 So, welcome to today's lecture, we will start with a new chapter today and which is called polarization transfer. So, polarization transfer has profound effect in many aspects of NMR spectroscopy. Polarization transfer is used to enhance the signal for a particular nuclei or it is also used to measure the distance between two nuclei because of these property actually it finds its wide application in chemistry and biology. So, we will just go and revise some of the concept that we had seen earlier. Previously like when we started the course we had seen that intensity of a resonance is proportional to the population difference between two states. So, suppose here I have a state say alpha state and beta state, how much is the population here and how much is the population here. So, this difference actually gives you what will be the intensity of your signal. Now, as we have seen that this population is governed by Boltzmann distribution. Now, Boltzmann dictates how many spins are going to be in the lower state and how many spins are going to be in higher state. Since the separation between these states is minimal. So, in NMR actually the difference between the ground state and the excited state is not much. Therefore, NMR is one of the insensitive technique. As we said that the difference between the population here and population here is not much. So, therefore intensity here is signal. So, to just give you an idea of how insensitive it is, if you record a fluorescence spectrum for a biomolecule, suppose we are probing a tryptophan which is a fluorophore and commonly used intrinsic fluorophore for doing fluorescence spectroscopy. So, for that you need maximum of 10 or 20 micromolar of sample. However, for getting a decent NMR spectrum for a biomolecule you need few 100 micromolar say 500 micromolar to 1 millimolar for doing 1D spectrum. Therefore, one can say that NMR is one of the insensitive technique that we have, but it has its own advantage and therefore, it is popular like getting the site specific resolution or information. The other important phenomena that this state difference also depends upon which type of nuclei is. So, that actually dictates the magnetic moment of the particular nuclei. So, carbon is 4 time less sensitive than the proton and therefore, if difference in the proton is this much then carbon will be less compared to that. And therefore, carbon becomes even less sensitive than the proton. Nitrogen is further like its gamma is 10 time less. So, its magnetic moment is less and therefore, the intensity that we obtain from nitrogen will be even less. So, these are the some of the phenomena. So, some are more sensitive nuclei like proton because of high magnetic moment. So, therefore, separation between these two states will be higher. Nuclei like carbon 13 or N15 will be less sensitive simply because the separation between these two states will be less and the population difference between these two states will be also less. So, this is one of the insensitive technique. So, just to summarize what we discussed, the intensity for a particular signal depends upon the difference in the population of the ground state to excited state like a typical electronic spectra like a fluorescence spectra or UV visible spectra. The difference between these two states ground state and excited state population difference between these two states is quite huge therefore, the signal intensity is remarkable. In case of NMR this the difference in population between these two states is a smaller therefore, it is one of the insensitive technique, this population is distributed by Boltzmann distribution and some of the nuclei like X nuclei nitrogen 15 or carbon 13 are even less sensitive. So, with this background we will move ahead for the polarization transfer and we try to understand the concept of polarization transfer. So, all the time we have to think how to increase the sensitivity of some of the lower sensitive nuclei even for many case proton is also not that sensitive compared with electronic spectra. However, among other NMR active nuclei proton is the most sensitive. So, can we manipulate somehow population difference between these two states? If we manipulate the difference between these two states we can enhance the sensitivity because now difference will be more. Now, manipulation of this population in two states actually energy level of the spins will be having now different population. So, here say we have a more population as expected because of Boltzmann distribution and here we have less, can we manipulate so that here becomes more and more and here becomes less and less. If we are probably able to do it we can increase the sensitivity of a particular resonance. The phenomena where we do manipulation between the population of these two states is called polarization transfer. Now, this polarization transfer can be between two same type of nuclei which is called homonuclear polarization transfer or it can be between two different kind of nuclei that is called heteronuclear. So, if we are doing this population difference manipulation between proton and proton this is homonuclear and carbon 13 and proton it is called heteronuclear. Now, this homonuclear polarization transfer gives you one of the important parameter which is used for measuring the distance between two nuclei. So, this gives you distance restraints. Now, in heteronuclear polarization transfer we will see further that actually it is used very much in multidimensional spectrum where we transfer the polarization from proton to carbon 13 then further to nitrogen 15 and that is how we enhance the sensitivity of carbon 13 and nitrogen 15. So, in multidimensional spectrum we do spin gymnastic or spin choreography where we transfer from one nuclei to another nuclei and take it back and then we record the information in macromolecule. So, we will see these concepts in coming lectures and this is essentially for