 Okay we are back and this is where we left in the last module the absorption and emission spectrum of 7 as a indole in hexane nxn it is difficult to get this kind of a result in protic solvents because as we discussed in the case of 3 hydroxyl flavone in some other cases you would get block structures that are formed so hexane is a better solvent and I am only showing you not even the tip of the iceberg tip of the tip the hundreds of papers on this where people have done temperature variation quantum chemical calculations different kinds of experiments and it was more or less agreed already by mid 1995 that double proton transfer takes place here and 7 as a indole dimer has been studied by people who are not spectroscopists also because it is a DNA base pair model so that biomimetic aspect is also there so lot of studies were there for our purpose what we need is upon increasing concentration from 10 to the power minus 4 to 10 to the power minus 2 molar small change in absorption is seen but what is most significant is that this monomer emission goes down and you do not see going down here because it is normalized here and totomer emission becomes very prominent between 400 to 700 nanometer emission maximum somewhere at 480, 490 nanometer this totomer emission becomes prominent in at higher concentrations right and this is the starting point of our time-resolved spectroscopic discussion and this data that you see here is from this 1998 Jeff Eskeme A paper by Takeuchi and Tahara. So what they started with is this starting point was very well non ambitious and I show you another paper that was published by Zuel group before this 1995 so there is some background so what they thought was this that alright this excited state double proton transfer takes place we know that this non proton transfer species the locally excited state has emission in 320 to say 400 nanometer region and beyond 400 nanometer it is predominantly the proton transfer species and there is another attractive feature look at the spectrum this locally excited state emission gets over by 400 nanometer and that is where the proton transferred species spectrum begins. So good thing here is that there is almost no overlap so there is almost no overlap the data are simpler if there is overlap between the two then there would be a significant region where you get signal from this as well as that actually it is there as you will see but it is not very much okay. So if that is the case then as we know then in the region of the non proton transferred locally excited dimeric excited state you expect a fast decay and in the region of emission of the proton transferred dimer you expect to see a rise okay this is the expectation and that is what they saw so let us go through the data a little carefully. So 320 and these are not normalized by the way that is why you see difference in heights at 320 nanometer of course that is a blue end of the spectrum the intensity is really really small so you see a decay it becomes more and more prominent as you go 350 nanometer 380 nanometer when you go to 420 nanometer once again intensity is small and you understand that if you remember the spectrum 420 nanometer is somewhere here so just before and just after 400 nanometer intensity is small but you have made the crossover already from the locally excited dimer to proton transferred dimer and here you see it looks like there is that fast decay still there but there is something that is very long lived and that becomes prominent at 440 nanometer 445 nanometer at 455 nanometer look at the data very closely what are the features that you see and look for features that are subtle what do you see I will give you the easiest you see a long lifetime right but there are two other features what are the two other features initial time that fast decay is still there that means some monomer emission is there even though you do not see it really in this steady state it is still there do you see the hint of a rise yeah do you see that there is a hint of a rise here of course the moment you go from 455 to 500 it is rise all the way followed by a long lifetime but the reason why I am spending so much time on this is that this is what you see a fast decay followed by a rise when you see emission when you are in the region of an emission spectrum where you have both generally our expectation is rise is for the destination state right the proton transferred state but since the non protons transferred excited the locally excited state also makes a contribution to fluorescence at this wavelength these are two independent things almost I mean this grows from there fine but you do see the decay there as well so you can get data like this so in our Jacob Fizz paper of 2010 I think in another system 2 to dash peri-dial benzimidazole we have observed something like this in up conversion these are all up conversion data perhaps do not need to say so after 455 nanometers so this is something that you might get if you do an experiment you should know you should not ignore it if you go more towards the and you can see that deliberately put in a gap 455 and 51 actually they are recorded decays at many wavelengths in between also but the gap is so that you see it nicely that there is a rise so what is this fast decay of the locally excited state what is the rise due to the rise is due to the formation of your proton transferred state and this decay on blue at blue end and