 We discussed last time a technique called selective population inversion, the idea was to do a polarization transfer from a more sensitive nucleus to a insensitive nucleus. So for example if I have a two spin system we have two lines here and then I have another like this and this is more sensitive. So this has more intensity and this we saw okay let us say we have this intensity of these two lines as 2 delta dou delta and this one has capital 2 delta capital 2 delta these are more insensitive. Then we saw that if I do an inversion on one of these transitions let us say I do an inversion here inversion means I apply a selective 180 degree pulse on this particular transition. So when I do this transition so as a result of this inversion I will get spectra where the intensity of these two weak lines they get enhanced. So let us say these ones were x1, x2 and this is these ones are a1, a2 and if a1 is inverted then what is the kind of a spectrum I will get we saw that we will get a huge enhancement in the intensity of these signals. So what we saw was this will become a get a signal like this for x1 and a signal like this for x2 and for x a1 it will be like this and a2 also it will be like this. So because we have inverted this a1 transition so this will have the intensity of minus 2 delta and this will have the intensity of plus 2 delta. This signal has an intensity of minus 2 delta plus 2 delta and this one has the intensity of 2 delta plus 2 delta of course this one should go longer compared to this there is no space there. So this can be extended below above there. So therefore you see this there is a substantial gain in the intensity of this signals and here of course delta is much greater than capital delta is greater than delta. So this was a population transfer as a result of the population transfer from the A spin one of the transitions then we get a significant enhancement in the intensities of the x transitions. However we had this problem that we have positive negative signals here and selectivity is a quite an issue. So applying a selective pulse was an issue and therefore we had some difficulties here that is what were the difficulties selectivity was an issue selectivity is a problem and we cannot do it in crowded spectra then we also have the positive or negative signals. So in order to get over this problem so there was a new technique which came up which is called as inept insensitive nuclei enhancement by polarization transfer. So the experiment is quite well described here I will go through it stepwise and we will use you will see that we will use here the principle of SPI also here at this point we will see where I will explain to you where we do use this. Pulse sequence goes like this so this is called insensitive nuclei enhancement by polarization transfer or in short inept. Experiment starts like this so you have the A spin here and the X spin there and the X spin is supposed to be the less sensitive one and the A spin is supposed to be the more sensitive nucleus. So now we apply a hard pulse to A hard pulse means it is not selective anymore so you invert you apply a hard pulse that is called as a hard pulse all the transitions of A spin are are excited. So we apply a 90 X pulse to the A spin wait for a period of time and then you apply simultaneously 180 degree pulses to both the A spin and the X spin and this is particularly easy if the A spin is for example a proton and X spin is like a carbon and then it is very easy to do it because these are two different channels and to apply pulses on two different channels is not a problem at all because they are independently they work so therefore you can apply without any issue of interference between the two. Then you wait for the same time tau again then you apply a selective not selective hard again 90 degree pulse on along the Y axis here and the 90 X pulse here it does not matter which one you take but more importantly this has to be a Y if this is X this has to be a Y. So therefore you make this sort of a pulse sequence and then you will see what happens that you will get a substantial enhancement of the X magnetization and that is what you will detect here. Now let us try and analyze this. So how does this work? Basically if you recall the spin echo experiment we had this spin echo from this is 90, 180, 90 tau, 180 tau this is the spin echo sequence. At the end of this two tau we have the echo appearing and then you apply the 90 degree pulse on both the channels the A channel and the X channel to transfer magnetization from the A spin to the X spin. How does that work? Let us see here. Let us assume that we sit on the rotating frame of the A spin and this is these are the time points indicated here 1, 2, 3, 4, 5. So at before this 90 degree pulse what is the magnetization? The magnetization is along the Z axis. At this point the magnetization this if I call this time point as 0 the magnetization is along the Z axis. If I say here if the time point is 0 here the magnetization here is along the Z axis. Now when I apply a 90 degree pulse the magnetization comes on to the minus Y axis. Now notice I am applying pulse only to the A spin therefore I need to consider only the A spin here. Now if it is coupling between A and X this will be transition there will be two transitions A1 and A2 and both they are both magnetizations are along the Y axis minus Y axis. So I just still represent that as A1 and A2 these are the X, Y magnetizations corresponding to the A1 and A2 transitions. Now what I do during the period 1 by 4 J during period 1 by 4 J what will happen these ones will start processing. Now as I said I