enhancing the sensitivity of heteronuclear atoms such as N15 or 13C. So, let us start with a homonuclear polarization transfer. The overhouser was one of the pioneer who actually discovered this and therefore this phenomena is called nuclear overhouser effect or NOE. And actually this experiment actually opened the avenue of NMR in structural biology because actually this gives direct measure of distance between two protons. So, if you can measure the distance between two protons, we measure the network of these distance and that distance is used for constructing the structure of a biomolecules like protein or DNA and or even a small molecules. Now, so that nuclear overhouser based spectroscopy which is called NOE and that we are going to see in coming lectures was one of the breakthrough in structural biology for protein or nucleic acid structure determination. However, organic chemists actually use also this concept for like deciphering the stereochemistry of a molecule. So, this again uses the more or less same concept how these group of spins are connected and the relative orientation of them can be measured and that fixes the stereochemistry of a small molecule. So, therefore the NOE or nuclear overhouser effect actually provides the information about the proximity of a molecule. So, if this proton in space if they are connected this will be shown in this experiment called nuclear overhouser effect. So, this is actually through a space through distance correlation through space correlation it is not through bond as we have seen that many experiments works through bond and here it is through a space correlation. Now, this also allows of filtering specific reason of the spectra that belongs to nuclei in close proximity in a space. So, these are the some of the useful point for NOE. So, what actually NOE is NOE can be defined as the change in the intensity of one of the NMR resonance line when another resonance line in the same spectrum is perturbed. So, let me explain you very well. So, suppose here are these two resonance and they are connected to each other via space. Now, if I perturb this resonance the effect of perturbation of this will be seen on this resonance. This effect is called like nuclear overhouser effect and the spectroscopy that was developed based on this is called nuclear overhouser effect spectroscopy or NOG which is going to come in future lecture. So, what happens because of this perturbation there is a enhancement of signal or actually decrease in the signal of this particular nuclei because we are perturbing the resonance of this nuclei and that is given by this formula. So, eta of S because of perturbation in I will be given by the difference in the intensity here is the I0 is unperturbed intensity, I is when we perturb the signal and the ratio of I minus I0 divided by I is actually NOE of any resonance I and here so we are perturbing this signal for S. So, now I0 is the intensity of resonance I in the absence of any perturbation and I is when we are perturbing it. So, that is what here we had S was being perturbed and we are looking how the intensity of I is changing whether increasing or decreasing or altered. So, that is given by this eta factor. Now, to achieve this NOE effect as we discussed the other resonance has to be perturbed and this perturbation can be by any means here is my resonance for S here is my resonance for I we are perturbing this. Now perturbing means you have to irradiate this resonance and that can be irradiation can be done by something called continuous wave. So, what we are doing we are applying a constant RA at this particular frequency that is that is called continuous irradiation and the perturbation in the continuous manner NOE is termed as steady state NOE. We can do also if we just apply a transient pulse here for a radiofrequency pulse at the S resonance and that is called transient NOE. So, NOE effect is between 2 nuclei not 2 resonance ok. So, if nuclei 1 which gives the resonance of I if the nuclei another gives the resonance of S the NOE has to be between these 2 different kind of nuclei not these 2 difference. So, just understand the difference in this. So, resonance is generally between the nuclei not between the resonance ok. So, that means for getting NOE we have to perturb a particular nuclei and that which gives a resonance. So, how we are going to perturb by continuous wave continuous irradiation. So, here is the schematic of that experiment that we are going to do. So, as we had discussed earlier we have 2 resonance one for I and another for S here is my S here is I. We are saying continuously we are irradiating this resonance which is shown here. And this continuous irradiation is done by a say low power RF we are just want to irradiate it in a continuous manner. Then after continuous irradiation we apply a 90 degree pulse which is a hard pulse means all these nuclei can be excited and once excitation is done. So, this is applied a 90 X pulse which actually effects all of the nuclei and then we record the spectrum. So, this RF continuous RF perturbation like done on S resonance at the midpoint here and this is by weak RF pulse. So, what happens now this S is irradiated and it can have a multiplied or singlet or whatever, but whole this spin system is irradiated. And the time period for irradiation how much we have to irradiate that depends upon what is the spin lattice relaxation. So, if you remember spin lattice relaxation is the like a time it takes to come back in the equilibrium state when we put it in the minus z direction. So, say suppose our spin was here and we put it in minus z direction how much time it takes to come back to equilibrium that is called spin lattice relaxation or T1 relaxation ok. So, that T1 determines for how long we have to irradiate because we want this guys to completely irradiated therefore, we need to know how much time it takes to come back to equilibrium. So, what essentially