 Hello everyone, I once again welcome you all to MSB lecture series on interpretive spectroscopy. In the last class I started discussion on NMR and also in the beginning what I would do is I would give little bit information about all these spectroscopic methods and then start detailed discussion one at a time. In my previous lecture I started with analytical methods and also some fundamentals about analytical methods and I started discussion on NMR and then I started IR. So, let me continue from where I had stopped the approximate time scale for structured determination using various techniques is very very important. So, that gives some information about the limitations or advantage of a particular technique when you want to use it as an analytical tool to understand the structure of a molecule. For example, if you see in case of electron diffraction we can use up to 10 to the power of minus 20 seconds or in case of x-ray it is about 10 to the power of minus 18 and in case of UV it is 10 to the power of minus 15. That means, whatever the dynamic process that happens up to 10 to the power of minus 15 can be analysed using UV visible spectroscopy and in case of visible it is the time scale is about 10 to the power of minus 14 and in case of IR and Raman it is about 10 to the power of minus 13 and in case of ESR it can range from 10 to the power of minus 4 to 10 to the power of minus 8 and in case of NMR it is 10 to the power of minus 1 to 10 to the power of minus 9. That means, basically whatever the dynamic process that is happening in the time scale of 10 to the power of minus 1 to 10 to the power of minus 9 can be analysed using NMR spectroscopy without any problem, but if there is any dynamic process that is much faster than 10 to the power of minus 9 let us say 10 to the power of minus 10 probably NMR would not identify. In that case what happens probably we have to suppress the thermic process by cooling the solution NMR sample to much lower temperature so that the dynamic process comes false within this range so that we can study through NMR what is happening and similarly if it is much slower than 10 to the power of minus 1 then probably we have to heat the sample so that dynamic process would fall in this range. So, this is what the information that gives in case of first kinetics this is about 10 to the power of minus 3 to 10 to the power of 2 and physical separation of isomers. If you see 2 isomers are formed in a reaction and then whether we can do separately after crystallization because if they have different morphology then at least we need 100 seconds that means for physical separation it should be greater than 10 to the power of minus 2 times scale that means the isomers form should not undergo isomeration within 100 seconds. As I mentioned NMR is the most powerful tool available for organic and inorganic structure determination it is used to study a wide variety of nuclei I have mentioned somewhere here it is 1 H 13 C is there both 11 boron and 10 boron are there and of course, 11 boron is about 80 percent natural abundances there remaining is 10 boron 10 boron nuclear spin is 3 whereas, 11 boron is 3 by 2 again 14 N I value is equals 1 and in case of 15 N I value is equals half and 19 F 31 P 29 silicon and 103 rhodium 195 platinum 183 tungsten all of them have nuclear spin value of I equals half, but their natural abundance varies we will see I have a table that I would be providing you in this lecture. We have some selectivity not all elements in the periodic table you know have nuclei which can be analyzed through NMR that means I have classified here different type of nuclei to three categories and even and even what does it mean? Nuclear containing even number of both protons and neutrons have I equals 0 and therefore, they cannot undergo NMR. So, that means whenever we come across nuclei having even number of both protons and neutrons then they have 0 nuclear spin in that case what happens we cannot use them in NMR measurement examples 4 helium 12 carbon 16 oxygen 32 S. Next odd odd that means, nuclei with odd number of both protons and neutrons have spin quantum numbers that are positive integers examples include 14 N we have I equals 1 2 H deuterium I equals 1 and 10 boron I equals 3 all others the remaining nuclei odd even or even odd combination of protons and neutrons all have spins that are half integral. For example, 1 H if you take I equals half is the 17 O I equals 5 by 2 19 F I equals half 23 sodium I equals 3 by 2 and 31 phosphorus I equals half. So, this is how we can classify. So, simply by looking into number of protons and neutrons in a given autumn we should be able to tell whether it is NMR active if not if it is NMR active what is its I value. So, this is NMR periodic table this will depict the elements which have NMR active nuclei and also it has all details one look for to use effectively is NMR and I have another table pretty good because here the color code is given for different nuclear spin you can see here red one is I equals half we have plenty of elements are there here starting from hydrogen is there phrancium and all elements the blocks in red are all having I equals half value and then I equals 1 we can see very few are there one is lithium is here one is nitrogen is here and when I equals 3 by 2 we have quite a few all in yellow color here you can see beryllium is there sodium potassium rubidium and all those things even among lanthanides and actinides we have and then I equals 5 by 2 are in green color and I equals 7 by 2 are in blue color and also 9 by 2 are in purple color. So, you can see here most of the elements show have some isotopes which are NMR active. Let us look into the interaction of these NMR active nucleus with the magnetic field. So, according to quantum mechanics the energy associated with the interaction of each different orientation of the magnetic moment with an external applied magnet will be equal to the component of mu. So, magnetic moment along with field B naught times the magnitude of B naught that means it can be represented using this equation here E equals mu z into B naught each value of mu z is associated with a different energy level. For example, I have shown here you can see orientation of nucleus with I equals 1 and angular momentum and magnetic moment vectors in a magnetic field. So, let us see if