 So, far we consider the conventional Fourier transform NMR and there what we had was one frequency axis and when the plotted we get the intensities on the other side on the second axis. So, now we enter into a new revolution which is called as multidimensional NMR the beginning of which is of course the two dimensional NMR this came into existence in the 1970s and this actually was the main revolution for applications in structural biology. In earlier situations it was all limited to chemistry and small molecules of few atoms and tens of atoms and things like that of simple molecules. Now it was unthinkable to go into things like proteins and nucleic acids and things like that which have hundreds of protons and so many other nuclei it was impossible to do it. To analyze this spectrum I will show you this by an illustration here, here is a spectrum of a protein, the spectrum of a protein this has about 400 protons and the proton spectrum the proton spectrum spans as it is here from 0 to 11 ppm of course we have some shifted once here minus 1 this is the spectrum of lysosyme recorded on a 900 megahertz spectrometer and you can see how much is the overlap of signals you cannot count the number of lines here forget about measuring the coupling constants forget about individual assignments to 400 different protons how will you assign them and how will you get to the structure of them. This is a quite an ambitious project to get to the structure with such a large protein such a large molecule with so many lines without the assignments you can do nothing in NMR you need to have to have the assignments first and this is the water line here we know from the chemical shift difference all of that what we have talked about is now coming into practical use. This is a water line quite substantially reduced and this sample is 1 millimolar in protein concentration recorded in water water is completely suppressed here in the 1 dimensional spectrum and these are all the aliphatic protons with the methyl here and these are the aromatics here and then you have the NH protons here in this area but you certainly cannot count them you cannot count them and therefore you cannot assign them ok then what do we do so this is where the revolution occurred that ok now you try to spread this information in two different axes instead of one frequency dimension here this is one frequency dimension why not we generate two frequency dimensions and establish a correlations between the various signals in the 1 dimensional spectrum in a 2 dimensional way and that is the motivation that was a fantastic idea but how to implement it you have to generate two frequency axis that is the first principle how do we generate two frequency axis and this is the idea which was put forward and this was initially given by Jane Jenner from Belgium and it was picked up later by Richard Ernst from Zurich and now it really caused a huge explosion in the applications of NMR in chemistry and biology now the idea is following in 2 dimensional NMR you have to generate two frequency axis in the normal FTNMR you had one time domain time domain signal and the time domain signal after Fourier transformation you get the frequency domain spectrum which will give you the spectrum ok now you want to generate two frequency axis so what we will do here is ok let us divide this time axis like this let us divide the time axis like this so let us say we have so called preparation period the preparation period means we can prepare the spin system in any manner we want it can be in equilibrium state or it can be non equilibrium state whatever you want here this is called the preparation period then you have a so called evolution time which we call it as T1 then you have what is called as a mixing time we have come across this mixing time and also such concepts earlier when you talked about the NOE we talked about the mixing ok and then we have the detection time which is called T2 this is where the actual FID is collected this evolution time is an indirect detection period as I will show you later this is the detection time actual FID is collected during this period only ok now how is the experiment done you do a series of experiments you do a series of experiments that is you do a preparation block remains the same and you do once with T1 value is equal to 0 then you have the mixing you collect the FID this is FID number 1 then you increment this T1 value give a small value here increment that means you separate this preparation and the mixing by certain value that is the increment and after that you collect the FID again this is FID number 2 then you continue to increment it in similar way if the increment here is delta T1 here it will be 2 delta T1 here it will be 3 delta T1 here 4 delta T1 so it systematically incremented this period and then you collect the FID every time so 2nd FID, 3rd FID, 4th FID so this is like doing the digitization when you are collecting the FID when you are collecting the FID so we have this FID when it is collected we are collecting in a digital manner right so we have various points here this is what this is what we are doing when you are collecting the FID also so here we are actually generating this another time domain here and this time is incremented so just as this time is increment 1.2 another point to 3rd point 4 5 6 7 like that so you keep doing the first point and then the 2nd point the 3rd point 4th point 5th point and so on so forth you generate a various set of experiments you collect so many FIDs therefore what you get so that is what is indicated here FID number 1 2 3 4 5 etc therefore you have so many FIDs so now each one of them is dependent on the value of this T1 whatever is the T1 value here that will modulate the signal that is detected in this FID so this FID what you are collecting will be dependent on this time because during this period the