 Hello all, my name is Arnab Dutta, I am an assistant professor in chemistry department IIT Bombay and today we will discuss the fundamentals of an interesting spectroscopic method known as NMR and we will also look into its application in the form of MRI. Let us start. So most of the nuclei we see around the world contains an intrinsic spin angular momentum and this spin angular momentum is the main reason behind the NMR spectroscopic. So this spin angular momentum is actually defined by the spin quantum number I, this spin quantum number I is actually how we define a spin system. The spin quantum number can have different values, it can be 0, it can be an integer value or it can be even a number like half or three half. The actual value of this I depends on how many neutrons and protons are actually present inside the nuclei. If I have a nuclei with even number of atomic number and mass number typically they give us a overall spin quantum number of 0. But if it deviates from it we can have different I values which are non-zero. The magnitude of the spin angular momentum is given by this term root over I into I plus 1 into H by 2 pi whereas the value M I can be in different forms plus I to minus I whereas M I into H by 2 pi defines the component of the angular momentum on a arbitrary axis. So let us define what do I mean over there. So we can have any particular direction we have a spin angular momentum which has this value I into I plus 1 into H by 2 pi. However if I want to find out what is the value at a particular axis it is the z axis. We try to find what is the projection of this spin angular momentum on this particular axis and they can have only particular values and over here I am showing in such a way that it can have values from plus I to minus I. It can be also on the opposite direction and the projection of that is over there say minus I over there it say it is plus I and defining that it is the M I values. Now with that thing sorted out we also found that when we have a spin angular momentum it also generates a spin magnetic momentum. The spin angular momentum also generate a spin magnetic momentum because the spin angular momentum actually has an electrical component. So obviously it also gives a magnetic component around it and this magnetic component is the reason to creation for the is the reason for the creation of a spin magnetic moment. And say I want to find out the spin magnetic moment the presence of the spin angular moment also is the main reason for the creation of a spin magnetic moment. The spin magnetic moment can be also found along with a particular axis. So over there how much spin magnetic moment is going to generate that depends on this particular equation shown over here mu j equal to gamma into M I into H by 2 pi. We already knew that M I into H by 2 pi is the component of the angular momentum if I multiply that with this term gamma which is a proportionately constant is gives us how much of the angular momentum is actually transferred to the spin magnetic momentum. So that is why this proportionately constant gamma also known as gyromagnetic ratio. So it defines how much of the angular momentum is actually converts into the magnetic moment and for each particular nuclei this value will be constant. Each of the nuclei has their own distinct gyromagnetic ratio. Now when this particular spin magnetic moment sees an external magnetic field what happens? The energy of these systems will be dependent on the magnetic field that we are producing the strength of the magnetic field. And following the equation we can say the energy of that particular system in presence of a magnetic field B 0 will be minus mu z into B 0 where mu z is nothing but the spin magnetic moment which is already given over there gamma into M I into H by 2 pi. So you have to just multiply B 0 into that. So this will be the energy of a particular state with a magnetic moment where M I is defining its nuclear spin. So taking proton as an example where the I value can be half we like to see what is actually happening over here with respect to its energy. So when we start with this particular spin state over here we said field is off that means there is no magnetic field is produced externally. So there is no presence of an external magnetic field. So all the states are in the same energy because they cannot be differed in the absence of a field. However at once we turn on the field the 2 M I states because proton has the I value of half so it can have the different M I values plus half and minus half. And in the presence of magnetic field it get differed in minus half and plus half. Over here the plus half is actually lower in energy why because as we know over here energy is actually given by minus gamma into M I into H by 2 pi into B 0. Now M I can have a value of plus half or minus half. So if I have a plus half value because of the presence of this minus sign that is going to be lower energy which will have a value of minus half into gamma into B 0 into H by 2 pi. Whereas when it is minus half state this minus sign from this M I value and minus sign already present in the equation will combine together and give me an higher energy state whose energy will be plus half into gamma into B 0 into H by 2 pi. So that is how they split it up and the difference of their energy if I subtract them down it will be gamma into B 0 into H by 2 pi which is given over there. Now again coming back to the system why this M I state differs because whenever we are putting a magnetic field from outside the magnetic moment present due to the spin state actually start precessing around this particular magnetic field. So say if this is the magnetic field it start precessing around it. So it will look like more of like a cone around which it is recessing. So this particular moment is actually generated which is also known as the Larmor frequency. So over