 So, we started discussing about two dimensional NMR spectroscopy in the last class. We introduced the general concept in a qualitative manner. We said this principle is like this that you have a time axis like this and you divide the time into multiple into two different segments and which in multiple segments we call the first one as the preparation period and then you have the evolution we call it evolution and labeled it as T1 period. Then we had the so-called mixing here and then we had this detection and which is where we actually collect our FIDs and this is the time period T2. So, we collect a series of FIDs incrementing the time T1 from one experiment to another experiment. Therefore, this will result in a two dimensional data body T1, T2 and you do a two dimensional Fourier transformation. This will generate a two dimensional spectrum which we call as F1, F2 or sometimes people also use this as omega 1, omega 2 does not matter either way it is the same thing. We need a two dimensional Fourier transformation. So, the concept which you have to be clear is that this is segmentation of the time axis. So, the idea can be extended further to multiple dimensions as well. We are introducing one evolution time T1, you can introduce other evolution times, you can use 2, 3, 4, 5, etc then accordingly will generate various kinds of evolution times. So, we took a particular examples of 2D spectra where we talked about the 2D J result spectroscopy and there along the two frequency axis we had one axis we had the J, other axis we had the delta. So, this became a 2D separation experiment the two coupling constant is on one axis and the chemical shift is on the other axis. And we are going to go into other kinds of 2D experiments and those are the correlation experiments. However, so correlation experiments before we actually embark on to the correlation experiments we need to clarify some of the other concepts and need to define certain terms. Some definitions we have to give because this will be required for all our future discussions, for all future discussions what sort of a magnetization, how do we generate various kinds of magnetizations, how do we generate different kind of information in different spectra. So, therefore, here we will have to make a slight digression and define certain terms. So, some definitions we will give here, some definitions because these are the terms which we will be using all the time. So, in a generalized multiples experiment you have various kinds of evolution periods, preparation periods as I mentioned here and there is what happens is you start from initial magnetization which is here and the magnetization flows through this various time periods. This may be T1, T2, T3 etc. So, the magnetization flows if I want to use a different color for the magnetization it will flow through this and ultimately we collect the data. So, this is called as the magnetization transfer, magnetization transfer or magnetization flow. So, it goes from one state to another from one T1 period to T2 period to the T3 period and so on so forth. So, here magnetization flow is something which one has to understand and that determines what magnetization is present in what time period determines what is the information in that time period. When you Fourier transform it in a multidimensional way the information that is present in the T1 will appear as F1, what is present in T2 will appear as F2, what is present in T3 will appear as F3 and so on so forth. And there is various time separations here which are there can be various kinds of mixing periods here which will allow transfer of magnetization that is why we are talking about magnetization flow. Magnetization terms will have to be defined here, we have to define certain types of magnetizations that is what we will do here. So, let us keep those definitions here now. Let us say we have the term called IKZ. IKZ implies Z magnetization of spin K and this has to do with the populations of the levels, populations of the levels of K spin which will cause K spin transitions. Then let us say I have, then I have IKX let us say this means X magnetization or the transverse magnetization, X magnetization of spin K and we are talking about spin half systems here. For all of these let us say we are talking about spin half systems. All K, L, etc. whatever label we use I have used as the label K that is to identify the spin K I can use it L, M, P, Q or whatever they all indicate different spins and they are all spin half systems. So therefore and we need two different symbols here. Similarly, if you have IKY, IKY would imply Y magnetization. Now among these what is it that we observe? It is a transverse magnetization when we measure we measure the transverse magnetization. So, we measure transverse magnetization always measure transverse magnetization and that is IKX or IKY. IKZ is not observable because you have to convert this Z magnetization into the transverse plane bring it to the transverse plane because your detector is in the transverse plane therefore you measure the transverse magnetization. Now if I measure the IKX term if I measure the IKX and after Fourier transformation etc we get the time domain signal you get the FID for this FID and if you do Fourier transformation you generate a suppose it is a spin it is coupled to another spin suppose it is coupled to another spin. We will generate two components like this is the doublet of K. If it is coupled to some other spin like L it will produce an in phase this is called as in phase doublet in phase signal. Similarly you can write for IKY IKY will give you antiphase terms IKY FID and this may generate you a dispersive signal this is in phase dispersive. You can choose either way I mean depends upon where the detector is if I choose IKX to produce this absorptive phase then the IKY will produce me in dispersive in phase and vice versa. Suppose