So, we will start on perturbation theory. Those who have already done 4 to 5 must have gone through a detailed perturbation. We will have a short review of the perturbation theory. But let me first tell that this perturbation theory can be used in quantum mechanics, in physics, even mechanics, engineering problems. It is a very general mathematical theory. It can be used in various fields. In quantum chemistry also, we can use it even to solve one particular problem. For example, if I give you a harmonic oscillator which is perturbed by an anharmonic force field, let us say x cube, then that x cube can be taken as a perturbation and you can calculate energy in what is called the orders of perturbation. So, it is not that perturbation theory is used for the improvement of Hartree form. It can be used in several problems. Right now, what we are going to do is to use perturbation theory to improve Hartree form. So, that will be our target. Can you look at perturbation theory as an improvement to Hartree form? And of course, when you say Hartree form, we have incidentally, you wanted to give the paper, did you give yesterday? So, can you give it to today with your doubts? To improve Hartree form for the many electron problem. So, I just want to revise the perturbation theory very quickly. I will not go through the order analysis right now, but let me tell you how the perturbation theory starts. It starts with a separation of the Hamiltonian into what is called a zeroth order Hamiltonian and the rest. Now, the idea of a zeroth order Hamiltonian comes from the following that it says that the zeroth order Hamiltonian must be such whose entire solutions, so let us say I am calling it psi i 0, must be known. Entire eigenvalue spectrum must be known. Of course, the underlying approximation assumes that I do not know the eigenfunction of the Hamiltonian. That is very clear because otherwise I will not do anything. So, I do not know the exact eigenfunction of the Hamiltonian, but I want to split the Hamiltonian into two parts. One part is a significant part H0 whose entire spectrum must be known. That is one of the preconditions of using perturbation theory. So, if you remember and then the rest is perturbation. So, V is perturbation and H0 is the dominant part of H. So, H0, I will lose the word it right now is the dominant part of the H, which means these solutions of H0 at least for the ground state is a dominant contribution to the ground state solution of H. So, let us assume that H has the solution which is psi i E i psi i and I order them as i equal to 0, 1, 2 etc. Such that E0 is less than equal to E1 etc. Similar ordering I can do here saying that E0 0 is less than E1 0 less than E2 0 and so on. Then what we are saying that since H0 is the dominant part of the Hamiltonian E0 0 is a good approximation to E0, psi 0 0 is a good approximation to psi 0 and we are only talking of ground state perturbation theory. So, we will not bother about the other approximations. So, that is the meaning of the dominant part of the Hamiltonian that the solutions of H0 are pretty good as far as the ground state is concerned, at least for the ground state is concerned. So, E0 0 and psi 0 0 are good approximations to E0 psi 0 respectively. Since we are only talking of ground state perturbation theory, we are not bothered whether correspondingly E1 0 is a good approximation to E1 or not. I mean you may also argue E1 0 is a good approximation to E1 and so on but at this point we are not bothered because we are looking at only ground state perturbation theory. I can only comment at this stage that the E1 0 is an approximation to E1 but it will not be as good an approximation to E1 as E0 0 is to E0. So, that is the only comment I will make. Beside that I will not worry about it. So, we must be able to write the Hamiltonian in this form that is our first job and then we will see the energy corrections and all that. I will actually since some people have not done perturbation theory, I will revise it again very quickly but that is when we require to do it. So, right now my first task is to have a Hamiltonian split into H0 plus V. Now, when you do that we notice that we have a wave function which is a pretty good approximation to the exact wave function. We already have a wave function. What is that? That is a Hartree Fock wave function. We have already done Hartree Fock. So, can I make Hartree Fock as a ground state wave function of some Hamiltonian? So, can Hartree Fock that we have done determinant be a Psi 0 0. So, I am now asking the reverse question instead of first finding H0. I already know that there is a good approximation to Psi 0 which exists. So, I already know that the Psi Hartree Fock can become my Psi 0 0 because it is a good approximation to the wave function although single determinant is not exact etc. It is a good approximation and from our experience we know that the E0 0 is 95 to 97 percent of the total E0. So, they are pretty good. They are higher than E0 but they are almost good. So, I can write Psi Hartree Fock as Psi 0 0 and somehow I should be able to get then H0. So, now can I rethink? Can I do a reverse manner that Psi 0 0 which is Psi Hartree Fock is not an Eigen function of H? I think all of you agree. Otherwise, we will not be here to discuss anymore. The quantum chemistry will be over. So, it is not an Eigen function of H but then we have to find out whose Eigen function it is because that will be my H0. Is it clear? If I know, if I can identify Hamiltonian whose Eigen function is Psi Hartree Fock, then I can think of that as a H0 and then I will see whether the entire solutions of that H0 is available or not because that is another condition. So, can you guess an H0 whose Eigen function would be Psi Hartree Fock, ground state Eigen function? Let us see. Who can guess? You have already done the Hartree Fock problem. Please re-look the Hartree Fock. Psi Hartree Fock is a slater determinant of spin orbitals. Those spin orbitals are Eigen functions of the Fock operator. So, let us say I am taking canonical Hartree Fock. Now, can you tell me what H0, what many particle H0 will give Psi Hartree Fock as a ground state Eigen function? Who can tell? Think in the reverse manner. We had a non-interacting theorem. Remember, we have a non-interacting theorem in which it says if an operator is a sum of some operators whose solutions are known, one particle operator, then the total Eigen function of that operator is a product of those one particle operators, one particle functions. So, now do a reverse analysis. I have Psi Hartree Fock which is a product of some spin orbitals, chi 1, chi 2, chi n. I know a one particle operator f of 1 whose Eigen functions are these chi i's. Now, can you tell me the operator H0 whose Eigen function will be Psi Hartree Fock? It is a very simple question. Sum of chi i, sum of the Fock operator. I hope all of you are able to think properly. Is it agreed? Because now we have a sum of the Fock operator. They have the Eigen functions of chi i. Hartree Fock is a product of that. So, of course, the Hartree Fock will be an Eigen function of H0. So, I can identify at least one H0. There may be others whose ground state solution is Psi Hartree Fock and what will be the Eigen value? E sum over E i. Is it clear to everybody? So, basically I am using the non-interacting theorem that H0 is sum of the Fock operator. Solution of the Fock operator is known. So, the Eigen function of this operator would be a product of this spin orbital. Of course, instead of product I am taking anti-semitic product, does not matter and the Eigen value will be sum of the orbital energies. Sum of the energies. Is it clear to everybody? So, now what I am suggesting is that we have got a Psi Hartree Fock which is not an Eigen function of the actual Hamiltonian. But it is an Eigen function of some other Hamiltonian H0. So, it is interesting that I have got a model Hamiltonian H0 whose Eigen function is Psi Hartree Fock with the Eigen value sum of epsilon i. Of course, this is a problem that we are not interested, but we have found a H0 to which Psi Hartree Fock would be an Eigen function. And we feel that since Psi Hartree Fock is a good approximation to Psi 0, exact Psi 0, the H0 is a good starting point for perturbation theorem. This H0 is a good starting point to do perturbation theorem. Is it clear the argument? So, why am I choosing this H0? Because this H0 has an Eigen function, ground state Eigen function, which is Psi Hartree Fock, which is a good approximation to exact Psi 0. Hence, we believe that this H0 can be a starting point to do a perturbation theorem. However, note one very important point here that the Eigen value of this problem is however not the Hartree Fock energy. And I want to repeat that because Hartree Fock energy and I have said this many times, the Hartree Fock energy has been defined as Psi Hartree Fock, 8th Psi Hartree Fock and which I have said many times not the sum of the orbital energy. In fact, it is sum of the orbital energy minus that over counted terms, half of whatever, Ig Ig at the symmetries. So, this is something that you must note, but I have no choice. You may wonder, can I get a H0? And I will come to this point whose Eigen function is Psi Hartree Fock and whose Eigen value is the Hartree Fock. That would be even better. So, I will come to that point if it is possible or not because that would be even nicer. At this point, I have something which is not the Hartree Fock energy, but let me start living with it first. So, what will I call this quantity? Sum of the epsilon i, i equal to 1 to n is by my definition here would be E0 0 because my definition of E0 0 is the ground state Eigen value of H0. So, what is my ground state Eigen value of H0? This is sum of the epsilon i which is actually E0 0. So, E0 0 is actually not the Hartree Fock energy unfortunately. So, that would have been a very nice idea that Psi 0 0 is Hartree Fock, E0 0 is Hartree Fock energy that would have been nice, but as I see so far it is not the case. E0 0 is actually just the sum of the orbital energy which is somewhat different from the Hartree Fock energy, but let us start living with this and see where we get. So, this H0 becomes a very nice starting point to do a perturbation theory. I have to of course remind you that there are another very important condition for doing a Hartree Fock that is I must have a complete solution of H0 not just a ground state solution. The ground state solution should be a good approximation to the exact ground state, but in addition to that and all solutions of H0 must be known. So, I have to now go back and see do I know all the solutions of H0. So, if you look at it very quickly the F has many solutions, in fact let us only talk of canonical Hartree Fock, F has many solutions N of them which are lowest energy are actually used in Hartree Fock to construct ground state, but there are other unoccupied orbitals through which I can construct others later determinants which I had discussed that all MCN determinants. If you now analyze this since all those spin orbitals are eigenfunctions of the Fock operator by very definition all those determinants are also eigenfunctions of H0, because all determinants are anti-symmetrious product of some set of spin orbitals occupied unoccupied altogether. So, let me write that down. So, I have MCN determinants, please note that the Hartree Fock itself I have not solved exactly, I have solved in some basis, m number of spin orbitals I have got whatever it is, actual Hartree Fock is infinity, infinite solutions. So, in fact everything I must also mention everything that we are talking is actually in a basis yesterday I mentioned this