 So, we discussed about two important experiments in the 2D series of experiments that was the COSY and double quantum filtered COSY. Now, so we will continue the discussion of that and then of course go over to other experimental schemes. Okay. So, in this context it is important to know some more concepts about the basics of the 2D experiment and that is one of the important thing is the resolution in 2D spectra. We should talk about the F1 dimension or all sometimes it calls the omega 1 dimension and the F2 dimensions. So, we have to worry about the resolution in the spectra in both these dimensions. What does the resolution depend upon? So, if we want to call resolution as R then this is proportional to the inverse of the acquisition time. So, this is the acquisition time, if T acquisition is the acquisition time then this is the resolution is inversely proportional to the acquisition time. What does that mean? This is similar to what we have talked in the case of the 1D spectra. Suppose I have the FID here and I have various points which are collected here, so many data points which are collected and then we say the total acquisition time is equal to, suppose I collected the n data points n times which is the dw, n times dw which is the dwell time. This is the time between two consecutive points. This is the acquisition time. So, if you collect more data points you have better resolution in your spectra. What does that mean? Then you have a line like this then you will have these peaks points coming appropriately at various places in your line. So, therefore the line will be represented better and the resolution will be higher if you collect more data points. In the case of the normal acquisition the one dimensional spectrum or even in the 2D the normal acquisition in the when you collect the FID it is simply the number of data points you collect. So, therefore it is very easy to increase this resolution by increasing this number of data points. In the case of F1 dimension the F1 dimension resolution will depend upon this is for the F2 dimension. Now, for the F1 dimension it will depend upon how many T1 increments we collect. Acquisition time along the T1 dimension will be let us say if I want to write as T1 acquisition is equal to T1 max let us say is equal to N let us say now I call it as N1 times the increment now I call this increment as let us say In. This is the same as the DW is the same as the DW except that increment this is these are collected one by one one by one this systematically that many FIDs are collected that means we have N1 FIDs collected. So, if you want to increase the acquisition time along the F1 dimension will have to increase the number of increments you have to increase the number of experiments the number of FIDs you collect. So, therefore it is a very time consuming process. So, for example, if I collect here 2048 data points in the F2 dimension this may go for let us say about 50 milliseconds assuming hypothetically. So, that is given the certain increment dwell time it may go for 50 milliseconds. But if you want to increase from this 2048 to 4096 then it will go to 100 milliseconds but that does not big deal. So, whether I collect the data for 50 milliseconds or 100 milliseconds or 200 milliseconds it is not going to increase my experimental time data collection time too much. But if I want to increase the same in the F1 dimension if I want to collect from 50 milliseconds acquisition time to 100 milliseconds acquisition time I have to do twice as many experiments twice as many FIDs. So, if the 50 milliseconds spectrum is going to take me about 10 hours then if I want to make it 100 milliseconds it will cost me how much did I say 10 hours 20 hours if it is going to collect 10 hours it is going to be 20 hours. So, therefore the number of increments is crucial here with regard to the acquisition in the F1 dimension. So, therefore experimental time along T1 dimension has to be optimally adjusted for the resolution we want. Now, why is the why is the resolution important in the case of F1 dimension? We have seen that in the cosy and the double quantum filtered cosy in the cosy in double quantum filtered cosy we let us say I have a cross peak like this this is the cross peak. So, this is in for cosy and dq of cosy we have seen that the cross peak for a two spin system has this kind of a structure for a two spin system and the separation between them is the coupling constant. Now we will be able to see all these four components if only you have enough resolution if these lines are properly separated. So, we can see this there is enough resolution. So, therefore along the F1 dimension it becomes crucial whereas along this is the F2 this is the F1. F2 dimension is not a problem I can easily increase from 1024 to 2048 or 4096 data points no problem at all I can separate these two. But the separation along this axis this is the crucial point. So, therefore always the limiting factor is the resolution along the F1 axis and this has to be optimally chosen. So, typically one does 512 T1 increments in a cosy or dq of cosy experiment. If the coupling constant is very small then you will have to collect more. So, what is the consequence if there is not enough resolution what will happen? If there is not enough resolution then this positive and the negative ones the positive and the negative components these come too close and then to cancel their intensities they will cancel their intensity therefore overall your signal to noise ratio in the cross peak will get reduced. And if you have good resolution here if these peaks are well separated along the F2 axis if this resolution is not enough if they are not well separated then they will cancel and your cross peak will have very low intensity and sometimes you may lose it also. If it is very small like 1 hertz or 2.5 hertz you may completely cancel it out and you may not see the cross peak at all. Therefore this actually is a quite a important limitation for those kind of experiments where you have cosy and where you have antiphase characters, antiphase characters meaning plus minus components along these cross peaks. So this is so far as the two spin systems are concerned now we should go and see how the spectra look like if you have three spins or more. So then let us look at the fine structures cross peak fine structures in three spin systems. Let us say the three spins are AMX these are all of spin half all of them are i is equal to half so we label them as AMX and of