 Okay. Thank you so much. Good afternoon. So my name is Imbrana. I'm from Islamabad. I teach at Chkaideasam University and this molecular energy level is not my subject. Umberto asked me to cover this, but we will do something. Okay. So it's just an outline, the brief introduction about molecules. What is the difference between atoms and molecule? What are the molecular orbital theory, molecular transitions and interaction of matter with radiation and types of molecular energy levels? Because in atom we have only the electronic levels, but in molecules we have different kinds of energy level. So usually in nature we say that there are exist 92 different atoms which have stable elements that corresponds to stable atoms. So these atoms can form large entities by using covalent bonding or ionic bonding. So those entities are called molecules. So number of atoms in a molecule can vary from to like in nitrogen, oxygen, but to many thousands like in DNA and protein we will see in the coming days. And molecules form when the total energy of the electron is lower in the molecule than in the individual atom. And this is the reason comes from above principle to put electron that states that to put electron into a lowest energy configuration in atoms. So the same principle goes for molecules as well as if like if you have 1s it should have 2 electron then 2s 2 electron 2p 6 electron that is the principle and it we follow this in molecules too. Okay. Properties of molecules depend on the specific kind of atoms they are composed of how the special structure of molecules, how they are arranged and the binding energy of atoms or the group of atoms present in a molecule. There are we there are different types of molecules we say them monoatomic molecules and sometime we call it just a monoatomic atom because it is a single atom molecule. And these are the elements that don't have tendency to form molecules. And at the standard temperature and pressure condition elements which are stable single atom molecules are the noble gases like helium, neon, argon, krypton and zeon. At higher temperature all the elements are in a gas form. So diatomic molecules are those molecules which consist of only 2 atoms of same or different kind like for example, hydrogen, oxygen and carbon monoxide nitric oxide they are 2 atom molecules and they are called diatomic molecules. And polyatomic molecules are consist of stable system consisting of 3 or more atoms. So sorry it skipped one slide this is atomic oxygen monoatomic we can it is stable and then this is diatomic and polyatomic ozone is a polyatomic form of oxygen. So there are 3 formulas basically that describe a molecule it is empirical formula, it is molecular formula and its structural formula. So empirical formula indicates the simplest whole number ratio of all the atoms present in a molecule. While the molecular formula describes the exact number of types and kinds of number and types of atom in a single molecule of a compound while the structural formula indicates not only the number of atoms present in molecule also their spatial arrangement. So this is the glucose molecule and you can see it is consist of carbon, hydrogen and oxygen. This is the structural form of this glucose molecule and here you can see that for our empirical molecule formula of glucose is CH2 it is just the whole number ratio of atoms present in glucose. But if you multiply this with 6 which is a whole number you get the molecular formula of glucose. So this is again another example of some empirical formulas, molecular formulas and the structure formula of methane, dinitrogen monoxide and benzene. So these are the 3 formulas are needed to explain a molecular structure. So we know that what is isotope because isotopes are same atoms which have same number of protons but different numbers of neutrons. So but it maintain their neutral character. So their physical behavior and their properties remain same. But isomers are 2 molecules with the same atom joined together in different shape that means their structure formula are different. So they have same molecular formula but different chemical structure for example butane and isobutane. I will show you their formula on the next slide. Then we have allotope they are different structural forms of same element when can exhibit quite different physical and chemical properties because we know that diamond, graphite, graphene they are all consist of pure carbon but due to their structure their properties are different. So we can see this is the butane or also it is pentane or isopentane they have same number of carbon, hydrogen but their structure is different. So they are called structural isomers then there are geometrical isomers and I think the third something like that. And this for carbon you can see this is the diamond structure of diamond and the second is the structure of graphite. So they are all consist of carbon the pure form of the same element and the different structure so they have the different properties. So in spectroscopy or in the molecular spectroscopy we study the interaction of electromagnetic radiations with matter and based on the analysis of electromagnetic radiation absorbed emitted we can gather information about the chemical analysis and molecular structure of that material. So what is an energy the question arises what is an energy level for any quantum mechanical system or a particle that is in a bound state is or bound states mean it is confined specially it can only take discrete values of energy and those discrete value of energies are called energy levels. So this term energy level is commonly used for the energy levels of electron in an atom ion or molecule which are bound by the electric