correlation energy as E0 minus E Hartree Fock or E Hartree Fock minus E0 depending on your sign. The point to note that this is exact energy this is Hartree Fock energy, but what is Hartree Fock energy? There is we are we cannot get exact Hartree Fock energy, because exact Hartree Fock energy will be obtained if I solve this exactly if I solve this exactly which I cannot solve, because for molecule I am introducing a basis. So, even the Hartree Fock has been approximated, even the Hartree Fock has been solved in an approximate manner. So, everything finally that we discussed is in a basis. So, this is in a given basis let us say m basis, this is also in a given basis, this is also in a given basis. So, when you say correlation energy that is also not a sacrosan number. In for a same molecule with a 20 basis whatever will be the correlation energy will be different from a 100 basis calculation, because all the numbers will change E0 will change, because when you do full CI your number of basis will number of determinants will increase if m increases. So, everything will change, but if you want exact values then all this m in the limit m tends to infinity everything will be exact. So, you have to go to the limit m tends to infinity in that basis then everything will become exact, then you will have exact energy exact Hartree Fock energy exact correlation energy. So, that is something that we do not do. So, it is important to realize that everything that we have been talking is in a finite basis. So, that is something that we have to leave you. So, with this finite basis we have only finite number of solutions of H0 which are all MCN. All MCN determinants are solutions, because they contain orbitals or spin orbital which are Eigen function of the Fock operator and my H0 is sum of the Fock operator. As long as H0 is sum of the Fock operators any product which is formed or any anti-symmetric product which is formed out of those Eigen functions of F are exact functions of H0. So, let us analyze these MCN determinants. One of the determinants is psi Hartree Fock. We have already said this. One of the determinants is psi Hartree Fock. What is the other class of determinants? Other class of determinants can be constructed in the following manner. Excite one electron from n occupied orbital to m-n virtual orbitals. So, I have n occupied orbitals, m-n virtual orbitals.  So, all possible psi AR, not one of them. Similarly, I can have two spin orbitals differing, A B to RS. I hope it is clear from the nomenclature and then you can have A, B, C, RS, T and so on, triples up to all n. How many I can excite? I can excite n. When all n have been excited that is the final thing. I cannot do any more. So, all MCN determinants I can categorize as first Hartree Fock with reference to Hartree Fock, singly excited, doubly excited, triply excited and so on up to n-toupley excited. So, let me write down those MCN determinants. So the MCN determinants, so let us assume that the Hartree Fock provides m solutions of chi i. That is the first assumption. Finite number, m solutions of chi i such that f of 1 chi i 1 is epsilon i chi i 1. So, that includes my occupied as well as virtual orbital. These m solutions, so m number of spin orbitals are now grouped into a subset of what I now call occupied n spin orbitals. Remember, these are one particle function. So, out of n spin orbitals I can actually have only one determinant for an n particle problem.  So, I have grouped them into two subset. One of them what I call occupied. Occupied by definition are the ones which constitute the Hartree Fock determinant. So, my Hartree Fock let us say provides m solution. m can be as large as possible depending on your basis whatever. So, then I have got n of them. So, let us say this is my n which constitute my Hartree Fock. So, together this is chi Hartree Fock. Note that chi Hartree Fock is not a orbital. It is a product of orbitals, a spin orbitals. So, all together is chi Hartree Fock. Then I have got m-n. So, rest of them are all virtual. So, this is a line. It is an imaginary line with a boundary between occupied and virtual. That is all. This is not an orbital line. So, many in solid state actually this is called the Fermi level. It is called the Fermi level in the solid. This is called the gap between valence and conduction band. So, this is the Fermi level. So, anyway in the quantum chemistry we do not call it Fermi level, but this is somewhere in between. Let us see. It does not matter. So, we then we are saying that all since there are m-spin orbitals I can construct m-c-n determinants. One of them is Hartree Fock and the rest can be generated by singly excited, doubly excited etc. So, lifting one electron from here anywhere, two electrons from anywhere here and so on. So, that is one way to look at it and maximum you will have all n lifted here. So, let us calculate the number. If you look at all m-c-n determinants they must be categorized only into these parts. With reference to Hartree Fock all occupied, one of them missing going to up, two of them going up, three of them going up, four of them going up and so on because there is nothing else left. So, if you calculate this number is of course one, how many psi ar is there? How many psi ar is there? n into m-n. Then I have psi abrs. So, psi abrs will be how many number? n-c-2 into m-n-c-2. Is it clear to everybody? Please those who are not understanding if you are in the back I want to hear your voices. So, how many ways I can lift two out of n? n-c-2 because I cannot lift from the same spin orbital. Obviously, two electrons are not there, Fermi principle. How many ways I can put them into m-n? This is m-n in number. This number is m-n, m-n-c-2. So, total number of determinants that I can find out is n-c-2 into m-n-c-2 and so on. So, triples will be n-c-3, m-n-c-3 and so on up to n-2 fully excited determinants. So, if I write this whole thing, there is a very nice mathematical combinatorial sum. The first number one can be written as n-c-0, m-n-c-0. So, it means by the same language or mathematics, I am not lifting anything and you can see this is 1, this is 1. So, 1 into 1 is 1, plus all singly excited, n-c-1 into m-n-c-1. I am writing everything in terms of combinator. Then I have plus n-c-2, m-n-c-2 plus n-c-3 and so on, m-n-c-3. This is number of triples and eventually I will go up to n-c-n, m-n-c-n and I will stop here. This is all the numbers that I have and the sum total of this number is how much? m-c-n. This must be because all the m-c-n numbers, I have grouped them in Hartree-Fock, which is just 1, plus all singly excited, all doubly excited, all triply excited and so on up to all n-toupley excited. All n-toupley excited, this is again 1, it is just m-n-c-n. In fact, there was a combination problems if somebody has done permutation combination, remember in high junior school, high school, wherever you have done it. This can be very nicely written as sum over r, 0 to n, n-c-r, m-n-c-r equal to m-c-n. They used to ask proof, I do not know if you remember, somewhere down the line you might have done. They used to ask proof this. Actually today you realize that the CI is just this we are doing actually. I am categorizing this in all singly excited, doubly excited. This was a math that was there. You can see the simple way to prove actually the way we proved it. Take this m, divide into two subsets and say that the entire combination is m-c-n and this is the different grouping. That is one way to prove this actually, this particular problem, but I think you have done it in many different ways. I do not know if you remember, at least I remember our time we have done it. Somewhere in the high school it was there, some such question. You have done more difficult things than CI. That is all I want to tell you. You have already done much more difficult things than what we will do. What we are now trying to say that CI is nothing but taking a linear combination of all such determinants. That is your full CI. You get what is called exact function, exact energy in this m basis. Of course we are never getting anything exact, remember. Whenever I am calling exact, it is in a basis, finite basis. Limit goes to m tends to infinity and that will go towards exact, only in that limit. Otherwise nothing is exact. This number of determinants can be categorized in this manner. Now our task is to come back to the problem. Do I know all solutions of H0? So I come back to the problem. Which means each of the determinants that I have written here must be an eigenfunction of the H0. That same H0. And quite clearly the answer is yes because they are constructed out of the same set of spin orbitals which are linear combination of the Fock operator.  So let me now write down what is the value. So let us say take one function H0 psi ar. This is an eigenfunction of H0, psi ar. Now can you tell me what is the eigenvalue? So how will you quickly write it? Some reference you have to use. So it is sum of all these energies of all these spin orbitals. That is clear. In the Hartree-Fock I had n of them. One of them is missing. A is missing. R is added. So the best way to write is the E00 which is sum of the orbital energy minus epsilon A plus epsilon R. This is nothing but sum of the orbital energies. Please remember this is nothing but sum of the orbital energies between i equal to 1 to n which are occupied in this occupied set. And then from there one of the A is always occupied. So again I remind you our notation at this stage. I am going to use A, B, C, etc. as occupied and then may be P, Q, R, S, T, etc. as virtual because now the notation has to be clear. So this is one of those n orbitals from where I have lifted the electron that is subtracted and to one which is added a new one virtual orbital that is added. So this becomes my Eigen value of this for this determinant. Eigen value of H0. And I can find out so on. Psi, A, B, R, S, all of them I can find out with reference to this. This is a very convenient reference because I do not want to write everything again. I will get lost. So this I know has all the Hartree-Fock orbitals energy summed up then subtract whichever has to be whichever are in the down. So if it is A, B, R, S, subtract epsilon A, epsilon B, add epsilon R, epsilon S. So that will become the energy of the WXRA determinant whose energy for H0 differs from psi Hartree-Fock energy by these numbers. By these numbers only the change of the orbital energies because for the ground state psi Hartree-Fock E00 is already sum of the orbital energies. Note that again please remember that E00 is not the Hartree-Fock energy however. So where is Hartree-Fock energy? We will see later. Everything is in talked in terms of orbital energies or sum of the orbital energies. There is nothing called Hartree-Fock energy yet. So please remember that. We will come back to that point little later. So I am now convinced that each of those MCN determinants is an Eigen function of H0 whose Eigen solutions are known completely. So H0 can be a very good starting point to do perturbation theory. So that is the first thing that I this H0 is a good starting point to do perturbation theory. Is that something that I want to first convince you? Then of course we will have to set the perturbation theory itself. How do I do perturbation theory? So first I will make a quick overview how the perturbation theory starts. So the perturbation theory starts with the following imaginary Hamiltonian H of lambda as H0 plus lambda. It is always good for those who have done it anyway. Remember good to have a small revision. Yes in that M basis of course. M basis you have only MCN number of determinants. Each of them can be written in