 Hello everyone, I once again welcome you all to MSP lecture series on interpretive spectroscopy. I started in discussion on EPR spectroscopy from my previous lecture. So let me continue from where I had stopped ESR or EPR measures the transition between the electron spin energy levels. So transition induced by the appropriate frequency of radiation and required frequency of radiation depends upon the strength of the magnetic field. As we increase the magnetic field, what happens? The energy gap between the nucleus spin steadily increases and if you go for higher field strength magnetic field, then higher microwave radiation is required to achieve the transition. So common field strength are anywhere between in the range of 0.34 to 1.24 Tesla, this about magnetic field B and then 9.5 and 35 gigahertz is the microwave region between 9.5 to 35 gigahertz is the microwave region that is used that is applied in a direction perpendicular to the applied magnetic field to perform transition of electron spins. And this is how the typical EPR instrument looks like, this is the magnetic field and the sample is kept here and the signals will go to the detector and then that goes to the plotter for plotting the spectrum. So how does the spectrometer work can be seen here, this is the source and this is the detector is there and sample cavity is here and this is the electromagnet and phase sensitive detector is here and modulation input comes from this part here. So that means the radiation source usually usually is called Klistron. Klistron are vacuum tubes known to be stable high power microwave sources which have low noise characteristics and thus give high intensity. That is the reason we use this source of microwave radiation called Klistron. The sample is placed in a resonant cavity in between the magnets I showed you which admits microwaves through an iris, the cavity is located in the middle of the electromagnet and helps to amplify the weak signals from the sample and most of the external components such as the source detector are contained within the microwave bridge control, additionally the other components such as attenuator, field modulator, amplifier also included to enhance the performance of the instrument. So EPR spectrometers typically use electromagnets and the microwave absorption is monitored as the field is varied. When an electron is placed within an applied magnetic field B naught the two possible spin states of the electron would have different energies. In the absence of magnetic field the spin states would have the same energy but the moment it is electron is placed in a magnetic field they possess two different energies. The lower energy state occurs when the magnetic moment of the electron is aligned with the magnetic field and a higher energy state where M is aligned against the magnetic field. So that means when the spin is aligned against the magnetic field we will be having here plus half. In case of NMR the one that is aligned with the magnetic field would have lowest energy that is to be plus half whereas here opposite of that one comes here. The lowest energy in case of NMR is plus half and higher energy is minus half in case of NMR. So here is opposite. So the two states are labeled by the projection of the electron spin MS and the direction of the magnetic field where MS equals minus half is the parallel state and MS half is the anti-parallel state. So this is actually aligned in this direction whereas this one is aligned in this direction here. Whereas here this is aligned in this direction and this is aligned in a direction opposite to the applied magnetic field and that is shown here and of course plus half you can see in this direction and that minus half is in this direction. And again it is always convenient to compare these two methodologies NMR and EPR. Similar to NMR EPR can be used to identify the geometry of a molecule through its magnetic moment and the difference in electron and nucleus mass and EPR is mainly used to use it for the detection and study of free radical species either in testing or analytical experiments. Pin labeling species of chemicals can be a powerful technique for both quantification and investigation of otherwise invisible factors that you cannot really detect using other methods. The EPR spectrum of a free electron shows only one line single peak whereas that of the hydrogen displays two lines two peaks due to the interaction between the nucleus and the unpaid electron. This is called hyperfine splitting so that means this electrons with spin half and minus half can also interact with nuclear spin and the lines can be further split and this we call it as hyperfine splitting. In NMR we call it as coupling spin-spin coupling. The distance between two lines is called hyperfine splitting constant A and then we call coupling constant in case of NMR spectroscopy. By using the simple 2Ni plus 1 rule number of hyperfine lines of a multiplet of a EPR transition can be calculated where N is number of spin and I is the number of equivalent nuclei. For example, for nitroxide radicals the nuclear spin of 14N is 1 so N equals 1 and I equals 1 therefore 2Ni plus 1 if you see we get three lines here. That means EPR transition for a nuclear spin equals 1 consists of a triplet. To observe microwave there must be unpaid electrons in the system that means of course only when we have an unpaid electron or a radical species that we subject for EPR study. So to observe microwave there must be unpaid electrons in the system. In a diamagnetic system or having no unpaid electrons no EPR signals will be observed as there will be no resonant absorption of micro energy that means EPR cannot be used for diamagnetic