field of nucleus because nucleus has protons and there is a binding between electron and proton that is also called the Coulomb's potential between these two. And this also this energy level scheme also refers to the energy levels of nuclei or the vibrational and rotational energy levels in molecules because in molecules we also apart from the electronic transition we have vibrational and rotational transitions we will see in couple of minutes that what are those energy levels. So ground state is when an electron is or molecule or ion is at the lowest possible energy so and it is and that electron that atom ion or molecule is called it is in its ground state because usually the electron is in the ground state and we call that atom ion or molecule is in its ground state when an electron have higher energy than its ground state we say that it is excited. And then there are some quantum mechanical state that have the same energy those states are called degenerate. So degenerate energy levels if they have the same energy and these are some basic things and then we have different kinds of chemical bonding between atoms which are which make those molecules and one is the covalent bond which involves the sharing of electron pair between atoms as atom approach each other to covalently bond their orbitals affect each other and others energy level to form bonding and anti-bonding. The energy level of bonding are metal is always lower and the energy level of the anti-bonding orbital is high and when molecules is in lower bonding state then it is stable. So the covalent bonding electron occupy the lower energy bonding orbital which may be signified by we call it by sigma or pi bonding in this molecular spectroscopy. So it is basically the covalent bonding that is based on the sharing of electrons. So more molecular orbital theory evolves from the atomic orbital theory because as the atoms approach towards each other they affect the orbits of each other due to this covalent attraction and repulsion. So we can say that orbitals of molecule can be specified by this capital phi and is a constant and this small phi represents the atomic orbitals. So molecule have discrete energy level there is no continuum between their electron electronic level vibrational level or rotational level. So they absorb electromagnetic radiation when the energy of the photon corresponds to the difference in energy between two states whether it is yeah no no you are right it is not always linear because sometime it is for linear molecule I think and but if it is a non-linear molecule and it has a group of atoms usually the problem is if it is the sharing of electron for the covalent bonds it is basically two electrons are involved between sharing of pair of an electron is involved then it is kind of this formula but for of course the molecules have many many different forms it is polyatomic and then they have different groups of atoms evolved and then it is a complicated thing. So energy can be stored either as a potential energy or the kinetic energy and there is a translational energy which is the small amount of energy stored as a kinetic energy of the molecule then we have rotational energy this is the kinetic energy associated with the rotational motion of the molecule then we have vibrational energy in case of molecules that is the oscillatory motion of the atoms which are or group of atom present within that molecule then we have the electronic energy which is stored as the potential energy because when the electron makes a transition from its ground state or the valence state to a some higher state so we have this electronic energy so all except translational energy are quantized so it means the vibrational rotational and electronic energy of molecules are quantized and they represent a quantum mechanical system because and what is the force it is the force due to the nucleus present there of all the constituent atoms okay so this is the molecule atomic and molecular vibration corresponds to excited energy level in quantum mechanics so if you have I think it will move okay atom is vibrating at some frequency and it absorbs it is it is oscillating between excited and the ground level so we can say that atom is at least partially in excited state atom is the quantum mechanical system and we talk only in terms of probability that there is a probability of finding the atom in excited or ground state but in the in the presence of a photon it is a finite probability that atom is in excited state or it can emit a photon and it can come back to the ground state so for any given frequency only one value of quantum energy of photon is possible transition between energy levels occur by absorption if there is a photon of frequency equal to the difference between excited and ground level there is a finite probability that electron will absorb the photon and go in the excited state and if it is in excited after the lifetime lifetime of molecule is quite in nanosecond so we can see that when an atom or molecule is in excited state it falls to a lower energy level eventually it has to and that is the reason it is quantum mechanically that it is the vacuum fluctuations that are associated with this spontaneous emission phenomena or the zero point energy that cause this transition so it emits a photon so atom is in excited state after some time in atom we can say it is the atomic lifetime which is of the order of 10 raised to power minus 8 second it is not for the metal stable state which can be for 10 raised to power minus 4 second or if it is a redberg atom that lifetime can be in the range of seconds but here in molecules they remain excited for few nanoseconds and upon the excitation emit a photon of light