 Welcome to laser spectroscopy for chemist. The purpose of this course is to discuss certain aspects of use of lasers in chemistry. We will mainly focus on ultrafast dynamics but we will talk about other applications of lasers in chemistry as well. So to start with what you see here is going to be our main textbook. It is available in the library, you can issue it and I have a copy as well. So to start with we all I think know what the properties of laser are. When I was a child or when I was in college lasers were a novelty, many of us had not seen lasers. The only lasers we saw were the laser guns in Flash Gordon movies or Star Trek or some such thing. But then the world has moved. You have lasers everywhere, right here you have a laser so you very well know what the properties of laser are. You can see the laser light and you can tell me perhaps some of the properties. So because can you tell me some properties of this laser? Monochromatic. Monochromatic, it is coloured light, unlike the light that comes out of tube light it looks coloured so lasers are monochromatic. Later on when we talk about ultrafast processes we are going to say that lasers may not always be as monochromatic as they think they are but still some element of colour will always be there. So monochromaticity is a property. Anything else? Intense. Of course I can see this light even though so many lights are on in this room I can still see this coloured green light that is there. So it is intense. Anything else? Let us leave that for the last. Anything else? No, something other than coherence will come to coherence but before that something easier, something even easier than polarised. Yes? High intensity. You have already said high intensity, I will say it, it is collimated, is not it? Right? It is collimated light from the tube light dissipates in all directions. But the very fact that laser travels all the photons sort of travel in the same direction that is why you can use them as laser pointers okay and then comes what you are all saying it is coherent. Of course that is a little more sophisticated term what it means is that all the photons actually move in phase okay you think of light as wave all the light waves that are there are moving in step that is the meaning of coherence. And coherence also has a very important role to play in some of the applications we are going to discuss later on but for now these are the properties and one thing that we did not say is that laser is capable of pulsed operation. I hope you all understand what the meaning of pulse is, pulse means light goes on for a very small amount of time and then it remains off and then after a while it goes on again. So for those of us who have worked in our lab we very well know what the meaning of pulse in its true essence but for beginners all of us have actually seen pulse in everyday life. Can you tell us some examples of pulse that we have seen outside the lab it is monsoon season so in this season lightning. Lightning is the perhaps easiest example of a pulse of light it goes on for a short time it is different from the pulses of light that we use in lasers because this lightning bolts are not correlated you can have lightning now then after few seconds there is no correlation between one lightning bolt and the other or you can think of but if you think of isolated flashes pulses then lightning bolt is definitely a pulse it is just that it does not repeat at a regular interval unlike laser anything else some man-made pulse of light that we have all encountered when you take photograph using flash that is also a pulse right now flash is there even in your mobile phone camera right take a photograph light goes on momentarily and then it goes off that is an example of a flash of a pulse. So laser as we are going to discuss later on some lasers are actually capable of pulsed operation by themselves naturally they are like that some lasers can be made to operate in pulsed mode by using some extrinsic external device or maybe even without using an external device we are going to come to a rather interesting pulse the interesting kind of pulsed operation when we talk about titanium sapphire laser where it is almost it looks like it has a mind of its own and it is getting pulsed by itself but actually not because titanium sapphire as we are going to discuss later that also actually gives a continuous wave I mean non pulsed operation unless some certain stringent conditions are made but these are the four properties and these four properties make lasers very useful in chemistry. So to start with let me give you a couple of examples the first example is from well it is from some research paper but you can read it in something as ubiquitous as Macquarie and Simon's physical chemistry book the spectrum of ICL. So first of all let me show you the spectrum of ICL in a spectrometer that is so called not high resolution low resolution spectrum in ordinary spectrometer of course when I say ordinary spectrometer it is not so ordinary also because as you can see the resolution is 0.03 cm inverse the resolution is much better than what we normally use for our absorption of fluorescence studies. But let us say that this is an ordinary spectrometer resolution is only 0.03 cm inverse in this kind of a spectrometer this is what the spectrum of ICL looks like you see two bands and the way we depicted it these bands look quite broad actually they are not so broad if you read the x axis it is 17,299.5 17,299.6 17,299.7 cm inverse. So even this so called ordinary spectrometer is a high resolution spectrometer okay let us see what happens when you use a laser spectrometer when you record the spectrum of ICL in a laser spectrometer the resolution there is 3 into 10 to the power minus 5 cm inverse. So