 So, we are now going to discuss the various 2 dimensional NMR experiments that have been developed over the years. A large number of experiments have been developed and these are generally categorized into 3 groups when we call them as resolution or separation experiments or correlation experiments, multiple quantum experiments. So, 3 categories of experiments are known and we put them as resolution or separation experiments or correlation experiments or multiple quantum experiments. And this is a very unique feature, multiple quantum experiments is a very unique feature of 2 dimensional NMR spectroscopy. This was not possible to observe in the conventional 1 dimensional NMR and that is, I will just briefly tell you what it is all about. And we know that in a 2 dimensional spectrum you have 2 frequency axis and we call this as F2 and F1. So, whatever the information present in the T1 domain of the 2 dimensional data body, it appears along the F1 dimension, what is present during the detection period appears along the F2 dimension. So, these experiments differ by the information content and what is present along the F1 axis or what is present in the map here in the 2 dimensional matrix. So, that is how these experiments can be classified and grouped into the 3 different types. You may have particular kind of information along the F1 axis, for example, you may only have the chemical shifts or you may have the coupling constants along the F1 axis and similarly you may have the coupling constants or the chemical shifts along the F2 axis, then it will lead to one kind of experiments. And if you have multiple quantum frequencies along the F1 dimension, then you have what are called as multiple quantum experiments. See typically multiple quantum signals are not observable as we discussed in the product operator fundamentalism, multiple quantum signals are not directly observable because the trace of these multiple quantum operators with the Ix or the Iy operators is 0, therefore they are not observable. But in the F1 dimension, since you are not doing any direct detection, it is possible to represent these frequencies here and the evolution under the multiple quantum frequencies modulates the detected signal in the F2 dimension and eventually we detect only the single quantum frequencies in the F2 dimension but the multiple quantum frequencies are obtained along the F1 dimension in an indirect manner. In J-resolve or resolution experiments, F2 dimension will have the normal frequency information and F1 dimension may have only the coupling information or the coupling plus chemical shift information so on so forth. So, this is the way these various experiments have been designed and we are going to discuss this in somewhat greater detail in the following slides. So, let us first look at 2D resolution and separation experiments. The primary aim in these experiments is to separate the different interactions in the Hamiltonian. So, we are talking about high resolution NMR here. In high resolution NMR, the Hamiltonian consists of 2 terms, one is the Hz or the second one is Hj and this is the Ziemann Hamiltonian, this is the J coupling Hamiltonian. So, Ziemann Hamiltonian is responsible for the chemical shifts and the J coupling Hamiltonian is responsible for the couplings. Now, different strategies can be defined depending upon the nature of the information required in the final spectrum. Let us take a few examples and try and see how we can analyze that. So, this is one example wherein you do the experiment in the following manner. So, you consider a heteronuclear system, carbon proton and we are talking about a natural abundance carbon 13. So, in a molecule which has only 1% carbon 13 and we are talking about those kinds of things and of course the proton is 100% abundant and there will be different kinds of carbons in a molecule. Some of them may be attached to 1 proton, some may be attached to 2 protons, some may be attached to 3 protons and so on and so forth. CH groups or CH2 groups or CH3 groups. The experiment is performed in the following manner. You first apply a 90 degree pulse to the carbon magnetization. Remember we are talking about the C13. So, that is at the natural abundance. So and when we apply the 90 degree pulse to this carbon and which is the initially the magnetization here is along the Z axis and it will after the 90 degree pulse this magnetization comes to the Y axis. Depending upon where you apply the pulse whether it comes to the Y axis or the X axis depending upon the phase of this pulse when you apply X pulse it will come to the minus Y axis and if you apply Y pulse it goes on to the X axis and so on and so forth. Now during the T1 period this is your indirect deduction period or the evolution period we apply a proton decoupler, broadband decoupler here which means so during this period the carbons will not evolve under the carbon proton coupling. They will only evolve under the carbon chemical shift. So the different kinds of carbons which are present they will evolve under the carbon chemical shift. So what is the information present here? Only the carbon chemical shift information is present here. So at the end of the T1 period we start the deduction period and there we turn off the proton decoupler. Therefore what is the information present in the T2 period? We have both the carbon chemical shifts and the carbon proton couplings. So therefore when you do a two dimensional experiment and do two dimensional Fourier transformation the spectrum will look like this. So this is my F1 dimension here. Here of course we have represented the F1 in a different way and conventionally we had written this as the F2 dimension, this as the F1 dimension but that does not matter you can choose whichever way you want. So we have put here as F1 and I put here as F2. So now if you see what is present along the F2 dimension? F2 dimension I have this chemical shift. This is the chemical shift of this particular triplet here and this center is the chemical shift of this quartet here and this is the doublet