here when it is recessing around this external magnetic field B 0 what is going to happen how much of the magnetic moment is actually projecting on that magnetic axis of the external magnetic field axis that is going to be having two different values it can be either plus half or minus half and depending on that we say we have these two particular values plus half and minus half. So that is the main reason behind the splitting of the magnetic spin state in the presence of a magnetic field otherwise the spin state cannot be differentiated only in the presence of magnetic field they get differentiated. So once they get differentiated now we have a particular energy gap and we can go from the ground state to the excited state if I can give an electromagnetic radiation whose energy perfectly matches that energy gap that we have created which is nothing but gamma into B 0 into H by 2 pi and when these two actually can be equated we can say the resonating condition has been made. So again just telling that thing one more time. So once this energy gap is created in the presence of the magnetic field this energy gap is gamma into B 0 into H by 2 pi you can see that this full system is depending on two factors one is the B 0 the strength of the magnetic field one is the gamma the gyromagnetic ratio which is actually property of the nuclear itself. And this part is going to equate with the resonating condition we can actually match that with an external electromagnetic radiation which can bring the ground state nuclear spin to the upper state by flipping it and when they match we have the resonating condition which says that it is going to be equal to H nu. And as we just said the difference of this energy state depends on two factors the gamma value and the B 0 value. So generally we actually use a magnetic field strength around 12 tesla so typically we use a magnetic field strength around 12 tesla with that amount of magnetic field we created enough space such a way that this space can be covered with H nu where the nu is actually belongs to the radio frequency region. So that says that this energy gap is actually pretty low because radio frequency is one of the weakest electromagnetic radiation with respect to energy. So if we look back again so it is a electromagnetic radiation can be the important factor to bring the lower magnetic spin state to the higher magnetic spin state where the spin can be flipped. Now the other important factor as we just discussed is the gamma factor which actually says that how much the energy gap will be the nuclear itself will have a say because each nuclear has their own electromagnetic ratio. And over there we can say if I use the same magnetic field 12 tesla the energy gap will be different for different nuclei and over there I am taking example of three different nuclei. So we have taken their three different nuclei proton 13C and 31P each of them has one common thing all of them has a nuclear spin of half. So that means in presence of magnetic field they will all split between plus half and minus half. If I use the same magnetic field of 12 tesla their energy gap will be different. Why they will be different because the gamma value the gamma value of these three different nuclei are different. And we can see the proton has the highest electromagnetic ratio has an energy gap that can be covered with a radio frequency of 500 megahertz whereas 13C is way too weaker than it and it requires only 126 megahertz. The 31P is stronger than 13C but weaker than proton as per the value of the gamma magnetic ratio of that particular nuclei and we have a resonating frequency of 202.5 megahertz. So over there we can say that the overall energy gap will differ in two different the overall energy gap between the different nuclear spin state in the presence of magnetic field will be dependent on two different factors. One is the external magnetic field its strength and the second is the gyromagnetic ratio it will be intrinsic property of the nuclei itself. Now how the NMR spectroscopy can be used to understand the property of a molecule. So whenever we produce an external magnetic field and try to see how it is affecting the splitting of the different nuclear spin state there is one more thing can be important and that is each of the nuclei in a molecule is present around electron field and the different molecule different nuclei not all the time their environment is same and depending on the environment they can have a little bit more electron density or less electron density coming from the structure of the molecule and those electronic environment around the system also creates a local magnetic field which is generated because those electrons are present in an orbital and orbital generates an orbital magnetic momentum which actually creates a local magnetic field which is given over here as B dash and this local magnetic field can come around the system along with the external magnetic field. So when we have the external magnetic field B0 this local magnetic field B dash can also come into there and they will combine to give the actual magnetic field actually felt by the nuclei. So this B dash can be positive or negative depending on their orientation of the electron and the actual resonating condition will be different now. So in a condition where there is almost negligible electronic effect what do we expect that the resonating condition will be made with gamma into H by 2 pi B0 because B0 is the magnetic field that is their experiencing and that can be resonated with the H new 0. New 0 is the condition where it matches the energy gap created by this magnetic field B0. However in a molecule the presence of the electronic environment creates an external magnetic field which gives us this value B dash so altogether the actual magnetic field the molecule is experiencing is that B0 plus B dash and if we now want to