 So, welcome to today's class. We were discussing polarization transfer and we will take some advanced topic in polarization transfer. So, in last class, we had looked at like how we can enhance the sensitivity of X nuclei by selective polarization inversion. So, that means if A and A spins were coupled, we were selectively inverting the population of one of the transition in A spin and because of that population inversion, the intensity of X spin got enhanced. Then we looked at another method called inept where we are transferring the polarization from A spin to X spin with help of series of these pulse sequences. We were starting with a 90 degree pulse but then we were evolving the magnetization for tau period and tau is 1 by 4j and then we were applying simultaneously 180 degree pulse on A spin and X spin. Then again evolving it for tau period which again 1 by 4j so total tau is 1 by 2j. Then we were applying a 90 degree Y pulse on A spin and 90 degree X pulse on X spin because of that magnetization was coming from here to here and we were detecting on X spin and because of that actually sensitivity of X spin got enhanced and that can be in order of the gamma of A by gamma of X. So, typically 4 times enhancement we can get it. We saw that there are some problem associated with this kind of inept because it depends upon J value. So J's dependency is there and then we can get a distortion in the peak pattern because of coupling how many protons or how many X are coupled. So, we can have a different kind of distortion like if you have A2X and A3X different kind of peak pattern will arise and some of them can be positive some of them can be negative. So, we looked at this to get rid of this we just saw that if we had additional spin echo system a spin echo sequence to the inept which is called a refocus inept we can get rid of this different sign of the multiple CT peak and all can be positive. So, here what we are doing so same like inept we are starting with a 90 degree pulse then applying 180 degree simultaneous pulse. Now magnetization was here at inept and then we are doing this is spin echo that means tau 180 tau and because of that all the lines which some of them were negative some of them are positive now all are positive. So, this refocus inept removes the problem that were associated with inept and all the lines here with a positive signal. So, we had finished up to this point and then we looked at how we can do transfer of the magnetization from a nuclei to X nuclei or proton to carbon using a concept called cross polarization. So, we will build up those concept today and we will take it forward for some of those topics that we want to discuss today. So, as we said that we have to do these in rotating frame of reference and two experiment that we are going to discuss today is spin lock and Hartman-Hann matching condition I briefly mentioned what is actually Hartman-Hann matching condition. So, today I am going to explain this in little more detail. So, what we have seen that till now we have we have actually discussed how the spins interacts with main magnetic field which is B0 and these interaction or this interaction Hamiltonian is called G-Man Hamiltonian. So, here B0 is in Z direction and our spins are interacting because of this phenomena we have different chemical shift for different spins. Now and so here we had looked so, but can we change this effective field direction for short duration? So, what is the benefit of changing the changing the direction of the effective field? How we can change it and why we can change it? So, you might have heard the concept of rotating frame reference are we discussed earlier. So, what we are trying to do from the live frame we are transforming it to rotating frame by changing the direction of effective field for a short duration. So, what we achieve by doing this? So, this idea is based on something called Hartman hand. So, these are two scientists who actually conceptualize this and propose the idea. So, this is actually used for improving the sensitivity of X nuclei in solid. So, as I said like in Z direction when the magnetization is in Z direction it is difficult to match the energy gap between proton and carbon. So, here say if it is for proton this is for delta E for proton. Now for carbon it is going to be 4 times less. So, this is our delta E for 13C. If they are interacting with the B0, but suppose we change the direction effective field direction by doing that we can match the energy gap between proton and carbon and we somehow match it then we in last class we conceptualize that we can transfer the polarization from proton to carbon that will enhance the sensitivity. So, how we are going to do that? For improving the sensitivity of X nuclei. So, this was conceptualizing solid, but this is also applicable in liquid state. So, the crux of the matter is we want to transfer the magnetization from high gamma nuclei to low gamma nuclei. That means high gamma nuclei such as proton to carbon 13 or nitrogen 15 or carbon 13 to nitrogen 15 and we can transfer this and these transfer will enhance the sensitivity or signal of the low gamma nuclei such as these nuclei. And we need to detect on X nuclei in solid that is why we need to transfer it. So, to enhance the sensitivity, why to detect? Because the dipolar coupling something called dipolar