why about photon of light when they emit this visible part of electromagnetic spectrum it means that they are doing fluorescence which we will discuss in my tomorrow's presentation what is fluorescence what is the difference between phosphorescence so this process is called fluorescence so this is the spontaneous emission okay leave it so atom and sorry yeah yeah it is just a spontaneous emission a general expression for atom and molecule I will explain fluorescence tomorrow in my presentation based on only for molecules the singlet states and triplet states the behavior of phosphorescence and fluorescence today we just want that if atom or molecule or any quantum mechanical system consists of a particle ion or molecule is in its excited state it doesn't stay there forever it eventually drops from the excited state to ground because nature prefers to live in its ground state so it if it is in excited state atom or molecule it de-excites and a bit of photon yeah yeah yeah that way I will discuss because fluorescence is if in a molecule with the corresponding to molecule because tomorrow we have to do this fluorescence so I that's why I mentioned that molecules typically remain excited for nanoseconds and of course there are some vibrational transitions involved before the fluorescence and we will go into the detail tomorrow okay so this is stimulated absorption absorption is always stimulated there is no such thing as spontaneous absorption so you have to they absorb photon provided the energy of this photon is equal to the difference of energy between excited and ground state of that quantum mechanical system that's why I'm saying quantum mechanical system instead of emphasizing on atoms or molecules right so a downward transition involves the mission of a photon of energy and it emits the energy difference between these two energy levels they can be vibrational level in a molecule they can be rotational level they can be electronic level in a molecule but for a quantum system it if it is in excited state it means that it has higher energy than its ground state so if atom is in excited state or electron of that quantum mechanical system is in excited state there is a finite probability that it if another incident photon is falls on this atom or molecule or ion which is in excited state there is a finite probability that it will emit another photon of same energy and phase so this process in 1916 Einstein showed that apart from spontaneous emission and stimulated absorption there is another process that is called stimulated emission and this laser is based on the light amplification of stimulated emission of radiation in order to get to behave a molecular system or an atomic system to be as an behave as an amplifier we need population inversion if the number of atoms molecules or ion are greater in its excited state as compared to their ground state then there is a this process is called population inversion and if there is a single even a single incident photon so it act as a avalanche and we have many photons of in phase photons which are coherent and this process is the basis of as I mentioned earlier about the laser. So these are the molecular the spontaneous emission it emits a photon it absorbs a photon and it go started stimulating if a photon is incident you get two photons in phase photons. So when what are the electromagnetic radiation there are different kind of things we know that higher the frequency higher because you know it there are many different principle we explain this thing because there is a model in which we say that this electron is in excited state it is already oscillating. So when it absorbs another frequency another photon of the same frequency which is equal to the difference between these two energy level it start oscillating with twice the frequency but in photon picture we say that it emits two photon but if you are talking about in terms of wave picture then it is the amplitude of the wave that is that has increased. So you can describe light by using wave picture or by using photon picture. So electromagnetic radiation consist of photons and the energy of the photon is directly proportional to the frequency yeah I am sorry I have to come near to you yeah please. Yeah you need lot of energy no it depends upon that you want what you want to do because I will compare because molecules have different energy levels it has electronic levels vibrational level and rotational level minimum energy is required to excite by rotationally and more energy is required as compared to the rotation you need more little more energy to excited in vibrational levels and lot of energy is needed to excite electronically. So we I will give you a comparison yeah any other question okay so energy is directly proportional to frequency this is the usual concept about the Planck's law that is equal to h nu and in spectroscopy limit spectroscopy people use wave number not me so wave number is actually equal to 1 over lambda so it is a meter inverse but the most commonly used are a centimeter inverse higher the wave number higher will be energy of that photon. So this is the electromagnetic spectrum which I think I am birth though no I am I do not think but I am positive birth so showed that so this is the radio frequency radio frequencies have you can see that it is of the order of 10 raised to power 3 and its wavelength is of the order of 10 raised to power 3 and frequency in hertz is 10 raised to power as you go from radio frequency to the gamma rays frequency increases as well as the energy of photon increases if you have an x-ray photon it will have a lot more energy as compared to microwave or infrared photon. So this is the visible part of an electromagnetic