now see everything is relative right. So 0.03 cm inverse is actually extraordinary compared to the measurements that we make in solution phase but when you are comparing it with a resolution of 3 into 10 to the power minus 5 cm inverse it looks quite ordinary right. So in this kind of a laser spectrometer the same spectrum looks like this you see there is so much of structure so many features are there so what look like 2 broad bands turn out to be 2 bunches of really narrow lines and in fact you can before going there just read the x axis once again now it reads 17,299.449 17,299.607 17,299.766 which means instead of going to the first place of decimal we have accuracy up to third place of decimal. In fact you perhaps appreciate it better if you zoom into it a little more zoom into this small region denoted by the dashed lines and this is what you see. Now look at the x axis 17,299.685 17,299.690 17,299.695 that is the kind of resolution that you can get if you use a really really monochromatic laser point to note not all lasers are monochromatic to this order and sometimes you might want lasers to be not so monochromatic but this is one application the first application that we start with for lasers where monochromaticity is used to the maximum possible extent it is difficult to imagine that it can get any better if you try to get resolution better than this perhaps you will be limited by what is called natural line width. So this is as good as it gets so using a laser which is sufficiently monochromatic you can actually see spectra with the maximum possible resolution that you can think of that is one application. Second application is in an area which is considered to be one of the holy grails of chemistry in chemistry as chemists our job is to carry out reactions and our job is to carry out reactions in the way that we want them to proceed of course in synthetic chemistry it is done by using by playing around with reagent or substrate or conditions and so on and so forth. But one of the holy grails that has remained almost elusive over the last few decades in chemistry is that can we make a reaction go in a particular direction at a molecular level very fine level and some success has been achieved in controlling the reaction path using lasers. And I will not give you an example here but I will just tell you the theory of it how it can happen to do that we will need to invoke what is called potential energy surfaces a potential energy surface basically tells us what kind of energy barrier is involved in the reaction depending on which path it takes and the way we have drawn it here is contours. So in this contours the reactant is here in the bottom right hand part the product is in the top left hand part and these lines of contours denote increasing values of energy. So as you see the reactant is in a minimum the product is in another minimum so as you go from reactant to product as you know usually you are going to encounter a reaction barrier which means you think in terms of energy the energy of the system will keep on going up up up until you reach a maximum and then it goes down as you proceed towards the product. So in this plot this is how it is drawn so it is like a mountain right so you go up energy keeps increasing until this point after which energy keeps decreasing and intentionally reactant product channels are shown to be perpendicular to each other. So you can think of this diagram as a mountain right in which this is a minimum this is a minimum and the path is you keep going up reach a maximum this is called a saddle point and then you go down this path to reach the product right. So this point here is called the saddle point look at this point if you go in any direction what happens if you go towards the reactant do you go up or down in energy you go down if you go towards the product do you go up or down if you go in a perpendicular direction then you go up okay see this is small energy this is small energy this is the next contour which means it is even higher energy so you need to visualize this so it is like a path it is sort of a pass in the mountain okay you go up turn right and then go down and if you go in perpendicular direction you have walls of a mountain it is like a pass in mountainous terrain alright why is it called a saddle point why is this called a saddle point because it looks like a saddle here if you have seen a saddle if you want to sit on a saddle your legs will be on the two sides so you go down and you do not want to fall from the horse so the saddle goes up in front of you and behind you. So that is what this place looks like that is why it is called a saddle point okay now this is a potential energy surface the way I have drawn it here it is an attractive potential energy surface which means the saddle point occurs quite early in the path of the reaction the other opposite example will of course be repulsive potential energy surface which means the saddle point occurs quite late in the reaction path now in depending on what kind of potential energy surface it is your reactant has to behave differently in order to reach the product okay let us see how let us say this is a reactant and now it is easiest if you think of the reactant to be a ball that is rolling up and then rolling down you give it some energy it rolls up and then rolls down suppose we start in such a way that the reactant does not vibrate does not vibrate means it goes straight what will happen will it cross the barrier let us see what happens let us say first the reactant is vibrating then what happens is now try to visualize the picture you have this path going up and down and the saddle point is quite early if the reactant vibrates then it will go up and down the path and finally it will come back