this is the applied magnetic field and if I equals 1 this is how we will be having the values of minus 1, 0 and plus 1 and if the I value is half again this is the one it is the same magnetic moment shown here and magnetic moment is shown here and then these orientations will be with respect to the magnetic field if this is magnetic field z naught. So, these are the orientations of 1 and 0 and minus 1 nuclear spins. The energy levels for the interaction of nuclei I equals 1 half or 3 by 2 with a magnetic field B naught and we are using another term called gamma. Gamma is nothing, but the gyromagnetic ratio or magneto gyric ratio and this is positive for I equals 1 and negative for I equals 3 by 2. So, that means, at a given value of B naught the spacings of the energy levels are equal at a given value of B naught the spacings of the energy levels are equal the difference in the energy levels increases as B increases. That one should remember the gap between the spacings of energy levels increases with increase in the magnetic field strength. This is actually a boon because many complicated spectra we get under low magnetic field can be enhanced for better refinement when we go for higher field. This is where the interest is there about making instruments having higher field strength. You see if the magneto gyric ratio is positive then mu z equals gamma mi h over 2 pi this implies that mu z and mi will have the same sign and because of that one E equals what we have is mu z B naught the energy level with the most negative will have the highest energy. So, this one. So, this is what it shows here as I said this orientations also you cannot have any orientations in between for example, here in case of I equals 1 we have 0 plus 1 0 and minus 1 and in case of half we have plus half and minus half whereas, in case of 3 by 2 we have plus 3 by 2 half minus half minus 3 by 2 and similarly, if we have 5 by 2 then we will be having plus 5 by 2 plus 3 by 2 plus half and minus half minus 3 by 2 and minus 5 by 2. So, it goes 7 by 2 also one can keep writing like this nuclei with negative magneto gyric ratio will have the highest energy for the most positive mi value. So, I have highlighted these parts are very important. So, nuclei with negative magneto gyric ratio will have highest energy for the most positive mi value. So, let us look into the effect of magnetic field on nucleus in a more classical way I will come back to that one. Since the value of mu z can never have the full value of mu z mu and n nuclear angular momentum vector can never be collinear with B naught if we imagine a spinning top as a nucleus the rotational axis cannot be aligned with B naught this is very very important that means, when the nucleus is persisting or rotating under the influence of the magnetic field the rotational axis can never be collinear with the direction of applied magnetic field it is always tilted at an angle must be oriented at some angle relative to B naught can be visualized with this spinning tops you can clearly visualize what I said here you can see here. A typical top can be compared to a persisting nuclei under the influence of the magnetic field and with respect to the magnetic field if you just try to see here this is not really collinear it is at an angle same thing is true in case of all these things this can be compared to the rotating magnetic field generated under the influence of a magnetic field on nuclei for example something like this if you see here although under the influence of this magnetic field they are rotating rotational axis is not collinear with this one it is at an angle. So, that means, a tilted spinning top when subjected to a force it precesses about the direction of the force that you saw in the previous slide. Similarly, a spinning nucleus precesses about the magnetic field B naught in that case the frequency of this precessional moment is given by omega is nothing, but omega equals gamma B naught. So, this omega is called precessional frequency or Larmor frequency you can see here this is how this in the absence of the magnetic field when the magnetic field is there it will be at an angle and then it will start precessing in this one with respect to applied magnetic field. So, B naught. So, this the frequency with which a nucleus precesses under the influence of the magnetic field is called omega and omega is directly proportional to the gyromagnetic ratio of that nucleus and also the magnetic field in which it is precessing. So, this precessional frequency omega is called Larmor frequency. Orientation of spinning nucleus in a magnetic field is shown here the orientation is not allowed by quantum mechanics to have this kind of things it does not precess like this here it will be at an angle here you can see and precision about B naught in this it goes like this. This is what exactly happens for a nonzero nuclear spin kept under the influence of a magnetic field with magnitude B naught. Again I am repeating here a tilted spinning top when subjected to a force precesses about the direction of the force similarly a spinning nucleus precesses about the applied magnetic field B naught the frequency of this precessional movement is given by omega equals gamma B naught if you want to change the angle of rotation with respect to B naught we must apply a force which moves the rotation axis of the nucleus away from this. So, that means, if it is something like this if it is precessing to increase and eventually to take it from this one away from this one what happens we have to apply another field which is perpendicular to the applied magnetic field. If we apply another field perpendicular to the magnetic field what happens it will tilt the precessing nucleus away from the direction of applied magnetic field and eventually when the flip changes we say resonance has occurred. In NMR this force is provided by a second magnetic field BI oriented at right angle or perpendicular to the B naught. So, that means, here basically we have the B naught is there and you apply another one here this is BI. So, this would take away the precessing the precessing frequency of this nucleus when matches the frequency of this applied magnetic field then transition occurs. When B 1 that is the applied magnetic field perpendicular to the B naught ok. So, that means, when B naught rotates about when B 1 rotates