 So, we have been discussing heteronuclear correlation experiments, two-dimensional experiments. We discussed last time various options and various ways of recording heteronuclear correlations. So, we will continue with that now, some more options which are present here. And so, one of them which I will now discuss is so called heteronuclear multiple quantum coherence spectroscopy and that is abbreviated as HMQC. The pulse sequence for that is given here. So, you start with a 90 degree pulse on the proton channel, so the magnetization comes down to the transverse plane and then you evolve it for the period 1 by 2j under the influence of the chemical shift as well as the coupling, but it is the coupling evolution which is important for us. And then after the 1 by 2j evolution under the coupling, you apply a 90 degree pulse on the X channel. So, at this point, this magnetization is converted into multiple quantum coherence at this point. This will now evolve during the period T1. In the middle of the T1 period, we apply 180 degree pulse onto the proton channel and then at the end of the T1 period, we apply a 90 degree pulse again on the X channel, so that the magnetization now is actually transferred back to the proton. And then at this point, the magnetization is anti-phase with respect to the X nucleus and anti-phase magnetization as we know is not observable. So, we evolve for the 1 by 2j period once more, so it is converted into in phase magnetization and after that you collect the data on the proton channel and you decouple the X nucleus by broadband decoupling. So, the product operator calculations can be done as we have discussed this quite extensively. So, I am only going to tell you about the salient features of these calculations which are relevant for this. Now, let us look at this 2 HX XY and of course, you notice here what I have given here is the phase cycling XX for this and X minus X for this and when you record the data, the first scan you add it and the second scan you subtract it, so that is plus and minus. So, the reason for that we will see soon. Now, first let us look at what happens here. We have got here relevant product operator term which is 2 HX XY. What is this? Recall the discussion of the product operators, this we know 2 HX XY is sum of double quantum coherence plus zero quantum coherence as double quantum goes with the sum of the two frequencies omega H plus omega X and the zero quantum should go as omega H minus omega X. Now, you notice in the middle of the T1 period, we apply 180 pulse on the proton channel, therefore from each one of those this frequency is refocused. So, till the time here and we come up to this point at the end of the T1 period, the omega H frequency in the double quantum and in the zero quantum is refocused. So, what remains is only omega X, therefore effectively during the T1 period I only have the X frequencies and X frequency the operator term and of course, they will evolve with the characteristic frequencies. The second thing is both these double quantum and zero quantum frequencies do not evolve under the coupling between H and X. If you are considering a two spin system, heteronuclear two spin system, for example the CH group or NH group where we are created the double quantum and zero quantum using the one bond coupling, the J is a one bond coupling here. It does not evolve under the coupling constant, therefore at the end of this T1 period, there is no coupling evolution contribution, there will only be chemical shift evolution at this point for the two spin system. Therefore, this operator term does not change because since there is no coupling evolution, we will remain as 2 HX XY or you may add HX XX. If you are considering chemical shift evolution, we can also cause another term which is XY plus X. So, but we consider one of these here, it does not matter which one you consider, that is you can do that by phase cycling and you get here 2 HX SY and then you will have a function which is F T1 which will dependent on the chemical shift evolution during this period T1. When you apply a 90 degree pulse on to the X channel now once more, this will get converted into a HX XZ because this is XY here, when you apply 90 X pulse that will get converted into XZ. So, now you see it is proton magnetization, here it was double quantum and zero quantum coherence, now it is proton magnetization, single quantum proton therefore I have here, now I come back here, so it is proton magnetization, anti phase proton magnetization. Now when you evolve it further now under the influence of the coupling between the two, this will evolve under the coupling, proton X coupling and it will evolve into HY, 2 HX XZ will evolve into HY, of course this F T1 will remain there. Now due this HY is now in phase magnetization of proton therefore we can actually collect the data and decouple the X during this acquisition time. So, now therefore what we have achieved we have only chemical shift information in the T1 period therefore when you do two dimensional Fourier transformation I have along the F1 axis X chemical shift and then here I have the proton magnetization here, it evolves with the chemical shift of the proton and there is no coupling therefore I only have along the F2 axis the proton magnetization therefore I have peaks here very similar to those we observed in the HSQC spectrum. So, one peak and no fine structure here for each HX pair. So, this therefore spectrum will appear very similar to the HSQC spectrum. There will be some other factors which you will consider and that will happen when you have more complex spin systems like if the proton is coupled to some other proton that proton will evolve the coupling between the two protons