spectrum which we see as color or the world we live in okay so in this is a whole range of electromagnetic but you can have interaction in microwave region infrared visible electromagnetic gamma is usually for nucleus so if interaction of radiation with matter there are different categories like he asked me the question that you have ultraviolet you have visible infrared or microwave so if you have a material and it there are levels available corresponding to microwave energy then there is a finite probability that molecule will get excited and go to the next rotational level under this microwave and if it is an infrared region and you have available energy levels and this proton corresponds to infrared will be get absorbed by that vibrational level of molecule and get excited and go to the next vibrational level if it is visible and ultraviolet region then it will the electronic transition will take place so you can see like I told you that less energy it is in the microwave region less frequencies so amount of energy is less next is the vibrational next is the electronic level so but if you have x-rays there are two process that can happen one is that is called the photo ionization that quantum energy of x-ray photons are too high to be absorbed by electronic transition in most atom so they ionize the atom and this process is called photo ionization and the second process that can take place with this x-ray interaction is the Compton scattering in this process how some part of the energy is given to an electron and it goes to an higher state and the rest of energy is given to a longer wavelength x-ray longer wavelength means it has less energy as compared to the incident energy so and the rest is to a lower energy photon Compton scattering x-ray will incident on atoms some energy will be used to ionize or photo ionize the electron and the rest of the energy can go as a longer wavelength electron yes because if it is just the ionization energy then it will take place the photo ionization if it is a Compton scattering then electron get okay so ultraviolet interaction if I go back to this picture you see that first is the photo ionization or the Compton effect if there are no energy level I forgot to mention then medium will behave as a transparent to those radiation if there is no possibility of having a microwave transition or rotational transition or vibrational transition or electron so material will be transparent to those radiation so first is the x-ray which are higher energies and they can do photo ionization and Compton scattering then we have this ultraviolet part of this electromagnetic spectrum and what they do the radiation is absorbed strongly with the surface of skin by electron okay this is a part of this medical physics that you know that they are absorbed by the electrons and they get excited ultraviolet is a process which is in the region of when electron moves from electron it is in the region of electronic transitions if you have ultraviolet or visible light photon so the transition which can happen is if possible is the electronic transition so what happens that electron can get excited from its ground level to higher level in ultraviolet and in also in the visible range so if we go here we can see that near UV radiation which is at the boundary of visible part is absorbed very strongly in the surface layer of skin if you are talking about the molecules present in our skin we get sunburns we get skin cancer if ionization process take place if it is just excited layer of the electron at higher energies ionization limit for many molecules are reached and the more dangerous photo ionization take place so it burns your skin UV always burns your skin and if ionization produced if it just only the excitation of the electron then it's sunburn if unfortunately it's ionization then there is a risk of skin cancer so I personally suffered these conditions so I added this slide I know I am I have problem of this acute photo sensitivity with the UVs and so then we have visible interaction it again corresponds to the electronic transitions so is always absorbed by electronic transition higher energies are absorbed more relative to the low energies so if we compare the visible part of electromagnetic spectrum we know that the wavelength of red light is longer and wavelength of blue light or frequency of blue light is higher so blue is higher energy as compared to red so higher energy means that red light is less strongly absorbed than blue light but we are all standing in this visible light we don't get burn we feed a bit heat but we don't get burns UV light can burn your skin it can damage very badly so absorption of visible light cause heating but no ionization so car windshields transmit visible light but absorb higher they make the windshield in such a manner that you can get some heat from the visible part of that spectrum but you can be protected from UV lights because okay so these are the infrared interactions the energy levels of infrared light corresponds to the energy required to cause molecular vibration the vibrations arises as molecular bonds are not rigid but they behave like because there is a kind of dipole moment between two due to a covalent bonding between a molecule atoms of a molecule so they stretch and they bend so there are two kinds of motions are involved and these bonds are not rigid it's not that electron one atom is here another and there is a rigid part in between so they are spring like they can bend they can stretch as molecular bands are not rigid but behave like spring so this is a symmetric stretch you can see that the both are going in this direction this is a symmetric and this is they are bending then there is a