coupling that we have seen the two spins are connected through a space by a coupling called dipolar coupling. So, in solid this dipolar coupling is huge and for proton dipolar coupling is very very large. So, that leads to the line broadening. Therefore, in solid generally X nuclei are detected. So, since X nuclei are detected therefore, it is imperative to enhance the signal of X nuclei and this is the way to enhance it transferring the polarization from more sensitive nuclei such as proton to less sensitive nuclei such as carbon or nitrogen. Now, so essentially if you look at the conceptual that we have learned in previous classes. So, sensitivity is given by the difference in the population between the ground state and the excited state or the first excited state or we can say alpha state and beta state. So, alpha state we have more number of particles, beta state we have less number of particles. So, a nuclei will be called sensitive if the difference is more. So, there are more in alpha state and less in beta state and that depends upon what is the delta E between these two states and also on T. So, T we cannot change too much. So, actually if you expand this T is generally ambient temperature that we see. Therefore, in NMR the difference between N alpha and N beta is comparatively quite less and if you look, if you expand this we get this formula where there is a B0 dependence. So, that is why the separation between these two states depend upon B. Now, so that means if the separation at the same B delta E is more for proton. So, proton is more sensitive if it is less then it is less sensitive. So, that is why proton is more sensitive and carbon 13 nitrogen 15 is less sensitive because here is a gamma and gamma for proton is high compared to carbon 13 and nitrogen 15. So, for a high gamma nuclei such as proton it has high N alpha divided by N beta that means ratio for proton is high and therefore, their spin temperature is low. So, that means proton are sitting at low temperature spin bath whereas, carbon 13 which is low gamma nuclei they have low ratio of N alpha and N beta and they are sitting at high temperature spin bath. So, the spin bath ratio is typically 4 to 1 because gamma of proton is 4 times more than carbon 13. So, T s that is spin temperature of carbon 13 is actually 4 times more than the spin temperature of proton. Now, by a mechanism suppose we have want to bring these two spin bath proton spin bath at low temperature carbon spin bath at high temperature or proton is more sensitive carbon is less sensitive somehow we bring these two spin bath together then what will happen the temperature will flow or spin temperature will flow from carbon to proton or we say sensitivity will flow or polarization will flow from proton to carbon and carbon sensitivity or polarization can be enhanced. So, if we bring these two nuclei in a thermal contact in sensitive nuclei will cool and therefore, there if they cool their sensitivity can be enhanced. So, this was we want to achieve we want to cool the spin temperature of insensitive nuclei by putting them in thermal contact with low spin temperature nuclei such as proton. So, how we can achieve that? So, that actually in homonuclear system for solid it can be done by spin-spin interaction. So, what happens since in solid spins are closer and they are not tumbling too much then actually dipolar coupling is active and spins are interacting. So, by something called flip-flop mechanism actually they can transfer this magnetization but say heteronuclear system such as like such as proton and carbon coupling. The gamma of B0 gamma H of B0 that is not equal to gamma of 13C. So, that means if you look at Ziemann field only the proton gamma B0 or we can write it omega gamma H B0 is which is omega H is not equal to omega 13C which is gamma 13C B0. Now, so that means if we keep in same field these two nuclei X and 13C even the thermal contact cannot be achieved when polarization transfer cannot happen. So, then we have to do a trick we have to shift from lab frame to rotating frame of reference and now that is what we are saying we want to change the direction of effective field by applying a B1 field and B1 field is applied on proton as well as on carbon. So, suppose we achieve this condition where we apply two B1 field one for proton and one for carbon then in that case we can achieve that gamma H of proton into B1 field which is a radio frequency pulse applied on proton this will be equal to gamma of 13C and an effective field applied along like a transverse plane or rotating frame of reference on 13C. So, if you do that we can achieve gamma omega of H equal to omega of 13C and this condition is called Hartmann-Hahn matching condition that means to visualize you simply now by applying this we want to match this for proton with of carbon 13. So, this is for 13C and this is for proton by applying two RF pulse or effective field in rotating frame of reference one on proton one on carbon 13. So, if you do that this frequency of proton and carbon 13 will match. This matching condition is known as Hartmann-Hahn matching condition and this will lead to polarization of transfer between proton and carbon. So, energy exchange will happen with both spin reservoir by something called cross polarization. So, polarization is coming from proton to carbon 13 therefore