am sitting in the middle of the A1 and the A2 transitions when I am this is exactly the spin echo sequence. The spin echo sequence meaning so I have this A1 and the A2 transitions here I am sitting here if I am sitting there so therefore the one of them goes faster other one goes slower. Therefore these ones will move in the two opposite directions. So these A1 and the A2 will move in opposite one will move like this other one will move like this because I am sitting in the middle. Now it will move a certain angle and what is that angle that angle is given by what is the frequency difference between the two and the delay you give because this separation between them is J and therefore 2 pi J and the tau we give that is the angle with which it will rotate. So the angle with which will rotate is let me write here angle theta what it will rotate is 2 pi J tau. So J is the frequency difference between the two therefore the separation between them will be 2 pi J tau. So if I say tau is equal to 1 by 4 J how much will be the angle if it is 4 J then it will be pi by 2. So angle between these two will be pi by 2 at this point it is pi by 2. So now I am applying A180 degree pulse on the A spin. So A spin what apply 180 degree pulse this A2 transition will come here and the A1 transition will come here that is what is indicated here and they will continue to move in the same direction this will continue to move in the same direction like this A1 will go like this and the A2 will go like that. Now the trick is here I apply also 180 degree pulse to the X spin as well. Remember what happens if I apply 180 pulse to the X spin it will invert the X and it will invert the alpha and the beta states of the X spin convert alpha to the beta this 180 degree pulse converts alpha to the beta of the X spin. So when that happens the two these two transitions will get interchanged A1 becomes A2 A2 becomes A1. Therefore there when you have this this will become A1 here this will go in the opposite direction this A2 this will go in this direction now. This one the slower becomes faster the faster becomes a slower. So therefore now this will go like this and this will go like this. So now during the next 1 by 4j what will happen they will again move I away from each other and another pi by 2 phase angle will be introduced. So this was pi by 2 here and this is also pi by 2 this was also pi but we did not do anything here this was also pi by 2 but when it moves now it is pi during the next one another pi by 2 is added there so therefore now they become opposite to each other. So they are along the now the X and the minus Y axis X and the minus Y axis. So now we apply a 90 degree Y pulse a 90 degree Y pulse here onto the A transition. So that means I am applying a pulse along the Y axis. So what will happen to these? These two which are along the X and the Y they will now go to the Z axis on the positive and the negative Z axis they will come along this okay. Now we compare this situation with what we had here in the beginning. In the beginning the two transitions were at time point zero at time point zero where they were at time point zero these two transitions were both along the Z axis right let me use that same color. At time point zero the both the transitions of A1 and A2 magnetizations were along the Z axis this is the Z axis A1 and A2. Magnetization corresponding to this they were along the positive Z axis. Now what I have achieved here at this point I have done inverting one of these inverting the A2 transition here the A1 is kept up there like that only nothing has happened to the A1 and the A2 is inverted this is like SPI populations are inverted as in SPI you see one transition is inverted okay. So therefore I get the same benefits as I will get from the SPI okay how much do I get now? So if you look back what did we have in this one I had minus 2 delta minus 2 delta plus 2 delta and 2 delta plus 2 the same when I will have there also and this will be minus 2 delta plus 2 delta that will be present there okay. So here therefore if I when I apply 90 y pulse to the next pulse if I apply the transitions of the A spin have gone on to the positive and the negative Z axis and the X now now X spin this is the first time applying a 90 pulse therefore the X magnetization will now come on to the transverse plane will now come on to the transverse plane. See before this point at this time point 4 these two transitions the intensities of these are along the Z axis only right these added is along the Z axis okay. So at this point the there is no transverse magnetization of the X spin it has got the populations of the 8 spin it has got at this point at this point the X spin use a different color the X spin have both the transitions along the Z axis but one of them is like this other one is like this along the Z axis part of this has come from the A spin transition how much has come from the A spin from the A spin as we said if it is 2 delta minus 2 delta to begin with it was 2 delta. So let us say this was 2 delta plus 2 delta and this was minus 2 delta plus 2 delta this is at this point after the 90 degree y pulse this will be at this point okay. Now notice here but I have also applied a 180 degree X on to the X spin. So therefore what was 2 small delta small delta here. So here there was the two transitions of the magnetization corresponding to the X spin where like this like this and these were 2 delta and 2 delta and but this is now inverted to this 2 delta 2 delta minus 2 delta minus 2 delta. This is great coming directly from the excitation of the X spin this is coming from the excitation of the X spin at