series ring and different names for these and this happened in the infrared region and it corresponds to the molecular vibrational transitions in a molecule so vibration transition are subdivided into two classes stretching symmetric and asymmetric so we see this is a symmetric stretch this is a symmetric stretch if the both molecules on this sides are moving with the same strength then it is a symmetric stretch so then there is a bending which is divided into many thing it is wiggling twisting so stretching frequencies are always higher when you are then cross bonding bending frequency it is you need less energy to bend something in as compared to to stretch something so are higher than cross bonding bending frequency it is easier to bend a bond than to stretch or compress it bonds to hydrogen have higher stretching frequency than those to heavier atom triple bonds have higher stretching frequency than cross bonding double bonds which in turn have higher frequency as compared to the single bonds so microwave interaction takes place in the region of rotational transitions of a molecule so quantum energy of molecular photon microwave photon is of the order at 10 is to power minus 5 to minus 3 electron volt matches the range of energies separating quantum states of molecular rotation so like electronic and vibrational transition rotational motion of molecule is also quantized it is a quantum mechanical system so absorption of microwave radiation cause heating due to increased molecular rotational activity so if the rotational is increased we all all see this thing happening in our life daily because we all use microwave amongst at our home so the food we want to heat contains water so when the microwave high-intensity microwaves are produced they start this rotational motion and in this way the food get warm or cooked so they use high-intensity microwaves to heat materials so there are it is only possible when there this molecular rotation is present and this kind of transition yeah no vibrational also created this kind of sunburns and these kind of things vibrational ultraviolet interactions they also creating heating oh yes yeah because if you see the electron the higher energy ionization many molecules are a more dangerous photo ionization occurs sunburn is basically when happens when it get burns and vibrational vibrational yeah so rotational also but it is in the microwave region and we know that microwave energy microwaves are not higher energy waves so it but their process how they transmit the energy they gain from that microwaves is by the rotational by increasing the rotational motion of the food you are cooking or you food you want to heat so it only microwaves are absorbed by the rotational levels of molecule whether it is a part of our skin or whether it is a part of a food or whether it is a part of a drink the coffee mug or anything you put in it is only the microwave will be absorbed if because they are quantum systems the absorption will only take place if there are two levels in between that microwave can be make transition from the lower rotational level to higher rotational level okay so these are the this is just a schematic that we have these blue lines shows the ground state electronic state then this blue is first excited state then these green ones are vibrational energy levels so basically an electronic state host a number of vibrational levels then on each vibrational level there is a set of rotational levels so this is how after starting the spectrum of many molecules compounds they assemble this data the tradition can be absorbed or emitted if the molecule changes any of its energy state so if you have an object you if you are not precise you know that there is a possibility you can excite this molecular object in vibrational level so you will provide the same energy if it is infrared its uv or it is in the visible part and if you know that the your source is producing visible light and you will get electronic transition if there are other kinds of frequencies involved that can be this infrared it can be microwave then there is a finite probability you will get some excitations in rotational level and some excitations in the vibrational level of molecule so these are the rotational levels these the first from their ground state of rotational level to excite is called the fundamental mode similarly in vibrational that is the fundamental mode in electronic transition this is the ground state and this is the first excited state I think I have a better like you said that you need it is the wave number it is given in the wave number the rotational transition is less than vibrational the energy required to do this rotational transition is less than the energy required to do vibrational transition and that is less than 2 energy required to do sorry why because there is a lot of separation between electronic level. So, you need a lot of because e 2 minus e 1 is too high as compared to the vibrational and rotational levels. So, these are the molecular energy level again the vibrational transition so the same thing the number on this figure and absorption spectrum of a molecule is that the molecule is determined by all allowed transition of course, if you want to see like I was telling you that if you shine a molecular object with if you do it with a known kind of radiation you know that you are using visible part of electromagnetic spectrum or infrared or ultraviolet or microwave region. So, you know that what kind of results you expect which frequencies will be absorbed and which will remain so you can measure your spectrum absorption spectrum and emission spectrum and then you can calculate the data. So, if it is so this is actually the electronic