it is called cross polarization. How we have to do that? So, essentially we have to apply a 90 degree pulse. So, let us see we write two channel one channel is for proton and another channel is for 13C. So, if we apply a 90 degree pulse on proton and then what we are doing 90 degree here and then we are locking it. So, we locking proton and carbon. So, because of that now here we brought it to XY plane and then we locked it and then we can detect X. So, this is called cross polarization experiment CEP cross polarization and this actually enhances the sensitivity of carbon that happens in solitude. So, essentially vectorially if you see it what we are doing here is our B0 field to start with we had magnetization in B0 field in Z direction and here is our B1 field which is like transfer direction. We applied a 90 degree pulse which is say on X pulse. Now our spin is in this direction and rotating in XY plane like here. Now we are locking it we are applying a pulse so that it is locked in the XY plane and by locking proton and carbon both in the same direction that means we are maintaining the thermal contact between X and 13C and that actually is the cause of sensitivity enhance. So, that we can do easily in solid CEP which means cross polarization plays an important role and in generally in solid state NMR experiment all experiment essentially where we are detecting on carbon starts with cross polarization. We transfer the magnetization from proton to carbon that is the first step in solid state experiment. But in liquid state actually CEP may not work because here what happens typically for in liquid state the T1 relaxation time and T2 relaxation times are more or less equal and therefore actually the like spins does not have dipolar coupling or simply you can visualize that the spins are orienting randomly at very rapid scale and therefore the dipolar coupling which is distance dependent will vanish because now direction is changing all the time and distance is changing. So, dipolar coupling vanishes completely and therefore if you do cross polarization the spin lock condition cannot be achieved. So, that cannot be achieved so that means whatever we were saying transferring the polarization from proton to carbon in liquid if you do like this we cannot enhance it however we can do another trick and then we can achieve the spin lock for homonuclear and heteronuclear system but how we can do it let us see it. So, here as you know although dipolar coupling is not active but we have one coupling which is active and that is J coupling the scalar coupling. So, scalar coupling is active using this scalar coupling we can still achieve the transfer of polarization for a homonuclear system and heteronuclear system. So, for homonuclear system the experiment is called ho-ha-ha homonuclear Hartmann-Hahn experiment and for heteronuclear it is called he-ha-ha that means heteronuclear Hartmann-Hahn ho-ha-ha is homonuclear Hartmann-Hahn. So, these two experiments can be done to achieve the polarization transfer. So, what we actually do during these experiments actually we have to remove the Giman contribution Giman contribution as we were saying B0 contribution. Now, so there is no chemical shift evolution what we have to do we have to remove that Giman contribution but we have to keep active the scalar coupling a scalar coupling Hamiltonian but still our coupling scalar couplings are active in the Hamiltonian. So, scalar coupling can act as a mixing operator. So, if you look at this is essentially sum of the i j between i and j spin. So, this is given by this formula H m equal to sigma sigma i j to j i i and j. So, that means two spins say a spin and x spin there is a coupling scalar coupling is active even if we remove the Giman contribution. Now, that actually helps in mixing of the of the polarization transfer of between two nuclei. So, how experimentally it is done I will just explain you. So, we are saying we are removing the Giman contribution but keeping active the scalar coupling contribution. So, experimentally it is done by something called multiple pulse decoupling experiment which is called MLAB. So, MLAB is actually has come from a name of scientist whose name is Malcolm and Levitt. So, Malcolm Levitt actually has developed this sequence and that is how it is MLAB or we can lock it the spins for a period and that is called spin lock period. So, what actually it is done? So, during this period either it is say spin lock period or the like a mixing period TSL or this TSL means spin lock period and this is mixing period. Essentially we want to achieve the Hartman-Hahn matching condition and this Hartman-Hahn matching condition if we achieve the transfer will happen. Transfer will happen from one nuclei to another nuclei more sensitive nuclei, less sensitive nuclei or even in the homonuclear fashion and this transfers of essentially what we are doing? We are starting with a Z magnetization we are bringing into XY plane and we are locking it there. So, this locking actually has a time dependence or so it actually reaches to maximum when the locking period or the spin lock period is more or less equal to 1 by 2 J and if we achieve this that magnetization can transfer or travel from more than one spin. So, like if you take a MX system it can transfer from A to M and then to X. So, that means multiple