some form like this and all of them Eigen solutions are known. Because there is nothing else. MCN determinants complete the full space. There is no other. So all of these determinants are Eigen solutions that it is not. And I am now if you are arguing that all these solutions yes, no it is only in this M basis. Everything is in the M basis and if M becomes larger then more solutions will come out. But then I will be able to find out because there will be also Eigen solutions of the Fock operator. So the perturbation theory starts with an imaginary Hamiltonian of this kind. When I have been able to separate a dominant part of H0 then you can very easily see that if lambda is 0 this particular revision I am doing little bit quickly because many of you have already done it. At lambda equal to 0 this fictitious Hamiltonian becomes the same as the 0th order Hamiltonian. At lambda equal to 1 this becomes a full H and of course at lambda different values they keep changing between H0 and V. So I can have lambda 0.5, 0.1, 0.2. So I can switch on the perturbation from lambda equal to 0 to lambda equal to 1. So lambda equal to 0 there is no perturbation and lambda equal to 1 I have got a full perturbation and I got the full Hamiltonian H. So in some way if you start from this switch from lambda equal to lambda equal to 0 to lambda equal to 1 you get the effect of the full perturbation taking place. Then what we do is to analyze the solutions of this H lambda. So if you look at the solutions of H lambda I can write in a very similar manner it will be psi i lambda E i lambda psi i lambda and I am particularly interested only in ground state. Again everything is ordered from i equal to 0, 1, 2, 3, etc. So I am particularly interested in H of lambda psi 0 lambda E 0 lambda psi 0 lambda and note when lambda equal to 0 the H of lambda becomes H0 and the entire solutions are known. Ground state as well as other solutions are known for lambda equal to 0 only but not for other values of lambda. So we will exploit these to find out what we can do. For the first order energy and that is what I will right now do it is quite easy to analyze this. So let me do the following. Write psi 0 lambda in general as a power series in terms of lambda. So at lambda equal to 0 its eigen solution is psi 0 0 because the operator becomes H0 its eigen function is psi 0 0. For all those I am actually addressing to them but for all those if you have doubt please raise hands you have done it already. Then I do a power series expansion. So lambda times some function which I call it psi 0 1. So this is basically a first order correction to this wave function and then I have lambda square psi 0 2. There are many ways of writing this. You can write a Taylor series expansion so that you put 1 by 2 factorial and so on. There is a mathematical series expansion. Each of these are called order corrections. So it is a first order correction, first order with respect to lambda. This is second order with respect to lambda and so on. Of course eventually my final solution is lambda equal to 1. So all these corrections once known the lambda does not appear. Only the coefficients will appear you know half one third one third three factorial and so on. Even you need not write this. You can absorb this in terms of psi 0 2. If you write only power series lambda square psi 0 2. This is a Taylor series expansion but does not matter. I mean that is sometimes even easier to understand. In the same way I can write E0 lambda as a power or Taylor series. So I can write E0 0 which is the 0th order for H0. Lambda E0 1 plus half lambda square E0 2 and so on. What is important to realize is that each of these are also derivatives of psi 0. Second derivative first derivative and so on at lambda equal to 0. I think you can do this expansion easily. If you take a second derivative of this what will you get? 2 lambda into 1 by 2. So that will become lambda times just this. So this psi 0 2 will then this lambda will also go in the next derivative. So you have 2 times psi 0 2. So that 2 will cancel out with 1 by 2 factorial. So you have just psi 0 2. So you have psi 0 2 as second derivative E0 2 as second derivative of E0 and so on. So each of these can be related to the derivatives of psi or energy with respect to lambda. So in some sense the order corrections are basically nothing but derivative corrections. More often we actually like not to put these factors half. We just like to write as a power series because they are just unnecessary terms. They can be absorbed in the definition. Then it becomes much easier to analyze this. Up to first order it does not matter. When you come to second order we will try to remove this. But right now we do not have to bother. We put this into this Strodinger equation. The main Strodinger equation for lambda and expand for the ground state. So what will you get? You will have this as H0 plus lambda E. Then psi 0 lambda will become psi 0 0 plus lambda psi 0 1 plus the rest. Rest I do not require right now. I will just write the rest and while writing the rest I will have to take care. If I am doing Taylor series or power series I have to be consistent. Then the right hand side similarly E 0 0 plus lambda E 0 1 etcetera. Again you write psi 0 0 plus lambda psi 0 1 etcetera. So I write this equation. Then what I do is to equate terms on the left and the right hand side. And I will get equation in orders of lambda. So the first equation that I get is H0 psi 0 0. Remember I am now first getting equation for lambda to the power 0. So I am extracting on the left and the right hand side terms which are independent of lambda. So I have only one term H0 psi 0 0. Rest have them all lambda. And the right hand side also I have got one term which is E 0 0 psi 0 0. This is no surprise because this is exactly the eigen value equation of H0. So it is a big deal. I have not got anything actually. But it is good to know that I have got what I know from this equation. What is important is the first order equation. So that is the first order perturbation equation. So that will now be H0 into psi 0 1. Note that I am not writing the lambda H0 into psi 0 1 plus what is the other term? V into psi 0 0. V into psi 0 0, good. And then on the right hand side I have similarly E 0 0 into psi 0 1 plus E 0 1 into psi 0 0. So this becomes the first order perturbation equation which will determine potentially psi 0 1 and E 0 1. That is something that I do not know. So I will get first order correction. And eventually I can write a second order, third order and get all orders corrections. So it is not really a big problem to do this. So what we want to do is to solve this first order equation. Before I solve this equation, I want to write this in a manner which I like better. That is to write this part on the everything on the left hand side. So H0 minus E 0 0 psi 0 1 plus V minus E 0 1 psi 0 0 equal to 0. You agree? So I have taken these two terms together. I have taken these two terms together. The reason I like this better because I can write it very easily from the original Schrodinger equation which is H minus E psi equal to 0. Original Schrodinger equation is just H minus E psi equal to 0. I am writing first order equation. So how do I write first order equation? First order of this into 0th order of this. Plus 0th order of this, first order of this. My total order has to be 1. So both cannot be first order. Then product will become second. So if you see this, the 0th order of this is H0 minus E 0 0 into first order of this. First order of this is V minus E 0 1 because first order of H is H0 plus lambda V. That is V. So V minus E 0 1 into psi 0 0 equal to 0. Actually you should be able to write second order onwards. We will do that in the next class. But it is easy to write it in this manner. So I just thought I will reflect you. Of course you could have argued that I can say H psi equal to E psi and do the same thing on the left and the right hand side. It is the same thing except that somehow I like it in this manner. I do not know why. So I have to now solve this equation. So for the solution to the first order energy is actually give away. It is a very cheap solution. Very quickly you can get and that is what I will do right now. And when you go to the second order I will come back to these equations again. So the way to solve this equation is the following. First you take this equation and project these with what is called psi 0 0 star and integrate. So how do you do this? You multiply by psi 0 0 star which is already known and integrate. So when you do the integration you have a scalar product H0 minus E 0 0 into psi 0 1 plus psi 0 0 V minus E 0 1 psi 0 0. Now you can quickly see that this part is 0 because psi 0 0 is an eigenfunction of H0 with an eigenvalue E0 0. So if you take the conjugate of that equation, you have already an equation which says H0 minus E 0 0 psi 0 0 equal to 0. So if you just take conjugate of this, this becomes 0 because H0 is a Hermitian operator. Of course I must say that when you split H as H0 plus V, H0 is Hermitian. Of course that is an important condition that you should remember. So it is a Hermitian operator. So this becomes 0. So I am only stuck with this final part. This whole thing is of course equal to 0 because right hand side is 0 anyway. So what I have now is psi 0 0 V psi 0 0 equal to E 0 1 because remember E 0 1 is a number and this is our normalized unity. So I just get psi 0 0 V psi 0 0 scalar product equal to 1. I will come back and make lot of other comments on how when I go for psi 0 1, how psi 0 1 is normalized to psi 0 0 and so on and those who have already done may recall intermediate normalization. But the point is I do not require at this point just for the first order. First order correction I do not care. They need not be normalized because that kind of terms are not coming. It will come for the first order correction to the wave function not for the energy. So up to first order correction to energy I really do not require to even assume that. So you can see that if I know the perturbation V and just take the expectation value of psi 0 0 I get E 0 1 and this side is already known. V I know by definition I have split H is H 0 plus V and this I already know of course because I have started with H 0. To get E 0 1 I really do not need to do anything. So now I will do this for my Hartree-Fock perturbation. So note that what is psi 0 0 psi Hartree-Fock? V psi Hartree-Fock equal to E 0 1. Let me write it down E 0 0 once more. What is E 0 0? Psi Hartree-Fock H 0 psi Hartree-Fock. Do you agree? Note that sorry note that Psi Hartree-Fock E 0 0 was an eigen function of eigen value of H 0 with psi Hartree-Fock as eigen function. So I can also write this equation. So if you remember H 0 psi 0 0 which is psi Hartree-Fock is equal to E 0 0 which is sum of the orbital energy psi Hartree-Fock. That is a ground state solution for H 0. So if I take an average value of H 0 with respect to psi Hartree-Fock. So integrate after projection with psi Hartree-Fock star then this psi right hand side will also become psi Hartree-Fock psi Hartree-Fock which is normalized unity so it is E 0 0. So this is another way of writing E 0 0 which is a ground state solution of H 0 and I can write it in this star. So if I put this together E 0 1 becomes the expectation value of the perturbation operator and the E 0 0 was the average value of H 0 both with respect to psi Hartree-Fock correct. Is it agreed? Because that is a trivial any eigen function solution any eigen value solution will always satisfy this. So that is a trivial nature. Add these two. If I add these two what will you get? You will have the operator added right everything else