resonate that cannot be happening at H new 0 it needs a totally different value which is given by new. So this will be the new resonating condition to balance the presence of this extra local magnetic field and the difference where and this new condition where we are actually resonating this new can be differentiated with respect to the new 0 where it should be in the absence of magnetic field and it can be given by this term delta which is given by this expression which is new minus new 0 divided by new 0 into 10 to the power 6. So why this particular expression? Because new minus new 0 by new 0 is giving an idea no matter what is the B0 or extra magnetic field I am using if I use this particular expression that will be independent of what is the strength of the extra magnetic field. So this will be a more of a universal number this delta value will be particularly constant at any particular condition all around the world. So that is why it is known as chemical shift and that is a universal factor when we are expressing that with this particular expression and over there we multiply that by 10 to the power 6 because the new 0 has a value of 500 megahertz if you are talking about the proton whereas the difference comes in the unit of hertz. So megahertz is 10 to the power 6 hertz and the difference is hertz. So we multiply that with 10 to the power 6 so we can have a number that we can play with very easily. So we have a number like 5 or 6 rather than 5 into 10 to the power minus 6. So that is why we multiply that with 10 to the power 6 and that is why there is a unit comes along with that which names as PPM parts per million which is not really an unit because over there you can see new minus new 0 divided by new 0 it should be dimensionless quantity. It is but we still consider this PPM written around it so that it can remind us that it actually gets multiplied by 10 to the power 6 or by a million number so that we can get this particular value. So that is known as chemical shift and again coming back to that this chemical shift is totally dependent how much local magnetic field I am creating. And that is why this delta value is nothing but a detector of what is the chemical environment around the system. Now the unique thing is that this particular delta value is going to be constant for a particular group in a particular molecule. And if we want to measure different molecules at a time we also need to know where is the new 0 value. So we need a standard molecule which we exactly know it has such a electronic field present around it that it cancel each other out and there is the local magnetic field is almost negligible it only fills the magnetic field created by the external one. So one of such molecule is tetramethyl silane in short from it is known as TMS which is nothing but a silica bound with 4 methyl groups. And this molecule gives us a delta value of 0 so that means if I am doing an experiment and use tetramethyl silane we know exactly where we should expect to see that graph and in that graph the signal is going to come at delta equal to 0 ppm. And why it is very easy to use because it has a very good solubility in all different kinds of solvents and all the same time we do not need to use a lot of this particular standard because it has 12 protons present there which are all in the similar environment. So we always got a very good signal even with a minute amount of this standard. So that is why this tetramethyl silane is used as a common standard all around the world especially for the proton and also for the 13C NMR spectroscopy. The chemical shift values as we just discussed is actually gives us an idea what is the electronic environment around the molecule especially around the nuclei we are discussing for an example say we are talking about proton NMR. So what we found for different compounds what we have produced what we have extracted over the years all of them we can record and proton NMR and for each particular group we can find a region where this particular signal comes out. And those are kind of the signature region for this particular groups for an example we can start with this alkene groups and we can see the alkene groups comes around the delta ppm value between 0 to 2 whereas whenever I put an alkyne group over here or a alkene group or a ketone group you can see they actually move towards a little bit higher value of delta. So it says that if you have this kind of electron withdrawing groups or electron reach environment then you are expected to have a shift in the delta value. Similarly if we have a aromatic group you can see it is way shifted towards almost 6.5 to 8.5 region. So it is actually signature region for aromatic compound. If you have a acid group you can see it shifted further beyond 10 ppm region. So each of this region is actually signifying the presence of one particular proton in a chemical environment. So that is why this chemical shift values can be a testament for the presence of particular groups. So with respect to that we can easily follow and find out not only whether this particular group is present or not and even can follow that change during an experiment. So that is why NMR spectroscopy is a very powerful tool for the structure elucidation of different compounds. Now we come to the second part of this NMR spectroscopy which is an application which is known as MRI or magnetic resonance imaging. MRI is quite a common term nowadays in the medical field because whenever we get injured in our body we generally try to do an MRI scan and it actually give us an idea what is actually happening around our body. So in MRI which is nothing but a particular kind of NMR where we actually follow the proton NMR and the proton NMR we follow from the water molecule because water molecule is quite common in a biological system and then we try to find out what is the behavior of the proton in