 Welcome to this new segment of CD spectroscopy and Mossberg spectroscopy for chemistry. Previously, we have discussed what is chirality and what is symmetry and we look through and we found in nature we have various examples of symmetry and chirality remaining there. And when we are talking about the symmetry, we found there are three different major oceans or segments of symmetry bilateral, radial and also spherical and we have also found chirality is one of the important aspect of this symmetry. The chirality is an important aspect because it has a huge role to play in biology. It helps it to do the molecular recognition whereas the chirality which means a particular object whose mirror image is not superimposable on each other is a key role to play when it comes to the proteins, carbohydrates or nucleic acid and that is why we are very much interested to know about chirality and we have also discussed that there are certain drug molecules whose properties are also dependent on its chirality. One form of the enantiomer can be a life saving drug whereas the other one looks very much similar to it other than one or two chiral centers can be lethal to us. So that is why a knowledge about chirality is very important. So now we have to connect a molecular structure chirality with certain properties by which we can differentiate a chiral molecule. So before jump into that let us know about how this molecular structure and its properties are connected. And for that we are looking into this structure function relationship and to understand how a structure of a molecule is controlling its properties we are going to take a little bit of help from quantum chemistry. So in quantum chemistry we have various equations comes to our mind but one of the most important equation that comes is the Schrodinger equation and what is a Schrodinger equation? A Schrodinger equation says this particular system H psi equal to E psi we all know this equation but what are the meaning of this equation? So this term H which is known as the Hamiltonian is nothing but a system which actually defines our surrounding we will come into that a little bit later this phi is known as the wave function E is quite obviously the energy and the psi is wave function back again. So when we draw this particular thing what is this particular wave function means? Wave function means typically when you are talking about an electronic system how the electron is moving the electron movement if I want to define that with a mathematical expression that is the wave function psi. Now this electron movement is controlled it cannot put anywhere as it want it is controlled by what? It is controlled by the nuclei it is controlled by other electrons and other forces around it and all those things control how the electron should move and if I can define the presence of nuclei other electrons or other forces around this system of the electron this is nothing but this Hamiltonian that we have written over there. So this factor A is Hamiltonian operator nothing but defines how my electron is surrounded by different particular segments or factors which can control the movement of the electron and that is known as the Hamiltonian operator. Now with this you can define that this surrounding has a lot to say because if I change the Hamiltonian factor it affects directly its energy it also controls how the psi would look like. So this Hamiltonian factor actually has a direct role to play on the psi a direct role to play on the energy. So that means by psi I am controlling the property and by E I am controlling the energy. So with these two factors the Hamiltonian is controlling that and it is controlled by the presence of the surrounding and the surrounding is nothing but the description of its structure. Just imagine I am talking about an electron where there are three nuclei in a regular triangle shape versus the same electron a shape like this. You can say the situation one versus situation two is not exactly the same situation one the electron will behave differently compared to the electron in the situation two and that is because the nuclei over here are in different position the other associated electrons are in different distance compared to this one in the situation one and that is why the behavior will be different because of the psi and E will be different because the surrounding or the structure is defined which can be defined by this H the Hamiltonian factor. So we can say the situation one is that H dot E dash dot this one whereas this one can be double dash and accordingly the energy and the wave function will also change. So because these are actually going to be different the property will be different the energy will be different and that is how the structure of a molecule controls what will be the behavior of the electron especially the electrons sitting on the valence bond and as you know valence bond electron controls the most important properties the acid base properties the redox properties the other important properties like electron negativity and all the periodic properties and that is why the surrounding on the structure has a big role to play over there. So now we understand what is the effect of structure and function does it really effect that much. So for that we will take an example and we will take an example of a very simple system. We will start a cube we will start with a cube they have the 3 sides. So let us say I am naming them A B and C and now if I put this cube on each of the different phases because it has 6 phases 2 A Bs 2 B Cs and 2 Cs and if I put them on a particular phase what will be their energy the potential