rise at red end of emission spectrum is something that you expect if you work out this kinetics of a two state model where one state depletes and as a result of that the other state grows you get a simple by exponential function where one of where the formation of the second species is associated with a negative amplitude and decay of course has positive amplitude fine so qualitatively nothing very surprising but when the decay was fitted and this is where fitting becomes very important as we have said several times earlier you can fit almost everything to a by exponential decay that may be appropriate may not be appropriate in this case they could fit the blue end decay to two components 0.2 picosecond and 1.1 picosecond so they had to be confident whenever you go to by exponential fitting there are still plenty of conservative people and for good reason who start doubting your fate as how do you know it is not try exponential how do you know how do you know that it is really by exponential because over parameterization always gives a better fit so one needs to be very very careful one needs to have a model in mind and one needs to be able to interpret the data correctly so 0.2 picosecond 1.1 picosecond here Takauchi and Tahara had some help from their prior work that we discussed in the previous module they are already established that the time required for S2 to S1 conversion is something like 100 200 picosecond 100 200 femtosecond so they were confident because they already had this kind of data in other systems the rise was fitted to a single term so what they did is for this kind of a sequential process where you excite and then you have a first precursor precursor 1 which makes way for precursor 2 with a time constant tau 1 the precursor 2 gives rise to P3 with time constant tau 2 which has a lifetime of tau 3 you have expression of fluorescence decay like this which is not unknown to us in this course I at time T after excitation is equal to K1 of lambda multiplied by P1 of T plus K2 of lambda multiplied by P2 of T plus K3 of lambda multiplied by P3 of T which simplifies into our well known tri exponential fit A1 e to the power minus T by tau 1 plus A2 e to the power minus T by tau 2 plus A3 e to the power minus T by tau 3 the reason why we are showing this line even is to emphasize the fact that many times it is not enough to just fit your data and work with the amplitudes you might want to do a simulation of the data when I say simulation I do not mean MD simulation simple kinetic simulation code small code that you can write using MATLAB you might want to actually work out the kinetics and you might want to get this functions P1 of T P2 of T and so on and so forth eventually it will be like this. So I recommend that you go through the work of floor Roderick's Prito they have done a very efficient very thorough Forster cycle analysis of the time resolved data of proton transfer in benzimidazoles well pyridyl benzimidazoles Forster cycle is something we are not discussed in this course but it is there in Lacovitch's book among other resources quite easy to understand generally when you have things like this it is good if you can do a Forster cycle analysis in case of proton transfer and get greater insight out of your amplitudes and lifetimes that is what Takeuchi and Tahara had done what is K1 of lambda that is the fluorescence intensity in lambda space and of course when you go from lambda to nu you have to multiply by this factor lambda square. If you integrate K1 of nu over all frequencies then that gives you an idea of the radiative decay rate radiative decay rate is the inverse of radiative lifetime. So remember in basic courses of spectroscopy we talk about Einstein's kinetic treatment of stimulated and spontaneous emission. So hence we get Einstein's a coefficient and B coefficient Einstein's a coefficient is associated it is basically the rate constant associated with spontaneous decay inverse of that is the radiative lifetime that we are talking about. And you can get the oscillator strength oscillator strength you might remember is something that tells you how well how strong the transition is. So oscillator strength is has a simple mathematical relationship with other parameters like the experimentally determined epsilon molar absorption coefficient or molar extinction coefficient and transition moment integral which is a theoretical quantity. Oscillator strength is a more classical concept and you can find it from this data by integrating K1 over all frequencies and dividing by 1 by nu square. So this is something that you can get from the emission and the premise of this discussion of getting oscillator strength from the emission when you excite and when emission become B1 equal to B2 B12 equal to B21 right from there you can actually relate it to absorption as well as we are going to say. So hence doing all this from the time resolved data Takeuchi and Tahara could construct the fluorescence spectrum of all the components. So this is the fluorescence of monomer not very difficult to find because it is there in the steady state this is the fluorescence of tautomer again not difficult to find because it is there in the steady state so that helps your time resolved data analysis also. Then in addition to monomer and tautomer they identified 2 precursors precursor 1 and precursor 2 precursor 1 is at smaller wavelengths and therefore higher frequency higher energies