usando un'altra struttura per la struttura di valori, per essere più scelta sul screen. Quindi questo è la struttura di valori che ho mostrato prima. Ora, magari, avremo un po' di carattere. E questo sarebbe l'energia del script PwTk. Sto usando la struttura di valori. Poi posso vedere questo script PwTk. Quindi è un po' più lungo che prima, perché qui abbiamo alcuni commenti, alcuni commenti. E due a questo, è un po' più lungo. E qui abbiamo questa struttura di valori. Per quelli di voi che non conoscono qual'è la struttura di valori, questo è anche un comando unico, che già la sua struttura di numeri, qualcosa di così. Quindi questo struttura di valori sarà solo 12, 16, 20, etc. Ok, quindi vedete l'unico o la struttura di valori che abbiamo detto che hanno una struttura di valori. E poi questa struttura PwTk è un comando di rinforzare la struttura PwTk. E ora lo esecuteremo. E questo è... Quindi la struttura di valori è girata. È molto veloce. Ok. E quindi questo è il mio risultato. E quindi ora abbiamo, diciamo, il primo risultato. Quindi cosa sarebbe la struttura di valori? Soposamente, diciamo che deve essere, diciamo, la struttura di valori convorcia lentamente, magari altre proprietà иногда può convorcire più velocemente. Ma diciamo come una struttura che dovrebbe essere convorciata tra Mili, Riedberg o so per atomi. Qui abbiamo due atomi che significa che più o meno, diciamo da 25% di Riedberg, è più o meno ok. Quindi si può vedere una struttura molto low cutoff. Il primo è cambiato molto rapidamente con l'energia e poi è saturata. E ora posso ricordare questo valore perché poi saranno usati questo valore, questo cutoff valore per calcolare la struttura di Riedberg. Quindi magari qualcosa di come la struttura di 25% o 30% di Riedberg dovrebbe essere più o meno sufficiente. Forse solo perché ho mostrato a voi questa struttura di WTK, io andrò qui. E quindi qui è una esponenza basica della logica tra la struttura di WTK. Quindi mi dispiace perché magari siamo davvero confusi a voi perché quelli di voi che sono nuovi per andare all'espresso sono iniziati con l'input. Sintax e ora abbiamo aggiunto qualcosa sui topo, ma credo non c'è rischio da questo perché se vogliamo fare una testa di convergenza bisogna fare per rendere molte calcolazioni e la struttura basicamente è l'unica possibilità di riuscire a fare. Quindi qui puoi vedere questo sarebbe una esponenza dell'input su la struttura e sulla struttura di WTK l'input è specifica molto simile, la differenza è qui abbiamo questa struttura di convergenza e poi nella struttura di WTK il termine è riuscito così. In struttura di WTK abbiamo la struttura di WTK calcolazione come con la struttura di WTK e dalla struttura di WTK la struttura di WTK come la struttura di WTK e la struttura di WTK ovviamente qui sulla struttura puoi vedere più informazioni su la struttura di WTK e poi all'inizio hai la struttura di WTK qui hai l'explonazione delle strutture che abbiamo usato l'input dalla struttura di WTK che è la struttura di WTK dalla struttura di WTK poi questa struttura di WTK o la struttura di WTK ritorna la struttura di WTK dall'output e così on e così on e poi se se vengono a Firefox se vengono a Firefox hai questa struttura qui e qui vedete l'informazione della struttura della struttura di WTK e magari se siete interessati se vuoi imparci qui è una struttura è una struttura di WTK questa struttura e poi per queste strutture qui ok ora quindi abbiamo fatto la prima testa quindi vediamo che alcuni 25 o 30 Riddberg è più o meno per questo caso e ora lasciamo andare al secondo esempio quindi posso andare una struttura di WTK e vediamo che il secondo esempio è K-Points quindi ovviamente in ogni struttura avete queste struttura di WTK quindi potete vedere cosa potrebbe essere fatto con questo esercizio ma penso che è molto ovvio abbiamo questa struttura K-Points scrittura quindi lascio lascio aprire lascio aprire e quindi cosa abbiamo qui vLoad input da alcun existing file che è una struttura di WTK e poi vediamo vediamo la struttura di K-Points 4, 6, 8 queste 2, 4, 6, 8 basically means you can see here so K-Points automatic and this automatic is what what Paolo described this morning that there is this automatic feature a feature which constructs the K-Point mesh for you and then it the code just uses the K-Points in the irreducible batch of the branch zone and of course the code knows how to calculate the way it leads of a particular key and so basically K2 means 2 by 2 by 2 K-Mesh and we use shifted K-Mesh so this means 1, 1, 1 and okay and then we collect the total energy and at the end we plot the result with the code so let us let us run this script so now we see 2, 4, 6, 8 and now I have the result and so what does this result tell me you can see how the total energy behaves so for the here is the total energy for the 2 by 2 by 2 mesh and then you can see that from 4 by 4 by 4 on the total energy is more or less converged so the answer for the silicon bulk is 4 by 4 by 4 K-Mesh is enough and now we know that something like I don't know 25 read works and 4 by 4 K-Mesh is okay for silicon bulk with doing that with finishing the first two examples we can go to example 3 and this has some let's say maybe not so clear name ALAT ALAT stands for a lattice parameter and so now you know what ALAT stands for and so the purpose of this exercise will be to determine the lattice parameter of to determine the lattice parameter of silicon bulk now so here we have the script which is prepared so let us open it and let us read it so again the logic is the same we load the input from this pre-existing input file but now let us read the comments here it says please uncomment and insert value as determined under e-cut wave function exercise so I will uncomment this and let me say okay silicon is a super fast example maybe I can take 30 readings sorry even maybe 25 would be more than enough please uncomment and insert values as determined in the k-points exercise so we just saw that for the silicon bulk 4 by 4 by 4 shifted mesh is more than okay and now I am more less ready and so here you can see for each ALAT so is a loop over the ALAT's parameters and so we use this sequence so we will scan from 9.7 bores to 10.7 bores with a step of 0.1 bore and so we see that for each ALAT we set in the system the cell dm of 1 basically which is which is basically ALAT's parameter in bore units then we run the calculation and we collect the result then we will plot the result with the new plot and then at the end we will also execute the evx code ev means energy versus