for these experiment we have to do we have to record two experiment one where we irradiate the S resonance, one where we do not irradiate and then we take the difference of these two and then difference will tell the NOE enhancement ok. So, because of irradiation it is enhancement in the ice spin. So, intensity in the enhanced spectrum minus intensity in the reference spectrum divided by intensity in the reference spectrum this is called actually NOE between the two spectrum. Now, this can only happen if these two spins are connected through a space. So, if they are not connected they will not happen and that is what we do in the reference spectrum. So, in reference spectrum we can irradiate far away from the resonance of the of the S spin in the actual spectrum we are irradiating at the S spin in the reference spectrum we are irradiating far away from the resonance and then we take a difference and we get a NOE. Now, in another experiment which is called transient NOE so, as we discussed transient NOE we are not going to give continuous pulse, but a small rf pulse of 180 degree. Now, this small rf pulse on 180 degree essentially will invert the resonance of that particular nuclei. So, perturbation is done by this selective rf pulse. If you see sign like this, this is for the selective rf pulse. The sign like square is for hard pulse means this non-selective everything is excited and this kind of Gaussian or various shape this is called soft pulse. So, this is soft pulse, this is hard pulse. Soft pulse is selective, selectively exciting particular resonance, this is hard pulse is non-selective. So, now this selective pulse is inverting a particular resonance or a group of resonance say S spin then after that we have to do something called mixing. So, mixing time and what happens during mixing time actually spin exchanges their magnetization and that actually leads to NOE. So, here this Tm is important so, now mixing between these two spins has happened then we apply a hard pulse 90 degree, hard pulse means that excites all the nuclei and after that we record as response this is FID. So, we record response as we discussed we have to do two experiment one where we irradiate it and another is a reference spectrum which we do off resonance spectrum is recorded by applying the inversion pulse at a frequency where there is no resonance in the spectrum and then we take a difference between two like a on resonance spectrum and off resonance spectrum and that difference gives you how much will be enhancement. Now, one of the parameter that we discussed in transient NOE is the mixing time Tm. So, Tm can be varied to monitor the time course of magnetization transfer as we discussed during this time two spins talk to each other. So, if we put it for longer time they will talk more and magnetization transfer will be more if we put it for shorter time then will their magnetization transfer will be less. So, this means this permits the identification of spins which are closer to the perturb spin or which are slightly further from the perturb spin and if you vary this Tm actually this can give you precise distance information from the perturb spin. So, if say just for an example A spin is here and we are perturbing that A spin, B spin is here and C spin is here. So, effect will be more seen here than the effect will be seen here. So, that means the intensity can change if the it is closer or it is far. Now, looking at the intensity we know that A is closer to B or A is closer to C. So, in this case C will be like intensity difference will tell the distance and that actually gives you the distance information. This whole experiment will be dictated by what is the spin lattice relaxation of the perturb spin. So, we have to determine how much is the T1 time spin lattice relaxation time for A. This is important parameter because this gives the time when it goes to equilibrium state. So, then perturbation we have to tune accordingly looking at the spin lattice relaxation time for this perturb spin. So, to summarize what we are doing the how we are going to get NOE in brief by two days, one is called a steady state NOE, one is called transient NOE. In a steady state NOE we are irradiating a particular resonance or a group of resonance in particular spin by a continuous wave. One parameter to look after is the T1 of the perturbed nuclei that we have to look at. In transient NOE we are doing same thing more or less, but here we are perturbing by a selective pulse and then again we are mixing the spin states so that the magnetization that perturbation effect can be transferred to another spin and that gives you distance information. So, here is a transient NOE spectrum for a large molecule. So, here is the off resonance spectrum where actually perturbation was done quite a far and one on resonance spectrum here the perturbation was done at this spin and then you see the effect at the sum of the resonances their intensity changing. So, if you take the difference between these two you can find that all these resonances which shows the some signal where actually in close proximity of the perturbed spin like here. So, now that gives the distance information and the distance information is not too long it is approximately about 5 angstrom, but we can find it out that and one thing can you can see it the intensity of this resonance and this resonance is more than this, this and this. So, what it says that these two resonances seems to be closer to the perturbed spin and that is how one can get the distance information in a macromolecule. So, if you do quantitative estimation of this intensity of NOE signal we know the distance between all these spins. So, we need to measure a standard distance and the NOE effect and with compare to all those intensity can be relatively calculated how much will be distance between these two nuclei or group of resonances. So, now we understood the importance of NOE. Now, next