 We have learnt about electronic energy states and we know how knowing the electron configuration including the spin states we can talk about electronic energy states. And we are now going to talk about the transitions between these states we are already familiar with n pi star and pi pi star transitions and we had closed the discussion in the previous module saying that not all transitions are going to take place. Some transitions are more probable some transitions are less probable according to that the intensity of transition is defined. In that connection we are going to study Lambert Beer's law and then we will talk about different kinds of spectra that one could get depending on the bond length of the ground and excited electronic states and then we will talk about some other kinds of transitions. But before that let us have a look at an actual spectrum reported in scientific literature. This here is an absorption spectrum of benzene dissolved in cyclohexane a an aromatic compound dissolved in a non aromatic organic solvent. So since it is benzene you might as well understand that these transitions that you see they are pi pi star transition because benzene does not have a nitrogen atom or oxygen atom or any such thing. So two things to note here are first of all what is the y axis what is the x axis x axis here is wavelength x axis in a spectrum has to be something that is related to energy. It is conventional to use wavelength because most of the measurements in the ultraviolet visible region is performed by using dispersive gratings or spectrometer detector kind of combinations and this dispersive gratings work on the principle of as we know Bragg's diffraction law. So there the diffraction is defined in terms of wavelength but it is not very difficult to convert from wavelength to energy. When we do that we have to do some correction called Jacobian correction to this but that is a different story altogether. The second thing is what is the y axis actually three things that we have to discuss the y axis is molar extinction coefficient in centimeter inverse per molar we are going to learn about this. The third aspect is look at the spectrum the spectrum is highly structured why is the spectrum highly structured and are all spectra highly structured by the time we are done today we will know the answer to these questions. But first let us remember what we learned in the last module there are selection rules spin selection rule which is more stringent requires that there cannot be any transition between a singlet and triplet state and orbital selection rule which is less stringent is based on symmetry of spatial wave functions. Spin selection rule can break down because of spin orbit coupling orbital selection rule can break down by vipronic coupling. So all those bands that you saw a little while ago they are actually vipronic bands they involve not only electronic levels but also vibration level we will come to that. But first before that since we are talking about transitions that are more probable and that are less probable we need some means by which we should be experimentally able to determine which transition is more probable which transition is less probable. An experimental parameter that tells us about the probability of transition and this is obtained in the form of Lambert Beer's law. If you remember the y axis of the spectrum that we just saw that is what it is. Well Lambert and Beer independently proposed something and then you combine them to get the law. Let us say this rectangle is a sample. The length of the sample along the direction of propagation of light is L, intensity of light impinging on the sample is I0 and intensity of light transmitted from the sample is I t. So what happens as the shading of the arrow also shows is that as light gets absorbed by the molecules that are there in the sample it loses intensity. Some of the light is absorbed so it does not go out. So intensity would decrease or an extinction to some extent would take place. So to find out the relationship between I0 and I t what Lambert and Beer separately did was they considered a thickness DL in the sample in the direction of propagation of light and the intensity of light impinging on this small element let us say that is I and intensity of a light that emerges from this element let us say that is I minus Di that means this narrow strip has caused a decrease in intensity by an amount Di. So Lambert and Beer's two scientists figure out that this minus Di is proportional to three things. The intensity of light that impinges on that element concentration of the sample. So how many molecules the light would have to pass through and DL the thickness of this element. So it is a proportionality can be written very easily in terms of an equation. But before that one thing that we should say is that in this treatment C is always written as molar concentration and L is always written in terms of centimeter that is what gives us the unit. So minus Di then is kappa into I into C into DL where kappa is the constant of proportionality not very difficult to figure out what has to be done minus Di by I equal to K multiplied by C DL all we have to do now is integrate both sides left side has to be integrated from I0 to I t right side has to be integrated from 0 to L. So this is what we need to do and when we do that right side is very simple integral of DL between limits 0 and L is just L left hand side is also simple Di by I integrated is going to be natural logarithm of I and the limits are I0 and I t anyway. So we get ln I0 by I t is equal to kappa CL and since we are more comfortable working with logarithm to the base 10 it is not difficult to convert ln to log base 10 you have to just multiply by a constant and do that you get log I0 by I t remember this log is base 10 is equal to epsilon CL this constant kappa is multiplied by a number and I will not say explicitly what the number is I think all students of this course should know what it is if you do not better check better remember this value alright. So log I0 by I t is equal