 Welcome to today's lecture. So we were discussing high resolution NMR spectra of molecules. If you remember in the last class we had discussed how to make chemical shift field independent because we remember that like if we record chemical shift at different field in terms of frequency or in terms of hertz the values were changing. So to get rid of that we started looking at the how to express the chemical shift in PPM value and that PPM value made it independent of field. Then we looked at that for referencing we need some compound which is inert and does not react with the solvent and the molecule of our interest. And therefore TMS and DSS were obvious choice because their resonance comes quite often shifted or lower PPM value their water like TMS is highly shielded and that is how it is used as a reference. DSS on the other hand is water soluble and it does not interact with any biomolecules and it is used for water soluble compound. So next we looked at the what are the factors that influence chemical shift and out of those many factors we looked at what ring current can do. So ring current effect we had looked at and ring current is 1 which causes the downfield shift or higher PPM value shift of resonance of CH protons of aromatic compound. Then we also looked at the contact effect this is this comes because of some unpaired electron are present and that can shift chemical shift significantly. Then after that we looked at the chemical shift variation due to different nuclei attached and that all we have summarized in the last class. So now from here we will move forward and we start looking at actually now the another very very crucial parameter that is called spin coupling or this is also called j coupling or scalar coupling. So let us start looking each of these parameter together. This is also called j coupling. Scalar coupling because this does not depend upon orientation and this is also called a scalar coupling. Now so we had looked at the first chemical shift spectra that were recorded on ethyl alcohol on 14 megahertz and it gave 3 line. The first line corresponds to CH3 methyl proton methylene proton and this is for OH proton. So this was for OH, this was for CH2 and this is for CH3 and the height of each of these peak was like 3 to 2 to 1. That is what we had looked at. So this was the first spectrum recorded by Dharmati and coworkers and then that actually opened the avenue of NMR in chemistry. Now in the same year almost in 5051 Proctor and Wu discovered one of the very very important parameter which is called actually the coupling constant. This helps in unambiguous characterization of molecule. So today we will look at how actually it helps in unambiguous characterization of molecule. So what happens that in the high resolution spectrum actually the one line of methyl proton that we had looked at here is not actually one line. However it is split into three lines and that is what here we see. In case of methylene actually this is also not one line and it is split into many lines and similarly OH also splits into many lines. So splitting of the resonance of line and the extent of this splitting, extent of this splitting actually reports for what is the strength of interaction between various spins and how these spins are interacting. So this actually this splitting pattern helps us in identifying the final structure of a molecule because this spin-spin coupling between the methyl and methylene proton actually tells the neighboring group effect and this is due to something called J coupling or spin-spin coupling or scalar coupling. So just to remind you here we should have if there is no coupling then in case of methyl there was only one P here and here also there was a one P and this is also a one P. Now this was 3, 1, 2. Now if you look at here this OH it is coming slightly upfield shifted then like CH2 and this spectra was recorded on generally very like neat alcohol, pure alcohol. So now we move forward and we look at how does this splitting occurs. So what is the reason behind the spin-spin coupling or J coupling? So this happens because of interaction of mediated by the electron in the intervening bond. So in a simple term what is happened like we had looked at the chemical shift is because there is a spin and around that there are electronic clouds. Now if you look at these spins is not in isolation there is another spin which is near here and that spin can influence the chemical shift or the resonance property of this spin and that coupling happens via the electrons that are between them. So that is why this is called through bond coupling. So through bond coupling because the two spins are now coupled by an electron. So in the bond that is intervening here. So a nuclear spin can polarize the electron spin adjacent to the bond orbital here it can polarize it and that polarizes the spin parameter of electron in the same orbital. So that can affect this one and then what happens this is through bond so can extend up to 4 to 5 bond but as you go far and far the strength of that effect decreases therefore the J coupling becomes smaller and smaller as we move far and far. So the strength of the coupling is called coupling constant or J coupling. So that means how much this spin affects its neighboring spin through bond it is called J coupling and as we say as we move from one spin to two spin this is quite strong but if you look at the effect of third spin the J coupling spin decreases because we are moving now far from spin number 1 to 2 to 3. Now what is happening here it is a concerted polarization of a nuclear spin and electron spin. So in a simple term suppose we have two spins here spin and there are some electron spin in between. So what is happening now if we are considering spin number 1 then it is near there is another spin and that spin can exist into form either up form