we want to understand what is the origin of this NOE. So, NOE arises because of the dipolar interaction between two spins. Now, as we know that each spin is a dipole and between these dipoles is a dipole and dipole there is a interaction. So, that means this interaction if you remember from your undergraduate physics dipolar interaction is a distance dependent and that is why we said that up to 5 angstrom the NOE effect can be seen. So, NOE arises because of dipolar interaction the also it depends upon if you look at there is a angular aspects to that. So, how spins are oriented with respect to each other. So, this actually gives you lots of information about the orientation of spins the distance and of these spins and many of those stuff. Now, so whenever a nuclei is perturbed from its equilibrium states equilibrium state what we mean where the lower states has more population than the higher state. So, that is equilibrium state. The perturbation is transferred to its neighboring nuclei by a dipolar interaction. So, suppose these two spins spin I and a spin S are connected by dipolar interaction we are perturbing the spin S. Now, perturbing means we are changing the population in these S spins. So, population between these two states the ground state and say the excited state or the alpha state and beta state. So, if you are changing the effect of that will be transferred to this spin and that is because they are interacting by a dipolar action. So, this extent of perturbation how much we are creating depends upon how they are relaxing. So, relaxation rate of this and how strongly we irradiate this what is the strength of that irradiation pulse what is the duration of that irradiation. So, all those plays effect and therefore, this effect is quite quantitative because we can change the irradiation strength and duration of irradiation and we can look at how far the irradiation effect has reached. So, extent of NOE depends upon various relaxation properties. So, we look at in a more qualitative and quantitative manner how the NOE is dependent upon relaxation property of particular spin. So, just for simplified treatment we will just look at two spin system like weakly coupled system that we had discussed earlier, AX system. Now, AX system will have four states say alpha alpha state, alpha beta state, beta alpha state and beta beta states. So, these are the four states for AX system. Now, the population in actually these four states let us write it P1, P2, P3 and P4. So, as we have seen so, these two transitions here A1 and A2 is for A spin, A spin suppose write and these two are for X spin. So, this transition will give one line and that transition will give another line and similarly here we have two transition giving one line and another line. So, that is the four states and the population A1, P1, P2, P3, P4 of these states. Now, as we have seen earlier this transition we define as omega 1, omega 1, omega 1 and omega 1 this is called single quantum transition. What is happening here? There is only one flip. So, alpha goes to beta state here. In this case first spin alpha goes to beta state. So, change in the quantum here is one again here, here and here. So, therefore, these are called single quantum transition. Now, here if you look at alpha alpha goes to beta beta states that is called double quantum transition and in this case there is a spin flip flop. So, alpha goes to beta and beta goes to alpha. So, this is called zero quantum transition. So, we have three kind of transition probability into a spin system omega 1, omega 2 and omega 0. So, we looked at the four these populations and the polarization of these four states. So, A1 and A2 are transition for A spin, X1 and X2 are transition for X spin. So, that is what we look that the omega 1 is transition called single quantum transition and omega 0 is called zero quantum transition and omega 2 is called double quantum transition. So, intensity of this case like A1 intensity will be dictated by what is the difference between P1 and P2. Similarly, intensity of A2 will depend upon population difference between 3 and 4, intensity of X1 depends upon the population difference between P1 and P3 and for X2 it is P2 and P4. So, at equilibrium all these will have equal population difference and resulting identical intensity of all four transition for a homonuclear system that we have seen previously. So, this is A1, A2 and this is X1, X2 all equal intensity because the difference between these populations are equal. Now, let the population difference be equal to D that let us define that. So, total intensity of A transition here A transition A1 and A2 will be equal to 2D. So, here that is what we measure the population difference let us define as D. So, for this single quantum we have 2D intensity for A line. Now, let the A transition be saturated we are irradiating A transition by continuous RF. So, now, population between the perturbate state is going to be P1 and P2 will be P1 minus D2 here and P3 P4 will be P3 minus D2 and A transition because we have irradiated A. So, like A transition will have 0 intensity and X transition will have like X1 plus X2 that will be here X1 plus X2 will be P1 minus P3. So, as we were saying now we had A and we had X, we irradiated this. So, here there is no signal and we get some signal which of equal intensity and minus P1 P2. But where is the enhancement of the signal? So, where is the signal enhancement? We got some intensity, but can we quantify that signal enhancement? Now that let us look at in the next lecture how we are going to get the enhancement in the X signal. You think over it and we will continue from here how using this concept we can enhance the signal of X spin if we are perturbing the A spin. So, we will continue from here. Looking forward to have you in the next class and let us have some questions. If you have any doubt do not hesitate to contact me again. Thank you very much.