volume and this ev will give us will give us will determine the minimum of the ev versus lattice parameter curve so it will give us the lattice parameter and it will also give us the bulk modulus and okay so i think is is time that we run this example so we say pwtk ALAT and so we go 9.7 9.8 9.9 10 so let us wait a bit we go to 10.7 10.7 so we're almost done okay so this is the result this is the result and so you can see that the lattice parameter should be around 10.2 bore and now let and in order to get rid of this new plot window either press this x or you just press enter in the terminal and now this is the output this is the output of the ev command which was run here and so here you can read this output of the of sorry the output of the ev dot x command equation of state so the input was here you can also run this code from the terminal so it will ask questions and then you can answer so we have chose mode Morgana equation of state and this would be the lattice parameter in Bore this would be atomic units in Bore radius this would be the lattice parameter in Engstems this is the bulk modulus here you can see lattice parameter and the calculated energies the fitted energies here is the pressure and here is the enthalpy and now just a homework se comparare la energia totale e l'entrappi potete vedere che se il parametro lattice è più piccolo che l'equilibrio di parametro lattice allora l'energia totale ha un valore low che l'entrappi ma se andiamo beyond il parametro lattice quindi potete vedere che l'energia totale ha un valore più alto che l'entrappi e quindi il homework è bisogna figurare perché questo è questo è ok quindi questo io credo abbiamo completato il primo esercizio quindi il primo test di conversazione quindi noi conosciamo l'energia totale noi conosciamo i punti k noi conosciamo il parametro lattice e ora possiamo fare il materiale bonus che sarà la struttura di band ora per il motivo di tempo io avrei scoperto questo esempio è un bel esempio ma io vorrei cercare come lo fai quindi luci questo file e questo file lo inserirò per editare la struttura di band pwtk script e quindi qui lo inserirei il parametro lattice lo inserirei il cutoff il cutoff di funzione e poi lo inserirei il punto key e ora qui vedete un remarko quindi il script è suggerirvi di usare una struttura di band e yesterday c'era una discussione quando usiamo la struttura di band e quando usiamo la struttura di band quindi in genere io vorrei dire che usiamo la struttura di band ma o magari io dovrei fare l'esempio ma se vogliamo portare diciamo la densità di stati è magari meglio usare la struttura di band che è la struttura di band perché quei punti critici come gamma x quindi nel centro della zona di Brian e della struttura di band della zona di Brian questi quanti punti simmetri sono basically una struttura di band e normalmente diciamo il bottimo di band e il topo di band sono questi punti critici e se non se usiamo la struttura di band ci misseranno questi punti e quindi supponere che vuoi avere un'idea da un punto di vista densitivo che è la struttura di band se non non inclusiva questi punti critici poi avrete un certo numero per la struttura di band quindi diciamo per la struttura di band è magari meglio usare la struttura di band se fai questo esempio e se prima usi struttura di band e la struttura di band sarà bloccata potete notare compare l'energia ferma potete notare che l'energia ferma extractiva dalla struttura di band sarà un po' bassa e poi diciamo il valore di diamo che dovrebbe essere occupato nel bottimo di band quindi potete figurare questo per te se lo fai l'esercito ok quindi con questo io credo che è il momento dobbiamo andare al secondo esempio che è l'aluminium che è l'aluminium ora vi faccio vedere i slide se non l'ho scoperto qualcosa quindi qui se avete tutte queste esplanazioni anche i plot e magari qui ho questo questo plot questa struttura di band oops questa struttura di band di silicone e vedete questo è un punto gamma questo è k 0 0 0 e se non inclusivo un punto gamma quindi se non uso non scoperto che è l'esercito io lo misserò a questo punto perché il massimo dovrebbe essere scoperto quindi questa è la serie questo è il tipo per questo silicone abbiamo il bottimo di band occupato e il topo di band occupato al punto gamma ok ora ve lo faccio alluminium che è un metallo ok quindi questo sarebbe il punto gamma guardate e se guardate questo in questo direttore nel simpote file ora vedete queste nuove varie varie occupazioni smigliati e garrini e quindi questo è ora come a discutere con queste discontinuiti metalli perché abbiamo un tipo di occupato occupato stati e poi non c'è una band di band e poi non c'è un cellulo da fermi energia i stati non sono più occupati e questo fa problemi questo fa problemi con la integrazione e uno deve usare una varie varie danza k-mesh o uno può usare una varie danza k-mesh e smigliati e poi, ovviamente, potere esplorare questa domanda per questo business e quindi l'esempio che vedete è che vedete un tipo di test di comprensione che sarà tre dimensioni quindi vedete scannati su k-points su di gaus value questo di gaus significa quanto scannati il gaus significa quanto lo smigliati e smigliati significa quali tipi di smigliati potrebbero usare quindi questo è un scannato tre dimensioni e lo prenderà un po' e quindi qui è un smigliato del pw tk come questo è fatto quindi è un scannato su di t-points poi è scannato su diversi tipi di smigliati gauscia smigliati metfeser paxna smigliati e marzari smigliati e poi c'è un scannato su diversi tipi di gauscia ora mi faccio prima mi faccio prima l'input file quindi questo è l'input file e oppure ok e questi sono i nuovi variabili questi sono i nuovi variabili che prima di noi non abbiamo un piccolo silicone e io penso che i resti dovrebbero essere più o meno dovrebbero essere più o meno o meno ora, quindi alluminum quindi alluminum ancora è fcc ovviamente ebra è uguale a un atom ma zero zero zero e qui sono i tipi di gauscia i tipi di gauscia e ora mi faccio un esempio di gauscia e ok qui sono le esplanazioni e questo sarebbe il script quindi facciamo l'opera quindi si dice ok ora è un po' più lungo di you know on the slides because there are some comments and ok so you see a scan over key points a scan over different type of smearing a scan over different the gaus values and now this script take a while because it's a three dimensional and so there is quite a number of examples to run and ok so maybe maybe we just wait for this to finish it should not take more than several minutes I suppose and