a particular region generally in thin slices of our body. And over there we try to find in three dimensional orientation how the protons are behaving. And over there we try to mostly find out the behavior of the proton under this particular condition where we put the external magnetic field of 1 to 1.5 tesla. You can imagine that it is almost 10 times lower than the 12 tesla we use for a 500 megahertz NMR machine. So over here the resonating condition met with much more lower energy with 40 to 70 megahertz of radio frequency. The NMR at the same time these are non-evasive techniques because we are not using very strong magnetic field or very strong radio frequency which can affect our body otherwise. And at the same time this NMR experiment we can find out what is happening in the water very quick from seconds to minutes so it is a fast and rapid diagnostic tool. So this is a diagram how the NMR actually looks like. So over here this is where we put ourselves in and over there you can find out two different coils one actually contains the magnetic field the other one is the radio frequency coil and we use both the magnetic field and radio frequency coil simultaneously to get the idea what is happening about the water around our body. And this is how it looks like from the outside the MRI instrument. Now when we look into the proton NMRs of water molecule in MRI we actually generally try to look into their intensity and we look into the intensity by following what happens to their relaxation dynamics. So what do I mean by relaxation dynamics? So whenever we actually put an external magnetic field the two states splits up i equal to half i equal to minus half and whenever we excite that with the electromagnetic radiation some of the spin flips and go to the excited state from plus half to minus half and then it relaxes back again and then we give the electromagnetic radiation so that it can go back again. And this process continues so when the high energy state nuclear magnetic spin state comes down to the ground state it is known as the spin relaxation. And this spin relaxation can give me an idea how the proton is behaving because the spin relaxation is dependent on its environment because it can relaxes through these two different methodologies spin lattice and spin-spin interaction. Spin lattice is the interaction between the spin and the other environment the electrical environment around it whereas the spin-spin relaxation happens when there is another spin moment present around it. So with this particular system it gets relaxed and we can follow what is actually happening and that is what we do in MRI. However, we generally use a paramagnetic agent which creates a huge amount of local magnetic field and that help us to understand what is actually happening when this paramagnetic sample present near the system we are diagnosing. And these are known as MRI contrast agent because they actually create a very good contrasting when they are present. For an example one of the system we use very regularly is the gadolinium plus 3 system. It is a F block element which has 7 unpaired electron in its plus 3 oxygen state so 7 unpaired electron which has a huge local magnetic field. And you can see over here I am showing it is an MRI of a brain and over there there is a tumor over here but we cannot see it very properly although we can see there is a difference when you are doing the MRI but we cannot see it very precisely exactly what is happening. But once we inject this gadolinium system near to it it actually clearly shows what is happening over there because in presence of this strong local magnetic field the water molecules over here behave differently compared to the other parts and that actually creates the contrast and over there we can easily see the tumor over here. So that is the effect of an MRI contrast agent which actually nothing but creates a local magnetic field around it and generally this gadolinium F7 system is the most common one that we actually use during an MRI. So with that we will come to the summary of our this segment. We start with the NMR which is nothing but a study of the spin magnetic moment and how it behaves when we create an external magnetic field around it. The spins actually deviates with respect to its spin quantum number and it can go to plus i to minus i values the most common one is proton which actually goes to plus i to minus i state and this energy gap depends on the strength of the magnetic field and also the gyromagnetic ratio. So that is why this difference is also very specific for particular nuclei. We can find out what is the energy gap because that is not only dependent on the external magnetic field but also the local magnetic field created by the electronic environment and that is why the actual resonating condition differs by small amount and that difference we actually expressed with this expression of this chemical shift or delta value and over there these delta values are quite specific for different groups. So with respect to that we can not only define a particular group but we can also follow their changes during the course of a reaction. MRI is one of the nice examples where we actually use it for diagnostic tool very regularly and very widely all over the world which actually nothing but monitors the spin relaxation dynamics around different biological system. Over there during this MRI we actually use a MRI contrast agent which is a system with a lot of unpaired electrons like gadolinium with 7 unpaired electrons which actually creates a strong local magnetic field which help us to see the environment much better in absence of that. So that is why it is known as the MRI contrasting agent which actually gives us a much better visualization when it is present. So with respect to that we would like to conclude this section of this NMR and its application over here. Thank you.