energy that I am going to measure and as we know potential energy V is equal to M G H say the mass and G remains same so the factor will be H. So if I put this particular system on the phase of B C as it is the energy will be dependent on only on this A. So the energy of B C will be somewhere around here now if I want to do and change the phase which is sitting on the base say if it is A B phase the height will be C but because C and A are same so the C A will also have the same energy same thing if we do for the A B phase the system will have the energy height of C. So heights will be over here A over here B over here C and because all of them are same over here in this case A equal to B equal to C this energy will be all same or in other words we can say they will remain degenerate. So now say I am taking a case number 2 where I am taking the similar system where the A and B remain the same but I am changing the C I am making it a bit longer this is my C over here A equal to B but they are less than C and C is much more higher. So now if I want to plot the energy then what will happen? Now I can put them in 3 different phases I can put them in B C and put them in C A we can put them in A B. Now B C will be this phase as it is written the height is A so the energy will be somewhere around here C A if I put that on the C A phase the height will be B and A or B are same over here so their energy will be also same. But when I put that in A B phase the height will be the C and C has much higher height so the energy will be higher. So previously all 3 are same because A equal to B equal to C over here I break the symmetry I make it less symmetric A equal to B but not equal to C or less than C and for that one of them got out the rest of them remains symmetric or degenerate but this one goes higher in energy it breaks the degeneracy. Now take an example the third case where it is such a case where I am breaking the symmetry further. So this is A this is B this is C and it is such a way A is less than B is less than C so all of them are now different. Now what will happen? The energy will be dependent on which of them is actually higher in energy so because you are measuring a potential energy over here height is the important factor. So C will be the height when I am talking about the phase A B then will come the B which will be the height when I put the system on the CFS and A will be the height when I put then the BC case. So this is A this is B this is C and as we say it is less than those so that is why the highest energy you will see on the A B then C A then BC and over here you can see there is no degeneracy at all all of them are different and you can kind of say previously where the system is very much symmetric I actually have all of them in the degenerate level. Now I slowly changing the symmetry so I am reducing the symmetry over there what happens I break only one part and two of them remain degenerate but one of them is going out of degeneracy over here and on the last hand when you actually totally vanish the symmetry all of them are different and similarly it is reflected on their energy all of them are different. So over here you can see symmetry and energy degeneracy is kind of holding hand and showing us their effect. So if I want a very symmetric system I would end up with a very energy degenerate system whereas if I take a symmetric system my energy degeneracy will be breaking down and this energy degeneracy and exactly what is the energy that will define the reactivity of a molecule and that is why symmetry and energy are very crucial point which we have to take a close look on to. So with that now we move to the definition of symmetry so we are talking about symmetry a long time we have also loosely defined what we mean by symmetry when you are talking about the natural system talking about the bilateral symmetry talking about the radial symmetry and spherical symmetry but if I want to define symmetry what is actually a symmetry and if I take this Oxford dictionary and over there try to find what is written there about symmetry and this is the system we are going to find. I am just writing it mutual relation of the parts of an object in respect to magnitude position relative measurement and arrangement of parts. So over there this is very important mutual relation that means I am going to change of the molecule in between such that one part of that whole object or molecule is going to be magnetically that means by the measurement the position the relative measurement and arrangement will be very much similar in relation and if you are seeing this we say we are having a symmetry so that is we actually try to define. So in the previous slide we actually just saw that so if I go back so you can see over there we saw that yes we are actually having this different symmetries and as you are going down we are changing the energy so similarly over here that is the definition of symmetry. So now we understand what is the definition of symmetry we understand yes the shape and symmetry can affect the energy but how does it come into a chemical molecule so for that we will take another example. The example we will take one of the very common molecule that we all aware of is benzene. So this is the benzene molecule I draw so the example we will be taking benzene is quite common molecule and this actually has six hydrogens and now if I try to follow up the symmetry of this molecule by doing an one H NMR spectroscopy how many signals we are going to get in one H NMR we are going to get only one signal why one signal because of this particular symmetry of this molecule we actually have all