in the meantime let me check the slides ok yeah here it will be the result and so that does now I am at k point 12 I can read here and k point 12 is here so I am but of course each next is a slower calculation because there is a lot the number of k points goes up as we go from 4 to 8 to 12 to 16 and maybe in the meantime while this is running I explained a very let's say one feature of PWTK because usually when we scan these parameters maybe we do not know in advance what would be the proper range of a given parameter test and then if this is the case the PWTK is smart in a sense and so you see this comment here what I can do is I say restart true and then I can add some I can expand the range of a given parameter let's say just for the sake of example that I will expand the range of the Gauss and I will add here 0.15 and 0.2 now I will not save the file and later on you will see how PWTK deals in such case where we expand let's say a range of scanning of a given parameter ok now this is the first result this is a Gaussian smilling and so this would be results for the 4x4 came 4x4x4 kmash this is a result for 8x8 kmash this is a result for 12x12x12 and this is 16x16x16 and so the first thing here are several things to notice the first thing to notice is that for metals let's say for aluminum in particular 4x4x4 kmash is not ok because you can see you remember before for silicon 4x4x4 was already perfect here it is not you can see that the total energy for 4x4x4 is sufficiently different from these more dense kmashes and then you can see that as we increase the smilling these curves come together this is this is why smilling helps so with the smilling we if we use a sufficient smilling maybe we can use coarser kmash so you can see how this difference between let's say 4 on the other curves goes down and also how the difference between 8 and this very fine kmash goes down as we increase the smilling but as Paolo explained this morning this Gaussian smilling the total energy will be affected with this smilling temperature quadratically basically this is what you are seeing here now I can so here it says press enter in the terminal for the next plot if I do this now I have a Marzari Vanderbilt smilling and this would be the previous Gaussian result now you can see because now this Marzari Vanderbilt is what Paolo referred to as smart smilling which was devised to let's say be less dependent on this smilling temperature and in effect you can see in particular for this let's say 8, 12 and 16 how flat it is with respect to the smilling and you can also see this 4x4 kmash when we increase the smilling this let's say difference gets smaller and smaller and smaller so it's meaning the message would be if it's meaning I can use coarser coarser kmash and now I press enter again and here I have a Fezdar Paxton smilling which is another type of this smart smilling as Paolo referred this morning and you can again see it is much less susceptible to the smilling than the Gaussian smilling ok and now in the meantime I prepare the script where I will expand the range of these digots so I added two new values and I say restart people through and now I need to save it if I rerun the script you can see that PWTK is smart and say some jobs are already done and so it will do only those which were not already done and so this for the convergence tests can be quite a useful feature now this should be much faster because we have just two big house values to calculate over these different types of kmash and different types of smilling so I am at kmash 16x16x16 which means it should be over soon and now of course I really used very very large smilling this was just let's say as an example this 0.2 liter of smilling this is quite high value ok so this is Gaussian you see it even goes outside with this such a large smilling it goes outside the range now this would be marzarev underbuilt so you can see it is flat up to a given point and then it starts the energy starts starts deviating from and then if we go to marzarev so this was marzarev underbuilt and now we go to MacPherson Paxton we can see that in fact it is more or less for this dancer kmash it is flat up to 0.2 liter so but this is really going too far and so what would be the message the message would be that one can use one can use for example for aluminum some smart smilling like marzarev underbuilt or MacPherson Paxton with this meaning parameter let's say something in range of 0.01 to I don't know 0.05 that it breaks you can see here it is it is quite flat and maybe this 8 by 8 by 8 you can see how it goes towards dancer the result of the dancer kmash and maybe for aluminum I don't know 8 by 8 by 8 kmash is it depends on the economy if you want a faster calculation you can use it but if you want a very good calculation you would use something like 12 by 12 by 12 kmash ok so with this we have finished this example so we can say that we can use I don't know 12 by 12 by 12 or if we want to make it calculation a bit faster maybe 8 by 8 by 8 and smitting something like I don't know 0.02 or 0.03 or 0.01 and now we can go to the next example and now this next example is not about convergence test it is about post processing it is about how to plot charge density so this ch dense this is ch dense stands for charge density ok and now let me just shift back to slides so here you see these results that we just saw for the aluminum and then here is the description how to plot the charge density and the scheme to plot the charge density in quantum espresso is first make an sef pw.x calculation and then with the post processing code pp.x we calculate the charge density and then of course this charge density is written to a given file and we can use some visualizer like excrision to plot the charge density now this you see for the charge density we have in the pp.x some parameter which is called plot num and this is equal to 0 means charge density and this plot num can go I don't know from 1 to about 20 so it's a code and maybe this code is sometimes difficult to remember so what is plot num 12 I have no idea what is plot num 12 but suppose that I want to plot a given property and here it is this graphical user interface that is very very useful so pw GUI so I open it so this is usually how I do then I open a blank pp.x input file and here you see I have this plot num and suppose yesterday we did psi square so I click psi square and then I can go here to view input file and you see that for psi square the plot number is 7 so this is I when I do post processing I always do