course these can be connected in two different ways AMX or this way also AMX. So this is the way you can have two different patterns here. So what will happen what will be the fine structure in the cross peaks? Let us look at once again the schematic here of the 2D spectrum so here we have F1, F2 we will have here 3 diagonal peaks let us say and let me call this as A call this as M and call this as X. Now what cross peaks do we see? So we will see a cross peak here and a cross peak here A to M in the case of if it were a linear system we will have two different things. So let me draw that here and of course we will have for the linear system how do you look let me draw that here for the linear system this we call it as the linear system. So MX this is A this is M this is X so A to M there is a cross peak here and therefore there will also be cross peak here and M to X also there will be coupling there is also cross peak here there is also cross peak here because remember these ones are J coupled this happens through J coupling this should be in the same line. So this happens through J coupling. Now in the case of this one this is the diagonal we are write it as A here, M here, X here I will have the same as before here and here but now I will also have this because I also have A to X coupling right A to X coupling I will also have M to X this also will be there this will be there and this will also be there. So in the case of this triangular coupling pattern I will have a different kinds of structure and the pattern overall pattern of the peaks of course in each of these peaks there will be a fine structure that is what we are going to see. So in this case depending upon which peak we are talking about which coupling constant is responsible for the peak that is important to see. So now if you are looking at this each one of them of course there is what will be the 1D spectrum for a such a kind of a thing if A MX let me draw the 1D spectrum of those that A has a coupling to M therefore it will be a doublet A will be a doublet and what will be M? M has 2 couplings therefore it will be a doublet of a doublet let me go and this is M and what will be X and X has only 1 coupling therefore that will also be a doublet. So this is X this is M this is A in the same order which I am writing here. So how this will be here now each of them here has 2 couplings each spin has 2 couplings. So therefore each one of them will be a doublet of a doublet so this is X this is M this is A and this fine structure will show up in the cross peaks and the diagonal peaks as well. Now which peak which coupling is responsible for which cross peak? Suppose I take here I will take the A M cross peak in the A M cross peak this is the rising from the coupling from A to M if I see here M this cross peak I use let me use a different colour let us say I take this cross peak or this cross peak it is coming from the coupling from A to M it is not coming from the coupling from M to X because the M to X peak will be here. So therefore there are 2 couplings in the M and these ones we distinguish them as active coupling and the passive coupling. So as we are looking at the particular peak I blow up this here and this side is the A and this side is the M I have this 2 things here so what will be the structure of these how many peaks will be there? So we will see that. Now the A is a doublet and M is a doublet of a doublet and therefore if I take this product here there will be that many peaks inside here. So therefore each one of these there will be peaks to all the 4 each one of these from this also there will be 4 peaks here from here also there will be 4 peaks there. So there will be total of 8 components in this peak this is my F2 axis this is my F1 axis there will be 8 components. Now what is the sign pattern here in the case of a 2 spin system we said plus minus plus minus how it will be here? So this peak is arising from JAM therefore JAM is called as active coupling and in the M there is also this MX splitting JMX which will be present only along the F2 axis this is called as the passive coupling. This is not responsible for the cross peak but details certainly contribute to the splitting. So now if I want to write the splitting pattern of both the spins A and M suppose I have this A chemical shift here and this splits because of the AM coupling as in the case of double counter filtered COSY or the COSY and this splits this produces inside there because of the active coupling plus and minus. So therefore inside here there will be pluses and minuses this splitting will lead to plus and minus and what about the M? This is the A this is the nu A let me write here nu M nu M will also show the AM coupling which is the active coupling active coupling leads to plus minus splitting as in the as you have seen in the double counter filtered COSY or the COSY. Now what does the MX coupling do because this will be further split because of the MX coupling therefore this will be further split into 2 but now this will not produce me plus and minuses it will produce plus plus minus minus and here this is JAM this is also JAM and this is JMX this is JMX okay. So now using this what I will do I will draw what will be the structure of this AM cross P let me draw that once more here this is this side is A A what is the structure I will have plus minus splitting along this side I will have plus plus minus minus because the M has this sort of a structure. So now if I multiply these 2 what I should get here I will get here plus plus minus minus now I multiply with the minus sign here therefore I will get here minus minus plus plus minus into minus gives me plus therefore inside here I will have this sort of a structure. This is provided JAM is greater than JMX okay. What happens if the MX coupling is larger than AM coupling let us also draw that. So if this is for that situation right so this is for JAM greater than JMX if the other thing happens let us say new M JAM is smaller than JMX this is JAM this is plus minus now I have splitting MX is larger okay. So now from here to here it is JMX so what will be the structure here this will be plus here and this will be minus minus here okay. So what is the thing we will get so therefore if I want to draw that here below this side will be plus minus as before but now this will be plus minus plus minus and this will be minus plus minus plus. So this is the case when JAM is smaller than JMX so this is JAM is smaller than JMX therefore it is very crucial to