 Hello everyone. I once again welcome you all to MSP lecture series on interpretive spectroscopy. Today I shall start discussion on EPR spectroscopy or ESR spectroscopy, electron paramagnetic resonance spectroscopy or electron spin resonance spectroscopy. Both are essentially same. EPR is fundamentally very similar to popular NMR spectroscopy. We are very much familiar with it with several important distinctions. While both the methods deal with the interaction of electromagnetic radiation with magnetic moments of particles, there are many differences between the two spectroscopic methods as well. For example, EPR focuses on the interaction between the external magnetic field and the unpaid electrons of whatever the system is delocalized to as opposed to the nuclei of individual atoms. Of course, in NMR spectroscopy we look into nuclear spin transition whereas in case of EPR we look into electron spin transition that is the major difference between EPR and NMR. The electromagnetic radiation is used in NMR is in the radio frequency range of 300 to 1000 MHz. Whatever the frequency we are applying in a direction perpendicular to the applied magnetic field to bring resonance with the Larmor frequency so that flipping or transition of a nucleus takes place that electromagnetic radiation comes in the radio frequency range of 300 to 1000 MHz whereas in case of EPR microwaves are used in the range of 3 to 400 GHz. So, in EPR the frequency is typically held constant this is the major difference between NMR and EPR. In EPR frequency is typically held constant microwave frequency whatever we are applying that is held constant while the magnetic field strength is varied. In contrast to this in NMR experiments the magnetic field is held constant B naught whatever we say and then we are tuning the radio frequency to match the Larmor frequency of the nuclei which is perturbed because of the local magnetic field generated which can either align with the magnetic field or oppose the magnetic field. So, that is the major difference. So, magnetic field is kept constant in case of NMR and the radio frequency is varied whereas here microwave radiation that is applied perpendicular to the applied magnetic field is held constant and magnetic field is varied. So, these are the major difference between EPR and NMR spectroscopic methods. Due to the short relaxation times of electrons spins compared to nuclei they have a very short relaxation time whereas in case of nuclei this is much larger as a result of this one EPR experiments must be performed at very low temperature often below 10 k and sometimes as low as 2 k this is typically request the use of liquid helium this is a major drawback that we face in case of EPR spectroscopy. EPR spectroscopy is roughly 1000 times more sensitive than NMR due to the higher frequency of electromagnetic radiation employed here. Advanced pulse EPR methods are also used directly to investigate specific couplings between paramagnetic spin systems and specific magnetic nuclei. That means we can also look into the interaction between paramagnetic spin systems as well as specific magnetic nuclei. So, the most widely used method is electron nuclear double resonance indoor called as in this method of EPR spectroscopy both microwave and radio frequencies are used to perp the spins of electrons and nuclei simultaneously in order to determine very specific coupling between these two entities which is not attainable through traditional continuous wave methods. So, this is the major difference between EPR and indoor. The objective of indoor is to look into the coupling between the nuclear spin as well as the electron spin. Let us look into the origin of the EPR signal. So, electron we all know that is a negatively charged particle with the certain mass that shows two kinds of movements. One is spinning around the nucleus in an orbital movement which brings orbital magnetic movement and also it spins around its own axis no the spin magnetic movement. This is again very similar to what we see in case of nuclear spin. Nuclear spin besides precessing on its own axis it also revolves around the magnetic field in an orbital fashion. So, magnetic moment of the molecule is primarily due to spin magnetic moment of unpaired electron that is given by m s equals square root of s and t s plus 1 into h over 2 pi. So, where m s is the total spin angular moment and s is the spin quantum number and h is Planck's constant. So, in the z direction if we consider the component of the total spin angular moment can have only two values m s equals small m s into h over 2 pi. So, m s can have 2 s plus 1 different values starting from plus s to minus s. So, that means, if you consider a single unpaired electron only two possible values are m s equals plus or minus half. The magnetic moment mu E is directly proportional to the spin angular moment. So, that can be related using this equation here mu E equals minus G E mu B and m s we are introducing a new term called G E. The negative sign in this expression is due to the fact that the magnetic momentum of electron is collinear collinear with the applied magnetic field, but anti parallel to the spin itself. As a result it the expression has negative charge the term this G E mu B is the magneto gyric ratio. So, gyromagnetic ratio I am sure you are familiar in case of nucleus NMR. The Bohr magneton mu B is the magnetic moment for one unit quantum mechanical angular momentum this mu B. So, of course, we also familiar with the term expression for mu B Bohr magneton that is given by mu B equals E h over 4 pi m E where E is the electron charge m E is the electron mass and G E is known as the free electron G factor which carries a very most accurate value of 2.002319304386 perhaps it is one of the most accurately known physical constant in physics or chemistry for that matter. So, this magnetic moment interacts with the applied magnetic field the interaction between the magnetic moment mu and the field can be described by a simple equation E equals mu into B. If we consider a single unpaired electron there will be 2 possible energy states this effect is called Zeeman