like that because I never remember what this plot num codes the other possibility is to go the other possibility is to go to description and then I go to plot num and here I have the description of the plot num so this is the other possibility and then of course okay with this now we will do charge density so I click on a charge density but then I need to specify the plot and so here are some data so dimensionality of the plot I say 3D format of the output and here I would say x-crease then x of a format who units it because this is super fast if you do 3D with this this is a slow option because here basically fast Fourier transform for calculating the density will not be used and this will be super slow this here basically in this fast option pp just dumps the density which is already pre calculated and now I can look how the input file looks like so you see I have plot number equals 0 and then I have the plot name list I have one file so the weight is 1 if like 3 so this is if like this is dimensionality of the plot and then format of the output 5 means x of a fast format because this will be really calculated quite quite rapidly with this now let us look let us look now I have too many windows is a bit difficult because I can just share one screen at a time and here we have two examples one will be charged density plotted with the use of zero potential and the other with the proper potential so it's a nice exercise you will notice the difference ok so here you will need to insert some values and then here you can see so this is the input for the pp and if I look here if like 3 if like 3 output format 5 output format 5 and then the file out is where to plot the charge density so it will be plotted in the file chdns.xsf and then the script will also execute x crystal with the same with the same trick as yesterday with with these orbiters with these orbital densities so there is a kind of a state script prepared so you squeeze them really immediately open and make a nice picture ok so here the comment says please insert smearing the Gaussian key points so smearing I don't know majority 100 the gauss zero point I don't know zero point two that should that should be ok key points now I think I can afford 12 by 12 by 12 this will be fast anyway and now I run this script so now it's doing scf calculation now it's doing post processing calculation so just to the scheme again first we do scf calculation in order to calculate to calculate to have a self consistent solution and then the pwx dumps files to the out there where there is a charge density by function and so on and so forth and then with pp we wrote read these files and in pp we instructed the code ok I want charge density and I want charge density to be plotted in 3D with x crystal format and ok this is now the charge density of aluminum and you will notice that there is no charge yet because black means no charge the the brighter the color means the more the electrons are there and you will notice there is no electrons around nuclear nuclearity and this is due to the use of pseudo potential so we will remember the talk of a Ralph Gevauer yesterday about this delta wave functions and so the answer why this is so is there and this talk and so for those of you maybe who are puzzled can go back and then realize why this is so and ok so this is this was just here what we see is a is a plane is a plane expanded on what is it 4x4 unit cell of of aluminum so maybe just to really give you the impression that this is a crystal but now we are looking at at the primitive right because the code calculate the primitive this does not give the impression that this is FCC right because the code calculate the charge density in the primitive cell which has just one atom in the cell and this primitive cell of the FCC is four times smaller than this conventional very nicely let's say tessellated unit cell ok now if we go back to slides you will notice here and then the example there is another example so I now run this one CH dense there is also example to CH dense no how is it called to CH dense pro and here we will use pro potential and so one warning when we will plot with this example we plot basically what we plot then you will find out this by yourself we plot all electron violence charge density so let's see what the number is this this is 17 and here I can see 17 maybe I should open it in max so the first is all electron violence you see plot number 17 and then eh we will also do all electron charge density so violence plus core this is possible with the plot and what number is this this is number 21 so if we go down you see here plot number 21 and but there is so when we use these features we should use a very large cut of energy for the charge density because if we look here at the charge density you can see these oscillations near the nucleus so remember the plot of around the power yesterday so there are these wiggles near the nucleus and to describe this with the plane waves we really need a huge number of them and this would be the all electron total charge density and now we really see that because the aluminum so let us open the periodic table aluminum has a 10 core electrons right and so these are located around the nuclei and so because in order to describe this we need a large cut off so here it is a 500 in Berg but typically when I use these features and when I want to calculate the bother charges for example from this all electron charge density difference I typically use 1000 ribber corso here I the example uses 500 ribber in order to be a bit faster but this is something that needs to be tested if you want to calculate the bother charge for example where you need this potential and all electron charge density you need to test what cut off should you use for the charge density in order to obtain the converged bother charges for example okay and then later on you will also run this example and you will obtain a picture something like this and something like that okay now we go to the last example of the day and this is a this is iron this is iron bulk iron and we keep if you look at the periodic table we see iron has three states and you will remember the talk of where have we have our yesterday 3D is a node less which means that if you would use uh noron consider in pseudo potential it would be quite hard and Ralph has very nicely explained yesterday this let's say smart idea of the ultrasound pseudo potential and for iron of course we will use ultra soft pseudo potential now iron is not an FCC but it is a BCC structure and a BCC