is the same. So you have psi Hartree-Fock H 0 plus V which is H psi Hartree-Fock what is that? Psi Hartree-Fock star H psi Hartree-Fock integration what is that? E Hartree-Fock remember we are struggling to see where is E Hartree-Fock. If you add this my left hand side is E Hartree-Fock and that is nothing but E 0 0 plus E 0 1. Remember we said E 0 0 is not E Hartree-Fock and we are very unhappy that my 0th order wave function is Hartree-Fock wave function but 0th order energy is not a Hartree-Fock energy. But now I am contending that with that H 0 perturbation if I do the first order correction and add the first order correction then I will get the Hartree-Fock energy because if I add H 0 plus V that is H and psi Hartree-Fock H psi Hartree-Fock is E Hartree-Fock. So together I get the Hartree-Fock energy yes no no no no I have not made any such statement. Where is the first order corrected wave function required here? So the question that is asking is the question that I asked can you find a Hamiltonian for which psi Hartree-Fock is an Eigen function and E Hartree-Fock is an Eigen value? Obviously the solution that I have written for H 0 it is not it is not. So I will come back to that how to do that in the next class yes that is something that is there but even if I have not been able to do I can recover Hartree-Fock energy by adding E 0 0 plus E 0 1 which means after doing first order energy correction I have actually got Hartree-Fock. So till now I have done nothing it is just to give you a comfort level that the Hartree-Fock is there somewhere it is not lost. So any improvement to Hartree-Fock energy any correction any correlation energy calculation will now start from second order and that is the reason you find that the first correction that you talk of is MP2 you never talk of MP1. So I just thought first I will tell you because the perturbation starts from a different point of view where the 0th order energy is not the Hartree-Fock energy 0th order energy is only some of the orbital energy after I added the first order correction I get the Hartree-Fock energy and hence the correction to Hartree-Fock energy which is what I am looking for actually starts from the next order. Now the question that I asked is that can I have H 0 for which Hartree-Fock energy is a 0th order solution. In that case my correction will start from first order I will come back to that question. So you may still say why there is no such theory where something dash 1 is a correlation correction you know we will come to that later. So I hope it is clear I have not written explicitly how V looks like we will do that in the next class how does V look like remember V is not just 1 by Rij what is V? V is V is H minus H0 what is H you should be able to write H is sum over H of I plus the average operator or the Fock operator let me call it now V Hartree-Fock. So this becomes my H0 sorry I should have written it later. So sum over H of I first I am writing H plus 1 by Rij correct that is my H minus H0 which is sum over H of I minus sum over Hartree-Fock potential I call it Hartree-Fock potential and this Hartree-Fock energy or Hartree-Fock operator will include the Coulomb and the exchange operator. So integral phi for Kij star 2 1 by R1 to all that is Kij 2 d tau 2 that is all stuck here in the Hartree-Fock potential. So if you see this part will get cancelled but your V is actually not 1 by Rij sum of 1 by Rij V is sum of 1 by Rij minus this Hartree-Fock potential and that is understandable because you have already added to H to your original sum of the one electron term this Hartree-Fock term in the H0. So when I do V your 1 by Rij must be reduced by the same term otherwise you will be over counting that Hartree-Fock potential. So I will write down formally what is V and then we will try to analyze what is E01 because although I know that together it is E Hartree-Fock I must say what is the difference of these two and of course the difference of these two you must now know already because you know that E00 is sum of the orbital energy. You know the difference from orbital energy to Hartree-Fock that must be E01 but I must get it by the application of this later rule also by allowing that V to act and so that everything should match. You already know how to get it. E Hartree-Fock is E00 minus half of I g, I g anti-symmetry. So you already know how to get it and we must get the same result by expanding this and adding to E00 we must ensure that you are getting Hartree-Fock energy. To do that I have to do a detailed analysis of V so I will start from the V but at this point I just want to mention that if I do a first order correction to the energy add that to 0th order actually get Hartree-Fock energy and hence any correction to Hartree-Fock energy any correlation energy contribution starts only from second order. This particular separation of Hamiltonian into H0 plus V was actually first done by Meuler and Placer. In the next class I will give the actual reference for those who are interested can also read the Meuler and Placer's original paper and there are lots of variations to this. One of the variations is what we discussed. Can I have H0 whose Eigen function is high Hartree-Fock whose Eigen value is E Hartree-Fock and what happens then for E01? Then I should have a correlation contribution from E01. So why is it not being talked about? I will say that in fact it is possible to have such H0 but we will see what happens to E01 in that case. So there are lots of variations to Meuler plus H but this is the beginning where H0 is just some of the Fock operator V is the rest so basically V is just the sum of 1 by Rij minus the Hartree-Fock potential. This is what I call Hartree-Fock potential in the Fock operator. So basically I have written one particle Fock operator as H plus V Hartree in a very simple manner. So that V Hartree-Fock has all the terms from other case so that has to be self consistently evaluated but if I write it in this manner this becomes my capital V and I will come back to this and evaluate this psi 0 V psi Hartree-Fock V psi Hartree-Fock and see that this actually gives me Hartree-Fock energy by even application of slater rule. I can use slater rule for this and you should get the same value that you know you should get. So we will come back to this.


Yeah, hello, I'm John from next job and also from open source design So I would just talk about combining two of the projects that I'm working on I want to have stickers later if you want to get some Gotta keep the sticker economy going So in this talk I'm going to show you five strategies By no means all, but five strategies that we're applying at the next job for open source design So first if you don't, like, can I have a show of hands when I know what the next job is? Okay, so most people, but I will explain it of course So next job essentially is a full suite of tools for keeping your data private within your organization or your personal data So we have file syncing and sharing, we have calendars, contacts, video calls, chats All sorts of things, we have an office suite, which is a bit of a collaboration We also have a bunch of AI integration, which is on-premise So you get the benefit of AI, but on your own server And yeah, it's kind of cool So, yeah, if you want to connect, there's my website, all the info is there But yeah, let me show you what I actually came here for So first strategy is structure So this is essentially like sort of the least you can do Or where you can start kind of category If you are an engineer, developer, or someone who has a project Or if you're not a developer, if you're someone within an open source project Then the basic thing you can do is give visibility to design And also to ensure that there is a place for designers that they have When they come, that they know where to continue or what to do And I will even show you some examples So one thing that we do, one of the first things that we do and what I always recommend to projects Is that you have an issue tag called design And I mean, some projects called UX slash UI or whatever, some people have different tags I just keep it simple, we just keep it simple in our project Just call it design, so just one design tag It's across the repositories and that's where you find the design issues That's where we open the issues That's where other designers can find the issues And that's where you can get started also, for example You can of course combine it with different other issue tags Like good first issue that you might be aware of that Which is an issue tag that can be used for people just getting started So if you combine design and good first issue You get good design and first issues So that's pretty cool And that is a really simple thing you can do in your project So if you don't do that right now, do it Yeah, first thing to do It's going to get harder now, but with the simplest one So next one is grouping design And this can be done in any sort of way This is one way we're doing As I said, next up is this whole suite of applications One thing that we have is the next up talk This is our chat and call and video call software And here we have a conversation called design to the public On our own instance This one, as it says, it's public, you can also join You can go there from next.com.com.slashdesign And this is a place where we group design So where you can join as a designer We're also a lot of developers hang out So people exchange information And yeah, just talk about design It's sort of, you don't have to be a designer To be in this group And there's, of course, other places as well Where you can group designers Like on GitHub or on whichever issue tracking system you use You can have these groups like apps We have apps to next talk slash designers So you can mention an entire group For review, for example, you can request a review from the designers So grouping people, giving them sort of a place to chat And not only among yourselves, but also with others With the engineers As something, for example, previously in this talk I said it's very important That design is not just a handover process But it's an iterative process Especially in open source Where there's traditionally very few designers Has to be very collaborative Then the third example For this section is the last example It has specific pages So this is our design page It's next.com.slashdesign It's not the whole page, of course It's more here with a whole bunch of text And info, a lot of what I'm talking about now Which serves as sort of an entry point And then a more advanced thing And yeah, this is probably a bit more difficult If you don't have it yet But it's having design guidelines of some sort Having components Having just saying, hey, this is the brand guidelines This is our logo These are our colors This is what we use Wording guidelines Is also something that is not very often used They're like being friendly Or which type of capitalization You use or which kind of language you use And they're like not of language As in English or German or whatever But which kind of type of tone You're friendly or you're serious and so on It's also very interesting to have guidelines from that All right, so that's the first one Having a structure The next one is having a process And making that process open So in this section we'll talk about specifications And mockups, how we do that And how we involve engineers and iterate Again, coming back to this, it's a very iterative process And a very collaborative process And some examples for that As I said before, we have labels here This design label There's a whole bunch of other labels And this is a specification That is done where the developers are on