or down form so spin state A and spin state B. So because of this orientation of the now this is our interest spin and this is its neighboring spin. So it has different state spin state 1, 1 state A and state B. So now this is influencing the electronic spin which is between these two spins and that is here that is shown here. So then the coupling interaction between these spins I1 and I2 is quantitatively given by spin interaction which is called J1, 2 I1 and I2. So this is the coupling strength where J1, 2 is a coupling constant. So in a simple term if there is a spin here and if there is another spin here now this spin is affecting the resonance frequency of this because spin number 2 here I2 and I1. So this is I1 and this is I2. So the interaction occurring between them because of this coupling is JI2. So now the resonance frequency of I1 is affected by I2 and vice versa and that is called spin-spin coupling or the scalar coupling. So let us define two spins like A and X. Now as we see that if these two spins are close by and they are connected by bond then there is a coupling between them which is called J coupling. Now then what happens? The energy of spin A, now actually it has 2 G minus state. So like here spin A, IA then it has 2 G minus spin alpha state and beta state. Now depends upon this state depends upon whether the X spin is in alpha state or beta state. So IA this state depends upon whether the X spin is in alpha state or X spin is in beta state. That affects the resonance frequency of this and this coupling can be positive. So because of that now what will happen between these two states, now there are two spins as we discussed spin A and spin say X. Now A spin has two state alpha and beta state and similarly X spin has alpha and beta state. So now because of this there are four state can be possible alpha alpha, alpha beta, beta alpha, beta beta. What it means in terms of vector? So here is alpha state and this beta state. Here is also alpha state and beta state. So it can be up, up both spin, up, down, down, up and down, down. That is all we are we were discussing. So because of this the all states that we were discussing it can exist here alpha alpha, alpha beta, beta alpha and beta state and these states will have different energy. So because now A spin is not in isolation it is coupled with B spin therefore the different energy will be. So coupling between them is positive if the energy of alpha state of spin A increases that means if the energy changes here and if it is increases and increases for X spin that is in alpha state and it decreases if X spin is in beta state. So what we are saying the energies of spin A and B can change. So suppose here here is the energy of A spin it can decrease or increase depending upon if the X spin is in alpha state or beta state it can increase or decrease. Now that is what we call coupled is positive. However the energy of beta state of spin A will increase if the X spin is in the beta state. So if X spin is beta state then it will increase and it will decrease if X spin is in alpha state. So that actually changes. So that is what now we can understood. So instead of now two energy here it can be depending upon whether what is the state of B and we can have four states here depending upon whether B is in alpha state or beta state. So that is what it is shown here. So again I will repeat it. So say spin A has two energy level one for alpha state one for beta state. Now depending upon what is the orientation of spin X if it is beta state or alpha state. So here if you look at this energy level it changing. If it is beta state the energy is decreasing. If it is alpha state energy is increasing and the separation between these two states is only few hertz. Similarly here also the energy of beta state also has changed depending upon whether X is in beta state or alpha state. So there are four energy level now created depending upon whether the X spin is in beta state or alpha state. So we can call this as a like alpha beta state as a 0 alpha alpha state as a 1 here beta alpha state as a 0 and beta beta state as a minus 1. So now the resonance for the spin A will have two line one will be mu 1A. So this is first line and this will be second line. Therefore the now earlier which was only one line here centered at the mu A now it will be split into two line and that separation between these two line will be J 1 2 or J coupling between these two states. So if you look at the energy level diagram. So if alpha alpha is alpha alpha state that is alpha A alpha X is this alpha beta is this beta alpha is this beta beta is this. So now we have four energy states one coming from here if the first spin is changing its state that is alpha is going to beta and here also if alpha is going to beta here again we have the energy state. So now spin A we have two lines one corresponds to this and another corresponds to this. Similarly it will happen also for beta and that will be given by these two lines here. So if A is coupled with X, X has split A into two line. Similarly if A is a half spin and X is also half spin as we said. So X will be also split it into two lines. So these are for A spin this is for X spin. Now that is the final structure. So now when A is coupled with X the transition will be called alpha A X beta A X. So this is here if you look at A is flipping. Similarly here again A is flipping and that is what this and this line corresponds to this and this line corresponds to. So now as we will say parallel orientation of these spins increases the energy states and anti-parallel will decrease the energy states. So here if you look at now we are looking at the coupling between this H and C and here it is coupled via C. So if they are anti-parallel here if the parallel orientation of spin increases the energy whereas the anti-parallel decreases the energy. So