chemical shift here and this is again a triplet of this. So this one therefore this triplet here this represents the CH2 group and this is a quartet which represents the CH3 group and this is a doublet which represents the CH group and this is again a triplet which represents the CH2 group. And this information this coupling information is present only along the F2 dimension here. Therefore you have a triplet here a quartet here a doublet here and a triplet there. Now along the F1 dimension what we have if you take the projection here you only have one line you take a projection here you have only one line similarly here and this is at the chemical shift of the particular carbon. And you see the line which has been drawn here this is to indicate the so called diagonal you see this chemical shift along this axis or this axis is the same this point is the same on this axis or this axis. Therefore here I have the chemical shift information and here also I have the chemical shift information at this position and if I come here I have the chemical shift information corresponding to this and similarly the chemical shift information is here this is the center of the multiplet this is the quartet and here the doublet and the doublet is of course the center of the doublet is here the chemical shift position is in the middle here and the two lines in the doublet are separated out from here. So if we were to take a cross section here like this then it will be a quartet of CH3 group, a quartet of a CH3 group how does it look? So let us just try and draw it here. So a triplet if we were to take a cross section here so that will look so this will be the cross section here. And if I were to take a cross section here it will look like it will be a quartet so this will be a quartet and the centre is here this is the chemical shift position, this is the chemical shift position. So likewise this one will be a doublet, the chemical shift position is in the middle and the last one will be a triplet again and this is due to the carbon proton coupling. Carbon proton one bond coupling these are, carbon proton one bond coupling is like 140, 150 hertz so therefore these are pretty well resolved and the centre is in this empty position here. So this is one way to separate out the interactions. Notice here we have both chemical shift and coupling information along the F2 dimension and along the F1 dimension we have only the chemical shift information. Let us see if we can do the other way round. Yes. So here we have the pulse sequence which is different compared to that one. You apply a 90 degree pulse along the carbon as before. Now during the T1 period now we do not apply decoupler. We apply the decoupler along the T2 axis. So during the T1 period therefore we have chemical shift plus the coupling constant of carbon and proton and therefore the appearance of the spectrum will now look different. Once again now if you see the diagonal is running like this, this is the centre which is the chemical shift of the multiplet and here again is the chemical shift of the multiplet, this is the chemical shift of the multiplet, this is the chemical shift of the multiplet. Now if you were to take cross section here then this will be a triplet as before and this will be a doublet and this will be a quartet with 4 lines and this will be a triplet. So on this axis now we have only chemical shift information if I were to take a projection here along this axis I only have one line and that will be the chemical shift. So similarly here. So the appearance of the spectrum looks different. Now if you were to record an NMR spectrum, experimental why is it useful to have this? If the chemical shifts are not very well separated sometimes this you may not be able to see this in the 1D spectrum. One may wonder whether these quartets if they are very clear in the 1D spectrum though we really need to do it. But you will see that sometimes it is not very clear and I will show you an example here. So here is an example which corresponds to the situation in the second pulse sequence which I showed you. And this was the first actually two dimensional spectrum recorded among all the 2D experiments recorded this was the first experiment that was recorded way back in 1975. So here the F1 axis this has the chemical shift and the coupling information this is the F2 axis which has only the chemical shift information that means we have applied decoupler along the F2 dimension proton decoupler. So now you see this one is a quartet this is a triplet and this is a triplet. This is the what molecule? This is molecule here n hexane and you have CH3, CH2, CH2, CH2, CH2, CH3 these two the two end carbons are equivalent the two again these two central carbons are equivalent and these two carbons are equivalent. So there are three types of carbons. The CH2's are triplets and CH3 is a quartet. Now if you were to take a projection this is what the one dimensional spectrum you will get. Now suppose you did not do a 2D experiment this is the kind of a one dimensional spectrum you will get. You see here it is impossible to figure out what sort of multiplets you have in your molecule. But by this separation you are able to see clearly that there are two triplets and one quartet. So this is the benefit of separating out the interactions in the two dimensional plane. Now you can do even more that is we want to completely separate out the chemical shifts in the coupling constants. So in the earlier cases we have one axis the chemical shift and the other axis both chemical shift and coupling constant. But can we do something better than that? So let us consider a sequence which is like this. So we have now a T1 period going from here to here but we apply 180 degree pulses in the middle of the T1 period on both carbon and proton. Now you recall this is like a spin echo sequence. This is a spin echo sequence from here to here it is a spin echo. So therefore when I apply this 180 pulses on both carbon and proton what I am retaining is the coupling information all the way from here to here. The