magnetization will be processing in the transverse plane it will be going around in the transverse plane ok so therefore these will have frequency labels this will have frequency labels during this period and the mixing is a crucial thing which allows you to establish correlations between the spins here and the spins there ok mixing establishes correlations between the evolution and the detection let me write that here mixing establishes correlations between frequencies in the T1 and T2 periods. In other words magnetization may get transferred from one spin to another spin what if a particular spin was processing with a certain frequency here during this period during this mixing it may get transferred to another spin and that will go with a different frequency it can go with a different frequency but whether this transfer will be complete or not complete one does not know it may be partially transferred. Now therefore what we have got here we have got a time domain data which has two dimensions that is what is indicated here ok so ok now let me go back here so you have a time domain data which has two dimensions that is a T1 and T2 therefore if I do a two dimensional Fourier transformation now I do a two dimensional Fourier transformation this is two dimensional Fourier transformation I generate two frequency axis which we call it as nu1 and nu2 whatever is the frequency present during the T1 period will appear along this axis whatever is the frequency present during this period T2 period will appear on the T2 axis on the nu2 axis therefore have generated two frequency axis by doing this trick I have given an additional T1 period additional evolution period during which the various spins persist with their characteristic frequencies now the mixing may cause transfer of magnetization from one spin to another spin we have seen this how it happens in the various examples we saw that in the case of inept we saw in the case of NOE how magnetization transfer can happen depending upon what you do it can go from one spin to another spin all this is boxed up in this so called mixing ok so therefore we can establish correlations when we transfer the magnetization meaning we establish correlations ok and the transfer may go 100 percent or it may go 50 percent or whatever so depending upon the way the mixing is done so you have a partial transfer or full transfer this is what happened in the case of NOE for example NOE entire magnetization is not going there part of the magnetization part of the perturbation is getting transferred to this period to another spin and therefore then that spin will carry the information of the past so this is the idea now since you increment this T1 I generate another time variable I generate another time variable and the evolution carries this information of the precessions during the T1 period therefore various frequencies are present here and I have the labeling can be done during this period ok therefore this evolution time can be called as indirect detection period evolution time is also called as indirect detection although there is no directly a 5D collected in the digitizer in the digitizer of the FTNMR spectrometer there is no direct data collection there but we collect the data in the form of many FIDs whose evolution is modulated by the evolution during the T1 period therefore that modulation is dependent on this T1 period therefore if a Fourier transform along the T1 axis then I get that information of modulation by the evolution here and this is explicitly shown in this particular example here so I have here various frequencies ok this is the first FID first FID after I do a Fourier transformation I get a line like this now I have the second FID I Fourier transform I can the second spectrum but now you see its intensity is not the same as this it is slightly reduced this is because of the attenuation here because of the evolution here because of the evolution in the T1 the FID is looking different the third one there is zero nothing there so therefore here also there is nothing the fourth one it has changed sign why does this happen this is because of the evolution during the T1 period what is the situation it has reached here the spin has reached here that shows up in this here that shows up in this initial point of the FID and then you see again this will now it has become negative this is more negative again the decrease in the negative because it starts going modulation right positive decrease zero negative increase negative decrease again go positive and so on so forth ok so therefore I get a series of spectra like this after I do a Fourier transformation along the F2 all the FIDs if a Fourier transform collect them like this now we look at this look at this various points this is look at this various points find out the condition of that in each of this spectra in the spectra I have this points A, B, C, D, E, F, G these are all the points on the on the line here in the F2 dimension this is my F2 dimension this is the T2 period therefore I have the F2 dimension here after the Fourier transformation I am collect looking at these points here at A, B, C, D, E in this and I see through this at this particular point what is the value here what is the value here and I plot that here I plot that here so therefore you see at the point A there is nothing it is all 0 all over and it is all 0 here now we come to the point B point B there is a small dip there is a small dip in the middle therefore if I were to Fourier transform this I get a small signal here now we go to point C there is a big dip as I go take point C and I go along like this and I plot the value of the signal here it will look like this now it has a time dependence right this is the what is along this axis this axis is T1 here this is T1 right so it is indicated here this is the T1 axis therefore if a Fourier transform this this is