structure has e brow equal three again uh so what are these numeric code for the e brow so we go we go to the firefox to the pw.ex explanation in the system name is e brow and you can hear see all these codes for the e brow zero is a free lattice one is uh primitive cubic two is FCC cubic three is BCC and so on and so forth is quite a number of uh lattices here okay and then uh what we will notice not only that we will now use ultra soft pseudo potential for iron but iron is magnetic everybody knows iron is magnetic and because it is magnetic we will notice a new variables in the input file and these are n spin equal to which uh is calling for uh which is let's say turning on spin polarization and then we need to set starting when the measurement magnetization we need to give to the code some input guess if you would say starting multiplication is zero we would end up with with a non magnetica with a non magnetic solution okay uh let me go back so i will close this so we are now example three iron and now there are two input files here inside iron afm and obviously afm is not the atomic force microscopy but it means anti ferromagnetic and afm means ferromagnetic okay so here okay first iron is metal so we have we have this occupation right then it is magnetic so n spin equal to and we give some initial guess for iron 0.6 this starting magnetization is from zero to one or from minus one to one if we have anti ferromagnetic and then as Ralf Gibauer yesterday explained if you see this US in the name of the pseudo potential then it is a ultra soft pseudo potential okay and so these are these new variables of today for this particular example these two variables now of course these magnetic business will be handled in more details next week but nevertheless let me just show you so how you do anti ferromagnetic setup and so I will open another input file and it is a it is very similar but there are important differences because now in bcc in the ebra 3 is bcc is just one atom per unit cell and because it's one atom per unit cell we cannot have two different atoms right so we can just with one atom per unit cell we can just have ferromagnetic so if you want to do anti ferromagnetic what we need to do we need to do in a sense a super cell which is twice bigger we need at least two atoms in the cell right at least two atoms in the cell and then we can say okay one is let's say spin up and the other is spin down or one is spin red the other is spin blue whatever you named it they have to be different and so for this reason what we will do we will take a primitive cubic this is ebra we call one and then there will be two atoms in the unit cell and they will be labeled differently you see with the same pseudo potential but we label it iron one and iron two and then we have two atoms in the let's say in the cell iron one and iron two and then we start we say okay starting manifestation of iron one is zero six and starting manifestation of iron two so the second iron is minus zero six and with this we have set up the anti ferromagnetic structure in a sense okay but for today okay you can do later on the exercise by yourself but now I will just run the ferromagnetic the ferromagnetic okay and so here okay let us just run this calculation so let me just for once open let me just for once open the rhythm file during the exercise okay so I can run the calculation oops didn't work okay I do it like that and this is what now I'm doing is another trick for those of you many of you know this so this I pipe to T and T will print to the file and to the standard output and so here if we look at output file you can see that it code prints total magnetization and absolute magnetization so we see to point something for magneton per cell which I think is not far from the experimental from the experimental value because we are now having the magnetic system okay now I think is a time we move on and we go okay here you will see the explanation for the anti ferromagnetic I will not do this example but now we go to the convergence test for the ultra soft pseudo potential you remember Paolo explained this morning when you have ultra soft pseudo potential for the charge density you will have two terms so you will have this let's say smooth charge density plus augmentation terms augmentation terms are much harder and requires a larger cut off for the for the charge density cut off and so here so what we will do we will scan different combinations of the wave function cut off and of the charge density cut off so these are these two e cut wave function and e cut row and so we go with dual dual is for historic reasons perché in the past in the very let's say initial versions it was e cut wave function and dual and the definition of dual you can you can see here it is just the wave function cut off multiplied by dual and this would be then the cut off for the charge density for the charge density in the past so it was wave function cut off on dual and so this is the reason I use here the name dual and so you see one feature of the pwtk you can write mathematical expressions and so we will look over a dual and we will look over over a wave function cut off so let me go to example so this will be example one so obviously it's just one script so I open it it should be the right one the right one because it's the only one okay so here you see so more or less the same as before but maybe a bit longer because we are also collecting collecting the results so dual from 4812 four would be default right because if you don't do not specify the cut off for the density it is taken four times that of the wave function right so this is here and eight and 12 is of course a higher number and then we will scan wave function cut off from 25 with a step of five down to or up to 50 okay so this is the script let us run it now it is running a bit slower because this zoom is taking apparently a sufficient amount of of CPU because when I test that without zoom it was much faster now we are in cut off 45 dual 4 so it will take it will take a while so maybe I should not wait I think I also have the result in the slides and the result is here so you see here the result and you can see for dual you could equal 4 this is the result and then for dual equal 8 and 12 the basically the two curves coincide and so what does this tell you this tells you the following if I want to use for the ultraswap for this particular case of course if I want to use dual or 4 then I need to go up with the wave function cut off to let's say 45 because here the two curves starts to