this point the X magnetization along the Z axis was corresponding to 2 small delta 2 small delta as in this one. Now this 180 X pulse makes this to minus 2 delta minus 2 delta with regard to the populations this will carry forward therefore I have to add that here whatever is coming here will be added here. So in that case what I will get I will get minus 2 delta let me add with a different color. So then I will have to add here minus 2 delta to this and minus 2 delta to this ok. So therefore what I got I got 2 delta and minus 2 delta as a result I get I will use the same color here I get this is 2 delta and this is minus 2 delta that is what I have shown here that is what I have shown here X 1 and X 2 as they are coming these are identical to this. So let me put a circle here to explain this to you. So this is the same. So when I do this the initial magnetization is along the populations are corresponding to this and when I apply a 90 X to 90 X here this magnetization gets transferred onto the transverse plane. So then I measure it then it will be 2 signals of equal amplitude but along the positive and the negative Z axis ok. So how much is the enhancement here what was delta earlier small delta earlier is now delta right. So therefore the enhancement is so therefore the let me write ok. So therefore in the AX case the enhancement is by factor delta by delta and these ones are dependent on the populations these are dependent on the populations or the sensitivity therefore this will be proportional to gamma A by gamma X ok. So this is the kind of an enhancement you will get for a simple 2X spin system ok and this will be for example this will be like factor of 4 for carbon 13 and factor of 10 for nitrogen 15. So this is a substantial enhancement ok. So now what happens but however we still have this problem of positive negative lines and that continues ok. So we have not gotten over that problem but we have gotten over the selectivity issue we do not need to apply selective pulse anymore we are applying a hard pulse by applying the hard pulse we have got the same result intensity enhancement and similar intensities for both the lines earlier you remember in SPI we did not have similar intensities for the 2 lines they were slightly different. Now here we get similar intensities for the 2 lines in the X spin. Now what happens suppose I consider an A2X system and this is the experimental spectrum here which shows exactly that point here see these are identical lines with similar intensities similarly here similarly here and of course we have more complex spin systems here because this is only not only AX but also we have A2X, A3X and things like that. Now of course in real life of course you not only have an AX not only have a CH group you also have a CH2 groups and CH3 groups and things like that. So what happens in the case of a CH2 group and that is indicated by this A2X, A2X spin system. The A2X indicates like a CH2, X is the C and A2 is the H2 but the transfer is considering we consider the transfer from the individual protons at a time individual protons at a time. So therefore how will we analyze this A2X system? Consider the X consider the X let to analyze this A2X system consider the X. Now this one is now split because of one coupling one transfer into two lines like this equal intensity. So when I apply when there is a next coupling there is a this is due to the 1JX coupling 1JAX coupling. The second coupling what it will do the second JX coupling will split this individual lines into two again. It will split this individual lines into but now this will be in phase splitting this will split like this and the other one will also split and that will happen it gives a different color here and that will happen like this the second line. So this line has split into these two and this line has split into these two because of the another coupling the second coupling because there are two A's there. The first A has resulted in this anti-phase separation this is called as anti-phase separation and this now is split further due to another coupling of the X to the second proton here and that results in this splitting. Now what happens these two central lines will cancel this will cancel. So then I will have only two lines now this will result in this will result in one line here and now there is a gap and there is another line here. So then the center there is nothing that is what will happen in the case of A2X the central portion has got 0. This separation is now 2 times JAX from here to here is not JAX but 2 times JAX. The central line which is there here it was JAX here it was in the single case there was JAX. Now this central line has vanished therefore in this case I get a 2 times JAX. So that is explanation for that. Now we can consider further suppose that is A3X if there is A3X these two will split again. So if you have another JA then these two will again split as like this and then the other one will also split but now it will come closer because it will go on to this side. This is what will happen for an A3X. So that A3X so therefore this will be the A3X and this will be the A2X. We still have the positive negative signals and the total separation from here to here is of course 3 times JAX. Separation from here to here because there are 3 couplings therefore there has to be 3 times JAX from here to here should be 3 times JAX. So that is this is 1 JAX and from here to here is 2 times JAX. These are one bond couplings remember JAX. So these are one bond couplings therefore there is a total of 3 bonds. So therefore A3X spin system will appear in this manner A2X will