species and molecules such as NO, NO2, O2 do have unpaid electrons in ground state and EPR can also be performed on proteins with paramagnetic ions such as MN2 plus, Fe3 plus and copper 2 plus and other relevant transfer metal ions. Additionally, molecules containing stable nitroxide radicals, nitroxide radicals such as 2, 2, 6, 6 tetramethyl, 1 pridinyl, oxyl that is called tempo and di-terstributyl nitroxide radical. Now let us look into the energy levels associated with these two spins. For a molecule with one unpaid electron in a magnetic field the energy states of the electron can be defined as this one. So E equals G mu B B naught M s that equals pressure minus half G mu naught B naught. So where G is the proportionality factor we call it as G factor and M B is the Bohr magneton, B is the applied magnetic field and M s is the electron spin quantum number. The two spin states have the same energy when there is no applied magnetic field that means E equals 0 in the absence of magnetic field. The energy difference between the two spin states increases linearly with increasing magnetic field strength. So the energy gap is directly proportional to the applied magnetic field strength. So we talk about proportionality constant. What is this one? This is measured from the center of the signal for a free electron this is 2.00232 that is G for organic radicals typically close to free electron value of 1.992 2.01. For transition metal compounds large variations due to spin orbit coupling and zero field splitting 1.4 to 3.0 is observed. Now let us look into the techniques that are employed in EPR spectroscopy and of course we know this energy difference between the two states even given by H nu equals G beta B naught. This can be recorded either by varying H nu the micro frequency or B naught. Usually B naught is varied at a constant microwave frequency. So microwave frequency is kept constant and magnetic field strength is varied in case of EPR technique and here in case of X band EPR typical magnetic field strength is 3000 Gauss and the nu is 8398 gigahertz or H nu equals 9 gigahertz and in case of Q band the magnetic field strength is 12500 Gauss and H nu equals 35 gigahertz and in case of W band EPR H nu equals 90 gigahertz and B naught equals 3.5 Tesla or 35000 Gauss and you can see here in this one E versus B naught you can see steadily the value is increasing when you go from X band to W band because of increase in the overall magnetic field strength. Of course if the magnetic field strength is increasing obviously the energy required to excite change the nuclear or to observe a spin transition microwave radiation also energy also increases. So this gives a correlation between various bands and the corresponding micro frequency employed in various EPR methods where we are using X band Q band or W band. And then if you look into the spin states energy of an electron in a magnetic field is denoted by mu B naught and then of course I already refer to this equation here mu equals G B MS and beta equals E HO 4 by MC E is charge of electron and negative for electron and beta is negative for electron atomic unit of magnetic moment is called Bohr magneton and E can be simplified as E equals G beta MS B naught and then of course S can have plus and MS can have plus or minus half when MS equals minus half the expression this is the expression and when MS equals plus half this is the expression here. So this becomes something like this as I said in the magnetic field they will be aligned and opposing the applied magnetic field this is the low energy one minus half and this is the high energy one plus half and then if we consider here the corresponding energy is also M I and MS is also shown here and this is the energy gap between these two is represented by this term this is what is shown here. And a typical EPR spectra can look like here number of peaks in the absorption curve equals number of maximum or minimum in the derivative curve. So that means when you look into a typical EPR spectrum you should observe the number of peaks in the absorption curve is equal to number of maximum or minimum in the derivative curve you can consider the maximums or minimums they will be essentially same. This absorption intensity when you look into it this is absorption curve it looks like that and this is B naught and this is A versus B naught is given the first derivative of the absorption intensity is represented by this one is how you can see a derivative curve. And again professionality factor is measured from this center of the signal for a free electron G equals 2.00232 for organic radicals typically close to free electron value that is between 1.99 to 2.01 for transcendental compounds large variation is observed due to spin orbit coupling and also larger variation is spin orbit coupling also observed as a result what happens and plus zero field splitting also we come across as a result the range is 1.4 to 3.0. Now let us look into few examples here. So even number of protons are neutrons here zero so you do not observe any EPR signals for those which have no unpaired electrons for example 12 carbon i equals zero 4 helium zero 16 oxygen zero you do not see and if you have odd number of protons or neutrons integral spin for example 2H 14N 10B i equals 1 and here in case of 10B i equals 3 and 11B i equals 3 by 2 odd mass even that means even or odd combination we have these things half integral spin this is very similar this is about nuclear spin I am talking about and then if we look into different main group elements and then the isotopes we have for these and also the spin abundance and also how many EPR lines are expected is given in this table for example H if we