the hydrogens are actually mutually very symmetric to each other. So that means this molecule the hydrogen although they are different they are not going to show their difference in an environment when you are doing this proton NMR spectroscopy they are going to be very much symmetric and that is why we are going to get only one signal because the structure defines this symmetry. Now take a variation of this same benzene molecule but over here what we are doing we are putting an X so instead of all hydrogen now I break down the symmetry by putting an system X over here and due to the presence of the X the previous symmetry is now gone. So if we talk about the symmetry symmetry is actually lowered as we put this X molecule over here X is anything but hydrogen. So then how many proton signals I am going to have now as we learn these two protons say like HA will be very similar these two protons will be similar this proton will be different. So these are nothing but the orthoprotons, metaprotons and paraprotons. So altogether I am expecting three different signals of proton in proton NMR and that is coming because the symmetry is now going down. So just by introducing one extra group other than hydrogen I can get difference stark difference in signal and that is showing that now the environment around the hydrogen is different and they are going to behave differently. So their behavior is directly connected to the structure which is can be defined by the symmetry terms. The next one we can have another portion of proton around the benzene and over here we are putting we are putting two X around it. So these are one this is the second so these are the two different X molecules you have and now if I want to define it how many hydrogen atoms you can find we are going to get only one hydrogen atoms why because all these hydrogens are similar in nature. So they are all symmetric because they are ortho to one X and the meta to other and it is true for all these hydrogens and that is why we are going to get only one signal. So again the change of the symmetry you can say from 1 to 2 I am getting more symmetric and as the symmetry changes my signal is actually varying. Now say I am taking this two X but putting that not in the para position like this how about I put them in the meta position. So over there how many hydrogen signals we are going to get. So obviously the first one would be this one which is ortho to both the X groups so that will be different. This one will be the other one which is para to one of the X and ortho to the other and this H, Hc which is also unique because this is meta position to both the Xs. So over here we are also getting three signals and you can say this molecule is actually have different symmetry lower symmetry compared to this one and as we are changing the symmetry we are changing the number of proton signals also. And the last one with bisubstituted benzene I can have that they are in ortho position and over here how many signals we are going to get. So over here this will be a hydrogen ortho to one and meta to other same for this one so one type and this one is para to one and meta to other similar for this. So over there I am going to get two different signals and that is what we are going to get for this particular molecule. So you can see from the starting from the benzene in the beginning which is very much symmetric I have only one signal this is case A. In case B we actually monosubstituted the benzene and over there we introduce a bit of asymmetry. So symmetry is going down and it is very much well signaled by this three different signature peaks in proton minima. Then case number C where you have a bisubstituted one where the parasubstituted quite symmetric and that is why we get only one proton. This is case D where we actually have again a bisubstituted but meta one which is actually have a little bit lower symmetry and we are going to get three signals. When you put them in the ortho position we get also two signals and you can see that symmetry has a direct role to play how many hydrogen signals I am getting and hydrogen signal in AMR defines how many different environment chemical environment these protons are facing. So with that it is showing that the symmetry is directly controlling the electronic environment of the molecule which we can say nothing but the property of the molecule and that is what is actually coming over here. Now we define the symmetry we define that yes it changes its energy it changes its symmetry along with the molecular properties and we also have a definition of symmetry with respect to the definition from English but how to define symmetry with mathematics that is one of the most important thing that we have to cover and that we will be covering in the next segment. So before going there we would like to just conclude in the beginning section that the symmetry is important aspect and that controls its energy and that controls is molecular property and all of them can be also defined by the Schrodinger equation H i equal to E psi where this H is nothing but an operator which actually reflects the definition of a surrounding that means the symmetry around the molecule. So with that we would like to conclude over there for this segment where we have defined how the symmetry and molecular property are interconnected and by following the symmetry how we can define the different properties or the structural effects on the energy on different molecules. In the next segment we are going to follow a little bit of mathematics to combine them properly. So with that we would like to conclude over here. Thank you, thank you very much.