will evolve here during this period although the chemical shift of the proton is refocused but the proton-proton coupling evolution will happen in case of more complicated spin systems that is you have one proton and another proton things like that and the proton-proton coupling evolve all that will enter into this F T1 and that can lead to some other complications in the spectrum. Now the second thing that will happen is if we are doing experiment at natural abundance so you see the proton is attached to every carbon all those carbon or the nitrogen which is evolved but the carbon natural abundance is 1.1% and N15 abundance is 0.37% but you are going to excite all the protons which are attached to carbon 12 as well. So, what happens to those ones? Those ones will not get transferred here because there is no coupling evolution for those ones and therefore they will continue to evolve like this and now you see this is the entire period this 180 pulse is in the middle of the entire period here from here to here. So, therefore this will get refocused at this point. Now if you add and subtract as you do in the receiver phase here once can you add others can you subtract and that magnetization which is coming from directly through without passing through this channel will get cancelled out. So, therefore that is the reason for this phase cycling here and this does not affect the magnetization which comes from this pathway and therefore you have to do this sort of a phase cycling to eliminate magnetization which is coming from the C12. If you have molecules which are carbon 13 level then it does not matter anyway everything will pass through this and it is not affected by this phase cycling you will get a clean signal. Now so therefore let us look at the magnetization transfer pathway once again in more explicit terms you start with the proton magnetization HZ convert it into HY and evolve it during the 1 by 2 J period and the relevant part of the product operated which is important for us and other things do not contribute and that will be 2 HX XY which I said is multiple quantum which is a summation of 0 quantum and double quantum they will both eventually be retained in this manner during the T1 period because if they do not evolve under the proton X coupling these are one bond they do not evolve under. So, this operated term remains as it is and then when you apply a 90 pulse on the X channel you convert it into proton magnetization which is anti phase to X and then during the next 1 by 2 J period you refocus this into in phase proton magnetization and then after that you can acquire with X du coupling. So, here are the salient features repeated once more the 180 pulse in the middle of the T1 period refocus is the proton chemical shifts multiple quantum coherence does not evolve under the HX coupling therefore there will be X chemical shifts only during the T1 period the multiple quantum coherence is converted into single quantum proton magnetization anti phase to X then anti phase proton magnetization is refocused to produce in phase proton magnetization which is detected with X decoupling. So, here is an experimental spectrum of a particular large molecule which is a protein. So, here on this axis you have the proton this axis you have the carbon here and see you can see lot of crowding of the peaks is there but all of the peaks are seen here these are the CH3 signals here and these are in the protein. So, these belong to the methyl because of the methyl protons appear at this chemical shift and the carbons of the methyl appear at this chemical shift and therefore this is the CH3 signals and here you have the gamma protons and the beta protons of the side chains in the proteins of the amino acids those ones appear here in the protons chemical shift and the carbon chemical shift occurs here. So, this is up to 20 ppm here this is between 20 to 40 ppm you have this beta and the gamma chemical shifts and of course you also have the deltas chemical shifts which are coming here the gammas and the deltas and the side chains of the amino acids they will come here and the glycine alphas also appear at this point which is around the 40 to 45 ppm and then in this place you have the alpha protons and the betas of the serines they will appear in this area the carbon chemical shifts will be in this between 50 to 65 ppm you will have the CH signals of the protein alphas and the betas of the serines and they will also appear in this area and these are coming from the aromatic signals. Notice however that the aromatic carbon chemical shifts appear between 100 to 120 ppm but they are appearing in this area and this is because you have allowed them to fold into this area you are not excited the carbon chemical shift all the way from 0 ppm to 200 ppm you have restricted the carbon excitation here up to 70 ppm only therefore the ones which are outside of that one will get folded into this area and therefore they are coming in this region you identify them on the basis of the proton chemical shift the proton chemical shifts are between 6 to 7.5 ppm and therefore you know that these are coming from the aromatic carbons and not from the aliphatic carbons. So, but this is fine so we can still analyze this so the reason why you choose only a small chemical shift range here is because you improve the resolution your spectral width is reduced so acquisition time can be increased along the F1 dimension so that you have a better resolution along the F1 dimension and this is particularly important in case of carbons because the carbon chemical shift range is quite large and generally it is not possible to excite a wide chemical shift range with simple hard pulses. So, the one special tricks will have to be