coincide right but if I use a larger cut off for the density like 8 times or 12 times then maybe I can go down all the way down to 25 reverse and I can use 25 reverts for the wave function and then let's say 8 times that which would be I think 200 reverts for 200 reverts for the charge density and so okay what is the advantage the advantage is that in the code itself there is a lot of a lot of operation with the wave function a lot of FFTs with the wave function and much less FFTs for the charge densities so we are doing a lot of business for the wave function and much less business for the density which means that if I am able to go down with the cut off okay here now I have the result if I am able to go down with the cut off for the wave function the calculation will run faster so this is the benefit so use the one or use cut off for the charge density which is 8 times or 10 times that you see for this particular example 8 times is okay 8 times that for the wave function and you can go down with the wave function cut off substantial so here you can see that this 812 are coinciding okay okay so this was about this let's say business of wave function versus density cut off when use of zero potential and now we can do let's say some example some analysis some post processing for the iron and this will be so we will plot the density of states and the density of states projected to atomic orbiters so we will see some electronic structure of iron and we will see how this magnetic solution looks like so we go to this example 2 DOS and okay you can see dimify and obviously there is just one script which is DOS.PWTK so I open it and here it says please insert e cut of wave function and e cut raw values as determined in the e cut exercise okay let us do it so I don't know we could let us take certain index and then of course we saw that for the cut off we need face times that right so I just do as a mathematical expression be careful when you do as a mathematical expression you should not write like that so it should be together or as the PWTK we do not know how to interpret that so this works together this will fail and okay let us just what this example is doing so we load input file for the ferromagnetic iron which has which we have in the pattern directory then we set the proper wave function cut off on the cut off for density we run pw.x calculation and then we do then we do NSF calculation with a denser mesh because here if I look back let us see what was in this file it was 8 by 8 by 8 here I just do a slightly denser mesh to have a better dose I'm using a tetrahedral occupations this is a kind of occupation which was not covered today it is basically taking decay points and then it is making a kind of not a cubes but a tetrahedra and then it is interpolating so if you plot if you plot a mesh three dimensional mesh then you can do let's say a little cubes right from one to the next and then each such cube can be subdivided into six tetrahedra and then with these occupations tetrahedra basically we are interpolating between 2k points this tetrahedra sometimes is nice for density of states and then okay so we are running this NSF calculation then we are running the dose calculation so okay maybe this is a new code you never you didn't see it before it is super simple we can go here we click dose so we see it has one English dose and here are some variables it is the prefix anoudir by this prefix anoudir this prefix anoudir this pops up more or less everywhere because this prefix anoudir tells to the program where are these files that pw.x calculated right when it did this self-consistent field calculation and so this prefix anoudir will be here for these two weeks so more or less every code not all but majority of them okay and then we do this dose calculation and then there is another code which is this project that way function this means you also have it here this is a similar than dose code so dose obviously from the name it calculates density of states and then you can plot the density of states this projected way function also calculate the density of states but it calculates density of states projected to atomic orbitals in this particular case to loading orbitals and then you will see later on we can have this dose projected to diron these states dose projected to diron s states and so on okay so at the end it is also running this and then it is executing a new plot script and we will see we will see the density of states of fire okay so let us run this example now is doing scf now is doing nscf with a dancer with a dancer game mesh now is calculating the density of states and if you write to our files now it is calculating projected density of states and now here is the result this was the result of this was the result of of the dose calculation so let me try to zoom so what we see a majority spin and this is typically usually how one plot this let's say speed or and spin polarized cases let's say spin up or majority spin is plotted like positive and then minority spin or spin down and is plotted as negative and then you can see the two together right and so you can really see that this is a majority spin later we will also see what is the Fermi energy and it will be here somewhere I hope you see my mouse and so this would be vacant states and you can really see that minority spin we have more vacant states than with majority spin this just means that in majority spin more states are occupied than in minority spin okay now whoops I press enter and now I get density of states projected to let's say atomic as an atomic distance and this is this is typical iron is transition metal more or less the electronic structure of transition metal that it is similar in a sand what if you look from the from from the from far it is similar for all of them so we have a very flat S band that spans I mean now 10, 10, 15, 20 EV so here it goes from I don't know this is 5 down to 20 it depends how many states we calculate and and so you see S, S is this right and this and so in the S state we have two electrons right per et S has two electrons per et and so we have these two electrons in the range of 20 electron volts which is why the dose is is why this band or why the dose is very low so it's a very flat right here on the other hand in the D state we have 10 electrons and it spans I don't know from here to here this is roughly 4 electron volts so with the D state we have 10 electrons in the range of 4 electron volts and then it is obvious that the density of states will be quite high and this is