 Welcome to this next segment of CD spectroscopy and MOSBA spectroscopy for chemistry. My name is Arnab Dutta and I am an associate professor in the department of chemistry IIT Bombay. So, in the previous segment we are discussing how we can find the different symmetry operators or elements present in a particular object or a molecule and how we can differentiate them in different groups. So, let us recap it a little bit and then we figure it out an easier route to figure it out how to find out what is the point group of a molecule. So, let us begin. So, previously we have looked into the different symmetry elements that is present and we found there are 5 of them starting with an identity operator, principal axis of rotation, plane of reflection, sigma h, sigma v, sigma d depending on its relation with the principal axis or cn then we also have improper axis of rotation and along with that we also have the center of symmetry inversion. And we found that there are different combinations of this particular symmetry elements can be present and which can be differentiated in 4 major groups. One is non-rotational group which is given by c1, cs or ci or we can have single axis rotation group which belongs to cn, cnh, cnv, s2n and c infinite v then we can have tihedral groups which is nothing but an extension of single axis rotation with an additional factor that it will have n number of c2 perpendicular to cn. If this is actually valid then you have dn, dnh, dnd and d infinite h point group and then at the last we can have cubic groups which belongs to tetrahedral and octahedral which are highly symmetric point groups and that is why we can call them like special groups because this particular tetrahedral octahedral have 24 and 48 symmetry elements respectively. So, that means they are very highly symmetric. So, these are the 4 different groups that we can divide it into. Now, the question is how to figure it out a particular molecule belongs to which particular point group? Do I need to find out all the symmetry elements present in the molecule or we can find out an easier now. So, that we will try to define from all these groups present over here and what are their difference. So, what is the difference between non-rotational and single axis rotation group? It is do we have the presence of axis of rotation or not where n is greater than 2. So, anything beyond c2 will go to either single axis or dihedral group. So, if I want to differentiate between non-rotational group and this single or dihedral group the question I have to ask whether I have a single axis of rotation or not. Difference between single axis rotation and dihedral angle groups we have already mentioned whether you have n number of c2's perpendicular cn or not. So, by asking this question I can differentiate between these two groups and cubic groups and non-rotational group are quite easy to figure it out because there is either not too many symmetry elements present or there are too many of symmetry elements present which are quite symmetric. And over there I also want to take your attention to the c infinite v or d infinite h group which is actually says that they are a linear molecule. So, that can be also figured out very easily. So, with all this information in my mind now we will try to develop a questionnaire that I am going to ask to a molecule and the answer will be binary yes or no and depending on that I will try to figure it out what is the point. So, let us take a look into it. So, this is very important this is figuring out the point group of a molecule and over here we are nothing but roll out a questionnaire. So, let us ask question to this molecule. The first question I am going to ask this molecule is the molecule linear that is going to be very easy to find out by looking into the molecular structure whether it is a linear or not. And again the answer can be 2 either yes or can be a resounding no. Now if the answer is yes then the next question I am going to ask do you have a center of symmetry in your molecule because if you remember that linear molecule can belong to two different point groups either c infinite v and d infinite h the special difference between these two are the d infinite h contains a center of symmetry the c infinite v is not because d infinite h actually both the sides of the line is similar it is a centrosymmetric molecule whereas a c infinite v this is linear but the both terminals are not same. So, with respect to this question I can separate them out if the answer is yes I am going to have a d infinite h point group if the answer is no I am going to have a c infinite v point group. So, that pretty easy for a linear molecule I can easily find out with only two question are you linear or do you have a center of symmetry or not. If the answer is no then we ask the question do you belong to any special symmetric group by special symmetric group I mean tetrahedral or octahedral the most common ones. If the answer is yes just looking into the structure we can figure it out whether it is tetrahedral or octahedral. So, from there I can figure it out what is the point group of the molecule. If the answer is no that means that does not belong to cubic group it does not belong to any linear groups. So, the only options possible is right now single axis rotation and non-rotational groups or dihedral groups. So, which particular factor defines the difference between a non-rotational and rotational groups by rotational group by mean I am considering the single axis rotation and the dihedral groups together. So, the question is going to ask do you have a cn or not where n is greater than 2 the answer can be again binary no or yes. If the answer is no that means it belongs to one of the non-rotational group and in the non-rotational group it can have c1, cs or ci and over here very importantly cs and ci cs means it has a sigma plane along with the operation E whereas, the ci has a symmetry element of i present along with the E the identity operator. Now in a molecule it will either have i or sigma the molecule cannot have cs or ci at the same time. So, if it is that mutually exclusive that it can be either cs or ci it does not matter which of the question I am asking first that whether you have a sigma plane or not if I ask it first and if give me the answer yes then it belongs to point group of cs. So, done if the answer is no then the next question I ask do you have an inversion center if the answer is yes it belongs to point group of ci if the answer is no that means this molecule does not have any linearity does not belong to symmetric group highly symmetric