like this right what happens if it does not vibrate then it goes straight and then it has a chance of crossing the saddle point more over once it crosses the saddle point so it is like it goes straight hits a wall so goes up a little bit and comes down so when it comes down the in the direction of the product it is going to oscillate like this okay so if you want if you happen to have an attractive potential energy surface and if you want the reaction to happen then you want the reactant to not vibrate at all it should only have translation energy no vibration energy right what happens if the potential energy surface is repulsive in nature where the saddle point is more towards the product now see if the reactant goes straight it cannot reach the saddle point in order to reach the saddle point it has to turn and the only way that can happen is if the reactant goes up the path in a vibrating manner otherwise it will not turn anyway right so it has to go like this and then it has to be in the right place when it goes down it should be on the other side of the wall okay something like this if it goes straight it hits a wall and comes back if it vibrates then this is what happens alright but now how are you going to tell the molecule that depending on the potential energy surface you go straight do not vibrate or you please vibrate yes and the amount of energy that is given is best given by using a laser so what you do is use this kind of a setup this is called a cross beam arrangement cross beam experiments are nothing new they are quite classical and their first design so that you would have two reactants coming in two directions gas phase reaction they would collide and then the product would be formed in this case what you do is you have the reactant coming and in the other path you do not have another reactant you have light going in in the first case where you do not want the molecule to vibrate what you do is you make it undergo what is called a supersonic expansion then there is no vibration energy to only goes straight if you want it to vibrate you excite it with an IL laser of appropriate frequency so this way you can make the reaction go in a particular direction or block a particular reaction so using lasers you can think of controlling the reaction path and then you can determine the trajectory right now let us come to the main theme of our discussion ultrafast dynamics before we start the discussion let us first understand what is the meaning of ultrafast what is the need of studying ultrafast reactions to do that let us go back to our maybe class 11 class 12 level knowledge of chemical kinetics we know that for many of the reactions we are able to write a rate law like this dx dt equal to minus dx dt equal to k into a minus x to the power n right it is a very simple rate law what is the order of this reaction n is it necessary that a reaction must always have an order no because I can have a rate law where you cannot write it like this it might be quite complicated ok it is not necessary that reaction must have a well defined order ok if you can write the rate law like this then n the exponent is the order of the reaction alright ok and what is k rate constant so for a faster reaction is k larger or is k smaller k larger right so suppose I give myself this challenge that I want to know what the k will be for the fastest possible chemical process let us see if we can get there but before that why do you even need to know n k you have already told me rate constant k tells us how fast the reaction proceeds what does n tell us I mean it tells the order n is the order but why do you even want to know n how many molecules are reacting might be a little dangerous it is not always correct so remember the definition of order is the exponent n to which you have to raise this concentration if it can be written that way that is the order of the reaction ok so what does it tell us why do you even study chemical kinetics the answer is mechanism right we talk about so many kinds of mechanisms SN1 SN2 U1 E2 how do you know which mechanism is being followed because if you propose a mechanism then you will invariably be able to work out a rate equation for it ok and then your job becomes to find out whether the experimentally observed rate equation matches the expectation from your mechanism if they match then it is possible but not always guaranteed that your mechanism is correct ok that is a little bit of a digression let us come back to this well this is what it is H2 plus Br to 2 HBr it looks very straight forward you might think that the rate constant is H2 concentration multiplied by Br to concentration multiplied by k but actually it is not it is found out that the rate law is quite complicated right rate law is quite complicated so that is because the reaction is not just H2 and we are coming together colliding and giving you 2 HBr that is more to it is a free radical reaction so when you propose a mechanism we actually come to this kind of a rate law right now let us come back to our main issue that we want to discuss what is the fastest possible reaction to do that let us again remind ourselves something temperature dependence I think we know that temperature dependence of rate constant is given by this kind of an Arrhenius equation k equal to a e to the power minus ea by RT where ea is the activation energy ok so and we are all familiar with this potentialized profile and so on and so forth now when we perform a little more detailed discussion on the activated complex then we arrive at the subject which is called molecular reaction dynamics and to understand that properly what you need to know is statistical mechanics right and using statistical mechanics statistical thermodynamics there you get an expression