brown state this is the first excited state energy increases in this direction. So, these are the vibrational level we represent them with the number nu or v and the rotation is represented by this J angular momentum. So, this is the vibrational quantum number this is the rotational quantum number. So, if you see molecular motion is governed by quantum mechanics molecules like atom like electrons or quantum mechanical system apart from their translation motion of those molecule all other energies are quantized whether it is an electronic energy vibrational energy or rotational energy. So, it is a quantum mechanical system. So, chemical bonds like covalent bond can act like a spring and can display simple harmonic motion like I showed you in a cartoon. So, they do stretching bending. So, these are like spring they are quantized these vibrations are quantized to because and these are quantized like harmonic oscillator. So, and you all know that a harmonic oscillator is the simplest quantum mechanical system with an energy that is equal to h ket omega with n plus half and that half h ket omega energy is 0 point energy which is present in each mode. Similarly, in each mode of this vibrational motion there is a 0 point energy. So, let us go here. So, chemical so energy due to vibrations are quantized. So, h ket omega v is the vibrational quantum number for harmonic oscillator you put here the number state or n which is the number of photons. So, vibrational quantum number is from 0 1 to 3 it is angular frequency is the spring constant and the effective mass of the atoms involved. If it is a diatomic atom you will have m 1 plus m 2 divided by this thing. So, an effective spring constant k for bond involved and effective mass I explained. So, half h ket omega comes from the quantum mechanics and represents 0 point energy do you know about 0 point energy? What is the 0 point energy? You know about vacuum fluctuations. So, what are the vacuum fluctuations? But he gave a right answer and what he is saying is when we quantized the electromagnetic field usually we all study the classical description of electromagnetic field which is given by the Maxwell's equation. When we quantize there are certain things which are not explained in the classical picture of electromagnetic radiations. So, we need to quantize we quantized electromagnetic field on the basis of harmonic oscillator we associate each mode of an harmonic oscillator with one frequency of an electromagnetic field. So, when you quantize you see that ground state energy is not equal to 0. We know we live in classical world we know that if there is a vacuum the energy of the vacuum is equal to 0. Classically this vacuum is described as something which has no energy, but quantum mechanically vacuum is not empty. Each there is a half cut half h ket omega omega cross bonds to it can be microwave it can be visible infrared ultraviolet gamma. So, half h ket omega energy is always present in quantum mechanical vacuum and it is and if we take into account that 0 point energy many theories becomes correct and the things which were not explained using this classical theory of electromagnetic radiation. For example, the spontaneous emission we used to say okay the atomic lifetime is 10 raise to power minus 8 after that it decades spontaneously no. These are the vacuum fluctuation which cause that push that atom in excited state to make a downward transition. So, these vacuum fluctuations are responsible for many phenomena which we can observe experimentally, but according to the Dirac theory we were not able to explain them. So, half h ket omega is a lot of energy and that is called the 0 point energy and that we get from the quantization of electromagnetic. So, it cannot be harvested or extracted its energy is there this half h ket omega is always present there still exist at absolute 0 it is even at the 0 temperature all molecules are in even if all the molecules are v is equal to 0 state, but this energy is yeah please yeah sure yeah that is half yeah n is equal to 0 is equal to this half right, but that is the way to how to calculate the energy. But the main thing is that you start with the actually the you start with the energy of an harmonic oscillator its kinetic energy plus its potential energy. Then you quantized your electric field or in magnetic field in quantization this electric field is also an operator which is given by a plus a dagger something if it is a kind of thing it is the special function similarly B is also a operators. So, what you are saying is the quantized and Hamiltonian is equal to h ket omega n plus half and even if n is equal to 0 n represents the Fox state or the number state even if we are in vacuum. So, then vacuum state is represented like this we still have ground state energy that will be equal to half h ket omega yeah. So, this is a lot of energy corresponding to each frequency. So, this energy level and we all know the energy levels of harmonic oscillator are separated by omega sorry sorry yeah yeah because look there are if I mean if I give you an example there is lamp shift if you are from spectroscopy everybody knows about lamp shift. This is the energy difference between 2 s half and 2 p half according to drug theory if we calculate experimentally observed shift is 1057 megahertz right. So, it is near to between the energy difference between 2 s half and 2 p half of hydrogen atom is and it is observed. No, no, but it is not the vacuum energy is there it is you are not going to measure it you are not going to extract it it is there because in actual sense your vacuum is not empty. In actual description of vacuum you do not have to if you are created a very class grade 1 vacuum broom