 Welcome to the lecture number 33 of the course quantum mechanics and molecular spectroscopy. Until the last class, we looked at the rotational and vibrational transitions and the associated selection rules. Today, we are going to look at the electronic transitions and the possible selection rules for them. Electronic transitions happen between two different electronic states. Now what does this two different electronic states mean? Two different electronic states mean, for example, you have a molecule and one can define an electronic configuration. Even for atoms, you can define electronic configuration and let us suppose there are all field orbitals using Pauli's exclusion principle or Offberg principle combination of them. So these are field orbiters and these are unfilled orbiters. And what I can do is that by applying energy or putting a photon, then I can go in presence of h nu. I can go from, I have now transformed the electron or I have replaced electron from the highest occupied atomic orbital or molecular orbital to a lowest unoccupied. So this is what we call as Homo and this is Lomo. Of course, one does not have to restrict to this. One can go to Lomo plus one to higher energy levels as well. So one can always excite from here to here to here to various levels. But this is the lowest energy transition. So what I am doing in this case is that I am promoting an electron from an occupied level to an unoccupied level. That is the electronic transition. So where you are displacing an electron from one orbital that is occupying to another orbital. These are called electronic transitions. By the way, when we have the absorption, electronic absorption or what is known as the UV visible spectroscopy in which you actually take out electron from one of the orbitals occupied orbitals and put it in the orbital that is unoccupied. Of course, you can also do from here to here. You can bring in the electrons that are lower than Homo. So many possibilities exist. So electronic transitions are many such possibilities. One can have Homo to Lomo or Homo minus one to Lomo or one can have Homo to Lomo plus one. So these are, this is Homo minus one, Homo minus two, minus three. So this is Lomo plus one, Lomo plus two, something like that. So one can have many, many combinations. And you will see that this one that is Homo to Lomo is the lowest energy possible transition. This is the lowest. Now it turns out that when you do that, now if you use the build-up principle and you can have a wave function called as psi ground. And this wave function will correspond to the electronic configuration. One could have a psi excited as to electronic configuration. This is Homo plus. Now there is one thing that I am trying to do here. If you see concentration Homo and Lomo, what I have done? I have started from here and I have, the other possibility is this. Now this state is represented by S is equal to 0. This state also is represented by S is equal to 0. This state is represented by S is equal to 1. So when we have S is equal to 0, this we call it as singlet state. When you have S is equal to singlet state and when you have S is equal to 1, we have triplet state. Now S is equal to 0, S is equal to 1, triplet state, singlet state. This is because of the degeneracy of the wave functions. Now there are two things that are possible. So when you have psi g, when you have this combination, this is Homo. So you could go to psi excited state in two possibilities. One is this, where S is equal to 0 or one would have psi e. So that is S is equal to 1. So this is singlet. So one could have, this is also singlet. So when I go from psi ground to psi excited state, I can go from psi ground S is equal to 0 to psi excited S is equal to 0 or I could go from a psi ground S is equal to 0 to psi excited S is equal to 1. So this is called singlet-singlet transition and this is called singlet triplet state. Now the exact wave function will depend on the molecule or atom in consideration. Now let us think of a transient moment integral. So Tmi will be equal to integral psi ground psi excited data that is going to be a transient moment integral. However, the way this transient moment integral has written has a problem because you see there is something called bond approximation. Now what does bond upon approximation it says that the electronic wave function parametrically depends on the nuclear coordinates. So psi electronic is dependent on the electron coordinates I would call it as I's okay and nuclear coordinates alphas. So that means whenever the nucleus changes its position the electronic wave function will change and this gives rise to concept of potential energy surfaces. Therefore your psi G okay will consist of two things. This will consist of psi G electronic multiplied by psi G nuclear okay and this comes out of the electronic transient or bonamino-prono apanamino approximation. Therefore it is similarly you have psi excited will have two possibilities psi excited okay. Let me call it as electronic electronic and psi excited nuclear. So this wave function that you use in the transient moment integral it is bit more complicated. So one can therefore write your TMI will be equal to psi G mu psi E or rather other way around d tau in fact this should be equal to the mu acts on psi G psi E mu psi G d tau. But you know this is a Hermitian operator so it does not really matter okay because overall the transient moment integral must be a the transient moment integral square which is equal to which is proportional to the probability of transient this is square and it has to be a positive number okay. So it does not really matter but technically this should be like this. So this will be equal to your psi E will be equal to psi E electronic multiplied by psi E nuclear and your psi G will be equal to psi G electronic multiplied by psi G nuclear and the transient moment integral or the dipole moment vector can also be seen you know there is electronic charge distribution and there is a nuclear charge distribution. So one can always write mu as a sum of mu E plus mu. Now I can separate this into two things this is equal to integral psi E electronic okay psi E nuclear mu E okay rather I can psi G electronics psi G nuclear d tau plus integral. So your total mu is written as mu E electronic plus psi E electronic psi E nuclear mu N psi G electronic psi G clear okay. So now the total transient moment integral can be now divided into two such integrals one because of the electronic dipole moment and other is the nuclear dipole. Now evaluation of these two integrals is not very it is going to be challenging. So one makes another approximation called Condon approximation. So essentially what are we looking at in this okay we are looking at how the electron wave function changes with respect to the nuclear coordinates okay. The electronic function does change with respect to nuclear coordinates however what we figure out is the dipole moment the nuclear dipole moment or the dipole or say nuclear dipole moment mu N depends equally on the electronic coordinates. So that means this dependence on these coordinates is very weak that is why we can neglect this term and this neglection is called Condon approximation. So your transient moment integral so your TMI or other way to write it is the following is that when you have integral mu electronic excited mu electronic nuclear mu E plus mu N psi ground electronic psi ground nuclear d tau is equal to now what in this what we do is mu N be equal to 0 and this is the Condon approximation. So essentially the dipole moment is enhanced or contribution comes from only the electronic coordinates. So this means what you have is mu E electronic sorry this must be psi E electronic not mu psi E electronic psi E nuclear mu E psi G electronic psi G nuclear d tau. Now we will see that the mu E electronic will only act on the psi E and psi G electronic okay. Once this will be equal to integral psi E electronic mu electronic psi G electronic d tau and integral over psi E nuclear psi G nuclear d tau prime. Because the nuclear coordinates are on the different the nuclear coordinates are different than the electronic coordinates so they are separate. So these two are the integral that need to so for getting the electronic transients one needs to evaluate these two integrals okay into evaluation of these two integrals I will take up in the next lecture we will stop it here now thank you.