here J will be positive and here J will be negative. So in case of one bond coupling like here one bond coupling the anti-parallel orientation of nuclear spin leads to lower energy and that coupling is called positive. Whereas two bonds separated spin like here two bond one bond here one bond here two bonds separated spin the parallel orientation of spins leads to lowering of the energy and this coupling is called negative. So we can have the value of J positive and negative. So now depending upon how the orientation of each spins the value is also changing. But one thing to remember this J coupling is field independent. Chemical shift was field dependent when we express that in PPM value it becomes field independent. J coupling invariably it is field independent. So positive and negative sign depends upon the orientation but does not depend upon which field we are recording this is a constant value. So what are the factors that influence the spin-spin coupling or J coupling? So first as we see the closeness of two spins depends what will be the strength of because these spins are coupled by a bond and in bond there are electron. So spin-spin coupling over one bond is denoted by J1 like here J is the scalar coupling and one denotes the one bond value. Now in the J-minial coupling which is say is two bonds so here these two bonds are called here like one bond here and one bond. So these are two bond coupling. Now visceral coupling is called three bond coupling. So if you look at one bond, two bond and three bond coupling. Similarly long range can be like more than four bond coupling. So depending upon one bond, two bond, three bond, four bond coupling. So h here and h here will be four bond coupling if it is connected like this or 1, 2, 3, 4. So that is more than this is called long range coupling. So if you look at the distance is increasing the strength of the coupling will decrease because this is connected through bond. So as for an example if you look at two bond coupling and we are saying this is minus 12.5 three bond coupling is four. However depending upon how they are oriented if long range coupling like five bond is 5.5 to 11 hertz. So but if you compare 2 to 3 actually as we move further the coupling constant strength is decreasing. So there are range of coupling constant. So a homonuclear coupling are generally small compared to heteronuclear. So for proton-proton like two bond coupling is generally 5 to 20 hertz whereas one bond coupling in heteronuclear system like 13C and proton it is a quite a bit 100 to 250 hertz. For nitrogen proton coupling here it is 80 to 100 hertz and then phosphorus proton coupling is typically around 17 to 12 hertz. Now here if you take three bond coupling this decreases four bond coupling further can decrease the proton-proton coupling. However this is called homonuclear coupling and these will be called heteronuclear coupling because that is between proton and proton and here our X nuclei like 13C and 15 and phosphorus are there. Till now we have understood that there is one parameter which is important is chemical shift. The another parameter is important coupling constant. Coupling constant is coming because of another spin coupled to the spin of our choice and this coupling is happening via electronic bond and as we move further the strength can decrease but the splitting the splitting cause because of this J coupling or scalar coupling. So now these two parameter chemical shift value and a J coupling these two are very important parameter because these are required for high resolution NMR spectrum analysis for any molecule even small molecule or bigger molecule. Now as we looked at the chemical shift value is for a particular nuclei. So that gives the particular resonance frequency for a nuclei and this is denoted by delta value so that is chemical shift value. The coupling constant actually determines the interaction between those nuclei. So a particular spin will have a chemical shift and another spin have another chemical shift and how strongly they are coupled or how strongly or weakly they are interacting that is given by J value. So the basic analysis for any molecule is requires these two parameter their chemical shift value and the coupling constant between these two. If you know this value one can identify the molecule. So this basic analysis of any molecule is done by using these two parameters and this is called first order analysis and there are certain basic rule to understand what is required first order analysis and then that I am going to come in a minute but for more complex analysis of these spin-spin coupling you require even more complex formalism and that we will look at later at the course which is called quantum mechanical calculation for if the spins are too strongly coupled. So now we move to first order analysis which is the simplest analysis of the molecules. So before we move ahead we define some of the spins nomenclature and spins are generally defined in terms of upper case of the alphabet like A, B and C. Now a spin will be called AB system or AX system depending upon what kind of chemical shift they have. If their chemical shift is quite close then they will be they will be called AB system because in alphabet A and B are close. If their chemical shift is far then they will be called AX system if you look at the alphabet A and X is quite apart. So AX system these two spin have a resonance frequency that are widely separated like something say here this will be A and X and on the same magnet AB system will be something like A and B. Now so ABX system will be like say AB and X here because A and B are quite close and X is far from them that is called ABX system. Now so AB are fairly close in relation to the in comparison to X. There is another parameter which is determined here is called coupling constant. So the coupling