used you need high power and all of those complications. So, therefore you allow them to fold so you can still analyze even the folded peaks here as well. So, now let us do a comparison of the spectra from HMQC and HSQC they looked similar but there are some differences between the two this is from a particular molecule this is HMQC spectrum and this is the HSQC spectrum by a large they look very similar but look except for this area these ones do not look very different. So, these are blobs here and what it shows is that the resolution in the HMQC appears to be smaller than the resolution in the HSQC spectrum and this happens because of the proton-proton coupling evolution during the T1 period which I mentioned to you. Then when the complicated spin systems are there it is not just a HC group or suppose it is a CH2 group or CH2-CH3 kind of a group where there is a proton-proton coupling evolved. So, every proton which is present here which is at the carbon chemical shift here will be coupled to some other proton and that proton-proton chemical shift leads to additional operator terms in your FT1 function and that leads to sort of complications in the F1 dimension. So, it leads to loss of resolution in this area and these ones are the projections along the carbon axis. So, you take projection like this and this is the projection of the spectrum from the HMQC and this is from the HSQC. By and large the resolution here is better although you cannot see it in this projection in the 1D when you blow them up and see as it is done here you can see that there will be a improvement in the resolution in the HSQC and no complications from the proton-proton coupling. So, typically therefore when you have complex spin systems one wants to record an HSQC spectrum. Now, we consider different ways of correlating protons and the X nucleus but now we can combine further these experiments with other proton-proton experiments to get more information on the molecule which you are having. See for example here the HSQC is combined with the Toxy spectrum. We discussed about the Toxy and the Toxy is kind of relay experiments in the homonuclear case. So, proton magnetization is transferred through the coupling network in the Toxy just to remind you what we discussed in the case of Toxy. So, if you have an AMX spin system magnetization is transferred from the A to the M in the Toxy. So, if you have a proton step of AMX and each one of them is of course attached to a carbon. Now, in the Toxy you remember that we had the transfer of coherence from here to here and then from here to here. So, this resulted in a cross peak between these two. So, that is the relay. So, the relay that happens is used now to correlate the X nucleus chemical shifts to the whole set of protons which are attached in the coupling network. And how is this experiment done? It is very simple. Let me write this is the Toxy. So, this is just to remind you because the HSQC is fresh in your mind toxin may not be fresh therefore, I just put that here or there. Now, this is the HSQC part all the way from here to here is the HSQC part. So, this is the NFC transfer to begin with from proton to the X nucleus tau is kept equal to 1 by 4 J. So, 2 tau is 1 by 2 J. So, with that adjustment magnetization is completely transferred to the X nucleus and this is antiphase here and this magnetization evolves during the T1 period and there is a 180 degree pulse applied in the middle. So, that there is no coupling evolution between the X nucleus and the proton that is decoupled there and then from here the magnetization is transferred back to the proton. This is antiphase proton magnetization with respect to the carbon or the X whatever is the X and then during the next 2 tau period the antiphase magnetization is refocused into the in phase magnetization. Now, we recall that the toxic transfer happens from in phase to in phase. So, here if I have the magnetization of A spin X here and this will be transferred to magnetization of M spin into the X magnetization only and this will also go to the I said X there and this is also X here X X. If it were Z then of course IAZ will go to IMZ which will IXZ. So, therefore in the toxic there is isotropic mixing and that leads to in phase magnetization gets transferred to the connected nuclei. So, here therefore if you started from one particular proton let us say a A proton which is coupled to a particular carbon and you will come here all the way up to that particular proton magnetization once more and then during this period you relate from A to M and M to X and then after that you collect the FID. So, therefore you have created transfer magnetization of all the 3 spins here which are coupled to each other and during that one all of since all of them are in phase magnetization we do a broadband decoupling of the carbon or the X nucleus then you will have the relay along the F2 axis and that is an important information you can identify spin systems on the basis of such a kind of a magnetization transfer. So, here is an example so you see here this is the normal HSQC spectrum for a particular molecule the molecule is shown here and you see here this is the carbon proton correlation spectrum you have here 2 peaks and this is 2 carbons there are 2 carbons here and they are connected to the protons as their respective chemical shifts or this particular carbon is connected to 2 protons and these are one bond correlations so you are seeing from here to here this is both the 2 protons on a particular one and then you will have here similarly the particular carbon connected to 2 protons which are non equivalent you will see 2 peaks here and this is another carbon coupled here and another carbon. So, therefore these