like this just believe me on this one k equal to well kt by h there are 2 ks here do not get confused that big k is the rate constant and the little k is Boltzmann constant kt by h q star by qa qb where qs are the partition coefficients e to the power minus e0 by RT now let us ask that from theory does this equation have a name adding equation. So from adding equation let us ask when are we going to get the maximum possible value of k first point what about e0 if e0 is large does k go up or go down down so what is the smallest possible value so small value of e0 is going to be a large value of rate constant what is the smallest possible value of e0 0 so when it is 0 then e to the power minus e0 by RT becomes 1 you do not have to worry about that and let me once again just believe me when I say that the best possible scenario is that this ratio of partition coefficients is also equal to 1 ok so what are you left with then you are left with kt by h kt by h is the maximum the largest value of rate constant that you could get ok and at room temperature this turns out to be a value of 6 into 10 to the power 12 per second ok so theoretically this is the limit you cannot have a rate constant that is larger than this for a chemical process and this is something that we would better remember when we do experiments like fluorescence quenching because there are many reports in which bimolecular quenching constants of 10 to the power 13 10 to the power 14 per second are reported they are all unphysical they are wrong those values come because something is wrong with the model that is being used but we will come to that later so this is the largest value of k you can get so what is the smallest time that would be associated with the chemical process inverse of this ok inverse of this turns out to be 170 femtosecond right so this is sort of the limit and that is why we want to study what is called femtochemistry because if we have an instrument that allows us to study a process that is as fast as 170 femtosecond then we will be able to study all chemical kinetics that is there you do not need anything faster than this in chemistry of course nowadays people do at a second spectroscopy but that is not chemistry that is beyond chemistry ok so this is what we learn that what is the limit of time constant or rate constant in chemistry the fastest chemical process takes place in about 170 femtosecond that is the expectation and there is another way of arriving at it what is the what is the fastest possible chemical process you can think of in generic very generic terms one breaking right breaking of a bond now very too simplistic way of calculating this as well if you want to know how much time it takes to break a bond well atomic motion is typically associated with speeds of 1 kilometer per second and the bond is typically about 1 angstrom right so if you can move the atoms by 1 angstrom then the bond is broken this is a very very simplistic way of thinking of it the earlier one was better so what is the time taken if speed is 1 kilometer per second what is the time taken to travel 1 angstrom the time turns out to be about 100 femtosecond ok so even though this is a very course way of thinking of it the number we get is not very different from the number that we get from iron equation so it is a 100 femtosecond 150 femtosecond that is the kind of capability that we need if you want to actually see a bond break ok so that is what takes us to ultrafast dynamics that is why you want to study ultrafast dynamics so that there is nothing in chemistry that you cannot study ok how do you follow such a fast process the problem is you cannot use a stop clock you cannot use electronics so easily because every electronics every electronic component has its own response time and that response time is much much larger than femtosecond so even before I go to femtosecond the easiest way of doing it is to create is to well let us say is to disturb an equilibrium you have a system in equilibrium you disturb it how do you disturb it you already discussed pulses of light and remember lasers can have pulsed operation to use a suitable pulse to disturb the equilibrium if you put it in very simple way use a laser pulse to create an excited state population ok and then what will happen the population is going to decay right if you can somehow follow this decay of population in time then you can find out the rate constant or time constant associated with it ok and capability of following faster and faster reaction has also increased exponentially as you see even in 1940s we could measure about milliseconds but between 1940 and 1980 capability went up from millisecond to femtosecond by using different experimental techniques this slide is quite famous this picture is quite famous it is called the arrow of time and it is taken from the Nobel lecture of Professor Ahmet Zuhl who got Nobel Prize in 1999 for well we see for what so this is the idea you need pulse excitation you need to produce an excited state population or a disturbed population or something and then you measure the relaxation time how you do that we will come to it one by one but let us end today but show by showing one of the pieces of data that one Zuhl is Nobel Prize you do not need to understand what this means right now but what it says is that he could sort of take photograph snap shots of the bond actually breaking and the way we could do it was by using very intense ultra short pulses of light ok and here you see you can see this oscillations right these oscillations come because of something called wave packet dynamics that is where this thing you are saying coherent that is where coherence of laser becomes very important ok so this is what we will study over the course slowly step by step.