GitHub now So this is for an improvement to a sharing design A flow that I wrote You see specification, first a bunch of text Down here there's some mockups And then there's some more text So it's a place where developers work It's on the issue tracker Where we also do the design specification It's very important because then everyone gets involved And it's not a fixed thing Then we're done with the mockups And then we throw it over the wall But it's like, it's a discussion Yeah, so specifications and issues That's a very important one Next example is maybe another software It's called PenPot It's basically an open source mockup tool You can also use it actually to create slides My colleague Namisha actually does her slides with it These slides were not done in the LibreOffice But she does her slides with PenPot Which is very cool So it's sort of an alternative to Figma Or Miro, these whiteboarding tools And we use that for mockups And it's very cool, very useful open source And I can only really wholeheartedly recommend it And yeah, we also do that in the open And so we invite new people who want to contribute And we also invite developers So yeah, because we're two full-time designers On the team only, with a lot of engineers But there's a whole bunch of people in this PenPot organization And you should be very liberal with inviting people Because then people can do stuff by themselves Yeah, developers of Groupware, for example Can do mockups Or any developer can mock up their own app, their own feature And then you can talk with them and do some modifications And that way you sort of teach designs well Which is a very important thing In tool Next example, or not next example So this was the last example for design process Next strategy is research And especially in open source Yeah, we don't have a lot of resources We're very, it's not a very small community And thankfully we're growing and we're big As you can see from the conference But designers in open source are still fewer So it's very important to use existing material And to also maximize the limited resources that you have And by that I mean, yeah, you can just get inspired a lot I mean, as everyone does, as every project does You look at other projects, you look at what works A lot of projects, in closed source projects blog about their usability tests Or about their design research There's a lot to learn that is out there And you don't need to always start from zero So, so again, here for our Next Cloud Talk app Which you see in this column There's a lot of nice green checkmarks Because we have a bunch of cool features that others don't have And we did this gap analysis with other solutions Like Microsoft Teams, Zoom, Google Meets, Slack and Discord And we also did others, of course, but these are the main ones And we just did a simple overview And this gives us a feeling of like Where are we missing things? Where are we positioned very well? What do we need to look into? Because then we would just, for example, yeah The last one is the disposal of the meetings Yeah, you see there's already an issue created for this We don't have an issue, yeah And then we would go to the other solutions Look at how they do it And simply see if there's like sort of a common thread That we can build on That we can sort of, yeah, make it look very similar Also to pick up people who are switching To an open source solution from a proprietary solution To make it look simpler As a next example, there's usability testing This is, of course, a bit more of an investment In this case, this was done with a partner organization sort of It's a usability agency or design agency Open source design agency called Pula Design And they did usability testing for our forms app For our next-gen forms And this, I think, is a very cool display of results, yeah So basically, you see it was done with five participants One participant per column And a bunch of tasks You see the first tasks were rather easy, yeah And then here, chairing the form was an issue, yeah So you immediately see if this is something you need to fix now And so it shows you immediately As someone who is not involved with the project Yeah, where the difficulties are Which is also very good, very important Because you as a person who works on the project You tend to not see the issues So usability testing is really good A really good tool And it doesn't have to be with five people Yeah, it can be three people Yeah, three people should be the minimum, I would say But it's, you should do it Agencies do it with 12 people That's like, yeah, you don't need that But just show it to a few people who are not so technical Yeah, to a few people who don't know the project To a few people at the conference, for example And just, yeah, see what they all they use it And then don't help out And let them make mistakes Because it's not their mistakes, it's mistakes with your software You already see that I can do it We'll talk about just what we did to test them But then we'll continue Next thing is surveys It's a very quick tool to see also, yeah Where you stand with your, with issues With features or anything Of course, this is more of a quantitative approach Where you just get, like you should get a lot of responses Where usability testing is quantitative So you get one-on-one feedback This is a quantitative approach So, yeah, you should get, you should spread it far and wide And you always need to be aware of a bias So if you, if you tweet it from your project account Maybe the people who are replying They already know your project well So you need to just keep that in mind, you know But yeah, you can also do that with next law forms Yeah, we have a forms app which is open source Google Forms And we periodically do surveys for next law apps Like about our Kanban board app Or about next law forms itself Just like here And this helps a bunch to just see, yeah Where we stand and what we can improve And what people are expecting So then, yeah, that was that with research Now we come to the fourth point Community It's one of you, hello So it's very important to get people, yeah Excited about design and involve a wider community Not just as I said before Not just the designers Or the people who would identify themselves with designers But also the engineers Because everyone sort of can, I mean You would think almost every engineer has something to say about design If you look at some open source communities So you should channel it into the right avenues So let me give you some examples We have lists from out of just talking with people At our next law conference in person And giving them design reviews We have a regular design review call every week It's at Tuesday at 2pm or whatever It doesn't really matter Yeah, except if you want to join You're very welcome But we have a weekly Regular review call for one hour So it's not that long So that's a short regular review call For anyone who wants their design reviewed In the community It can be an app that an employee works on Or a community member, whatever But we have this open forum sort of And where also everyone can join Yeah, it's a Whether a designer studied or whatever Or an engineer or a marketing person No background whatsoever Yeah, it's all cool Everyone can give feedback on what's off Or if something is weird or not understandable So this is a very, very cool tool And then we take notes during the calls And they're then put into issues Then sort of a checklist That's a Directly a checklist for the developer What is very important is that This needs to come Like you need to involve the people The maintainers of the app So the developers need to come to you You can't just do this review without them present And then give them a list This is a recipe for disaster Essentially So what this is We're just very open We ask like a lot Yeah, we have to ask a lot again and again But when people come It's usually very helpful to them And yeah So that's one example And I can really recommend it If you want to get involved also Come join this course Next example And this is a very current one Because you can actually participate This is something that we posted about yesterday Because for our current Next to Hub 5 development cycle We're looking for you to design Document templates So we have these I mean when you create a new file Create a new document Or presentation Or a card sheet Or a drawing document We have these templates Yeah So these are two templates that I actually designed Yeah Captured rather simple Because creating templates Actually very difficult But maybe you have some cool templates Maybe you have some nice ideas And you can submit them So this is a current community contribution effort Yeah, you can go to next.com slash blog And there's a post with more info on that Would be cool to have your designs submitted to them They will be It's much like the Maybe you know from Google to the Or some other open source projects I think this background For background It's called Background photo submission process Yeah For the desktop background So in this case it's a document template That will be shipped with maximum Yeah So yeah community involvement Very important And then like that You can grow a community And make people like at the very least Even if they don't join It's first you have a very cool template And they can say hey I contributed to an open source project In a very visible way And it's a very cool thing That they can show their friends And then maybe they can work So yeah Next thing And this is the last strategy Is collaboration Because I mean we're open source Yeah, we're all here But I often see And what I've seen through the years Basically of working in open source Is that oftentimes the projects Are still very insular I mean oftentimes there's collaboration But more often than not It's sort of a very very I mean I don't want to say world guard I mean because that has a certain connotation But you need to understand That you are not the only project There's a whole bunch of other projects out there That you can do cool collaborations with And there's of course also community developers Which are not necessarily in your direct sphere Of influence So let me show you some examples So for example with Collabra We will probably know They will be in our office online And Collabra will partner it To create next cloud office This is basically built on Collabra online And we work very closely with them Yeah, we will call every week To do adjustments And to see what a very interesting strategy And stuff And really helps us to integrate Very very very closely So you have a very nicely integrated Office suite Directly inside next cloud And they also get a lot of feedback From our side And this is really a very cool partnership We have because we both Yeah, we have a limited amount of designers But every time we do like this ping pong Among us we get new ideas and everything It's very cool So partnerships with other projects We really really recommend This is the first example So the next one is community developers So we have our app store Our next cloud app store They see community apps like Forms that I mentioned before And next cloud maps actually Tasks in this case And the next one news The news reader like As to Google news That they shopped on a few years ago And so these community developers Also often come to our design team channel And ask if they can have a design review And then it's very useful for them Because then we do the review And we have a bunch of other people Who are also engineers Or developers from other apps And they say oh but in my app It's different or in my app We do it like that And that way even It gets like sort of Gets consistent