precisely what we are looking at and typically transition metal black transition metals have one S electron one electron in the S band because the Fermi energy would be somewhere here we will do later on the exercise where is the Fermi energy somewhere here which means that roughly half of the band is occupied half of the S band is empty now to complete the exercise so here we did we did not see where the Fermi energy is right and now okay so how to figure out the Fermi energy well suppose that I am new with the quantum espresso I don't know how to do it because now everything is prepared I can look the read me file and there will be a recipe how to get how to get the Fermi energy so one way is that we grab this NSEF file this is one way and here I say that I got the Fermi energy is 12.8541 electron volts other way we will be to look at the the output file and maybe this I think was explained today with Paolo so we can we can look because now we are dealing with the metal so we have number of atoms in the cell one number of atomic types one because it's just iron right number of electrons it is 8 so how many conchamp states do I need to for 8 electrons obviously 4 why the code is taking the number of conchamp states equal 8 because it is a metal and we specified occupation or we specified explicitly the number of beds so this is also possible and I think this was covered yesterday by by Pietro del US so you can say number of states is that high but even for metals as soon as you occupy smiring the code will take some percentage larger number of states than let's say the minimum needed then I can go down I can go down and I can so I'm trying to find where is it where is it okay it is printed here the Fermi energy is so this the output is NSF calculation is a bit different than for the SEF calculation another way to find the Fermi energy I think was also explained yesterday by Pietro del Lugas is to look at the dose file and you have it here you have it here now we can edit the group plot file so all the group plot files I have the GP extension all the PWTK scripts has the PWTK extension all the inputs has a dot in extension all the shares script has dot SH extension so this is good to know because by extension you can you can recognize a lot of values and so here you see the instruction set Fermi energy to correct value okay so here I have it or if I lost it by now I look at this dose file it's here I put it here and then I can re-plot I can re-plot and now we can see this vertical line this is the Fermi energy and this is more or less where I showed before you with the mouse and this would be now this density of states projected to atomic estimates so this basically is density of states projected to S states and density of states projected to B states and now you can really see that this is this is vacant this is not occupied because we have the states occupied only up to Fermi energy and with this you can immediately figure out that this is really the minority display and this is the majority display so I think with this we have more or less completed completed the hands on for today so here you also have an explanation of the scheme how to do this dose in prior for prior wave function calculation so you have you need to do but I already described to you this SCF calculation with non SCF we have a denser K-mesh then we do dose projection project project the wave function calculation and so on and so forth so with this I think I am finished and and if there are some questions I can answer them and otherwise I wish you productive afternoons so that you will be able to do those exercises for those of you who did not follow me who have just listened me but I believe that some of you have followed followed me and have already completed some of those exercises so thank you very much for your attention thank you very much Tony yes there are many questions on Slack which have been answered by other tutors and other speakers and we have a few questions here in the chat do you want me to read them or you do yourself no please read okay yeah these are from the streaming the youtube streaming channel so the first one is for lattice parameter convergence should not be no okay this is sorry this question has been already answered by paulo here and in the Slack so we can go ahead shall we do k point convergence e cut convergence before or after this relax starting from the experimental strapper so the previous question was whether to perform the difference between relax and vc relax and paulo answered relax does not change the cell volume vc relax does it's an alternative procedure for simple materials the equation of state is simple and effective and then the question the following question is should we do the k point convergence e cut convergence before or after vc relax starting from the experimental structure so i think that in this case i think that the answer is is relatively simple so even if you take so for example we treated silicon and we treated iron and we treated aluminum so as far as k point is are concerned if you take a lot experimental lattice parameter and you you do a k point test i think that that will do that will do of course the true lattice parameter will be a bit different but i don't think this will change this will affect the k point convergence so as far as the cutoff is concerned it really does not depend on the structure because it's more atomic property so the cutoff for the wave function depends on which pseudo potentials you take so now for iron we took ultra soft pseudo potential if it would take anorum conserving the cutoff would be much higher and this cutoff is atomic so it depends on the pseudo potential and the lattice parameter doesn't really have a role here so i think that for both of course maybe with these k points we can we need to have some provision if if i compress the structure and for example the structure becomes metallic then yes then of course this k point convergence can be significantly affected because we can go from non-metal to metallic but these are let's say special cases normally i would say that this k point convergence does not let's say critically depend on the lattice parameter and taking experimental lattice parameter would be just fine this would be my answer to this and is it convenient is it convenient to do the convergence of e cut rho we've done that we've done that this was this dual so and the answer is here so dual so dual is let me open the window because you can still see my so we have e cut wave function right this is for the wave