precursor 2 is at lower longer wavelength therefore lower energies and they established that the 0.2 picosecond time constant is the time associated with precursor 1 to precursor 2 transformation 1.1 picosecond is the time associated with not only the decay of precursor 2 but also the rise of tautomer emission and here in starts the debate. So what they are saying essentially is that you have some precursor to start with from which no proton transfer is taking place no tautomer is formed from there you get another precursor which is associated with the slightly longer time 1.1 picosecond and from there you get that tautomer okay so it is I will tell you why this was a one of the starting points of the debate but well this we have said already they also determined the oscillator strength and to summarize the data that they had this is neglect the first line for the moment even though I have shown it to you so you already know the answer they had this 3 components right 0.2 picosecond 1.1 picosecond and a 3 nanosecond or so peak wavelengths are for the first one 330 nanometer for the first decay the species has peak wavelength emission wavelength of 350 nanometer this one this tautomer emission 490 nanometer. So this life time turns out to be 0.2 picosecond 1.1 picosecond 3.2 nanosecond and radiative life time turns out to be 13 nanosecond 38 nanosecond 160 nanosecond okay what is radiative life time 1 by kr remember what is life time life time is 1 by kr plus knr 1 by kr is 13 nanosecond 1 by kr plus knr is 0.2 picosecond what does that mean means there is some very efficient non radiative process going on here that is why you do not get so much because 13 nanosecond radiative life time is not actually bad it is quite good but due to this non radiative process it does not get a chance. So remember I refer to this Einstein kinetic treatment little while ago one thing that is not included in the treatment is non radiative process in Einstein's treatment you get to learn that spontaneous emission is a reality and it is always there we also get to learn that the rate constant of excitation is equal to rate constant of stimulated emission these are the 2 important things that we learnt from the treatment rather simple treatment but what is still not done there is non radiative rate constant which is of utmost importance when you discuss ultrafast processes okay. So this is a very good piece of data also to sensitize us to the fact that non radiative processes can bring about a sea change if you can somehow stop the non radiative process then this species will have lifetime of 13 nanosecond suppose there is no non radiative processes at all lifetime will go up from less than picosecond to 13 nanosecond and you will see a huge increase in fluorescence you do not see it because of the non radiative process okay. And the associated quantum is you know how to calculate them A i tau i divided by sum over i A i tau i for the ultrafast component it is 1.5 into 10 to the power minus 5 really very small first component 2.9 into 10 to the power minus 5 marginally better slow component 2 into 10 to the power minus 2 now 2 into 10 to the power minus 2 may not seem attractive for somebody who is looking for a brightly fluorescent molecule but then compared to 10 to the power minus 5 10 to the power minus 2 is 1000 times more yeah alright. Now the oscillator strength calculated from the fluorescence spectra well not fluorescence spectra fluorescence data turn out to be 0.13 for ultrafast 0.048 for fast and 0.023 for the slow component and then if you add this to 0.13 plus 0.048 that turns out to be 0.16 which closely matches the oscillator strength that you determine experimentally from the absorption spectrum remember what I said a little while ago oscillator strength generally when you say oscillator strength you think of absorption spectrum from there there is a straight forward determination from epsilon that turns out to be about 0.16. And when you sort of back calculate from the fluorescence data it turns out that almost the entire oscillator strength is accounted for by excitation to the species associated with ultrafast and fast components. So that means ultrafast and fast components together make up sort of a 2 fold excited state ensemble to which excitation is taking place remember excitation that we do here is by ultrafast pulse ultrafast pulse is not monochromatic. So if you have 2 states that are closely lying to each other then you might end up exciting both together okay. So this is the state of affairs here up to here that oscillator strength is accounted for by excitation to not 1 but 2 species and what are the 2 species now the first line that was written in the table the ultrafast one was associated is assigned to dimeric s2 state the first decay is associated with the dimeric s1 state why did they think this should be the assignment because they had prior knowledge that they in other compounds they had shown that you actually can look at the emission spectrum originating in s2 if you look at ultrafast time scales without that they could not have achieved this right. So this was the assignment that was done and the main contention here is that excitation is taking place to not 1 but 2 excited states 1 is s1 1 is s2 what are these 2 closely lying excited states what is the do we have some additional evidence to support what has been said so far we will take that up in the next module.