appear like this and this is again a disadvantage for the in-app sequence because of the middle sequence is gone. Now you may tend to think that if I get a spectrum like this this is actually an AX with a coupling constant which is twice that of the normal coupling. Now one bond coupling which is not the case. It is actually an A2X but this is because of the sequence you will get a separation which is twice that and the central line has vanished. So this is while you have circumvented the problem of sensitivity I mean the problem of selectivity problem you have still got the anti-phase problems and you have some missing signals in the middle. So that will be a kind of a disadvantage. So therefore here we will have missing signals, missing central line. So this is what I indicated there with regard to the in-app sequence how it will increase the sensitivity. So therefore the in-app use non-selective pulses. So you have gain identical intensities for the two lines in the X doublet. And the gain is by the fact is gamma A by gamma X. So this much gain we will get in the case of in-app. Now the disadvantage of course will be are still disadvantages. Disadvantages are so you have the positive negative signals still present still present but missing line in A2X systems. So to get over this problem there was one more technique which came into existence and this is called as the refocused in-app. What it does it is until here it is the same as the in-app until here it is the same as the in-app and then you have introduced another block here another block here which is tau it can be tau dash or tau dash or it can be tau or tau also in the simplest case it is tau and tau. So then what happens here? So at this point if I draw the X transitions if you recall the X transitions were along the X axis or the Y axis whatever that is. So if this is minus Y this is minus Y and the two transitions were oriented like this and such a signal is called as anti-phase magnetization. This is called as anti-phase magnetization because two transitions have opposite phases. Now what we have done is you continued the spin echo, you continued the spin echo in an identical manner. You notice the tau and tau suppose tau dash is equal to tau, tau dash is equal to tau. You are simply repeating that same sequence. Therefore as a result of this during the next two tau period, what will happen? This one will again clear another 180 degree phase difference and then they will become oriented like this. They will refocus. So they will come here along they will refocus the separation of 180 degree phase difference which was there that would be gone because it roses by another 180 degrees. Another 180 degree is meaning they will come back in phase. This is called the refocusing. So when they refocus now if you would now take a spectrum of this you will get in phase lines because the magnetizations are not along the opposite directions and this magnetization here was like this and like this and when you do a refocusing so you will get magnetization along this axis here and we will get your phase after use to phase correction etc. you will get in phase magnetization. This is called as in phase magnetization. Now of course you notice here of course the tau dash is a variable tau dash can be optimized for certain purposes. We will not go into those details here and there is also one other pulse which is applied as a modification to a refocused inept is called as inept plus and this is a modification to remove some artifacts and this actually pulse sequence is called as inept plus. With that modification it is called as inept plus but we will not go into those details here if that requires more of theoretical calculations and but this is enough to understand that we can actually do a refocusing. If you refocus what is the advantage we collect the data here we collect the data then magnetization is now in phase therefore we can decouple it also. So now if you do decoupling you can do decoupling here you can decouple they can get a one line you can get one line which has the some of the intensities of these two. So decoupling so this is possible this decoupling can be introduced here this is decoupling. So the proton can be decoupled while you are observing the X when you observe the X now you get a very huge gain in the now the splitting is gone you do not need this splitting this is one bond coupling one bond coupling is not of much use therefore you can remove that coupling then you will get a single line for the particular carbon or the nitrogen or whatever you are talking about. So you will have a substantial gain in the signal to noise ratio and this is the benefit of this refocusing every time you want to decouple you have to remove this anti phase character bring them into in phase in phase means they both go in the same direction like this. So therefore then you can collapse them there if they are like this so you know decouple it becomes 0 but if they are going like this if they are too like this if you decouple they will become like that and of course they will add on intensity. So there will be substantial gain in the intensity because of that. So and here is an example of such a spectrum is a practical example you can see all in phase lines and with much higher signal to noise ratios intensities and all multiplied structures will get retained so you will not have any problems with this missing peaks and all the things will be retained. So this is the ideal technique one can use and most of the time this is what one uses all multidimensional NMR experiments and I think we will stop here with the polarization transfer.