splitting that means plus half and minus half. So, this term can be rewritten as E plus half equals half G mu B B and E minus half for the another one with minus half level minus half into G mu B B that means both of them have different energies when they are kept in the magnetic field when the magnetic field is applied in the absence of external magnetic field E plus is equal to E minus that is equal to 0. So, that we can relate them with this equation the energy difference between the 2 levels is h mu equals G mu B into B B naught or B that is applied magnetic field. So, in the presence of external magnetic field the energy difference between the 2 states can be represented using this diagram here energy versus applied magnetic field steadily increasing as the energy the applied magnetic field strength increases the gap between these 2 levels also increases and here the gap between these 2 levels is given by the energy different delta E equals h mu equals G mu B into B naught from this equation we can calculate the energy required to excite the nuclear spin from one state to another state and this comes from the macro region. So, with the intensity of the applied magnetic field increasing the energy difference between the energy levels widens until it matches with the microwave radiation and results in absorption of photons. So, this is the fundamental basis for EPR spectroscopy. So, in case of NMR we talk about Larmor frequency and when the radio frequency applied in a direction perpendicular to the applied magnetic field when that radio frequency achieves the Larmor frequency of the precessing nucleus the resonance occurs and flipping of the spin or spin transition a nuclear transition takes place. So, EPR spectrometers typically vary the magnetic field and hold the microwave frequency this is very very important. So, magnetic field is varied whereas the microwave frequency is kept constant whereas in case of NMR again magnetic field is kept constant and radio frequency is varied. So, EPR spectrometers are available in several frequency ranges and the X band is currently the most commonly used and also more popular range of frequency used. So, here I have given a list of different micro bands for EPR spectroscopy and they carry different names they call S band X band K band Q band and W and the corresponding frequency I have shown here in gigahertz and also corresponding wavelength in centimeter is also given and also for corresponding particular microwave bands the magnetic field strength used is also given here in Tesla in case of S band 0.107 in case of X band it is 0.339 Tesla in case of K band it is 0.82 in case of Q band it is 1.25 and in case of W it is 3.3 you can go up to 4 Tesla. So, EPR is often used to investigate systems in which electrons have both orbital and spin angular momentum which needs the use of scaling factor to account for the coupling between the two momenta. So, we should look into coupling between two. So, this is called the G factor. So, G factor arrives to account for interaction between orbital and spin angular momentum and it is roughly equivalent in utility how chemical shift is used in NMR. The utility of this one is very similar to the utility of chemical shift in case of NMR the G factor is associated with the quantum number J the total angular momentum where J can take L plus S value. In case of UV visible spectroscopy J pin orbit coupling can have values of L plus or minus S and we know that it takes L minus S when the sub shell is less than half field and it takes L plus S value when it is when the sub shell is more than half field. For example, if you take D4 we consider J equals L minus S and if you take D6 we are considering J equals L plus S. So, that term is shown here this is how we can write the term here of course the same term without these two G factors we use it for calculating mu effective in case of paramagnetic species. So, in this term GL is the orbital G value and GSC the spin G value for most spin systems with angular and spin magnetic momenta it can be approximated that GL is exactly 1 and GSC is exactly 2. Then this equation reduces to a new expression called land F formula and that is represented by this expression here G J equals 3 by 2 minus L into L plus 1 minus S into S plus 1 over 2 J into J plus 1. The resultant electronic magnetic dipole is mu J equals minus G J mu B J. So, this is how we can represent the resultant electronic magnetic dipole. So, often these approximations do not always hold true as there are many systems in which J coupling does occur especially in transcendental clusters where the unpaid spin is highly delocalized over several nuclei that accounts for metal metal bonding anyway. So, but for the purpose of an elementary examination of PPR theory it is usual for the understanding of how this G factor is derived. In general this simply refer to as the G factor or the land A G factor for a free electron with zero angular momentum G factor has a small quantum mechanical corrective value of G equals 2.0023193. So, in addition to considering the total magnetic dipole moment of a paramagnetic species the G value takes into account the local environments of the spin system. Of course that is true in case of NMR also we define in a different way the net magnetic field experienced by the nucleus when it is surrounded by electrons would differ because of shielding or de-shielding effects. So, here the existence of local magnetic field produced by other magnetic species. So, electric quadruples, a magnetic nuclei, ligand fields etcetera and ligand fields comes into picture when we talk about EPR of a transmitter complexes which are paramagnetic in nature. All can change the effective magnetic field experienced by the electron. So, similarly the net magnetic field experienced by the electron spin is given like this B naught plus B local and this is also again very similar to NMR that magnetic field experienced by the nucleus is also shown in the very similar way that we call B naught plus B i where it is a induced magnetic field, but whereas here we call it as local magnetic field. So, the local field