spins can be coupled or network of spin can be the transfer in network of spin coupled spin can be achieved. So, how actually it is done? The experiment is simple don't worry at the moment about this. Here it is a pulse sequence for 2D but essentially if you remove this T1 period here it is a sequence for transferring from magnetization transferring from one spin to another spin. So, what essentially we are doing? Applying a 90 degree pulse. Applying a 90 degree pulse means bringing them to XY plane and then we are spin locking it. I mean locking in the XY plane. So, because of locking that means we are applying a weak RF pulse, weak RF pulse bringing them to like a rotating frame of reference and here the Hartmann hand matching condition happening and then we detect it and that is FID. So, similar in case of TOXI total correlation spectroscopy that we are going to learn after few class. So, this is also essentially the achieving this Hartmann hand matching condition. So, start with a 90 degree pulse and then a series of decoupling pulses is applied which is called MLAB and then you detect it. So, this is mixing time and this is spin lock time. So, essentially the concept is similar. Now, we same experiment can be extended to two dimension just we have to add a T1 evolution here that again we are going to discuss after few class. So, that means from one dimension we can add two dimension and we can actually achieve the magnetization transfer relay from one spin to another spin to third spin to fourth spin something like that. So, that is what essentially is Hohaha or TOXI experiment. So, for an example I will just give you where actually it is used. So, say we have a glucose molecule D-glucose which actually which is in equilibrium beta glucose and alpha glucose the difference you can notice is at this position. So, now there are so many protons here if you record one D we get all these peaks. So, here is a water peak and these are other proton that are these are coming from beta conformation beta glucose these are beta glucose this is alpha glucose because here is the difference. Now, if you record 2D on glucose molecule say with a mixing time of 30 millisecond. So, this 30 millisecond when we spin lock in XY plane now because of this mixing there is a relay transfer of magnetization from one spin to another spin you can see it here this is between 2, 3, 1, 2 like if you go in this line there are transfer happening 1, 2, 1, 2, 1, 2, 1, 2, 3. So, that means relay transfer happens. So, we can transfer from magnetization say from here to here to here and so on and so forth and that helps in getting the structural information for any of such molecules details we are going to discuss when we start actually looking at the 2D experiments some such as Koji, Toxy and all those. But at the moment this is this concept is important because you can now achieve the correlation between 3 bond, 4 bond coupling. Simplified version of this can be also done in 1D 1D fashion. So, now I am going to discuss with you 1D selective Toxy experiments. Toxy is total correlation spectroscopy don't worry too much at the moment about name. So, it is a same spin lock period 90 degree spin lock period and detection. Now this can be used for a structural information why actually generally say 2D takes 3 hours. But the 1D version of same experiment you can achieve and you can save lots of time. So, this polarization concept actually polarization concept can be used for transferring the magnetization in 1D fashion and you save lots of time. And the like whatever example we showed in the last slide it can be nicely used for identification of protons say in carbohydrate. So, how we are going to do experiment? Let us see we do two experiment and we take difference between them that is called difference experiment. So, essentially we are trying to do something like this two experiment. Experiment number one, we want to apply a 180 degree selective pulse on resonance. So, say I have 5 peaks here 1, 2, 3, 4 and 5 peaks. So, in first experiment I apply 180 degree pulse selectively on this spin. Then we apply a 90 degree pulse. So, 180 degree selective. Then we apply a 90 degree pulse on all spins. Then we have a mixing period here spin lock period or mixing period here tau mixing and then we detect FID. So, this is our first experiment. In the next experiment we are so this is on resonance. In next experiment we are doing same thing we are applying 180 degree pulse but not this time on resonance but off resonance somewhere here. And then we apply a 90 degree pulse and then we have a mixing time and then we detect FID. And then we take difference between these two whatever spectra comes take a difference between S1 and S2. So, this will this will depot only where magnetization transfer has happened because here we have inverted and then we mixed it. So, difference between these two actually gives us information where the magnetization transfer happens and that will tell you the connected proton. So, here is a one of the examples. So, let us see the same molecule beta glucose if you take. Now, just we record say beta glucose is always in equilibrium with alpha glucose. So, here we getting the spectrum coming from a mixture of alpha and beta glucose. Here are those peaks that appears we have seen in the last slide. So, these are this is the H1 alpha and this is H1 beta. So, that tells that we have both confirmation in same solution. This is water peak. Now, we did a Toxy. So, Toxy means total correlation spectroscopy. So, all those are directly coupled will come. Therefore, if you notice here this peak is not coming because this is from different conformers. So, all those has come 1, 2, like here 6, 6 prime 3, 5, 4, 2. So, here 1, 2, 3, 4, 5, 6 all protons have come. Now, we have a complete spectrum. So, now what experiment we are doing same Toxy with increasing mixing time we are doing. So, if we say start with 1, we selectively in what 1 and then we want to apply a 90 degree pulse and then we are increasing the mixing time. So, first one which is near to that will be appearing and that is how we get a 2 signal coming from 2. 