or clean broom still your vacuum is not empty it has energy it is there, but there are certain quantities we can calculate by using classical theory of electromagnetism and it agrees with experimentally observation. So, but like for example, I give you a spectroscopic example the 2 s half and 2 p half if you calculate in theory. So, you will get that they have same energy, but experimentally if you measure the energy difference between 2 s half and 2 p half it is 1057 megahertz frequency difference and that agrees with the quantum theory. If you take into account the zero point energy then your theory matches the experiment. Why we need quantum mechanics if classical mechanics was enough because there are certain things we cannot explain using the classical mechanics. So, we need, but we did not discarded classical mechanics as we started using of course, you cannot describe the motion of a car or a bus or airplane by using quantum mechanics you need classical mechanics. So, there are different regimes. So, vacuum classical it is empty quantum mechanically it is not empty in reality it is not empty it has energy. So, that energy cause many things are you satisfied with? So, this is so diatomic molecule this is the effective mass as I mentioned you can multiply and divide with the sum. So, energy scale for molecular vibration is much less than that for electronic transitions excitation energies correspond to the our region of the electromagnetic these are about vibrational transition in a molecule. So, a vibration levels are built on electronic state each electronic state will host the whole range of a vibrational levels. So, this is a kind of picture you can see that this is a fundamental IR transition which is between 0 to 1 these are all the vibrational level this first one is the electron n is equal to 1, n is the principal quantum number, n is equal to 2 is the principal quantum number it is the first excited state and these are the fundamental IR transition. So, you can make transitions from here to here by visible radiations you can make transitions by using IR radiation between these vibrational levels because they are separated by an energy range which corresponds to the IR spectrum of electromagnetic radiation. If you need to excite between vibrational levels you have to use IR radiation if you need to excite between electronic levels you need visible or ultraviolet. So, this is again the repetition of molecular levels you can see these are the diatomic which can be N2 oxygen or CO. So, they it is a symmetric this thing these are the linear atomic molecule CO2 is the linear molecule this is a symmetric stretch that they move in opposite direction this is bending they are bending like this and this is an asymmetric stretch that this moves toward this this moves away and this the center one moves this thing. So, there can be many possibilities in a molecule there are many complicated we will see in DNA structure and RNA structure that those molecules are quite complicated they do not follow these simple kind of vibrational modes. The now the rotational rotational energy of molecule is again quantized. So, it is its energy is given by this which is J is the angular momentum given like this. So, this is the moment of inertia. So, it is rotating with this thing. So, you know how the angular momentum is related with moment of inertia and the angular velocity those all formula came from that is a moment hence rotational parameter can be different for each rotation axis. So, this is also quantized this is a quantum number which is given here. So, this is an integral number. So, these energies which cross bonds to the rotation of a molecular transition is also quantized. So, excitation energy and cross bonds to the microwave region we saw before that if we shine a molecular molecule with microwave energy then what will happen if there is a possibility of transition between rotational level then it will take place. So, energy scale for rotation is much less than vibrational and for vibrational it is much less than electronic transition. Each vibrational level has rotational bands built on it and selection rule is plus minus 1 these are the rotational levels. So, if you compare this picture with the previous of this kind you can see that here this is visible radiation which means the transition can take place between one electronic states to another electronic state yeah. Non a pi and sigma are two kinds of bonding covalential bonding one is called pi. So, this is I took it from some website. So, this is what sigma also and it can be pi anti orbit if it is anti orbital then it can be is steric on pi and sigma there are different kind of bonding. So, this is a visible radiation and here you can see between these consecutive vibrational mode you need IR radiation if you go to this cartoon. So, you can see these are IR radiation now these are vibrational levels these this side you have vibrational levels and in order to go from one vibrational level to another vibrational level the part of electromagnetic spectrum you need is in IRR region and for rotational you need microwave radiations. So, if you want to go from 0 to 1 which is the fundamental of vibrational mode you need to shine this molecule with the microwave. Sorry yeah more or less here that is for vibration not the electronic yeah and for this one it depends on you can see that it depends on H cut it is also quantized it depends on this J and J plus 1 and it is also quantized this is the moment of inertia because we know that if there is a kind of router or something or a kind of gyroscope you know what is its moment of inertia and what is the angular velocity and you relate these things with this. So, in