about B naught with Larmor frequency the two rotation fields are in phase two rotation phase are in phase. Now, nucleus experiences another magnetic field about which it can precess. So, now it will make an attempt to precess about the new applied magnetic field also that can be seen here in this diagram you can see here. Earlier it was B 1 was not applied under the influence of B naught it was precessing about B naught in this fashion and the moment we applied a magnetic field perpendicular to the B naught and if the frequency of this one matches the Larmor frequency of this one what happens the nuclear transition happens ok it will move away and then the flipping of the spin takes place and it will be flipping and it will be going in this direction. So, changing the precessing angle with perpendicular rotating magnetic field. So, this is when it rotates with Larmor frequency nuclear spin flips the precessal frequency of nucleus about B 1 is much lower than omega. Quantum mechanics limits the magnetic moment to own the certain orientations rotation of B at Larmor frequency causes nuclear spin from one orientation to another one. So, that means, basically that is what we do of knowing the precessal frequency of a nucleus under the influence of B naught we apply another magnetic field that is perpendicular B naught with the frequency matching the Larmor frequency of that nucleus to have nuclear transition that means, we say nuclear spin flips what is the selection rule for nuclear transition this is very important. So, for selection rule for nuclear transition is delta M i equals plus or minus 1 that means, basically when the nuclear spin it should change its value from plus 1 to minus 1 or minus 1 to plus 1. So, this is against we come across spin selection rule in case of electronic transition in case of electronic transition we say equals 0 whereas, here it is plus or minus 1 we should remember that one. If we consider a nucleus with spin equals i equals half let us say simple as simple as proton have only 2 energy levels plus half and minus half it is placed in the magnetic field we can calculate its Larmor frequency or energy necessary for the transition. So, whatever the Larmor frequency is there that is the energy required for the transition from plus half to minus half level. If a proton is placed in the magnetic field of 2 tesla then delta E which gives the transition energy can be directly calculated using these formulas. For example, transition from energy level 1 to 2 is mu z 1 B naught minus mu z 2 B naught that is equal to M i gamma H B naught that is equal to gamma H B naught. Now, if the change in energy is produced by electromagnetic radiation then we know that delta E equals H nu that is equal to gamma H B naught. So, that was given here if we consider the Larmor frequency in place of nu then it will become 2 because it is angular it is rotating. So, as a result what happens omega becomes 2 pi nu then nu equals gamma B naught over 2 pi. So, that means, we can now calculate the present frequency under different magnitude of B naught we can calculate. So, here what is only known is if we know the magnetic field strength and gyromagnetic ratio is constant unique for each nucleus and then we should be able to calculate this Larmor frequency very easily. So, once we know that we can tune the NMR instrument. So, this equation is very very important and this equation is nu equals gamma B naught over 2 pi is what you should remember that is all nothing else you should remember this one. So, once you remember most of the problems we come across can be understood and solved as far as NMR is concerned. So, now for example, let us say non-zero nuclear spin we will be having all possible orientations in the absence of the magnetic field. The moment we apply magnetic field what happens. So, they align some of them will be aligned with the magnetic field some of them will be opposing the magnetic field you can see here. So, for example, this is precessing with respect to B naught and yes when we apply another magnetic field B i perpendicular to B naught what happens it flips you can see here how this is flipping this is what exactly happens in case of NMR. So, here as I mentioned this equation is very very important for protons in a magnetic field of 2 Tesla we know that gamma value is given we should calculate now nu for this proton 2 Tesla. So, now it is very simple you add your 226.78 into 10 raise to 7 so B naught is there. So, into B naught and divided by 2 into 22 by 7 if you calculate for example, 26.75 into 2 into 10 raise to 7 over 2 into 22 7 comes here. If you simplify this one it would come around I would say 90 megahertz. So, this is how you can calculate the frequency starting from the gyromagnetic ratio and also the magnetic field strength. So, similarly one can calculate the radio frequency necessary for the transition of 11 boron 31 phosphorus 13 C at magnetic field strength of 2 Tesla and 10 Tesla. So, this is how the orientations are there in the in the absence of magnetic field the moment you apply magnetic field they will align in such a way that some of them will be having plus half and some of them will be having minus half. So, nuclear spin what is nuclear spin nucleus with an odd atomic number and an odd mass number has a nuclear spin that is what I was telling you the spinning charged nucleus generates a magnetic field. The any charged species generates a magnetic field and when you apply that one in the magnetic field it will start rotating about the magnetic field. So, that means, here you can see here this the spinning protons under the influence of the magnetic field generate a loop of current here and loop of current as a result what happens you can see they behave like tiny magnets and aligning in this direction they behave like a bar magnet. Typically I have shown here B naught is there in the absence of magnetic field they can be having all kind of rotations or orientations and when you apply magnetic field it will flip and probably it will go something like this and this is low energy more stable and then if it has like this orientation this high energy less stable. So, this one we call it as plus half and this we call it as minus half. So, let me continue in the next class let me stop at this stage and continue more discussion on NMR in my next class.