 Now we change here and we start talking about molecular spectroscopy which is an experimental technique. What we will do in this course is that we will develop the theoretical foundation of spectroscopy. All this time we have been talking about quantum mechanics. In quantum mechanics we learnt about wave mechanics we were introduced to operator algebra. We learnt that boundary conditions take us to quantum numbers. We learnt about Eigen values and expectation values which to use when we did a at least preliminary treatment of hydrogen atom where Schrodinger equation is partially solvable. We solved at least one part of it and that is going to be handy in our subsequent discussion and we arrived at the orbitals, atomic orbitals. And the same atomic orbitals were used to build molecular orbitals when we tried to build a quantum mechanical description of molecules using molecular orbital theory. And from there we said that we get an idea of bond length, bond energy so on and so forth. We really did not talk about length so much but bond energy definitely. So now the question that arises is that all these things that we have said is this true? Is it a fact or are we just making things up? Is there anything called wave functions? Well before going further I would like to show you a quotation by someone who is a father figure of quantum mechanics Max Planck. Max Planck had said experimental experiments are the only means of knowledge at our disposal. The rest is poetry and imagination not to undermine poetry and imagination but in the pursuit of truth in the pursuit of understanding what everything is about we must have experiments that will give us insight into the systems actually. And the experiments that are most related in this context are of molecular spectroscopy. In molecular spectroscopy, in molecular spectroscopy we study the interaction of radiation with matter. We are already exposed to molecular spectroscopy to some extent because we did talk about photo electron spectrum we will talk about some other forms of spectroscopy here. Analyzation energies is something that we have already access to. Now we are going to learn how do we determine bond length experimentally using spectroscopy? How do we determine bond strength? Can we can we determine bond strength? Can we talk about intermolecular interactions? We might not go into very deep detail of this but we will see. Can we tell which functional group it is? And can we talk about structured in solution? Can we talk about dynamics of processes going on a solution? Unfortunately, we will not go into all of these but at least some of the questions I hope will be answered by the time we are done discussing spectroscopy. Now when we do spectroscopy the most important relationship is this h nu equal to E2 minus E1. This is called Bohr resonance condition and this has to be fulfilled for light to be absorbed. Energy of a photon must match some energy gap in the molecule E1 and E2 are the energies of two stationary states in the molecule. And if you look at the electromagnetic spectrum it spans all the way from gamma rays very very high energy to radio waves very very low energy. And there are different regions you have radio waves, microwaves, IR radiation, visible radiation, ultraviolet radiation, x rays and finally gamma rays. Note how small the visible radiation is. If we talk in terms of say wavelength, light wavelength spans 10 to the power 3 to 10 to the power minus 11 centimeter. Our visible one is somewhere here 10 to the power minus 4 maybe 2 10 to the power minus 5, not even that not even like one order of magnitude. This is this very narrow region of electromagnetic spectrum that we can actually see. But using instruments we can have access to everything from radio waves to gamma rays. In this course we are going to focus our attention in this microwave to ultraviolet region. Microwave is what we will talk about first, then we will go on to IR, then we will discuss UV visible. The reason why these different regions are important is that in different regions you can probe different kinds of energies. If you want to put it that way different kinds of motion within atoms and molecules. This is the window we are going to talk about as we said. So, as you see energy is 10 to the power 2 kilocalorie for UV visible, 1 kilocalorie for IR, 10 to the power minus 2 kilocalorie for microwave. In terms of frequency we are going to span 6 decades 10 to the power 9 hertz for microwave to 10 to the power minus 15 hertz for UV visible. And in times of time scale which may not be important in our discussion we actually go from nanosecond to femtosecond. Now this IR and microwave radiation these have energies that are more or less comparable to energies of nuclear motion. Whereas UV visible light has energy that matches the energy gaps associated with electronic levels. So, when I say nuclear motion what do I mean? I mean two kinds of motion, one is rotation and the other is vibration. Rotational energies are associated with lower energy microwave region, vibrational energies are a little higher in IR region. So, these are the two regions we are going to talk about first we start with microwave. So, if I do microwave