 So, first of all, happy new year to all of you and welcome. So, I just thought I would tell you that this is a this course is officially titled Quantum Chemistry CH 560 and the prerequisites are kind of CH 425, which was the first year MSC course. So, that is the kind of prerequisite. I hope all of you have done a similar course somewhere, somewhere in the country, you might have done a similar course to CH 425, which is basically the basic quantum mechanics, postulates and simple problems like hydrogen atom and so on. So, that is very important that we must realize that this is a prerequisite although I would do a revision, but the revision would be a very quick revision. Now, in case somebody has not done that prerequisite, please raise hands first, who has no exposure of quantum mechanics. What is your background? So, you are doing what we take now or PSD, PSD, classical simulation. You are doing with whom are you working? So, do you require it for your research, the quantum or you are doing one thing. What about you? Same, same, same group. You are also doing classical simulation. So, you have to excuse little bit in the same that you have to read on your own, the basics though I will revise. So, the topics that have been covered in 425 I will definitely mention. So, you must make a revision. The basic course will start with many electron problems. So, this will be the focus of this course. Many of the exactly solvable one particle problems we will skip except making a revision. So, the basic idea will be the many electron problem and that is what we need to learn in chemistry. One particle problems are model problems. They are exactly solvable, but model problems. So, many times they are useful, but of course, when you do actual chemistry, you have to learn how to deal with many electrons. So, that is something that I want to tell you. Rest of the people have some kind of exposure. I think many of you have done 425 here. So, at some point of time, some of your second year MSc students, most of your second year MSc students, those who are taking class, three of you and the rest are 5 year integrated, some of them. BS, BSMS, BS, just BS. So, third year of BS or fourth year and the rest are some of them are PhD students. So, let me first state that for those who are doing classical simulation, we actually discussed in the 425 three important experiments, three important experiments which highlighted the failure of classical mechanics in the atomic and molecular regime. That is the reason because you may first wonder why not classical mechanics for electrons. That is the first thing that you would think. So, the failures were actually highlighted more than 100 years back by one major experiment was, one of the major experiments was the Planck's blackbody radiation in which in the ultraviolet region, the radiation could not be explained. The change of the intensity with the wavelength could not be explained because Rayleigh-Jean's catenary tells that the intensity is proportional to 1 by lambda to the power 4. So, as lambda, so this is the classical Rayleigh-Jean's. So, if you use classical mechanics, the intensity of a radiation in a blackbody, so this was basically a blackbody, blackbody which perfectly absorbs and then radiates. So, the radiation intensity is proportional to lambda to the power 4 which means as lambda increases, intensity should decrease. However, in the actual experiment, it was not like that, it actually increased initially and then decreased whereas Rayleigh-Jean's would predict a completely different curve. So, this low wavelength, so this is the low wavelength, wavelength is increasing, is called the ultraviolet wavelength. So, this ultraviolet region could not be explained by classical mechanics because this region it fails and that is the reason this blackbody, so this is basically the blackbody radiation. So, this is why this is called the ultraviolet catastrophe. So, this was one of the experiments which actually signal the failure of classical mechanics in the quantum regime. Now, these bodies were of course quantum bodies which means they are very small. So, atomic and molecular length, so it is a length scale is very, very important. This was one of the experiments. The second one was the very famous experiments of the Einstein date of photoelectric effect. So, that was the second experiment. So, the photoelectric experiment essentially is that it signs a light on the metal of certain frequency and intensity and then you expect that the energy that is given on this metal would be sufficient at some point to eject the electrons, ionize the electrons. What was interesting is that it was shown that if nu is less than some cutoff frequency, no electrons were ejected. So, that was a very important experiment to see and this cutoff frequency depends on the metal. So, this is actually metal dependent. So, no electrons are ejected. So, that was the experiment A and the B it shows that if nu is greater than nu cutoff, then of course the energy of the electrons would increase and the kinetic energy of the emitted electrons is proportional to the frequency. So, these two experiments essentially showed that the energy and this is the first time it was shown that the energy is proportional to the frequency and this was actually later told by the Planck as energy of a single photon is energy as h which is the Planck's constant times the frequency. So, this was a very important experiment. What was the failure of classical mechanics is the following that once again if I increase the intensity, nothing happens if it is below the cutoff. So, once again it shows that the intensity is not proportional to energy. Both the experiments show the intensity is not proportional to energy which is what the classical mechanics essentially assume that if I have a high intense light, it has a more energy that is not true. Energy is dependent on the frequency even if the intensity is low. What happens when I increase the intensity, more number of electrons are emitted that is all but their kinetic energy of each electron is the same. So, this was one experiment that again showed that the classical mechanics failed and the final experiment that I would end with is of course the hydrogen atom spectra. So, that was important experiment which again showed that the energy spectra, the emission spectroscopy or emissions is discrete. Depending on where from where it emits, you have a different wavelengths but they are all discrete. So, you have only discrete at discrete frequencies or wavelength emission is observed and not proportional. So, this was again showed that essentially energy is quantized. So, this is the first time this concept came because of the atomic spectra that the energy is quantized that essentially means that the classical thinking that the energy can change continuously was again wrong. Like if you take a cricket ball, you can increase the energy continuously. There is no reason that energy is quantized. You