 So, I think at the end of the class, we said that why for outer valence IP, the Koopman's approximation works very well. If you remember, the argument was that this is the N minus 1 electron energy and this is the N electron energy for the Hartree-Pock and this is the N minus 1 Koopman's. Then this gets depressed because of correlation, so this is delta correlation for the N electron system, so this is exact and this gets depressed twice once because of the Hartree-Pock that the SCF that is what we call relaxation and again because of the correlation of N minus 1. However, this correlation is larger than this correlation, so hopefully for outer valence IP, this and this plus this match so that this difference from this is the N minus 1 exact, so this difference and this difference become almost same. So, this is your Koopman's IP, this is your exact IP, so that is almost the same because you know the relaxation and correlation correction, this is exactly what is called relaxation and correlation correction, so both of them work in a way that they cancel each other, but assume the reverse case of an electron affinity, so let's say I have taken electron affinity where I have a positive electron affinity, so that means what is positive electron affinity? That means the negative ion is more stable, lower energy. In such a case, EN plus 1 will be lower than EN because it is a positive electron affinity, so let's say this is EN SCF, so let's do the same thing again but now note that the EN plus 1 is actually lower and this is EN plus 1 Koopman's, so without doing Hartree-Fock, so this is your Koopman's electron affinity. Now what will happen is that EN plus 1 will relax, just like N minus 1 relaxed because that is where we have frozen the orbitals, so this will have a relaxation energy, so let's say this is EN plus 1 SCF, so this is your relaxation energy R and then both of them will have a correlation, so again this is delta 1 for N and then there is a delta 2 for N and this is EN exact, this is EN plus 1 exact, so your exact electron affinity is this. Now you can see the reverse thing happening because we said that the correlation energy is proportional to N, delta 2 is now going to be greater than delta 1, so this is going to be actually greater than delta 1 because this is EN plus 1, this is EN but this has a further depression, so this is depressed more compared to this but this is a further depression because of relaxation. So in fact in this case it's a classic problem where relaxation and correlation are not only not cancelling, they are actually working in opposite direction. To make the error significantly bad, if relaxation was not there at least this point would not have been there, so the difference would have been only this minus this but now the EN plus 1 Koopman is going down this much whereas EN is going down only this much. So there is a relaxation correlation error, so wherever there is a positive electron affinity Koopman's EA gets much worse, Koopman's EA is very bad because the errors that you have neglected which is correlation and SCF relaxation are actually working in opposite directions and the problem becomes much worse whereas in the IP fortunately it is in the other direction, so they kind of cancel that is simply because your EN plus 1 is lower than EN whereas EN minus 1 is higher than EN that was the main reason why it happened. So depending on how the systems change for example if you have a system where there is a negative electron affinity where again EN plus 1 is higher then again it will actually have a situation more somewhat like the Koopman's but not IP not exactly even there EN plus 1 correlation will be at least higher but it will probably do an over correction in that case. So in any case electron affinity it is very hard to get a good result by Koopman that is one important conclusion the IP it works much better because one that is higher is actually EN minus 1 and that EN minus 1 correlation is lower than EN in this case even if EN plus 1 goes higher EN plus 1 correlation is actually higher than EN. So the correction will never take place properly for the electron affinity and if it is positive electron affinity then system becomes much bad much worse. So that is the problem of the Koopman's so obviously for IP so the basic message is although Koopman's did this variation method for both EN and EN minus 1 and EN plus 1 for IP it works much better than the electron affinity so that is the essential message to show this alright.