like an FID also right this is also like an FID so if a Fourier transform this I get a signal so go to point D greater dip greater intensity go to E dip has decreased smaller intensity go to F again it has decreased further small intensity go to G here then no signal 0 intensity therefore you see here as a result of this kind of an experiment I have got the frequencies along both the F1 and the F2 axis okay so this is what is the principle of two dimensional NMR which is summarily described here so you have the two dimensional NMR you have S, T1, T2 time domain signal has two time components T1 and T2 you have to do a two dimensional Fourier transformation and generate a frequency two frequency axis F1 and F2 okay so and these are independent Fourier transformations you can do either one whichever order you want to do it does not matter okay alright so now that was the principle of two dimensional I do a certain examples here what all things whereas various kinds of 2D experiments we will not go into the theory of these calculations we are going to use these ideas and describe some experiments how these experiments what are the pulse sequences here and what is the information that comes in this experiments one of the very early experiments that was done was 2D J resolved spectroscopy okay the J resolved spectroscopy is done in this following manner okay so you have a first a 90 degree pulse 90 degree pulse now the evolution period is from here to here evolution period is from here to here okay but we have put a 180 degree pulse in the middle itself that does not matter you can do that but the time is incremented here now what is the consequence of this the consequence is from here to here this is an incrementable time we are going to collect various FIDs with incremented t values right so as a function of t2 now from here to here it is the same as the spin echo okay this point is the spin echo so this sequence 90 180 tau 90 tau 180 tau okay that is the spin echo so during the spin echo what happens that is indicated here during the spin echo chemical shifts are refocused right in the spin echo chemical shifts are refocused but the J remains the J information remains the coupling constants are not refocused in the spin echo this is what we saw earlier and also in the inept experiment we explain that how the J information is not refocused in the spin echo period and therefore the J information is present here and this is my evolution therefore what is the information present during the evolution period that t1 period that is a J J information so frequencies correspond which describe the J are present okay so it is like sitting in the center of the line and looking at the two transitions A1 and A2 transitions how they are processing how they are processing you sit at the center of one line they let A1 and A2 are the two transitions of the A spin you are sitting in the center because your chemical shifts are refocused the chemical shift information is not present here anymore so during this t1 increment what is changing the two transitions A1 and A2 they keep moving let me write that here so they keep moving during the t1 period they keep evolving okay they are in the center okay this happens for every spin for every spin because the chemical shift information is removed what it is at zero frequency chemical shift does not have information at all so only the J values are present during this period okay that is the effect of the spin echo I repeat here again the chemical shifts are refocused no matter what the chemical shifts are that is completely eliminated at the time of the echo until this period which means it is like sitting at the center of the multiplet for every nucleus because the chemical shift information is not present it is like sitting at the center of every multiplet for in your spectrum therefore we consider only this kind of attack to single doublet the two transitions keep evolving as a function of t1 okay therefore what is getting modulated as a result here so what is the modulation that is happening J evolution is contributing to the modulation so therefore J evolution therefore if I were to Fourier transform along the t1 period what I am supposed to get I should get the J information J is a frequency I should get that frequency right the angle modulation creates a different phases and the affidies will be modulated by that evolution therefore if a Fourier transform along this I should be getting the J information what happens here in the t2 period t2 period I have done nothing I am collecting the data as if it is a normal one-dimensional spectrum I collect the data as if it is a normal one-dimensional spectrum one-dimensional spectrum has both chemical shift and the coupling constant therefore I have the J plus delta both informations are present here during the detection period so during the spin echo during the t1 period I only have J and during the detection period I have plot J plus delta therefore this experiment is called as J resolved spectroscopy okay how does this look so you see this is explained here it is called as 2d separation here now this is a consider this sort of a system here you have a 1 doublet and a triplet there now along the f2 period I have both the J and the delta now this axis is delta plus J this axis is delta plus J and this axis is only J okay so delta plus J and J what it will give me along this frequency axis I will have the J information this axis I have the chemical shift information therefore for a doublet I will have these two lines oriented at a certain degree at a 45 degree here they will be oriented a 45 degree with the central line because there is a J by 2 and J by 2 both places right so this is the center and this is the doublet right so this is J by 2 here and this is also J by 2 the doublet so the doublet this is J this total is J from the center to the end it is J by 