are all simple one bond correlations between the carbons and the connected protons then what happens here now this is the corresponding toxic spectrum HSQC toxic therefore magnetization is transferred from this carbon to this proton or to this proton and then then from this proton it is relayed further to other protons which are located on another carbon not on the same carbon these 2 protons are located on the same carbon and therefore you got them at the same carbon chemical shift this. Now at the same carbon chemical shift because of the proton-proton relay that happens through the toxic and there is a relay to a proton which is on another carbon therefore you will see these ones will go to these protons here which are connected a different carbon and that will show up here as well and where they are present for example this one is you can see here there is a carbon here and this another one is appearing at this point so this one for example this carbon is appearing at this point and that shows relay to these 3 protons here there is only one carbon one proton but this proton is coupled to 2 other proton 3 other protons there that is this one here this one is this one here and it is connected to 2 other protons which have this chemical shift which are this proton chemical shifts here. So this is how you establish a network of coupled spins in a molecule it will allow you to identify the resonances in an ambiguous manner. We can do the same thing with HMQC HMQC also allows the same thing to be done so you go through the HMQC spectrum until this point and introduce the Toxy block if the Toxy block here allows you to relay the magnetization through the proton coupling network and collect the data here proton magnetization and do the decoupling. So the spectrum will look very similar except of course for the proton-proton coupling complications which happen as I indicated in the HMQC spectrum. Now so we you can also introduce the nosies so now what you do is up till here the pulse sequence is the same as HHQC right. So this is HHQC from here you come up to this and which is the nosy so at this point therefore I have the magnetization of the proton but now this is along the z axis when I apply the 90 degree pulse here I put the magnetization along the z axis. So now during this time period this is a mixing time during this mixing time then I have relay of magnetization from a particular proton to another proton which is close by in space and this happens through the dipolar coupling. Therefore this is a nosy mixing so earlier it was j coupling mixing in the Toxy now here it is a dipolar coupling mixing so there is a relay of magnetization from this z of one particular proton to another proton and then after that of course you have at this point both the z magnetizations of if I take two protons A and M then I will have here relay I have the mixture of IAZ and IMZ which the relay has happened through the dipolar interaction and through the mixing period and then of course you collect the data since it is z magnetization this last 90 degree pulse converts the z magnetization in the transverse magnetization and so that we can generate in phase transverse magnetization and you collect the data here as an FID and this will contain frequencies of both of the spins and you can decouple here since it is all in phase magnetization you can decouple. So and then all other parameters remain as they are in the HSQC mixing time you can optimize to get what information you want in your spectrum how much relay you want to do and you can optimize a mixing time and intensities will get affected accordingly. So here is an experimental spectrum incidentally if when you are working with a small molecule the correlation peaks and the nosy peaks will have opposite signs and is very helpful because you can then identify which are the peaks which are coming from nosy and which ones are coming from the normal HSQC correlation. So all these black peaks which are present in this experiment they are all coming from the normal HSQC correlations proton carbon correlations and then these red ones which are present here these ones are coming because of the NOE transfer this is proton-proton NOE transfer and they appear with a different sign and therefore it becomes very easy to figure out which protons are close by in space and that is an important information for structure determination of small molecules. If you have a large molecule of course this situation will change in large molecules the NOE will have an opposite sign compared to that for the small molecules therefore in that case these ones will also appear with the same sign as the these direct correlation peaks. The same experiment can do with HMQC nosy as well and the same block is introduced here until this point it is HMQC and you apply 90 degree pulse here to convert that magnetization into the Z axis and once you put it in the Z axis then you can do a nosy mixing at this point then you have the last 90 degree pulse to convert that Z magnetization back into the transverse magnetization you collect the data and then you decouple the X nucleus. So I think we have covered here important heteronuclear experiments and also we have shown how to combine this heteronuclear correlations with proton-proton correlations to extend the information content of the two-dimensional spectra. You can relay the magnetization within the proton network either using the toxic scheme or using the nosy scheme and you can combine this with the heteronuclear correlations either through HSQC experiment or through the HMQC experiment. So this will be extremely useful in obtaining resonance assignments in small molecules big molecules and likewise so I think we will stop here.