group like tetraloctahedral no cn no sigma no i it has nothing but a identity operator. So, the molecule belongs to c1 point group the absolutely unsymmetrical molecule. So, this is how we differentiate between all the non-rotational group. However, there are two other things still present if there is a cn present in a molecule over here and if the answer is yes what are the possibilities the possibilities are two either your molecule is a single axis rotation or a dihedral group and we have mentioned this earlier what is the factor differentiators do you have a number of c2 perpendicular to the cn or not and again the answer can be 2 either no or yes if it is an answer no that means now it belongs to a single axis rotation and in single axis rotation I can have cn, cna, cnv all these point groups. So, to figure it out first the question I ask do you have a sigma h I am asking this because if you have a particular cn you can have only one set of perpendicular sigma h to it so it is easier to find. So, that is the first question we ask and the answer can be yes or no if the answer is yes this molecule belongs to cnh point group and if this molecule does not have a sigma h the next question I ask do you have n number of sigma v is present because if the molecule has a principal axis rotation of cn n is the integer which comes from the 360 degree divided by the angular rotation which actually allows us to achieve a superimposable and indistinguishable configuration if it has it it will have all n number of them or nothing say if it is a c3 it will have 3 sigma v if it is a c4 it has to have 4 sigma v or nothing, nothing in between. So, this is the next question we ask and the answer can be yes or no if the answer is yes I belongs to point group of cnv if the answer is no then I belong to point group of cn where I have only the cn over there but nothing else. So, that is how we can figure it out or differentiate single axis rotation groups. The next thing is that I can have n number of c2 perpendicular to cn and the answer is yes that means I am now belonging to the dihedral group and that I want to figure it out how we can differentiate the other different groups present in that dihedral group dA and dNh dNd. So, for that we are going to ask some question the next question we are going to ask is very much similar what we have asked to this cn point group do you have sigma h present and then the answer can be yes or no if the answer is yes it belongs to point group of dNh you can see the similarity. Then the next question is do you have n number of sigma d's if it does not contain the sigma h here I am writing sigma d because all the sigma we present in this molecule will be bisecting this c2's which is perpendicular to cn that way there will be all sigma d's. So, again it will have n number of sigma d's or nothing. So, if it has it then I belongs to point group of dNd if none then it belongs to the point group of dN. So, by that I can separate out all the dihedral groups and this is the special group or cubic symmetry groups and these are the two linear molecules and with that we cover up all the different groups possible in the molecule. So, you can see that I do not have to remember each and every symmetry elements and I do not have to find out each and every of them we have to rationally only figure it out which of them are important. For an example a molecule linear or not we can easily find it out just looking into the structure. So, that is the first question we ask over here that whether the molecule is linear or not then the question we ask whether it is a centrosymmetric or not. If it is then it will be d infinite h if it is not it will be c infinite v. If it is not linear then the next question we ask whether it is tetrahedral or octahedral. If it is tetrahedral or octahedral we can easily find it out looking into the structure. So, you can easily find out whether it belongs to this cubic group or not. Obviously, these are the easier ones and in the real life most of the molecule specifically are not linear or does not belong to this very highly symmetric cubic groups. So, then we look into the next one because now we have three different options either we have a non-rotational group or single axis or dihedral group. The similarity between dihedral and single axis rotation group both of them are cn or single axis of rotation. However, the non-rotational group does not have that. So, this will be the question I will ask that whether I have a cn or not where n is greater than 2. If the answer is no I belong to this non-rotational groups either cs or ci or c1 that we differentiate by asking the question whether you have a sigma or not or i or not. Does not matter which question you ask first i or sigma because it will have only one of them if it has and with that it will have cs and ci and then if it has nothing it will be c1. So, one thing I want to mention when I say sigma or i only one will be present that belongs to when the molecule has nothing else no other symmetry limits does not have any cn. The molecule does not have any single axis of rotation and then I am trying to find out whether it is having a sigma plane or not or there is a center of symmetry or not and that is where only one of them will be present and by that you can differentiate between ci, cs and if nothing is present then it is c1. Now, if the molecule have this cn axis then the possibility is it will be single axis rotation group cn based or dihedral groups or dn based. The main factor which differentiates them whether you have n number of c2 perpendicular to it or not. If it is then it belongs to dihedral group if it is not it belongs to single axis rotation group and then the questionnaire is quite similar for both these cases whether you have a sigma h or not if it is yes cnh or dnh. Then whether you have n number of sigma v or n number of sigma d or not if yes cnv or dnd and if nothing is present other than the cn axis of rotation then cn and nothing other than cn and n number of c2 perpendicular to cn then it belongs to point group of dn. So, that is how we can separate out all the different molecules present by asking this very simple question. So, we like to conclude it over here for this particular segment how to figure it out a point group of molecule. In the next segment we will perform this particular exercise on 10 different examples and figure it out how to find out a point group of molecule and over there we will learn this process and practice it a little bit more. So, with that we would like to conclude this particular session. Thank you. Thank you very much.