coupling is not refocused but this 180 degree pulses on the carbon channel refocused with the carbon chemical shifts because you have created carbon magnetization at this point and it will refocus the carbon chemical shifts. But the coupling information to the proton is retained and during the T2 period the chemical shifts are evolving but I do a decoupling of the proton. So therefore along the T2 axis I have only the chemical shift information. Now if I represent the F2 axis here and the F1 axis here so what is it we have? We have the F2 axis I have only the chemical shift information and along the F1 axis I do not have chemical shift information but only the coupling information. Therefore it will spectrum will look much more simpler here as compared to the previous ones and this you see is the scalar coupling. So the doublet will appear like this and the quartet will appear like this and the triplet will appear like this. So if you were to take cross sections here of this then of course they will all be as indicated before let me just show that this is a, see if I were to take a cross section here so this will be a doublet with the chemical shift in the middle and this will be a quartet with the chemical shift in the middle again and this will be a triplet. Now the chemical shift will be on the middle again which will be it will fall on the line in the center. So this is the way you separate out the interactions as though we have rotated this the whole multiplet along the orthogonal axis so you have put the multiplet structure along the orthogonal F1 axis and the chemical shifts are kept along the F2 axis. This is extremely a useful technique and to do a little bit more rigorous analysis we can do a product operator calculation of this which is pretty simple as we have discussed in the previous classes. So in order to do that what we will do is consider the time points explicitly here. So this is the initial magnetization therefore I call this as the time point 1 then I have here time point 2 then the T1 by 2 evolution and T1 by 2 evolution this is the spin echo sequence so therefore this here I will directly evolve the coupling information therefore I can directly go to this point here is labeled as 3 and I level this time point as 4. So therefore we will calculate the density operator using the product operator formalism as to how the spin system will evolve through this pulse sequence this is pretty straight forward and let us see what is rho 1 rho 1 is the Z magnetization of the carbon I have applied the 90 degree pulse to the carbon right. So therefore initially I have the Z magnetization of the carbon this is for a single carbon proton system. Of course we will not do the calculation for the CH2's in the CH3's but that will be easily doable but we will demonstrate it for a simple CH system how it will a doublet will appear how doublet will come from here. Now when I apply 90 degree expulse I create Y magnetization which will be minus CY now what I do during this whole period from here to here it is a spin echo sequence there is no chemical shift evolution of carbon there is only carbon proton evolution coupling information right. So therefore I evolve this under carbon proton coupling so therefore this is minus the CY gives me cosine pi J HCT1 notice this C is actually capital C H is not a small C this is has to represent carbon this is supposed to represent carbon same is here sine pi J HCT1 minus 2 X HZ sine pi J HCT1. The second term does not lead to observable magnetization in T2 because of proton decoupling right. So this is enti-phase magnetization when you decouple the two enti-phase terms will simply collapse and therefore you will not have any signal coming from this to C X HZ term. So what will remain is only CY and we need to consider the evolution of this CY term only. So now we consider the CY evolution during the T2 under the influence of the chemical shift or the Zeeman Hamiltonian only. So this what does it give me this CY gives me CY cosine omega C T2 minus C X sine omega C T2. Now we can detect only the Y magnetization and if you do so then of course I will have here the row 4 is CY cosine omega C T2 cosine pi J HCT1 okay. Now this is once again capital C. Now you see in the T2 domain I only the frequency omega C the chemical shift therefore if a Fourier transform along the T2 axis I will get only the frequency information. Now along the T1 dimension I only the coupling information this is pi J HCT1 therefore when a Fourier transform along the T1 dimension I only have the coupling information okay. So therefore this results in exclusively coupling information along the T1 dimension and chemical shift information along the T2 dimension. And that is indicated here in this schematic drawn here we have exclusively coupling information along the F1 dimension and exclusively chemical shift information along the F2 dimension. So in all of these experiments we had considered carbon proton coupling right and we are talking about experiments at natural abundance of carbon 13 therefore there was no question of carbon carbon couplings evolution there. But if you were to do these experiments for protons then of course it will it can lead to more difficulties because there are proton-proton couplings which will be present in your experiment and then you will have to deal with what is called as homonuclear 2DJ spectrum and this would result in more complications. The pulse sequence of course remains the same except that you do not have the thing on the another channel you only have the proton channel here and if it were of course also if you have carbon 13 labeled molecules then also you can do the same thing except that you are going to apply a decoupler along the proton channels if you want to eliminate carbon proton couplings you want to measure only the homonuclear couplings. Therefore for a homonuclear 2D experiments we define experimental sequence like this so T1 by 2, T1 by 2 and T2 a detailed theoretical analysis of this we will postpone to the next class so this will take time we stop here.