 Previously we talked about that in absorbance we can write it as a function of epsilon into C into a simple bare numbers law. And over there the most important term is the epsilon in the way because it is a molecular property or I should say an intrinsic molecular property that means it is coming from the molecule and you cannot change it and this is known as the molar extinction coefficient and this is connected with the oscillatory motion, oscillatory strength. So, we discussed earlier again this creates this darn particularly says that how much the incoming electromagnetic radiation can interact with the wave function of the existing electron density and exchange the energy. However, what happens if my electric field, so over here we are talking about the simple absorbance it is only the electrical dipole moment active but now we want to consider both what happens if mu e and mu m both are active then what happens. Now imagine how it is going to happen first you are going to have a mu e then you are going to have a mu m all together it is not going to be dependent only on a oscillatory because there is a magnetic field also important and this magnetic field as it is dependent on the rotation this is going to be a rotational strength factor for the magnetic moment. The electrical dipole moment going with respect to the oscillation the magnetic dipole moment is going with a rotation. So, this rotatory strength will come in and when we talk about both of them both of them will come together as a rotatory strength which will be a function of mu e and mu m together. So, what I am looking into if I can make a molecule such that its electronic excitation can happen not only with the electrical dipole moment but also with the magnetic dipole moment and over here this particular term rotatory strength comes which is very much analogous to the oscillatory strength for a simple electronic distribution. Now what is the implication that I want both this electrical dipole moment and magnetical dipole moment activity in a system so let us take a look into it. So previously we have said if I have a electrical dipole moment active system how the electron should move in a linear way and if it is a magnetic dipole moment it is going to be a circular way. I am going in such a way that this circular motion is actually happening perpendicular to the board I have brought. Now say I have a system where mu e and mu m both are active so what will happen? That means the linear motion and circular motion both will happen together. Now think about that you want to move forward in a line and perpendicularly want to do a circular rotation so what will be the movement will look like? So let us take a look for this particular system. So over there what happened I am moving in circle but at the same time I want to move forward so how it will look like? I am doing circular motion but at the same time I am moving forward. So I am going to end up to have a helical motion and this is very important because once you have a helical motion that means you have a helix you have created a chirality because depending on which direction the circular motion is happening you can have two opposite systems which will be exactly mirror image to each other this is also a helical motion mirror image to each other but not superimposable. That means if you can create a molecule with such an electronic distribution that it can be excited by both linear and circular motion that means by both electrical dipole movement and magnetic dipole movement you are going to create a helical motion of the electron density in the molecule. Once you created this helical motion what will be the effect now it can detect the incoming if you remember in the molecule I am actually giving a RCP or LCP which are helical in motion and now say you have a molecule present such a way its electronic distribution is such a way that it can create this kind of helical motion and once it creates the helical motion because if the molecule is chiral that means it have only one particular enantiomer it will create only one of them and at that moment what will happen it can create the helical motion but the helical motion will have different interaction with RCP and LCP because one of them will be in the same direction one of them will be in the opposite direction and depending on that it can differentiate the difference between RCP and LCP and depending on that it can different not only differentiate but it can absorb it differently that means it is going to show circular dichroism or electricity or it can allow one of them to go faster slow other one down due to the interaction and create the optical rotation due to circular bi-refringence so that is the main reason what is actually giving up an optical activity because in the molecule electronic distribution is such that it can be excited by both electrical and magnetic dipole volume so if an absorbance I am talking about circular dichroism now if an absorbance is both electrically and magnetically dipole moment allowed only then that molecule will be optically active any questions up to here before you go further that why a molecule is showing optical activity where the physical origin of a molecule actually having those motions so far we know that it has to have a electrical dipole and magnetic dipole moment allowed transition only then it can have this optical activity I haven't really connected to the molecular structure yet but before that step the main reason for that is that it has to be electrical and magnetic dipole moment allowed both allowed if only one of them is allowed one of them is not it will not be kind of just imagine if it is only linear magnetic mode disallow linear motion you cannot have any quality or electrical development disallowed forbidden but only magnetically dipole moment allowed you are going to have a circular motion you cannot really have a quality with respect to that so that it can interact with the RCP and LCP so now the question come what is the character of a molecule that can come into the picture over here which can be connected to this particular helical motion possibly in a model so for that we are going to again look back the electrical dipole moment and magnetical dipole moment so what we just said that both of them has to be active at the same time so how we can differentiate both of them either by x axis direction for electrical dipole moment and the corresponding magnetic dipole moment will be Rx so now during a transition when you say that it should be electrically magnetically dipole moment active it has what is actually saying that it has to be for the corresponding axis you can have a axis and Rx both of them has to be active you cannot have a x versus ry or z versus rx that will not be possible because the electrical field and magnetic field are connected the electrical field if you are going to one direction the magnetic field you need with respect to that is a magnetic field perpendicular that means x needs rx similarly you can have y direction the magnetic moment corresponds to that will be ry and you have to have z direction and rz right so if you want to have an optically active compound you have to create the helical motion and to create the helical motion both electrical dipole and magnetical dipole moment active transition should be allowed that means these two things should play together rx and x y and ry z and rz they have to active with the same motion they have to active together either this or this or this and depending on them which particular one is actually active for both of them that is actually going to tell you that which direction the helical moment will be active and which direction if you give a polarized light you are going to see a optical activity now what do I mean by a directionality activity so when we actually pass a light a electromagnetic radiation to observe a optical