Without the desires necessarily Always having like The funds on it And so it creates this exchange Between the maintainers of the different apps as well So the For example the different Android apps Or the different iOS apps from next cloud They all exchange sort of They're like oh this is how you do it Oh yeah we have this library and so on So this is very cool And creating this flow of information Between the teams as well Then next example And the second to last example I think Is the GNOME online account So probably no GNOME The open source desktop Has this online accounts functionality Which I think is super cool Because this is also in Google actually Immediately when you install it When you start it for the first time You see the screen And you can add an account So of course they show When you see the sign on And then Google is popular But then they show next cloud So you can add your next cloud account Directly when you install your system So this has been an effort Like I actually initially started out In the GNOME community sort of Because they are very designed For the community Really like thanks to the GNOME community I have to say Because a lot of these techniques Are also inspired by GNOME And so this Yeah it's already there since a long time Comes through partnership to talking with them And we're always trying to link up more apps So that they can be synced Because like that you have a whole experience Yeah just like I mean We need to compete against the lights of Apple Which sync everything You don't even need to think about And we have the moving parts We just need to talk to each other And make it work So this is another very cool thing Yeah just talk to projects that are relevant to you They do similar things Just on a different platform On mobile and desktop or whatever And make it work Last example Or last yeah Last example I would say The open source design community As I mentioned that Samsung as well And me are involved in We're a loose collective of designers And developers as well Anyone who cares about design And open source And wants to raise the profile of it You can join Yeah anyone of you can be part of it We're at opensourcedesign.net Now you will find this page We also have a job award You can find job postings From open source companies About design roles You can post one Yeah if you need a design Yeah you can find a job We have a forum where you can get involved Yeah so engage with the wider audience And come to a conference like this I don't need to tell you all that But yeah And that's that To get involved at nexthelp.com slash design Or get involved with any open source project As a designer yeah We need more designers In open source And yeah So come to Nexthel Or come to open source design And get some stickers Thank you Thank you Thank you Thank you Thank you Thank you for talking to me Yeah are there any questions Thank you Thank you So I'll give you the So you mentioned in strategy number four That you have a conference for every Tuesday At central european time Yeah so that's why I said like The time doesn't really matter Like in our case Unfortunately it's central european time On tuesday it's two yeah So it's Spring is really out Exactly yeah So I was actually in japan for two and a half months Just just now So it was in the evening like at 10 I think So I mean yeah I participated But it's a tough thing So what you could do is like Depending on how your community is Is distributed Like for example with open source design We have a monthly call And we have two Yeah we have one For like more european Equest sort of Time zone African time zone And one for more asian Sort of pacific time zone So you could do that for example Yeah it's unfortunately Time zones I think so And yeah That's a glow right I mean we're not on a flatter What more questions? You mentioned about the design of the process So are those limited to be nice Cloud projects that you take with it Or any teleprompter that can come at it That's for a new Yeah so in our case In the design we recall that I mentioned Those are specifically related to next-told And next-told apps But with open source design for example We have a forum So you could ask for a review there Or we're often at conferences For example I mean we also had a track at FossAsia I think in 2017 And we should get a booth up and running again Maybe next year But we often do We have a track every year at FossDamn Actually in Brussels And there we sometimes also have a table Where we have people come to us And they can do ad hoc reviews I mean you can also Maybe just I don't know what it's like I'm just going to say you can come to us And just ask it Like if we want to have a look at your app And we're going to give you some hints or something Right? Thank you


If you're a fan of music and technology, you've probably used Pandora, maybe even today, maybe even right now. I hope not. Please be listening to the Future Music Summit. If that's the case, you'll probably want to hit pause, as I said, and tune into this conversation. With all the media focus on rate setting and the future of online radio, we thought this was absolutely the perfect moment to hear from Pandora founder and chief strategy officer Tim Westergren. He'll be joined by Chicago Tribunes Greg Hott, who we know can ask all kinds of questions. Musicians and indeed the musicians care about. We're thrilled to have both of them with us here at the Future of Music E-Summit. So please join me in welcoming Tim Westergren and Greg Hott. All right, good. Thanks for getting here early. I think it's a great forum. FMC is a great forum to have a hopefully rational discussion about something that stirred up a lot of emotion in the last few weeks, for sure. Tim, let's get a little context first. 2000, you co-started Pandora. And very much different landscape than a lot of promise, but a lot of doubt about whether this thing, this entity, would even make it. So congratulations for even getting your company here today, still alive. I can't imagine how many startups there were in 2000 that didn't make it. Tell us about the business model then and now. How has it changed? Well, it's pretty radically different. We didn't actually launch the business thinking we would become a radio product. We built what we thought would be a recommendation technology that we'd license out to other services that had their own consumers that needed navigation. And it took us about five years sort of wandering in the wilderness before we realized that the best use of our technology was in the world of personalized radio. That really came about partly through sort of thinking about our own product, but also looking at what was happening with infrastructure and consumers and broadband penetration and so on. So it took a while for the market, I think, to be ready for it. And it wasn't until 2005 that we kind of came to that decision in 2007 when we actually launched the service. So it's been a long, circuitous path, for sure. Now, we had a conversation in, it's been a decade-long process. I mean, there's no way to sugarcoat that. A lot of years of struggle, I would imagine. I talked to you in 2009, and even though Pandora at the time was obviously a growing business, you were saying at the time it was not a profitable one, you said you were losing money at that time. What's the reality now? We're kind of keeping our chin just about the waterline right now. Like when we last spoke in 09, it was on the heels of the first major decision to come out of that copyright royalty board for Web Radio. And the decision that came out then, which was ultimately reduced after a lengthy lobbying and renegotiation effort, that original decision would have put Pandora under. Without a doubt, it would have eaten up every all, if had that been in place and had we been operating under that ruling, we would virtually all of our revenue would be going to royalties right now. So it was a sobering experience to go through that. We got some relief through the subsequent negotiation. And what that left us with was a survivable rate, is how we would describe it. But the business now still really struggles to make ends meet. Now there were some numbers put out. You had your IPO, your initial public offering, last year. Some numbers associated with that. I've heard figures of the company being valued at $2.5 billion. And you can correct me on these users, tens of millions of users. I've heard figures 55 million, 80 million. People look at those numbers and say, man, this guy is kicking butt. He's got a seriously working company here that's making money. Most record companies today would kill to be valued at $2.5 billion. You might be able to put them all together. I'm not sure they'd be worth that right now. Irving Azoff, that genius of the 20th century record business, had some caddy remarks to make about that a few days ago. What's the reality of that? The perception versus your reality of where the company's at? Yeah, so it's kind of a Jekyll and Hyde business. I guess you could say that on the growth side, it's been a wonderful story. Our listenership just keeps exploding. And so does our revenue. I mean, Pandora has been doubling its revenue every year for some time. And that's been a really good story. Profitability is a completely different story for us. We're really struggling to make that happen. Although I think that for this topic of webcast rates, I think focusing just purely on Pandora's profitability misses, I think, a larger picture, which is Pandora is essentially all alone in internet radio right now. We have 75% market share of internet radio. And I think if you measure just music, it's probably higher than that. And I think any economist would tell you that's a sign that something is broken, that you have one company that has such a huge share. And it's because nobody wants any part of this business. Everybody gets to read our quarterly statements. And most businesses are reluctant to enter it. And not only have there been some large technology companies, Yahoo, MSN, AOL, who had large audiences and essentially walked away from the business, you've also got broadcast companies who are avoiding it. And to me, that's an enormous signal, because I think you could argue that radio is on this inevitable march to internet-connected delivery.  And in spite of that, they're sitting on the sidelines by and large. I mean, Clear Channel has made some efforts, but I think that the last seven years for us has been notable for the lack of competition. I think that should send off alarm bells. All right, so alarm bells, a lot of alarm bells went off a few weeks ago. In my gut, anytime the government gets involved in anything, I'm right away throwing up the red flag on what's going on here. Why? Internet Radio Fairness Act is now a bill before Congress. Whether you want it to be or not, you've become the public face of that bill in some ways.  