 Hello and welcome to this new segment of CD spectroscopy and MOSBA spectroscopy for chemistry. So far we are discussing symmetry and we have discussed the mathematical version of symmetry where we looked into the different symmetry elements and out of them 5 of them come out to be very important. They are identity operator E rotation around an axis Cn reflection through a plane sigma improper accept rotation Sn and reflection through a point center of inversion I. So let me jot down those points. So the different symmetry elements, so first is the identity operator. Second is the rotation around an axis. Third is reflection through a plane which you call them sigma and we have discussed that with relation with respect to the Cn or proper axis of rotation or rotational axis. It can be distinguished in three different versions sigma H or sigma horizontal which is a reflection plane which is perpendicular to the axis of rotation. Then we can also have sigma V's sigma vertical where the plane of reflection actually contains the rotational axis and then there is also sigma D which is a version of sigma V but over here they actually bisects to C2's perpendicular to that principal axis. So these are the different reflection plane. Fourth one is the reflection through a point as we call them inversion center and we put them as I and the last one was improper axis of rotation where we do two different operation consecutively first there is a rotation around an axis and secondly a reflection through a plane perpendicular to that Cn we have just done. So it is basically nothing but a sigma H. So over here we are doing two operations together Cn followed by sigma H. So this is nothing but S n axis. So these are the five different components of symmetry elements we have found and we have also found that these five can be combined in different particular groups and those groups are known as the mathematical groups and this mathematical groups that we have found can be divide in four broad areas one rotational group where we have Cs, Ci and C1 point groups then we can have single axis rotation group where we have Cn, CnH, CnV, S2n and C infinite V point group C infinite V point group for a linear molecule. Then comes the dihedral group which is very much similar to the single axis rotational Cn groups but over here we have an additional n number of C2 perpendicular to that principal axis Cn and that is why this group becomes Dn, DnH, DnD and D infinite H point group Dn infinite H again is for the linear molecule the difference between C infinite V and D infinite H is whether you have a center of symmetry or not whether the linear molecule both sides are same or not if it is same it belongs to D infinite H it has a center of symmetry if it is not then it does not have a center of symmetry it belongs to C infinite V point group and the last one is the cubic group which are very highly symmetric point group and we have two of them tetrahedral and octahedral which contain 24 and 48 symmetry elements respectively. So these are the four groups we have found that can be present in a system and all our molecules can be mostly distributed among all these particular point groups. Now the question is how to find out this point group and over there we have learned that we can do that by particular questioning first we start with whether this molecule is linear or not then if it is yes then we ask whether we have a center of symmetry or not and then if it is yes or no answer yes it is infinite H no it is infinite V then we the molecule is not linear if it is a no then the next question we ask to them whether you belong to a cubic group or not and if the answer is yes then we will find out whether it is a tetrahedral or octahedral geometry if the answer is no the next question we ask do you have a principal accessor rotation or not if the answer is no then the next question you ask do you have a center of symmetry I if the answer is yes you belong to C I if the answer is no then next question you ask do you have a plane of reflection or not if the answer is yes then you belong to C S group if the answer is no you belong to C I point group sorry C 1 point group so these are the different point groups you can find over here but if the molecule does have a C N then the next question we ask do you have N number of C 2 perpendicular to C N or not so we are differentiating between dihedral and single axis rotation group if the answer is yes and if the answer is no so let me just change this say this is no this is yes if the answer is no then you ask whether they have a sigma H or not if the answer is yes they belong to C N H if the answer is no then you ask do you have N number of sigma V is or not if the answer is yes then either C N V if the answer is no it belongs to C N point group so these are the different point groups you can find for single axis rotation group in dihedral angle all the rest remains same only it has extra number of C 2 is perpendicular to C N if the answer is yes is belong to D N H if the answer is no then we ask do you have N number of sigma D is or not if the answer is yes the answer will be D N D if the answer is no it belongs to D N point group so we have gone through that in details last class and over here this D N D is coming because you have sigma D so if you have N number of C 2 present C N and if it is present in this molecule this sigma V is will be obviously going to bisect those C 2 so they are actually defined as sigma D so you have gone through that part now the question is how chirality is connected to point group so that is the question we would like to find the answer towards to it so for that we are going to define what is chirality so if we ask what is a chirality we say a molecule is chiral if its mirror image is not super imposable and indistinguishable original molecule so just imagine my hand is one of those molecules and over there if I reflect it I get this particular hand you can see they are mirror image to each other but they are not super imposable on each other or they are not indistinguishable that is why these are known as the enantiomers the two mirror images this enantiomers actually is originated because of the presence of chirality in the molecule chirality is again coming from a Greek term which meant handedness so like our hand is mirror image but not super imposable indistinguishable so that is one of the definition but now if I have a molecule do I always have to draw their mirror image and try to fit and fix whether it is actually its mirror image or not so the second definition there are multiple definition of it the second definition was there if there is a molecule you