activity generally we shine light in all possible direction x y z all possible direction but if I want to send the light in either x or y or z direction then what will happen then what will happen that it depends in which particular direction either the mu e or mu m is actually active and if it follows the rule of allowed transition with respect to mu e and mu m so what we mean is the following we have all together said that the transition moment integral is given by psi excited state into the operator into the ground state theta now I want to find out whether the value is zero or one if it is zero it is forbidden if it is one it is allowed now this full thing I can define with respect to symmetry what do I mean by symmetry so all of you when we talk about electronic transition we generally say it is a pi to pi star transition into pi star transition so when we say this is a pi orbital it's a pi star orbital this is actually a symmetry we are talking about so this pi sigma these terms are nothing but a symmetry recognition or a symmetry element term so similarly depending on the molecule that we are actually talking about and depending on its point group each orbital I can define with respect to a particular symmetry a recognition term or a symmetry uh uh uh elemental term for an example if we take a water molecule the water molecule belongs to c 2 v point group and if you look into c 2 v point group we found the symmetry can be defined as a 1 a 2 b 1 and b 2 symmetry that means any orbital present in water molecule can be separated in either of these four symmetric configurations a 1 a 2 b 1 b 2 so that means on water molecule the ground state orbital or excited state orbital I can define it as different terms say it is a 1 a 2 b 1 b 2 whatever depending on the particular point similarly this operator can be also defined as with a symmetry recognition how to do that it is very simple any particular point group has a corresponding table known as character table if I look into point group and each point group has something called a character table and in this character table there are defined where x y z r x r y r z etc false so you know exactly what is their particular symmetric notion find out that symmetry notion say it is a 1 a 2 b 1 b 2 whatever put it over here so now instead of putting all these three terms you can put all of them as a combination of different symmetry representation a 1 a 2 b 1 b 2 all those things together and then once you have the symmetry representation you can multiply them and find out what is the result if and only if the result of the multiplications are such that they are giving me fully symmetric representation fully symmetric representation is such that all the character for that particular representation is 1 that means whatever you do for the symmetry element on that particular representation nothing is going to change for example for c 2 v it is a 1 generally the first symmetry representation if you get that you are going to get a value of 1 that means that will be allowed if you get anything else that will be 0 that means all we do so I'm just going to give you an example of that for an example say excited state operator ground state so say my ground state is a 1 my excited state is a 2 this one I don't know so what I will do a 2 into unknown say x into a 1 what I want to find that totally symmetric representation that means a 1 and this is only possible because this is already a 1 that means these two have to get multiply and give you a 1 back you will learn those things when professor lila will go through I'm just giving a little brief on that because a 1 is a totally symmetric so if you multiply anything with that it will give you that other term back and you require a 1 so that means all these things to come together and should give you a 1 only then a 1 into a 1 will give you an a 1 now I want to have a totally symmetric representation a 1 by multiplying a 2 into x it is only possible if the x is an 8 if you multiply the same representation with each other you will get a totally symmetric representation these are the corollaries so that means I know exactly which particular symmetry representation will make this particular transition allowed it is the 8 then what I do look into the character table find out whether it is x y or z direction if it is connected with this or not if it is connected with particular x axis y axis or z axis only for that particular polarization this optical transition will be allowed if it is not there no matter what you do you cannot do a a 1 to a 2 transition say find example I'm just taking a random example that it is allowed only with x the a 2 has an x but no y or z so if you only give a x polarized light only then you will see the transition if you give y or z polarized it will not see any transition for optical absorption it is not possible so it is completely controlled by the symmetry of the molecule that is molecular structure and the mathematics is helping us to get there which particular axis is going to show me so from there we can find out whether it is x y or z allowed or not now for the same transition for the same symmetry we'll find out if it is for an example this a 2 is x allowed if it is rx allowed or not if it is rx allowed that means for the same motion I can have x and rx allowed that means electrical dipole and magnetical dipole moment allowed transition and only then this molecule will be optically active because previously we have already learned that if you want to have an optical activity you have to have x rx active together or y r y or z r z otherwise it's not possible and over there now we know from the symmetry elements and character table that which particular representation is going to allow me particular optical transition x axis y axis or z axis and then I have to just simply find out if it is also rx allowed or not so in the character table we'll try to find out if rx is also retained site on the side of x or not because it's may not be true rx can be a1 rx can be b1 and it may not be live with a2 if it doesn't lie no matter what you do with the molecule you cannot get an optical activity so altogether what our main goal is to find is x rx y r y and z r z are they staying together in the same symmetry representation or not in a character table or not that is the main thing we are trying to find out not sure so x r x y r y z r z are they combined or not in a character table in the same symmetric representation so that means it is totally possible I just look into all random character table and find out that which particular point group only have this together and only molecules belong to those point group will be optically active and that is what we defined earlier if you have a point group of cn and dn these are the only two point groups that actually satisfy this any other point group doesn't satisfy and that is why any other molecule falls in a point group other than cn and dn they cannot be optically active the only optical activity is possible if they belong to cn and dn y because in cn and dn point group you can have x rx y r y z r z activated together why it is important because that will ensure my electrical dipole moment and magnetical dipole moment will be activated together what is the consequence that you are going to create a linear and circular motion together that means you are going to create a helical motion unless you create a helical motion you cannot create a chirality inside the molecule because once we create the helical motion now you create a chirality because these two are not same they are mirror image and non super impossible to each other and only once you created it then it can differentiate between rcp and lcp you can have either optical rotation if it is a circular bidefringence we are talking about or we are going to see a ellipticity if you are talking about circular dichroism okay