180 degree applied on 1 then we started mixing we got 2 then we are getting 2 plus 3. So, now we know that 2 and 3 are connected. Similarly, we are getting 2, 3, 4, we are getting now 2, 3, 4, 5 and if we keep increasing we can get everything. So, now by increasing time. So, here we are we can assign it which is closer to 1 proton. Now, the nearest one appears at a shorter mixing time, the farthest one will appear at a longer mixing time. So, we can get like we can see the relay in the magnetization transfer from 1 to 2 to 3 to 4 to 5 and 6 and that is the beauty of this experiment. Now, we can do a spectral editing by doing the multiple 1D Toxy experiment. So, essentially alternatively Toxy that I discussed we can also do by a simple experiment. So, 90 degrees selective pulse say 90 degrees selective we do on spin number 1, then we are doing a mixing time here tau m or Tm and then we do FID. So, essentially same experiment you can do by just selectively applying a 90 degree pulse on a spin number 1, then mix it and then we detect it. So, if we increase mixing we first see the proton number 2, then we see proton number 3, then we see proton number 4 and so on and so forth. So, that is beauty of 1D Toxy experiment can be done easily and in a quicker time. We had discussed this earlier that generally for a large molecule we have a negative NOE, but there is a one good part of rotating frame of reference. Here NOE is always positive and that can be used to do something called like a again something called a NOE best experiment. So, in rotating frame these experiments are called ROG, rotational frame over Hauser effect spectroscopy that is a ROG. So, if you look at here we can get still positive NOE enhancement even for the bigger molecule which was difficult in the NOG, NOE enhancement that we have seen in the previous lectures, but if you do in rotating frame we still get positive enhancement and that positive enhancement is almost 67 percent. So, using this concept whatever we just discussed this is 1D ROG experiment. We apply a 90 degree pulse then we have a like a time period. So, we apply a 90 degree pulse then we have a time period where we spin lock it 90 degree pulse then we spin lock it tau SL and then FID. So, now this actually spin locking is slightly different than Toxy. Toxy uses J coupling for transferring the magnetization. Here we want to make sure that transfer happens by a cross relaxation rate. So, still it can use dipolar coupling. So, one can have this period where or the alternate experiment where we selectively invert one of the spins. So, by applying a 180 degree pulse then a 90 degree and then a spin lock and FID. So, now if you apply 180 degree pulse it starts the cross relaxation. So, if you take the difference of these experiment number 2 minus experiment number 1, one can get the ROE effect and that is exclusively coming from the dipolar coupling contribution and that is called ROG. So, still we get NOE enhancement by putting them in rotating frame and spin locking it. The signal enhancement is always positive up to 67 percent and one can achieve a nice dipolar coupling based correlation that we had seen earlier. So, here in this regime that is what we are talking ROG works better and pulse sequence for 2D even one can have a 90 degree pulse. T1 evolution again I said just after few lectures we will get into 2D, but at the moment if you delete this you have a 90 degree pulse isotropic mixing which is generally achieved by applying a weak RF pulse and then we detect. So, this is ROG experiment and during this spin lock period magnetization transfer happens via dipolar coupling and good part of this ROG experiment that it is less susceptible to spin diffusion therefore we can achieve a longer transfer through dipolar coupling and this is quite a bit used for identification of the distance proton that are connected through dipolar coupling in many of the spectrum and here one of the spectrum that we show here the cross peaks comes of opposite sign and then the diagonal peak. So, this is ROG spectrum for any of the molecule and now for peptides or for aldehyde saccharides the NOG experiment people do ROG experiment where they can mix it for longer time and that is less susceptible to spin diffusion which was a problem of NOG aspect. So, I think we covered more or less the polarization transfer and now we will move to next topic from next lecture. So, if you have any question on these topics don't hesitate to write us we will be happy to answer all of your question. Thank you very much.