to epsilon CL C is concentration L is length of the sample what is there on the left hand side log I0 by I t that essentially tells us how much of the incident light has been absorbed this is called absorbance it is an extrinsic quantity depends on C and L also and what is epsilon since epsilon is multiplied by C and L the parameters that have got to do with how much of sample there is how much of sample the photons have to pass through epsilon is actually intrinsic quantity it is something that gives us an idea about how probable the transition is. So this is called molar extinction coefficient or molar absorption coefficient I always called it molar extinction coefficient but few years ago I had a student who told me unequivocally that molar extinction coefficient is apparently outdated and I have to call it molar absorption coefficient I like the term extinction because look at this arrow it is actually light is getting extinguished to some extent but anyway molar absorption coefficient is the more modern term both work. So molar extinction or molar absorption coefficient tells us about probability of transition an experimental parameter that tells us how probable the transition is in fact with a little bit of theory one can find a relationship between this experimentally observed quantity and the theoretically calculated probability of transition this is worked out in many standard textbooks Barrow is what I studied but then Barrow is out of print so you could study this from I think Macquarie and Simons book and maybe even Atkins physical chemistry book by the way I did not mention any textbooks so far you can study all this from Atkins by and large people who are interested in a little more you can study Banwell's molecular spectroscopy book those who are interested in a lot more I recommend molecular spectroscopy by Jack D. Greveld but that book is way beyond the scope of the current course. Let us come back to this we have this equation absorbance is equal to epsilon cl so if I measure absorbance at different concentrations then what happens absorbance should increase within a certain range so if I plot absorbance against concentration if I know concentration then the slope should give me epsilon it is as simple as that. Now high absorbance what does that mean high absorbance means that very little light will emerge from the sample so the sample is nearing opacity I leave it to you to work out what is the percentage of light that is transmitted it divided by I0 multiplied by 100 when absorbance is 0.01 0.1 1 and 10 please work this out and I think you will understand why I would like you to do this absorbance tells us how opaque or how transparent the sample is for that particular wavelength what are the factors that epsilon depend upon definitely depends upon the wavelength that is why in the spectrum that I showed you the plot was actually epsilon against wavelength or energy because some transitions are more probable some transitions are less probable and if you remember the unit that was written in the spectrum the unit was I think they had written centimeter inverse per molar I have written per molar per centimeter inverse very easy to work out from this expression left hand side absorbance has no unit please remember absorbance has no unit it is a logarithm of a ratio there is no way it can have any unit right hand side C has a unit L has a unit so epsilon also has a unit per molar per centimeter so this is Lambert Beer's law epsilon tells us probability of transition now if you recall the kind of transitions that we know already there are transitions that are spin forbidden but allowed a little bit by spin orbit coupling you have there are transitions that are maybe spin allowed but or vitally forbidden allowed a little bit by fibronic coupling so and some there are some transitions that are completely allowed spin allowed as well as or vitally allowed the difference in the probability among these shows up very nicely in the comparative values of the excellence the molar absorption coefficients and this table summarizes it quite nicely for fully allowed transitions spin allowed as well as or vitally allowed the molar extinction coefficient in per molar per centimeter ranges from 10 to the power 3 to create to the power 5 I have taken log to the base 10 that is why it is 3 to 5 for spin allowed transitions which are or vitally forbidden they come next in line and epsilon ranges from 10 to the power 0 1 2 3 4 that kind of thing to 10 to the power 3 1000 2000 so on and so forth for or vitally allowed but spin forbidden transition as I said if you remember spin selection rule is more stringent so epsilon ranges from 10 to the power minus 5 to 10 to the power 0 really really small transitions less intense transitions and I will not discuss this in detail but this here is a collection of spectra of different aromatic hydrocarbons benzene phenanthrene and athicene I leave it to you to figure out which ones are fully allowed which ones which of these transitions are spin allowed which ones of these transitions are or vitally allowed but what we are going to discuss today in the remaining 10 12 minutes is that why is it that they are all structured even in the benzene spectrum that I showed you earlier if you remember they are all structured so why is it that they are structured why are the spectra structured they are structured because see we were talking about this this is let us say the ground state S 0 and this is let us say S 1 the excited state these are electronic levels but electronic levels are associated with vibrational sub levels and these levels are characterized by vibrational quantum numbers that range from 0 1 2 so on and so forth and even S 1 they are characterized by vibrational levels it is conversional to denote those quantum numbers by V dashed equal to I will write 0 dashed 1 dashed 2 dashed 3 dashed now the difference between vibrational levels is high enough so only these 0s vibrational level of S 0 is populated at room temperature so any upward transition has to originate in V equal to 0 