can be either induced by the applied field and as a result have magnitude dependence on B naught. If the local field generated is because of the applied magnetic field then the result will have a dependence that have a dependence on the magnitude of B naught. The local fields may be permanent and can be independent of B naught also. So, in the case of former where the local field depends on the applied magnetic field it is ideal to consider the net field experienced by the electron as a function of B naught. So, here we use the term B effective equals B naught into 1 minus sigma and we same terminology we used in case of NMR also to assess the net magnetic field experienced by the nucleus and here it can be simplified B effective equals B naught into g over g effective. So, since many organic radicals and radical ions have unpaid electrons with L equals 0 and hence J becomes S of course it is L plus S if L value is 0. Obviously, J becomes same as that of S value as a result G value will be close to 2. So, however, transmit lines are complexes due to unpaid electrons have larger value of L and S and hence the G value diverge from the observed value of 2 here. In view of this the energy levels corresponds to the spins in an applied magnetic field can be expressed using this equation here E M S equals M S G E mu B B naught always when E subscript is coming that refers to electron and thus the energy difference associated with a transition is delta E M S equals delta M S G E mu B into B naught is the applied magnetic field. These two equations expressions are important in EPR. Typically EPR is performed in a perpendicular mode where the magnetic field component of the microwave radiation is oriented perpendicular to the applied magnetic field. Of course, this is also very similar to the NMR where a magnetic field of frequency is similar to Larmor frequency that comes from the radio frequency range. It is applied in a direction perpendicular to the applied magnetic field B naught. So, this very similar in the same way here microwave radiation is also applied or it is oriented in a direction perpendicular to the applied magnetic field. So, the selection rule for allowed EPR transition is also similar to nuclear transition in which we are considering delta S equals plus or minus 1 and similarly in case of EPR also we are considering delta M S equals plus or minus 1. So, the energy of the transition can be simplified as follows like this and there is a method called parallel mode. In parallel mode what happens a microwave radiation is applied in a direction parallel to the magnetic field in which microwaves are applied parallel to the magnetic field changing the selection rule to this one. This is the special case in this case the selection rule is M S equals plus or minus 2. Otherwise when it is applied perpendicular to the magnetic field microwave this is very similar to what we see or what we use in case of NMR delta M S equals plus or minus 1. So, this kind of theory that explains applying microwave radiation parallel to the applied magnetic field is called parallel mode EPR theory and I am not going to the details of parallel mode EPR theory. Let me focus only on perpendicular mode of EPR theory. So, now I have shown a typical spectrum here. So, EPR again EPR electron paramagnetic resonance and ESR is electron spin resonance apply this is applicable for species with one or more unpaid electrons. So, in order to use EPR to study a molecule it should have one or more unpaid electrons or it can be free radicals or transient metals with odd number of electrons or high spin complexes or at least in the excited state they should have nonzero S value. And again this is a non-destructive technique very similar to NMR and IR this is a non-destructive technique only destructive technique is mass spectrometry. And now let us look into more points concerned with EPR spectroscopy. So, EPR what are the information we can extract from EPR spectra of a molecule which has at least one unpaid electron. So, it says what type of what types of paramagnetic species are present and what is the local structure and symmetry of this species also we can get about this and what is the nature of the wave function containing the unpaid electrons where are the unpaid spins delocalized all this vital information we can get from EPR spectrum. So, and what are the major disadvantages then typically required odd integer spins. So, that means diamagnetic species we cannot use it and here spin should have half 3 by 2 5 by 2 7 by 2 etcetera. And resolution is not as good as in NMR broad futures are observed and often requires very low temperature for good resolution. So, that is the major drawback because of very fast relaxation in order to slow down the relaxation in case of EPR we have to go to much lower temperature for that one we need liquid helium this is the major disadvantage or these are the major disadvantages associated with EPR spectroscopic method. Now, let us look into the energy transition how that happens. So, ESR measures the transition between electron spin energy levels and transition induced by the appropriate frequency radiation. That means basically when we know that in the absence of magnetic field the nuclear spin possess zero energy and the moment field is applied they align with plus half and minus half values. So, transition induced by the appropriate so once we can achieve transition and electron spin transition by applying the corresponding microwave radiation. So, required frequency of radiation depends upon the strength of the magnetic field you saw that one energy is associated with the energy difference between the two states is directly proportional to the applied magnetic field. If the field strength increases the energy the separation also increases and we need high frequency microwave radiation. So, common field strengths are 0.34 to 1.24 tesla and 9.5 to 335 gigahertz microwave region is employed here in this perpendicular mode of EPR module. So, let me stop here and continue more discussion on EPR spectroscopic methods in my next lecture until then have an excellent time. Thank you.