between them is called JAB and coupling between them will be called JAX. So now here AX system because their chemical shift is quite far AX system or AMX system or AMQX system because they are like separated in the alphabet these will be called weakly coupled system whereas AB system or AB system will be called a strongly coupled system. So what is happening here A and X their chemical shift quite far and the separation between say delta A and delta X is greater than the coupling between them JAX and this is the consideration to define that as a weakly system whereas JA and JB will be equal to these splitting between them JAB and this will be called strongly coupled system. So if you look at strongly coupled or weakly coupled system are not reflection of the strength of the coupling constant alone however it is the consideration of the chemical shift. So how far the chemical shift is in comparison to the coupling constant that determines whether the systems are weakly coupled system or strongly coupled system. So typically heteronuclear system are weakly coupled system and many of the homonuclear system are strongly coupled system not all but there in homonuclear system we have a strongly coupled system. So if I look at the 13 C chemical shift like 13 C chemical shift and proton chemical shift so here on 600 megahertz this will be near to 600 megahertz chemical shift and this chemical shift will be near to 150 megahertz however the coupling constant between them will be around say 150 hertz. So this separation between the chemical shift is quite far from the strength of coupling constant and these will be weakly coupled system. This cannot be case for the homonuclear system here it can be like equal as we were saying here or almost equal. So these will be a strongly coupled system. So first order analysis or simplistic analysis are generally done for weakly coupled system not for strongly coupled system. For those we need a quantum mechanical calculation to understand. Now one more concept I will explain that this is called chemically equivalent and magnetically equivalent nuclei. Now a group of nuclei we can define as magnetically equivalent if all of them have a same chemical shift and each of them has a same coupling constant to every other nuclei outside that group. So these will be called magnetically equivalent nuclei. So similarly like here a to x now a here if you look at here we have a three kind of proton this proton and this proton will have same chemical shift and they have a same coupling constant with x. So this will be called magnetically equivalent nuclei. So that is why this system can be written as a to x that means two a are equivalent but that are different from the x that is why it is called a to x. So spin coupling between these magnetically equivalent nuclei does not appear in the spectrum that means the a to there the spin coupling between them will not appear in the spectrum whereas the coupling constant between this a and x and this will be appear. So these they are not magnetically equivalent to x however among themselves they are magnetically equivalent. Now look at the another system and here we define as another type of nuclei which is called chemically equivalent nuclei or isochronous. So chemically equivalent nuclei will not be magnetically equivalent if they have a different coupling constant to other nuclei in the molecule. So like if I look at here here look at this molecule the one substitution is NO2 and another OH. Now here the Hx and Hx prime here Ha and Ha prime. So these are actually chemically equivalent but not magnetically equivalent. So they have there will be coupling constant between these they are not magnetically and there will be coupling constant between them. So they are not magnetically equivalent they are chemically equivalent. Like similarly if you look at here here Ha and Hb they are not magnetically equivalent neither they are chemically equivalent. So there will be coupling constant exists between them. If I look at these nuclei so fluorine and proton their resonance frequency is quite close. So they are also there will be coupled and there will be coupling constant between them and they can be also called different chemical like they will be not magnetically equivalent neither chemically equivalent. So now these all will be important in interpretation of multiplied structure of a compound. Now multiplied pattern so when we do analysis the multiplied pattern of different groups of line will be different and that will be also dictated by the relative intensity of individual group like as we see different group like CH3 was like this and CH2 was even more complicated. So CH2 like it was split into 4. So that we will look at how the splitting comes from and intensity how it changes the intensity. So that again is very important when we are interpreting the multiplied structure. And measurement of coupling constant what I mean by measurement of coupling constant is this measuring JAB from the splitting of individual group is important because that helps in identification of group having same coupling constant. So here this measurement is so all these parameters we are going to discuss in detail the intensity the pattern as well as the strength and that helps us in analyzing the first order spectrum of the molecule. So that I am going to discuss in the next class how to do the multiplied analysis of different groups and what is the basis of different intensity in the group and how we can measure or how we identify the coupling constant to identify the groups are similar or different and that all comes under first order of analysis. So if you have any question for today's lecture you are welcome to ask and we will try to respond each and every point that we have discussed for today. Look forward for your attendance in the next class. Thank you very much.