see what sort of a pattern you will get in your finds in the cross peak and this will tell you what kind of precautions one should take in doing your experiments. So analysis of the spectra has to take care of all of these factors when you want to measure the coupling constants from the COSY spectra and this is true for both COSY as well as double quantum filtered COSY. Now what will be the nature of the AX coupling in there is no AX peak here we are talked about the AM and similar thing will be for the MX also MX also will be for in the same manner you will have in the linear system we are talking about the linear system here. Now this is for the linear system so the pattern will be similar for MX cross peak and what about this peak let us look at the peak where this side is M this side is A and what will be that here we have a doublet so this will be a doublet and here we will have plus plus minus minus so therefore and this will produce me plus minus plus minus minus plus minus plus. So therefore you see the symmetry is broken the peaks do not look identical in other words what I am trying to say here is so if I look in the 2D spectrum this is my M and this is my A this is my X so I had here AMX so I have the cross peak here the cross peak here and the cross peak here and the cross peak here. So this is what we are looking at right so I showed you what is the structure for the AM cross peak and that was A was on this side M was in this side in this case this case is the case what I shown here and this is M so this side is plus plus minus minus this is plus minus so I will have plus plus plus plus minus minus minus minus sorry plus minus plus minus minus plus minus plus. So this will be the structure for the other peak yeah so therefore depending upon which peak you are looking at you will have the final structure so point you remember therefore is the active coupling leads to plus minus splitting a passive coupling leads to plus plus splitting ok. So this is so far as the linear spin system is concerned now if I want to take a triangular spin system this sort of a thing now I will have here this is the diagonal this is AMX I will have a cross peak here a cross peak there cross peak here cross peak there a cross peak here cross peak there ok. So all these are cross peaks now in each one of them we will have one active coupling and one passive coupling ok the same line so each one of them will have let us say I have this is AX that is this peak that is this peak AX so what will be the active coupling here? Here JAX is active coupling because this cross peak is arising as a result of coupling between A and X this is the same here ok and the X is also coupled to M ok so the X multiplied will have A coupling and also the M coupling and JAX is the passive coupling accordingly one can draw the various structures now suppose I take a different cross peak let me say I take this cross peak what is this cross peak this cross peak is M on this side because this is all AMX this cross peak if I am taking remember I am not taking this when I draw here if I draw here M if I draw here X then it is this cross peak active and passive couplings will be the same in both cases but the fine structures will be different depending upon which cross peak you are taking the if I take M here and X here then which is this active coupling JMX is active coupling and what is the other coupling it has X along this side I have the MX coupling and AX coupling ok now JAX notice this side this side I have X multiplied this side I have M multiplied so therefore all the three couplings are appearing here right so AX is is the is the passive coupling and JM is also passive coupling let me demonstrate that here ok let us draw the M multiplied ok for this particular case the M multiplied is plus minus from JMX and let us say MX is greater than AM this is plus plus minus minus and this is JM coupling and now this is for M I draw let me draw the same thing for A for the X and X again I will draw here JMX is plus minus because this is active coupling number those now this will have a different coupling here and what is this one here this is JAX here it was AM here it is AX because we are talking about the multiplet structure of the X spin therefore the patterns will be can be different depending upon what is the relative magnitudes of the two couplings therefore the fine structure of this is plus plus minus minus and this is also plus plus minus minus so if I draw that here now this is this side is X and this side is M and here we wrote as plus plus minus minus and this side also was plus plus minus minus so what will be the structure multiply these two once plus plus minus minus once again plus plus minus minus minus plus plus minus plus plus so 16 components so each of the cross peak here will have 16 components unlike in the previous case depending upon how many couplings are present in each multiplet structure you will have you have to multiply that by that many components so if one side has 4 components other side has 2 then there will be 8 components in the cross peak if both sides have 4 4 then you will have 16 components in the structure and the combination of the plus of the locations of the pluses and the minuses will depend upon relative magnitudes of the coupling constants the fine structure on one the active and passive couplings and two relative magnitudes of the active passive couplings third the peak appearances appearances on the two sides of the diagonal okay so these are the important features of cosy and double quantum filtered cosy spectra they I mean there can be more combinations of course if you have 4 spins there will be further splitting if you have more spins there will be further splitting but the active coupling will always be 1 remember this no matter how many spins are there how many couplings are there the active coupling will always be 1 all others will be passive couplings so therefore that is what is important in calculating the fine structure in each of the cross peak these will be directly used I am going through this so much detail because this will be directly used when we actually look at the splitting patterns in the spectra of nucleic acids and proteins and this is our ultimate aim is that we will see how we can analyze the 2d spectra and the 3d spectra of proteins and nucleic acids the very later on from the point of view of structural biology calculating the structures of the molecules these becomes very important okay so we will stop here