are actually seeing does not have a plane of reflection it will be chiral so again it does not have so let me just properly does not have a plane of reflection it will be chiral that means you do not want any kind of sigma present in its symmetry element so go to the next one the other definition we found if the molecule does not have a center of symmetry I should not say will be I should say can be it can be chiral so no center of symmetry a center of inversion should be present and with all those things when we actually look into that we find like is there any connection between the chirality and the point obviously some of the symmetry elements coming but they are not really general how I can further generalize it and connect it to point so for that we go back to the first definition first what we do we take a molecule say it is a we take its mirror image and try to find what is the mirror image and this particular mirror image we try to find whether they are super imposable and indistinguishable now how we do this thing so what first we are doing we are taking a reflection of the molecule so basically in our term we are doing a sigma operation and then whatever this reflection we got we try to move it around so that it can go and match with the original position so basically after this we are rotating in all different orientation orientation possible basically we are doing a CN operation because that is what we do reflection is already done now we are just rotating it in all different orientations possible to fit with the original system that means you are doing a sigma we doing a CN and because this sigma plane what we are actually doing this operation it does not have to be present in the molecule at this moment we are just doing the operation that is why we can say this sigma can be any place and the mirror image we are going to take is going to be the same a molecule is going to have a mirror image of it it can be similar depending on wherever I put the sigma plane is so with respect to that we find that we are doing a sigma operation and CN operation next to each other so basically we are doing a S n operation or improper axis of rotation and we have discussed this earlier why this improper axis of rotation is very important because it has a direct connection to chirality so now if I am able to do the reflection do the rotation and find that this molecule can be indistinguishable and superimposable that means this molecule is going to have an SN axis so that means if a molecule has a SN axis then this molecule cannot be chiral so what in other terms I am saying that if a molecule has a SN axis it cannot be chiral that means presence of SN axis can be crucial factor to determine whether my molecule will be chiral or not and there are some corollaries to this factor we have already discussed that S1 where n equal to 1 is nothing but C1 into sigma so this is equivalent to a sigma plane and that is the corollary we are finding in number 2 that means if you have a sigma plane of reflection that means you have S1 it cannot be chiral so that is what is actually happening there so if you do not have a sigma there is a possibility that molecule can be chiral then the next one we have also defined if a S2 is equivalent to center of symmetry so this is also getting connected over here if you have a S2 it means it is saying that you have a molecule which is belonging to S2 you have a C2 and sigma you do this operation you find another molecule which is exactly superimposable and indistinguishable to the original structure and from there we say yes if a molecule have a center of symmetry it cannot be chiral so molecule cannot be chiral where it has S1, S2 or any other SN axis of rotation so that is where we are actually getting into some again trying to make it much general a molecule cannot be chiral the molecule possess SN axis of rotation this SN axis of rotation means S1 to sigma S2 to i and so on and so forth so S1 means sigma plane S2 means i so those are covered say molecule cannot be chiral if the molecule have an SN axis and why SN axis because as we just said what we generally do we have a mirror image and try to fit it sigma CN so that is basically we are doing an SN axis of rotation where we are doing a reflection and a rotation next to each other without probably confirming it that we are trying to find out whether the molecule is chiral or not and that is basically we are doing an SN axis of rotation and try to find whether it is chiral or not so that means SN axis the presence of SN axis is going to be crucial factor is a key factor and with which we can figure it out whether a molecule is chiral or not now what we can do I can find a molecule find out this point group and find out in that particular point group do we have an SN or not and the SN we can have SN where N is greater than 3 if S1 that becomes actually sigma phase 2 that becomes actually center of symmetry so this is what we actually try to find out now the thing is that do I really need to go through all the point groups and try to find out where do I have an SN axis or not and if we look all the point groups that is possible in the system only two point groups actually going to give you a system where there is no SN axis present and those are CN and DN point group and over here one of the extension of C1 is basically C1 where the molecule have totally asymmetric does not have any symmetry element present other than identity operator that is C1 where N equal to 1 so if you have a CN or DN point group molecule you can say that means that does not have any SN axis of rotation where N equal to 1 2 or 3 or greater than that and that means this molecule will be chiral in nature so only CN and DN point group molecules can be chiral and again C1 is a special case of CN so with that respect in mind so what we generally do to do take a molecule again find out the point group and just just see whether there CN or DN if it is yes then it is actually a chiral molecule and it is not belong to CN or DN then it cannot be chiral it is going to be a chiral molecule so with respect to that we would like to close this particular segment of this CD spectroscopy and MOSBUS spectroscopy for chemist where we define the connection between chirality and point group and what we figure it out that a molecule cannot be chiral if the molecule possesses an SN axis and over there we bring it further and we find out that if a molecule does not belong to CN or DN point group that will be a chiral if a molecule is among the CN or DN point group then the molecule will be chiral so with that we would like to stop this particular segment thank you thank you very much