function right and then we have e cut rho e cut rho this is for the charge right but here in this example what we had so here is a here is a e cut wave function for different duals and so as i explained e cut rho e cut rho equal e cut wave function times dual so basically what we are looking at this plot is we could also plot this in two dimensions if we would if kind of plot in basically projection of three dimensional surface projected to two dimension so basically what we are looking at this plot here is wave function cutoff and then each curve here means a different in a sense a different e cut rho right because okay but it's case so for example for for a dual equal four this would mean this would mean 100 read back for e cut rho here it would mean 120 read back for e cut rho and of course 30 read back for e cut wave function and so on and so forth this point here so let me no now i need to okay suppose that this is a 12 curve right so this point here the cutoff rho is 12 times 25 this point here is 12 times 30 so in a sense we're doing this we have run both e cut rho and e cut wave function test and we have determined that let's say with dual 8 we can use e cut wave function of 25 and so at 25 with dual 8 this means that e cut rho would be 200 right so this we did in a sense thank you another question from streaming thanks well understood i agree maybe okay this was still related to the vc relax and i think okay here another one from streaming for systems with more than 100 atoms can you do vc relax at gamma point okay i i think so if you remember the talk of uh ralph ghebabri yesterday he he plotted these i think at the given point these k points right is a brianon zone and now the larger the unit cell right the larger the lattice parameters of of the unit cell the smaller are the reciprocal lattice vectors the smaller are the reciprocal lattice vector the smaller is the brianon zone the last k points now if you if you go back to the talk of ralph ghebabri where he plotted these k points and now imagine that you shrink the brianon zone which means that less and less and less and less key points are there and this implies yes for a very big super cell you can take a gamma point so a single k point if your super cell is super big a single k point is sufficient so you can take gamma point but of course so what would be what would be again this is something that is to be tested and suppose that we have for a cubic for a cubic for a cubic unit cell this is super simple suppose that my lattice parameter is a right and for this a lattice parameter we saw that we needed let's say for aluminum 12 k points right now suppose that I do a super cell and I do I do a 2a by 2a by 2a super cell now because my super cell is twice bigger this means that the brianon zone will be twice smaller per direction so I can take 12 divided by 2 for the 2 by 2 by 2 so I can take 6 by 6 by 6 now imagine I go to 3 by 3 by 3 super cell a 3 times larger cell means a 3 times smaller brianon zone per direction so I can go to 12 divided by 3 so 4 by 4 by 4 would be fine right then I go to 4 by 4 by 4 super cell which means 12 by 4 so 3 by 3 by 3 k points would be okay and now you see this is the reason why I like 12 by 12 by 12 k mesh so much because it has a lot of these divisors so you can divide by 2 you can divide by 3 you can divide by 4 you can divide by 6 which means that if you go from a unit cell to a 2 by 2 by 2 super cell to a 4 by 4 to a 6 by 6 you can figure out what would be the equivalent k meshes so for 6 a super cell 2 k points would be enough but if I do 12 a super cell then at this point because I saw that for example aluminum 12 by 12 by 12 k meshes enough if my super cell is 12 by 12 by 12 this implies that I can easily take a single k point and I will be at the same precision us for the unit cell when I use 12 by 12 by 12 k mesh thank you another question of course for participants since now Tonya has finished the explanation you can write here on zoom if you want some questions to be explained on voice by Tonya or otherwise you write tons luck in the way you are doing so far so here another question here for which total energy difference should I consider the calculation as converged is there a rule of or rule of thumb or some safe value that I can be satisfied with okay this is this is a this is um in a sense a tough question which does not have a single answer let's say there does a rule of thumb if you converge to a milli readberg per atom this should be more or less okay but uh so uh this should be tested in principle this should be tested for every property that you are interested in it depends on the context right it depends on the context now I wanted to say something more here I had in my but now I forgot what I wanted to say is another issue but I just forgot is another issue uh is another issue even can you repeat the question maybe sure sure for which total energy difference should I consider the calculation as converged is there a rule of thumb or some safe value that I can be satisfied with yeah so as I said it depends on the context so maybe one little bit per atom but then you can test for every property you're interested in but so even uh I'm sorry because I I wanted to tell something more but now I forgot what so I cannot remember I'm sorry you're the question didn't help if if I will remember then I'll be right on the slack okay no problem the question is are supposed to do slack on the two channel made in there is there is something more I wanted to tell but I'm really sorry I forgot why I was speaking yeah yeah sure we have slack and many other occasions so yeah no problem has uh now I remember now I remember so suppose that you have a semi core states uh in uh that you treat semi core states explicitly then these are these are uh very hard usually and if you would uh if you would uh want to converge the energy to within a million read work per atom then this would require a super high um color right in such cases maybe you can do another test so you're interested I don't know in in the structure or you're interested in in the cell volume you can instead of doing a convergence test with respect to the total energy for such a pseudo potential with the semi core states treated explicitly you can do a convergence test with respect to I don't know life is parameter with respect to forces with respect to to the property you're interested in thank you so another one thanks here for this great presentation can we optimize the atomic position and keep unit cell I guess yeah yeah this is