I put the detector along the Y axis and I measure the Y magnetization I get absorptive signals for the IKY magnetization and IKX will give me dispersive signal so these are interchangeable. So this is one set of terms which we will always use IKX, IKY, ILZ and when we have other kinds of what are the other kinds of magnetization terms. Let me define few other types of magnetization terms. So we also will come across terms something like this I 2 times IKX ILZ and this is called as antiphase magnetization of K which is antiphase with respect to spin L. Antiphase with respect to spin L. What does that mean? What does that mean? So if I take term like this 2 IKX ILZ now I do this is evolves during the generate an FID from here because FID generate means this has to evolve various kinds of evolutions will happen and then of course after you do a FID then I do a Fourier transformation and collect the signal this will generate is the same 2 lines but they will have appearance like this. So this is called as antiphase magnetization. So IKX ILZ this kind of a magnetization this is the magnetization term and which this evolves in the FID free induction decay because there is a J evolution that will happen there and after you do Fourier transformation of the resultant magnetization that is will produce you a spectrum which is like this. So these are called as antiphase signals same will apply for 2 IKY ILZ as well IKY ILZ or suppose I take ILX IKZ suppose I do this 2 ILX IZ what does this mean? This will mean the same sort of a term we will get but this is antiphase magnetization spin L this is spin L which is antiphase with respect to spin K. See the KZ indicates that it is with respect to skin K and LX means it is X magnetization this is X antiphase magnetization. Similarly I can also have 2 ILY IKZ this will be Y magnetization of spin L antiphase with respect to spin K. So these are the kinds of terms which you will get when you are actually considering a series of transfers from one time period to another time period during the mixing periods. When you do mixing times during the mixing time we generate transfers from one spin to another spin. See if I go from KX to let us say 2 KX LY 2 KX LZ to 2 LX KZ it would mean that I have transferred from the K spin to the L spin. So this sort of a transfers will happen when you are doing this mixing periods during the mixing times this sort of transfers will happen. That is why it is important to understand these terminologies how this will happen. So and there will be other kinds of terms and all of these are so all of these are called single quantum transitions also. So I will have to explain that in this context using a energy level diagram there. Suppose I am taking a 2-spin system so then I will have here these are all let us say alpha alpha alpha beta beta alpha and beta beta for the 2-spin system. So I will have transitions here transitions here transitions here transitions here transitions here and all of these are delta these are delta M is equal to plus minus 1 therefore these are called as single quantum transitions or coherences. And notice when I say transits and coherences the transfers magnetization always represents the phase coherence between spins whereas the Z magnetization represents populations as I mentioned earlier the transitions the transfers magnetization refers to single quantum coherences. These are all single quantum because what is the M value here? M value here is 1.0, M is 1.0, here it is 0, here it is 0, here it is minus 1. Therefore the transitions which I have indicated there these are all delta M is equal to plus minus 1 therefore these are single quantum. Now what are the other transitions possible? There are other transitions possible you can have a transition here and this is dq double quantum coherence because the delta M is equal to 2.0. These are not directly observable of course with selection rules when we consider double quantum are not directly observable but these will be created in the course of your pathway magnetization flow this quantum terms will also be created coherences will be created and then you also have a third kind of a thing possible. Let me see here and this is Zq 0 quantum. So Zq is called 0 quantum coherence dq is called double quantum coherence. So during the magnetization flow such kind of magnetization terms will be created. How do we know these ones? What are the kinds of magnetization terms which represent this? This is what we will see now here. You can have things such as 2 ikx ily or 2 iky ilx or 2 ikx ilx or 2 iky ily. This kind of terms indicate these indicate mixtures of double quantum plus 0 quantum coherences a combination of these can create pure double quantum or pure 0 quantum. Combinations of these can generate pure dq or pure Zq. So for example 2 ikx ily for example ikx ikx ily plus 2 iky ilx this represents pure dq this represents a pure dq. So similarly I can also make 2 ikx ily minus 2 iky ilx that will represent a 0 quantum. So such kind of combinations are possible you will generate pure double quantum or 0 quantum or mixtures of double quantum, 0 quantum and double quantum or in general multiple quantum. In general these are called multiple quantum coherences. You can also have triple quantum coherences but these are not directly observable. When you put detector these are not directly observable in a detector and they have to be converted into single quantum coherences for detection but these can appear in your transfer pathway. So these are not directly measurable, directly measurable in the detector systems they can appear in the magnetization flow. So therefore when you are having multiple experiments various kinds of transfers at various places all these kinds of terms will appear. So and we are going to use this in all these multidimensional and SMRM experiments which we will discuss as various kinds