but then for vibronically allowed transitions it is not as if only the 0 0 dashed transition will take place 0 1 dashed 0 2 dashed 0 3 dashed all these transitions can take place with different probabilities sorry about my poor artistic skills please remember that these vertical lines are all straight lines they are not really the curvy lines that I have drawn but the point is for a given vibrational for a given electronic energy gap there can be multiple transitions involving the vibrational sub levels of the higher electronic state and that is what we are going to dwell upon a little bit and that is what gives the structure to these absorption spectrum so you can think that this is S 0 2 in which direction is energy increasing from left to right wavelength increases so energy increases from right to left so this one is S 0 to well V equal to 0 to V dashed equal to 1 dash transition this is V equal to 0 to V dashed equal to 2 to 3 dashed 4 dashed and so on and so forth and as you see that these vibronic transitions are not all equally probable also there are two kinds of spectra in for naphtha scene you see the 0 0 dashed transition seems to be the most intense whereas for benzene some other transition seems to be most intense why is that so that is what we learn in the next 10 minutes or so but before that one more thing that we want to talk about is solvent effect and how do you know which transition is what first of all we have discussed already that n pi star transitions are less probable because they are orbitally forbidden so if in a molecule you have a less probable transition in a little lower energy region then you can think that it is n pi star transition compared to pi pi star transitions which are expected to be stronger and in higher energy smaller wavelength region. What happens if I add acid where acid the lone pairs would get engaged with the proton so n pi star transition would gradually vanish if you add enough acid it would decrease with increasing acid amount finally it would vanish. For polar solvents n pi star transitions show blue shift or hypsochromic shift that means the shift to higher energies blue and red are relative terms pi pi star transitions show very small bathochromic or red shift why is that so because when you have these polar solvents the energy levels actually get stabilized to different extents the pi level gets stabilized to some extent n level gets stabilized to a much greater extent because in non-bonding orbitals you have this electron pairs that are more strongly directed so it is easier for solvent to lower their energies pi star also gets stabilized to an extent that is greater than that of pi because it is more delocalized but not as much as that of n all these stabilizations are they are not to scale they are grossly over emphasized. So what would I get in a polar solvent let us say left hand side this is a situation in non-polar solvent right hand side situation is in a polar solvent this n pi star gap actually is more than the n pi star gap in non-polar solvent that is why n pi star transition shows a hypsochromic or blue shift whereas pi pi star transition can show a little small bathochromic shift because pi star is stabilized to a greater extent than pi another kind of transitions that take place very often are charge transfer transitions what is that suppose you have a donor and an acceptor something that likes to donate electron something that likes to accept electron let us say you have an organic molecule some kind of a kumarin and let us say you have aniline aniline is a good donor and kumarin is a good electron acceptor so when they are close together of course they have to be in close proximity so we will see how they are brought in close proximity then if you shine with the right amount of light right wavelength of light then there can be a transition from the donor to the acceptor so these transitions always occur in low energies because they take place only when the energy gap is not very large they are broad and structure less why are they broad and structure less well see this donor acceptor energy levels are two different systems related to each other they can have a big spread that is why they are broad and they are structure less because this is unbound states so there is no really vibration that holds them together except for some very loose vibration involving the donor and acceptor moieties so they are by and large structure less they show strong solvent effect because there is a charge transfer charge separation so naturally when you have a polar solvent it is going to stabilize charge transfer states to a very large extent and now how do you get the donor and acceptor together one easy way of doing it is that if the solvent itself is either donor or acceptor then the solute is surrounded by the donor or acceptor or whatever it might be then you can have charge transfer with the solvent otherwise if both solutes are involved in charge transfer then their concentration would better be very large otherwise it does not happen the third option is a donor and an acceptor that are bonded together that is when charge transfer can happen very easily. In metal ion complexes the charge transfer often involves the ligand as well as the metal depending on the direction of charge transfer it is called metal to legal charge transfer or ligand to metal charge transfer about which you might study a little more in your discussion of inorganic chemistry but before leaving this slide this year is a schematic representation of the absorption spectra let us say this is the absorption spectrum of acceptor this is the absorption spectrum of donor charge transfer band would appear only when donor and acceptor are present together in sufficiently high concentration or covalently bonded together as you see it appears at longer wavelength that is smaller wave smaller energy it is broad and it is structure less these are the characteristics of charge transfer bands so we stop here and in the next module we will talk about this time not structure less but structured absorption