You're a supporter of this bill. Explain why, in your view, it's necessary for the government to get involved in this private sector issue. It's a great question. And I guess the weird focus is one of the critical ingredients to I think a healthy long-term music industry is a robust compulsory licensing system. So a methodology that businesses can take advantage of, a platform to get the rights to play music in one central way. So Pandora, for all intents and purposes, signs one piece of paper, the Digital Millennium Copyright Act and its associated webcast license that gives us the permission to play all the music that we play legally. It has a whole bunch of stipulations, but from a business standpoint, that's a fantastically efficient way to make rights available for businesses to build businesses offer products. That compulsory license comes from the government and it's a vital ingredient for our system. And one of the reasons is, in the case of Pandora, part of what I think has made the service appealing and has made it grow so fast is we play this enormous breadth of music. We have over 100,000 artists on Pandora. The majority of whom are actually independent, so not associated with a major label. An absent compulsory licensing system that allows us to get permission to play all that music, a lot of that stuff would just never get to participate because the economics of chasing down one independent label after another to get the rights to play their music just wouldn't add up. So I'd say sort of first and foremost, government involvement is absolutely essential for the health of, I think not just web streaming, but any other arena that could benefit from compulsory licenses. In terms of this act in particular, the focus of the Internet Radio Fairness Act, contrary to some of what's been written, it doesn't set rates. The act is intended to do one very specific thing, which is to extend to internet radio the same standard for setting rates called the 801B standard that's used by virtually every other sort of copyright arbitration process around us, including our competition, satellite radio, cable radio. The bill is really designed to create a level playing field in terms of the rate setting process. Doesn't necessarily mean we have the same outcome, but it's putting us on a par in terms of rate setting, which we see as a reasonable request. Mm-hmm. All right, so the idea being that satellite radio, cable radio has a better rate than you.  Obviously you would like your rates to go lower than they are. You feel your rate right now is unfair. That right? Yes, we do. And is it simply a case of it's unfair because everybody's paying a lot less? I think there's, that's a good question. That's for sure. I think that there's an inequity. It's hard to deny and literally we operate under two different standards. Ours is separate and unequal and worse. It's hard to look at them. It's impossible to look at those different rates and say that there's not discrimination against this one category. But I think that the net impact of this rate, while on the surface it leads to a higher per song fee, it leads to greater revenue per song, it's actually ultimately detrimental to the artist community because it suffocates an industry that could be doing so much more than it is. You're saying that basically right now the artist should look at it as this is a long-term kind of thing. Because if I'm an artist, I'm looking at this and I'm saying, wait a minute, you wanna cut my rates? I think I've seen figures, basically 80%, right? That would be kind of the hit that they would take. No, that's a huge misnomer. That's a very dangerous. Okay, let's clarify that. How much lower would the rate, in your ideal world, where would the rate be compared to where it is right now? How much of a hit? Yeah, so it's really important for artists especially to try and parse the rhetoric around this because that is not true. Again, what this legislation proposes to do is to provide us with the same rate setting standard so that when the Copyright Rulity Board judges consider our situation and they hear from everybody, they get to consider that evidence and information under the same sort of rubric as our other forms of radio. It doesn't set a rate. And we don't know what the outcome would be. It's been unpredictable in the past. I wouldn't want to even bet on what the outcome would be. So it's not setting a specific rate. It's just allowing us to operate on a more level playing field. But potentially the rate, you would like to see the rate lower. Yes, that's true, absolutely. And how low do you want to go? Again, this is probably not the place for me to sort of put forward what our number is, but the way I think about this is, so Pandora has maybe 30 to 40 engineers in that ballpark. Lots of companies operating in our space have hundreds if not thousands of engineers working on product. Internet radio as a category has been massively under invested in in many, many different dimensions. And that's because these economics prevented. Having a more reasonable economic structure would drive a lot more investment into this space. And frankly, I think in this day and age, in the music industry, when we see win-win opportunities, we all need to embrace them. And I think this is one of them. I think internet radio is an enormous bright spot in music. There is the opportunity here where there's an intersection of what consumers clearly want. I mean, without really a marketing budget, Pandora's audience has grown, as you mentioned, to tens of millions of listeners. An intersection of what consumers want. An intersection of what artists want. I'm not just talking about promotion, exposure, et cetera, but also revenue from performance and an intersection with business. It's an area in which you could build healthy, successful, and yes, public, well-capitalized companies. And the key to a healthy industry is recognizing that and embracing all that. Not saying, oh, I don't wanna do it because this company has gone public and has this market cap, or because consumers are getting money and music for less than it's worth. It's really saying, okay, there's a win-win-win to be had here. How do we all sort of ante up to make that happen? An artist is saying, when does that win-win take place? Because I understand right now, I'm gonna lose short-term. You're basically saying long-term we're all gonna win.  That if internet radio could operate under better economics, there would be more participants, it would grow faster, and it would easily swamp whatever sort of near-term change there was. And I think that's basic economics. I really think that would be, that's true. Now, it's taken 12 years for your industry. Just one, as you said, you're basically the dominant radio internet voice out there. It's been a 10, 12-year process for you to even get to this stage. And an artist is going away, I'm gonna have to wait 10 or 12 years to get my, because basically your industry is based on my work as an artist. And again, you were a musician. Maybe still in. Yeah, let me stop you there. I think I agree with that. The industry is based on their work and our work. That's part of what this conversation has to be about. Of course, these services would not exist with music. Some of my music's in Pandora. I'm part of that. But at the same time, a huge amount of effort has gone into building the services themselves. There's a, it's a partnership. And you have to view it that way. You have to see again a win-win. And I am an artist myself, and I'm no longer sort of performing artist, but I understand why it's awfully hard for an artist to hear anybody say anything about lowering anything ever right now. But again, focusing on the long term, I think if you can embrace that perspective, that a healthier business in the long run will grow faster, it leads to a very, I think obvious answer. And I think it's a much short time horizon than you talk about.  And still, 90% of radio listening is on broadcast radio. From the consumer's standpoint, that makes no sense. What consumers want is personalized listening. It's hit every other form of media. It's behind. And so consumers want it, and you've got this enormous technical infrastructure now, not just sort of the broadband infrastructure, but all these devices and car companies and everyone who is tooling up their systems to be able to deliver internet radio as easily and as ubiquitously as broadcast radio, it's ready to go. It just needs a little fuel. Artists have been hearing that argument for decades now. Help us form this business. Is it a new boss, old boss scenario here? Because there are a lot of businesses that have been built that way. And we still see a lot of starving artists, as it were. You do have some interest. You did post a blog the other day, which I thought was interesting, where you did talk about Pandora's payouts to artists. I guess technically to their service that pays them. 2000 artists making $10,000 a year from just royalties from Pandora, right? 800 at $50,000 a year. Now, these aren't extraordinary numbers, but there's an indication that streaming revenue can provide a certain amount of income over an annual basis. What is the possibility, you raise this possibility of creating an artist mill class. You're talking about these micro payments per stream. And obviously certain artists are doing it. You're asking us to say lower the rate, but we're gonna increase the number of plays, right? I mean, that's basically what's gonna happen. Is that basically the formula? I don't wanna sound like a broken record, but we're asking for a standard parody, which we think could lead to a lower rate, hopefully it will. But yes, fundamentally you're right, that we're saying that if you reduce this burden that internet radio as a category would grow a lot faster and would generate that kind of, a rising tide lifting all boats. Right. How realistic is that? I think there, I've seen some figures, 80 million songs somewhere in the, is that way overstated that are available in Pandora? No, a little over a million. A million, but how many artists are represented on Pandora? So it's over 100,000 artists, and I think this is interesting, over a million songs, over 95% of those songs play every month. So internet radio is, I say, arguably the first online music category to deliver on the long tail. When we talk about, for lack of a better word, the musician's middle class, it's not just lip service. I mean, we actually on Pandora are playing a huge breadth of music, and it's not just Pandora, there are tons of internet radio companies, there are hundreds of them, all of them kind of on shaky ground, but on internet radio you hear bluegrass in classic country and classical and bebop and standard jazz.  All the stuff that doesn't get played on any other form of radio. So the opportunity here is for the whole, a huge gamut of artists that otherwise I don't think would have much in the way of public exposure. How is an artist supposed to view this in the context of a career, though, because what I'm hearing is the success rate under the old industry was about five percent. You know, you had about five percent halves, 95 percent who really weren't seeing anything from recorded music. Do you see a scenario where these numbers would actually increase to the point where you would see roughly 30, 40, 50 percent of the people on Pandora making, you know, a significant enough income to sort of live off that? I mean, is that what you're saying? That's our dream, absolutely. I mean, how big is that number? I think that's an interesting question. You know, how many artists have sort of a combination of the songs, the tenacity, the, you know, all the requisite skills. It's a hard career in lots of different dimensions that have all it takes to build that. But I think this platform has the potential to, you know, to unleash that. And granted, my experience is a little old now, but years ago when I was in bands touring, you know, I saw so many bands and I'd always think to myself, man, if only this audience that likes this kind of music could hear this band, you know, they wouldn't be playing to 12 people. They'd actually maybe be making a living at it. And so I sort of feel like I can scientifically say now, based on the seven years of experience since we launched our service, that there is an audience large enough with an appetite big enough and broad enough to support a lot more than the number of artists that are currently being supported. So you've got this successful, or it's starting to become successful business. You're the only player, or the main player in internet right now in terms of this kind of service. And the argument comes back at you, instead of lowering the rates or getting a more equitable rate, why not sell more advertising?  