spectroscopy I essentially talk about rotating molecules. If I do IR spectroscopy infrared spectroscopy I talk about vibration of molecules and what is the molecular parameter that they lead to we will see. And when we talk about UV visible spectroscopy we are doing electronic spectroscopy which itself is a very very rich field of slurry. So, vibrational motion gives us an idea actually about bond strength as we are going to see and rotational motion gives us an idea about bond length. So, even though we are not really discussed yet see this is sort of a spoiler which is an answer to the question that we asked a little while ago. Can we experimentally determine bond length and bond strength? The answer is yes by doing microwave spectroscopy and IR spectroscopy. And the reason why we can do it, why we can explore different regions is that well there are so many different kinds of molecular energy levels you have electronic levels, vibrational levels, rotational levels. But Born-Neuponheimer approximation that we encountered earlier tells us essentially that these different kinds of energies can be handled one at a time. Atomic motion of nuclei and motion of electrons can be separated that is what Born-Neuponheimer approximation says in very very simple terms we have encountered this earlier also. But let us before starting a discussion of micro spectroscopy or anything there is this thing what is the spectrum and what is the information it contains. Let us say I have 3 levels in a molecule for now do not worry about what kind of levels these are just 3 levels energies are 10, 20, 40 centimeter inverse. Let us say the transition between E1 and E2 levels 1 and 2 is allowed. Now in spectroscopy we are going to encounter these terms allowed transition and forbidden transition allowed transitions are those that happen forbidden transitions or transitions that do not happen it comes from a little more sophisticated quantum mechanical treatment time dependent perturbation theoretical treatment of interaction of radiation with matter when we do that we arrive at a quantity called transition moment integral. The essential condition for a transition between 2 levels to take place is that the transition moment integral must be non-zero. So let us say in this particular molecule this first one is allowed. Let us say this one is not allowed 1, 2, 3 transition is not allowed and let us say this 2 to 3 transition is allowed. Now when I try to plot the spectrum, a spectrum is essentially a plot of intensity versus energy in some form it can be wavelength, it can be wave number, it can be energy in electron volt, it can be energy in kilocalorie, it can be joule whatever. So essentially it is a plot of some energy parameter in x axis and intensity in y axis. Where should I get the lines? This energy gap is 10 centimeter inverse. So I should get a line at 10 centimeter inverse and this energy gap between 2 and 3 is 20 centimeter inverse. So I should get another line at 20 centimeter inverse and I should not get a line at 30 centimeter inverse because this transition from 1 to 3 is forbidden. So that is what takes care of the x axis. What about y axis? Is it going to be stronger, the lower energy transition? Is it going to be weaker? Is there a correlation? We will come to that as well. For now let us say for whatever reason the transition for this 1 to 2 is twice as intense as the transition from 2 to 3. What do you expect in the spectrum? You expect 2 lines like the dotted lines that are shown here. What you get in reality is this. The lines always have some finite width, they are not delta functions. It is not as if they have nonzero value only at a particular value of energy of transition, there is a width spread. And also you see this horizontal, vertical up and down jiggly structure that is basically noise. When you do any experimental measurement, it is invariably associated with noise. So this vertical wiggle and jiggle that you see is essentially noise. So this is what a spectrum would look like for this system. Now let us think what is it that determines the y axis? One thing is probability of transition. I talked about transition dipole moment or transition moment integral little while ago. That is what tells us how probable a transition is. So another quantity that is often used for this is oscillator strength especially for UV visible transition, electronic transition. Yet another term that is used very often is well for absorption spectroscopy absorption cross-section. They are all interrelated and they talk about sort of probability of transition. So this is an intrinsic quantity. What is the per molecule quantity? Take one isolated molecule, what is the probability of transition? There is another factor and that factor is population. How are the states populated? And how they are populated is determined by Boltzmann distribution where number of molecules in level j at equilibrium is proportional to degeneracy of the state multiplied by e to the power minus epsilon j by kT. So let us say degeneracy is the same everywhere. You expect the population of the state 1 to be more than the population of state 2. And that is what is reflected in the schematic spectrum