can keep on pumping more and more energy and energy increases continuously but in this case energy is quantized. So, this was also a non classical explanation to this experiment and there are no way the classical mechanics could explain. So, some of these experiments gave birth to a new mechanics and the exact evolution of the quantum mechanics is of course there is a lot of history behind it and it is not very easy to kind of say that what brought the other but essentially there are a lot of thoughts that are going on and because of the people like Schrodinger, Heisenberg, Niels Bohr, Wolfgang Pauli, many of these people who actually in later Dirac, Feynman, many of these people actually kind of put quantum mechanics on a very hard footing. Ironically of course Einstein himself although he is experiment started photoelectric effect this experiment started quantum mechanics and it actually won the Nobel Prize also was not initially convinced about quantum mechanics. That is a very ironic thing that Einstein thought that the and we will say which are the parts which Einstein disagreed but eventually of course he could not disprove quantum mechanics. So, that is another part of the history that I always quote and particularly there is very nice exchange between Einstein versus Schrodinger, Einstein versus Heisenberg. So, it is a Schrodinger and Heisenberg who actually billered quantum mechanics in the early days. So, with that what we did was of course in the original in the basic quantum mechanics class was to tell the postulates of quantum mechanics. So, after that it is very hard to say the history of quantum mechanics in a sequential manner because a lot of things happened and sometimes they happened in a haphazard manner people started working in different directions. So, one of the important things that came up was actually an uncertainty principle at that time. So, these two were very very important one is the energy is proportional to frequency another is uncertainty principle which says that the uncertainty in position and momentum must be greater than some number like h cross over 2. So, that essentially means that if you have a finite energy system you cannot find the electron or an atom or a molecule at a specific place because if it has a specific place what will happen to delta x it will become 0 and if delta x becomes 0 according to this equation delta p will become infinity which means energy itself will become infinity. So, for any finite energy particle it is impossible to locate the quantum particle. So, the only issue is what is a quantum particle? So, that was very very important of course cricket ball you can locate where the cricket ball is. So, the quantum particles are of course defined as particles with very small size. So, which are basically atoms molecules electrons and there have been lots of exciting discussion how small is small how large is large all right because there are something between atoms and molecules clusters of atoms and molecules and the cricket ball. So, cricket ball contains Avogadro number of molecules all right a cluster can be 1000 10000. So, when do I stop using quantum mechanics and can use classical mechanics? So, that is an exciting discussion by itself which is basically the quantum classical transition and there again there is a very nice theory that it says that if I have if I can assume limit as h tends to 0 then the quantum principles move over to the classical mechanics. So, this also is another important principle and you can see that this actually follows the uncertainty principle because in the limit h cross tends to 0 the product of the uncertainties can become 0. I can make it 0 which means that means the particle can now be a classical. But when is this limit reached that is a question when do I reach this limit of h tending to 0 h is actually not 0 Planck's constant remember Planck's constant never changes. So, when I say in the limit h tends to 0 it means I can assume for all practical purposes of my measurements that the value of h is close to 0. So, when does that happen when the values are very large actual values are very large which again means if the particle size is larger and so on and so forth question again is exactly when. So, the point I am not trying to kind of satisfy you I am not trying to avoid but at the same time this point is a very important point when can I say that the quantum principles will become close to the classical. So, that is a very important question that we will answer and this question is still unresolved. So, the question are unresolved today people are using nano materials which are actually in the bridging length scales. So, is the nano material a length scale where I can stop using quantum mechanics is sufficiently big and if you look at the bulk from the bulk it is sufficiently small then you can argue that you have to use quantum mechanics. So, none of these are very clearly defined. So, that is a region that may be a gray region where many people use quantum mechanics many people use classical mechanics many use semi classical. In fact, there is a whole bunch of theory which is called semi classical. So, that can also be used in this region. So, this again was a very very important theory apart from the fact that E is H. At the same time the de Broglie actually postulated that every electron has a wave and particle such that the wavelength of the electron is related to the momentum of itself by the following relation of lambda equal to H by T. Now, many of these were actually the founding principles of quantum mechanics based on which essentially the full quantum mechanics was postulated. Remember while doing this Niels Bohr was already looking at the Bohr's atom 1913. In fact, Bohr's theory came many of you have read this in the schools these days or at least in class 11, 12 that is the Bohr's theory which made an ad hoc quantization. Bohr's theory was initially to explain the hydrogen atom spectrum remember the hydrogen atom spectrum. So, Bohr actually came up with a theory that the angular momentum is quantized. So, you remember this m v r equal to n H cross angular momentum is quantized and from this actually Bohr came up with the energy of the atom of a hydrogen atom which depends on a quantum number because this quantization brings in a quantum number. So, essentially m v r is multiple integer multiple of H cross. So, that brings in the multiple integer n and that n actually gives you the energy which essentially shows for hydrogen atom it was minus 1 by n square and hydrogen like atom Bohr essentially said that this would be minus z square by n square hydrogen like atom or atoms with one electron but charge z. So, all of you know what it is like helium plus, elite 2 plus and so on. So, this came about independently in 1913 and remember the quantum mechanics has still not started. In fact, at some point of time I can show you the slides of history of quantum mechanics how the quantum mechanics started.