What do you say to that? Well, you can trust that we're doing absolutely everything we possibly can to build that as fast as we can. We have every incentive to do that. And I think that to focus on that misses a much more important question, which is how do we maximize this opportunity period? And I think the way you do that is a create incentives for a much broader base of businesses to go in and invest in it and market in it. That's how you turn this into a much bigger industry. So any business that goes in that has, that's an advertising supportive business that has these content costs is fundamentally motivated to do everything they can. You know, we have over 600 employees at Pandora, well over half of them are involved directly in advertising selling in some capacity. You know, you can be sure that any web radio company that's serious about this business, it does not need any extra incentive to build their revenues fast as they can. All right, we got, we're running out of time but I want to take some questions and the operative word is questions. Please no political statements right now. Those can happen afterward, but we've got a question over here. David Lowry, we've met before actually, Tim. I'm from the Tri-Cordist and also from the Bands Cracker and Camper Van Beethoven. When I read this bill, I'd say 90% of it actually isn't about rates. So I don't want to ask you about rates. I want to ask you about this one particular clause in the bill. Nothing in this paragraph shall be construed to permit any copyright owners of sound recordings acting jointly or any common agent or collective representing such copyright owners to take any action that would prohibit, interfere with or impede direct licensing by copyright owners of sound recordings in competition with licensing by any common agent or collective and any such action that affects interstate commerce shall be deemed a contract, a combination or conspiracy in restraint of trade in violation of section one of the Sherman Act. Okay, so basically what this says, says groups of copyright owners can't say anything about direct licensing deals going on or suggested. So what do you mean by any group of copyright owners? Is this a musical group? A pair of songwriters? An alliance between two indie labels? Artist unions? Also what is impede? I assume that it means the same thing that Sirius is suing the American Association of Independent Musicians for, which is simply for speaking out negatively about direct licensing deals. I see this as a terrible, perhaps unconstitutional infringement of an artist's right to speak out and I wonder how you feel about that. So I definitely don't wanna get into the legal and legislative language stuff. I'd be speaking out of turn if I did that. I think the sort of, the spirit of that section is really about, on the one hand, the collective licensing of music has these great benefits of centralizing how you get rights and how you administer them and you have bodies that are empowered to sort of offer up this huge bundle of content in one central place. In some ways copyright itself and the aggregation of copyrights around PROs like ASCAP, et cetera, have this huge benefit. The danger on the other side is it creates monopoly. In a music group, it could be anybody, any reader. It's as any copyright of any group of copyright owners. I mean, it could be two people, it could be my band. We would be under threat of prosecution under the Sherman Act. We would be restricted from saying, hey, you guys really shouldn't do that direct licensing deal. Or hey, we think that direct licensing deal is actually, you know, it's not beneficial for all artists. We would actually literally have our speech infringed. So you're, yeah, I would be out of turn trying to debate sort of the legal and legislative meaning of these words. I just can't answer that specific question. I can really just sort of answer this. The spirit of this is that you have to balance the centralization of rights with the centralization of rights with the potential for monopoly abuse of it. That's what it's there for. I would restrict them from saying that. Yeah, I think I've answered your question as best I could. Kurt Hansen, you might have some clarity. I thought, Tim, it was that if Sony and Universal NEMI conspired to stop direct licensing that that could be prosecuted and that a couple of musicians wouldn't be considered monopoly. Yeah, but would two musicians be, you know, would be monopolists? It's hard to imagine that they would qualify as monopolists. And there's also some future conversation about this at the next panel that Michael Brace has been at this afternoon. Sorry, we're gonna move on to Ann. Hi, you mentioned this. Oh, I'm Ann Chaitovitz. I now work at the Patent Trademark Office but I'm a longtime future of music coalition person. And so you mentioned that this should be win-win and that the services should be able to compete on a level playing field and artists should get more of a bigger pot. Do you think either of these are possible until broadcast radio pays because you're not on a level playing field and the pot is small and the international pots aren't available? Yeah, it's a great question. It's obviously a big longstanding issue that's been fought over as recently as just a couple of years ago. You know, my answer to that is I think it's becoming a less and less relevant question. I mean, I think that radio is moving in this direction and the right way to think about this is sure we can keep fighting and refighting the broadcast royalty issue as was done literally like in the last Congress. But I think the right way to sort of build this business is to say, look, internet radio is the future. Personalized radio is the future. Let's get that right. And let's accelerate that transition. Granted, massively self-serving to say that. But every hour that goes to internet radio is a net positive for artists and that's where we should focus. And that's our, we are an internet radio company. We're not a broadcast company. It's not sort of our fight to fight per se. Hi, my name's Tim Anderson. I'm from Old Dominion University. I had a question about ads. You mentioned that you're trying to build more ad revenue and I've read elsewhere that you've talked about extending to local markets. And I was actually kind of interested in how you built that local ad revenue infrastructure. Are you building sales teams or how are you going about this process given that you're going all over the US and it's so hard to do it on a local basis? Yeah, so I think one of the really exciting developments in internet radio is the fact that it's become large on a local scale which has introduced this whole new complexion to the business. Pandora now is the largest radio station in I think 20 of the 25 largest radio markets in the US. And that offers up the opportunity to become a local advertising seller. And we are hiring local ad sales people all over the country to sell to the local mattress store and the local grocery chain and the local car dealer. And it's tapping into this enormous advertising business that's been the sole domain of broadcast radio historically. And I think what is so significant about this for musicians is for the first time ever performers are getting to participate in the advertising revenue part of their business which by the way has been the largest since radio was invented a long time ago. So you're going to become stakeholders in the advertising, we, I'm a musician too, are going to be stakeholders in the advertising business including local advertising. And that's, I think the stakes for this are enormous. I think that radio holds within it one of the keys to a long-term health of this business because it is an enormous and healthy and growing area and radio still accounts for 80% of the hours people spend with music. So to get it right is key. Could you, to follow up on that, you also have this internet radio thing is obviously huge from a data standpoint too. You're able to sort of determine where audiences are for particular bands. And you've done some work in that area where you've enabled bands to sort of play concerts where they may not even be aware that there was an audience but through the fact that they had a high Pandora listenership. Can you speak on that just for a few minutes? I'm glad you, we haven't even touched on that. I mean, setting aside the financial side of things, one of the great distinguishing characteristics of internet radio listening is you're connected. So you can talk to individuals and you know who they are. I mean, speaking for ourselves, you know, on Pandora we have over 20 billion pieces of thumb feedback we've received from listeners. And we know their zip codes and we know their email addresses and we can talk to them. And we've begun to do things where we'll actually do a show where we'll find a band that's coming through a city and we'll email listeners on Pandora who have thumbed up their music that live within driving distance of a given club and invite them to a show. Not just who've thumbed up that band but who have thumbed up bands that sound like them.  And it doesn't take much to sort of extend that and say, you know, internet radio is about 10% of listening right now. What if it was 50 or 60 or 70 and you were taking all this capability to connect people and activate locally to bear on a phenomenon that large that gets back to that earlier question about the musician's middle class. Like that's where you really start to see things happen. So at a scale of 100 or 200 people at a show can make a difference for a band. I mean, when we were, when I was playing in a band, you know, the difference for us in making a living or not or surviving was, you know, a difference between 50 or 250 people at a show and that's within our reach. We got time for one question? Yeah, yeah. Okay. Oh, hi. My name is Bill Rosenblatt and from Copyright and Technology and for these purposes, I was an expert witness in the satellite radio CRB hearings and I'm a little mystified by your statement or your sort of assumption that royalty rates are scaring off competition from the internet radio space and, you know, that you don't have so much competition. The statistics that I've seen don't jive with that. Like for example, there's, I mean, you're the leaders and you have a lot of listeners but there's like maybe order of magnitude, half as many listeners that listen to simulcast internet radio that carries advertising that's covered under the same royalty rates and that runs pretty much on autopilot without 30 or 40 engineers. So, and therefore has a much lower cost base so how do you account for that? Well, our share of the market is growing and I don't think those of simulcast is a robust part of internet radio and I think you'd be hard pressed to talk to, executive of a major broadcaster who's enthusiastic about internet radio right now and again, the three largest players when we started AOL, Yahoo, MSN who had all built enormous online audiences, they left the business. I don't think, I mean, I'm not sure why our evidence is so different but I don't look at that market and say that people are coming into it. Okay, for example, well our experience and data says otherwise, so. All right, we have to run unfortunately but we appreciate the participation. Thank you, Tim. Yeah, thanks.