consider we are considering 1 as well as 2 that means hydrogen as well as deuterium and then in case of hydrogen plus half is there in case of deuterium plus 1 is there so this is 0.015 percent abundance and then we can see in case of first one two lines in case of the deuterium we see three lines in EPR spectrum and in case of carbon we have 12 carbon and 13 carbon 12 carbon shows no signal I mean i equals 0 and whereas in case of 13C we have i equals half this constitutes about 1.1 percent and in case of 1 we get only one line because 2 Ni plus 1 if you take plus this whole term will be 0 so 1 will be there and in case of half we get two lines and in case of nitrogen we have both 14N and 15N 14N has i equals 1 and in case of 15N we have half that is only about 0.4 percent so we get three lines and two lines respectively in case of 14N and 15N and in case of oxygen we have 16, 17 and 18 and 16, 0 and in case of 17 we have 5 by 2 0.04 percent and 18 can be ignored so in case of 5 by 2 we get 6 lines 2 Ni plus 1 if we use here 2 into 1 we get 6 lines here and in case of 0 we get simply one line. In case of F only one isotope is there 19F i equals half so we get two lines and similarly in case of 31P also 100 percent abundant 31P isotope we get spin is half and we get two lines. In case of sulphur we have three isotopes 32, 33, 34 again 32 has spin i equals 0 and whereas 33 and 34 have 3 by 2 that constitute about 0.8 percent so in case of 32 we get 1 in case of 33 or 34 we get four lines in EPR spectrum and in case of chlorine we have two isotopes 35 and 37 both have 3 by 2 and in both the cases we get four lines and in case of arsenic we have 75 is the only 75 is the isotope have 3 by 2 value and we get 4 and in case of selenium we have several isotopes 76, 77, 78, 80, 82 and 76 is 0 and others have half spin value and that constitute about 0.76 that is 77 so we see 1.1 and 4 lines. Again in case of bromine very similar to chlorine we have two isotopes 79 and 81 both have i equals 3 by 2 and we see 4 lines here and in case of iodine again 127 we have 5 by 2 spin we see 6 lines here and similarly we can have a table for transfer metals also if you consider vanadium in plus 4 state isotope 51 and spin is 7 by 2 so we get 8 lines in EPR spectrum in case of manganese 2 plus 55 isotope 5 by 2 is the spin i value and we get 6 lines here in case of iron 3 we have 54, 56, 57, 58, 54 has 0 spin and whereas 56 and 57 can show half there is about 2 percent so we see 2 lines whereas in case of 0 we get only 1 line here and in case of cobalt we have 2 cobalt 2 59 isotope 7 by 2 we see again 8 lines here and in case of nickel we have nickel 3 as well as nickel 1 again 58 is 0 in case of 60 to 62 and 64 we constitute only about 1 percent and we see 3 by 2 4 lines there is about 0.25 percent and in case of copper 2 we have 63, 65 and again spin 3 by 2 we observe 4 lines in case of malbdenum in plus 5 state 92, 94 to 98 and 100 and 92 is 0 and in case of other one we see 5 by 2 is about 25 percent and constitutes and whereas we see 6 lines only in case of 4 percent and here tungsten also very similar 5 oxygen state 180, 182 to 184 and 186 again 14 percent has half and other one is 0 so what we see is we see about 1 and 2 lines and that is about 97 percent. Now let us look into hyperfine interaction like spin-spin splitting in case of NMR that is very similar here in addition to the applied magnetic field unpaid electrons are also sensitive to their local environments frequently the nuclei of the atoms in a molecular complex have a magnetic moment which produces a local magnetic field at the electron the resulting interactions between the electrons and the nuclei is called as hyperfine interaction because of the induced magnetic field generated at electrons and other nuclei surrounding the nuclei we are considering we see spin-spin coupling so here in a similar way this is the interactions between the electrons and the local magnetic field generated either independently or depending on the applied magnetic field so that results in the further splitting of the line this we call it as hyperfine interaction so that means here the resulting interaction between the electron and the nuclei is what decides the number of lines in the hyperfine interaction so number of lines again is given by 2 ni plus 1 n number of equivalent nuclei and i equals spin value the relative intensities of the lines is determined by the number of interacting nuclei so same thing in case of NMR as well so for example if you consider here we have half and minus half minus half and plus half here and they further interact and then nucleus with spin half to give four lines like this here so now let us look into hyperfine splitting with the different nuclei having a nuclear spin and also how many such nuclei are there for example when no interaction is there here so we see single peak for one unpaired electron when the interaction with nucleus with i equals half one nucleus with i equals half when it interacts it splits into two lines and then when this electron interacts with the nucleus spin i equals 1 this will be three lines here and then in case of nucleus spin i equals 3 by 2 there will be four lines four lines and then two equivalent nuclei with i equals half we will see again three lines and then three equivalent nuclei with i equals half we will see the four lines and then four equivalent nuclei with i equals one you can see nine lines will be there 2 ni plus 1 2 into 4 so we will see nine lines here so this gives some idea about hyperfine splitting so let me take some specific examples in my next lecture and then continue discussion on EPR spectroscopy until then have an excellent time thank you.