of correlation experiment which I mentioned to you. They will come across all of these kinds of terms and therefore it is important to understand what we are talking about here. So in the general scheme which you have various kinds of teams here you can have single quantum here, you can have double quantum here or 0 quantum there or you can have z magnetization, you can have pure double quantum. I am just randomly writing here what all things can happen coherences and here you have z magnetization. So these are the pathways, this is the pathway along the time and when you detect here this will be pure, this will be single quantum coherences only. You can detect only single quantum coherences and here it because this is the selection rule delta m is equal to plus minus 1, only that thing can be detected but these ones can appear anywhere in the pathway. So this actually represents the pathway of flow of magnetization. So therefore one can do design various kinds of experiments at what you want to have in a particular time period. I may want to have single quantum here, I may not want to have single quantum there, I want to have double quantum there, I might want to have I can delete some of those ones, how to manipulate those ones. This is the thing which actually generates a whole lot of experimental schemes which are required for generating a specific type of information in your spectra and that is what is the power of this multidimensional spectroscopy. You can use different kinds of nuclei, generate different kinds of coherences in this experiment. So and then I will have terms such as 2ikz ilz, I will also have such kind of terms and this is called as 2spin alder, 2spin zz alder. This can be converted into single quantum or double quantum, this can be converted into can be converted to sqc or dqc or zqc, all such kind of terms can be there. This is so far as 2spins are concerned. Now let us consider what kind of things can happen for 3spins. 3spins again I can have let us say these spins are klm, suppose I have 3spins then I can have terms like ikx, individual ones ilx imx, these are all mklm spin magnetizations, klm individually, x magnetizations of these are all x magnetizations of klm spins. So and the 2 spin terms will also be available, you can make combinations of 2ikx ilz or 2ikx imz and so on so forth. So there will be 2spin terms also there. Now there can be 3spin terms, 3spin terms are like suppose I have things like that 2 4ikx ily imz, suppose I have a term like this, I get term magnetization in the pathway I get things like that. What does this imply? This will imply dq plus zq of k and l spins antiphase with respect to m, mspin note whichever one is z it is antiphase with respect to mspin. So this will lead to a particular kind of a pattern in your final spectrum when we generate it or that I can also have things like this 4ikx ilz imz. So now I have 2z parts, transverse is only 1, transverse is only with respect to the kspin but I will have the z with respect to l and m. So this will be single quantum of k antiphase single quantum what? Transverse magnetization xspin, this is x magnetization antiphase with respect to both l and m spins. This will generate different kind of terms when you actually do a measurement. So if you have such a kind of a term let us take for example ikx ilz. Now in the 3spin system, how will the ikx look like? So then with the 3spin system is like this I have the kspin lspin mspin and there is a j for each one of those j1, j2, j3. Let us say if I have those how will the ikx look like? After this generates a fid and then you measure take the ft and this will give me for the k, I am only writing for the k because this is the kspin. So the kspin will be 4 lines which is a doublet of a doublet because it is 2 couplings j1 and j3 couplings. This will generate a doublet of a doublet. So if this coupling constants are not equal then it will be a doublet of a doublet. In the same one suppose I have a term which is like this 2ikx ilz. So what it will generate to me? This will this term in the fid and then you do ft and this will produce spectrum like this. In the spectrum it will appear like this 2ikx ilz. Notice here this repeats here positive negative positive negative. So it repeats. This is called as it is antiphate with respect to the lspin. Now suppose I have this kind of a term 4ikx ilz imz. This generates an fid and then I have the ft and this will produce a pattern like this after Fourier transformation. Now you see this is positive or negative. This came from the antiphate with respect to the lspin and then again now negative of this. So therefore positive negative negative positive. So therefore this is plus minus plus minus and here I have plus minus minus plus. So 2 negatives. So one negative coming from the k to l and the second negative coming from k to m. So therefore we get this kind of a pattern. So this is doubly antiphase magnetization. Therefore this is called as doubly antiphase magnetization. So alright then let me also write one more term which is to complete the story here ikx ily imx or any combinations of those. If I write like this, these are called as triple quantum coherences. Once again this will not be directly observable. These will have to be converted into single quantum coherences before actually you can observe and then we will generate the various kinds of spectral features as I indicated in different things like this. So we will be dealing with such kind of magnetization transfer pathways as we go into the multidimensional NMR experiments. In fact this is when we want to talk about the cosy and the nosies and things like that these are required. That is why I introduced these ones beforehand so that we will have no difficulty in understanding these kind of situations. So alright so then I think we can stop here and we go into the next phase into the next class.