2 therefore one of them goes up here and this is and then the total from here to here is J that is what is called as the J separation along one axis I have the J information along the other axis I have both J plus delta so therefore when I consider in the two-dimensional spectrum I will have these peaks appearing at an angle of 45 degrees because you have J by 2 and J by 2 means these are isosceles triangle isosceles triangle means it is a 45 degree angle therefore I will have here the doublet appearing like this and the triplet will also appear like this and we have the in the triplet of course we will have the one line at the center therefore triplet appearing now what we do we do not want this angle we do not want this angle what we do is during the processing process we will move this fellow to this center we will move this fellow here we will move this fellow to the left move this fellow to the right and similarly we move this fellow to the left move this fellow to the right so that we bring all of these on the same line and we bring these two in the same line. That is what is done here. This is done by moving one of them this way, other one this way and here this also again move this way and move this way. So let me indicate that here. When you move this, so they will all come on the same line. So as a result, I will have this spectrum. Now you see on the, this is the F1 axis or it is also called as the J axis. Now I have simply looking at the separations here, I can measure the coupling constant. And if I take the projection of this, I will have only one line. If I take the projection here, I will have only one line, correct? Which means I have decoupled them, which have decoupled the two spins. What was a doublet here now appears as a single line. What was a triplet here will also appear as a single line. So this is a homonuclear broadband decoupling. So this amounts to broadband decoupling. The coupling information is removed. Therefore your lines will get simplified, right? So your spectrum will get simplified. You will have multiple information, multiplicity is removed. So you will have one line per spin. Therefore you will have, you have a very higher resolution in this kind of a spectrum. But you are not lost to the coupling information though. The coupling information is retained along the other dimension. So therefore this experiment is called as 2D separation or J delta separation. In a 2 dimensional experiment, we have achieved this sort of a result, okay? So now you see here it is a more complex system there. We have many spins and I have just shown this spectrum here for your information. And I do not even know what molecule it is but nevertheless it does not matter. You have here a doublet. You have a triplet. Then you have a doublet of a doublet here. Then you have again possibly a triplet here but with a smaller coupling constant. So here you have a triplet. Again a single line. Then you have a doublet of a doublet. Again doublet of a doublet. So you can see all the coupling information can be obtained. And look at the range here. The range is minus 10 hertz to plus 10 hertz. So 20 hertz. This is about, I mean you do not have any fine splitting which is more than that. So you will have here the separation which is like about 10 hertz. You are able to measure this 10 hertz separation and this will be 20 hertz here and so on so forth. The coupling information is present and if you take the projection down here each one of them will give a single line. All of them will give a single line. So this will be a single line. This will be a single line. A single line here. A single line there. A single line there. Again a single line there. A single line there. A single line there. If you took this projection on to this axis you will have only one line. So there is a completely chemical shift information is on one axis and the coupling information is on the other axis. So therefore this is an extremely useful technique for handling large molecules because you have achieved a good resolution enhancement along the F2 dimension by decoupling and but you have retained the coupling information along the F1 axis. Therefore you can extend the coupling constant also. You have not lost it. So it is like sitting on the line the spectrum and rotating it by 90 degree like this. So you have the spectrum like this, sit in the center and rotate it by 90 degree. Therefore you have a much better resolution in your final spectrum. Well so this is a little bit more modified technique of refocused inept and we already discussed the refocused inept earlier and this experiment is now converted into a two dimensional J inept experiment. In this case what we have seen this earlier this experiment we discussed earlier to refocused inept. So basically and we do a decoupling of course we can get this. Now what we do is instead of this period being a constant time period what we do is we make it as an evolution time. We make as an evolution time when we do that you generate the second frequency axis here. When you do the second frequency axis you are able to produce the frequency axis along the F1 dimension, Fourier transformation you get such a beautiful clean spectrum and 2D, J and F, identification of carbon types. By looking at this you can identify what kind of a carbon it is. Along this axis you have the carbon frequencies and along this axis you have the J's. So the single doublet therefore this is the CH group and this is the CH2. CH2 you have a much larger separation here in this then another CH2, then you have the CH here, then you have the CH3 which we saw earlier we saw in the case of one dimensional spectrum how these ones will appear. So you can identify the carbon types by looking at by doing such a kind of an experiment. So I think we can stop here we will go into this next kind of 2 dimensional experiments in the next class.