that we have shown here. What happens when you have degeneracy of more than 1? We will see when we talk about microwave spectrum. Now let me introduce you very very briefly to the schematics of a spectrophotometer. And here I am talking about a UV visible spectrophotometer an instrument on which you record the absorption spectrum. First of all you have a light source. Light source does not really look like a bulb this is just a schematic remember. Most typically for UV visible measurements the light source is a combination of deuterium lamp and tungsten halogen lamp. Tungsten halogen lamp gives you light in visible region and the deuterium lamp gives you light in ultraviolet region. Now this light is made to go through a monochromator. What is a monochromator? Chroma means color mono means one. So monochromator essentially means something that produces one color. How it does it? We will come to that also. But for now let us just see what happens after the monochromator. So white light goes in and let us say some colored light comes out depending on what your monochromator settings are. Now what you do is let us discuss what is there inside a monochromator. Inside a monochromator you have essentially a reflection grating. We are going to discuss Bragg's law later. Bragg's law essentially says n lambda equal to 2D sin theta which means that when light of multiple wavelengths is incident together on a grating different wavelengths travel in different directions according to this relationship Bragg's law. So when light falls on this grating you see blue light goes in one direction, red light goes in another direction. So initially what you have is when light gets into the monochromator there is a slit and this slit acts as a point source. Then you have a mirror which is placed in such a way that the slit is at its focal point focal plane. So light from a focal point coming and being incident on a concave mirror becomes parallel after reflection that is very important otherwise you will still get a mixture of colors. Now you see you get two kinds of beams in the scheme that I have shown. One beam of parallel blue light, one beam of parallel red light of course you have many different colors between and beyond them. Now what happens? Now since this blue light rays are all parallel they are going to be focused at some point because this is also concave mirror. Red light beams they are also parallel they will be focused to some other point and all these points are going to be on the focal plane. So what you do is you keep a slit here and keep the slit in such a way that if the focal plane is like this if the focal plane is like this the slit is like this. So what happens is red light is focused here blue light is focused here yellow light is focused here in this position if this is the slit only yellow light would go through. Now if you turn the grating a little bit turn this grating a little bit what will happen? This was the situation yellow light was going through now this entire thing will move and maybe blue light or red light will go through depending on in which direction you have turned the grating. This is how you have point by point collection of different wavelengths. Of course there is always a spread this is how monochromatic works. So after the monochromatic light comes out of monochromatic you place a beam splitter. A beam splitter is essentially a piece of glass or quartz which in this case divides the beam into two equal halves. 50-50 beam splitter is what is typically used in spectrophotometers. So one part goes straight the other arm is reflected by another plane mirror and made parallel to the original direction. Now one of these goes through the sample the other goes through the reference and then they are detected by some detector like photodiode or photomultiplier. These detectors what they do is that when light falls from the detector it generates a photo current and this photo current can tell you how much of light has fallen on the detector. It gives you an idea about the intensity of light that impinges upon the detector. From here you calculate absorbance log i0 by i and according to Lambert Beer's law this log i0 by i absorbance is actually equal to epsilon cl where c is the concentration in mole per liter, l is the length and epsilon is called molar extinction coefficient or molar absorption coefficient. Your homework is to find out what is the unit of molar absorption coefficient. So this is how a spectrophotometer roughly works. This is the introduction that we wanted to provide to spectroscopy. With this background we are going to discuss rotational spectroscopy with a caveat. Usually rotational spectroscopy is not performed using this monochromator. There is some other technique called Fourier transformation which we are not going to discuss here but you hear about it all the time. If you actually do research involving spectroscopy you keep hearing about FT NMR and FT IR and FT Raman, FT Microwave spectroscopy. So that is what is usually used. So we did not think that it is the same spectrometer that is used here but we are not even going to get into that. We are going to talk about the very fundamentals of microwave spectroscopy.