case of rotational motion the molecules is also doing the same kind of thing like a gyroscope doer. So, this is this energy is also quantized, but this energy lies in the range of microwave part of electromagnetic spectrum for vibrational it lies in IR region for electronic it lies in ultraviolet and visible part for photo ionization it lies in x-rays. So, there are different parts of electromagnetic spectrum and each does a different kind of transition. So, this is they are divided into P, Q and R branches depending upon the selection rule if delta J is equal to minus 1 that means that if it goes from this rotational level of higher J value to lower J value because selection rule delta J is equal to plus minus 1 is allowed. So, and delta J equals to 0 means there is this is not a rotational motion it is only the vibrational transition because if delta J is equal to 0 that means you are going from J is equal to 1 to J is equal to 1 or J is equal to 2 to J is equal to 2 and actually you are changing from one vibrational level to other. So, this branch corresponds to pure vibration and this is when the J value is less. So, you can see here that this is the vibration if you it is only possible if you go from 1 to 1 that you are changing vibrational levels otherwise from here you go from plus and minus. So, these are called P branches if delta J is moving from J is equal to 2 of this vibrational level to J is equal to 1 you will get minus 1. So, if it is going from J is equal to 2 to J is equal to 3 in this range then you get plus 1. So, delta J plus minus 1 is the selection rule and delta J equals to 0 to corresponds to the vibrational transitions. In molecule we have two opposing force the repelling force of nuclei when there are atoms and their nuclei nucleus repel each other and the binding force of the electrons towards the nucleus. If the orbit of electron change then the binding force will change the net potential energy of the that is net potential energy of the if you excite an electron from this level to this level of course, now the potential energy is changed. You know how what is the Coulomb's potential between nucleus and if we consider the example of hydrogen atom which consists of a single proton and an electron orbiting around that nucleus. So, what is the scale of energy between electron and proton in a hydrogen atom? Inverse square law it obeys the. So, this means the inner atomic distance will change different electronic level will have different rotational and vibrational constants. So, if you draw all these kind of. So, taking rotation vibration excitation you need these all energies you have to add rotational vibrational and electronic and everything is quantized. So, complex molecule may have many vibration like you asked before. So, there it is easy to say in theory, but in reality these molecules are quite complicated. So, may have many vibrational modes rotational mode in the combination of these different modes lead to the smearing of discrete spectrum. So, the broad bumps appear rather than discrete lines it is hard to distinguish between the lines because there is an overlapping and I think it is the next cartoon. It is a kind of this is a simple or a linear symmetric molecule and this is for a complex molecule. You can see if E is the electronic transition. So, this is E 1 or E 2 or you can say this is cross bonds to N is equal to 1 level this cross bonds to N is equal to 2 level. So, these blue ones are vibrational modes of this level and these red ones are rotational level of these that host on this vibrational level. So, the sum of energy for a simple or symmetric molecule can be a discrete some of these discrete bands which you can distinguish that it is the sum of this it is the sum of all these kind of. But for asymmetric or complex molecules these energies are different these vibrational energies can be different. So, if you take you can see that here we have very narrow spacing here there is a very narrow spacing between these two. So, then you can get a different there you can find a broad band instead of discrete lines. So, it there is a molecule spectrum can change for a simple molecule to a complex molecule. So, ignoring electronic the total energy of the molecule yeah black line is electronically N is equal to we will go into the fluorescence tomorrow. But these are two electronic level that can be the ground level and N is equal to 1 or N is equal to 2 level with the principal quantum number. If electron is making transition between these two electronic level it needs this much energy to be absorbed. So, that electron can make transition from here to here. These are very symmetric vibrational level in case every level has a h cut omega spacing they are because there is nothing to this is a kind of simple molecule and then there is a very symmetric vibrational level host on rotational level on this vibration. So, if you see the spectrum absorption spectrum or the emission spectrum of a simple molecule you can get a symmetric pattern it absorbs symmetrically it emits symmetrically because there are in the presence of an sorry you will. So, but if you have a complex molecule because these kind of bondings between covalent bonding between a complex molecule ionic bonding between a. So, they will affect these if molecule is consist of group of atoms. So, they affect the orb molecular orbits in different manner. So, now this e 1 and 2 are they are different they are their spacing is different they are not symmetric like this one. So, when you get a spectrum. So, you can identify this is a complex molecule they affect their electronic vibrational and rotational level I hope that I satisfied you yeah. Look you know I am not an experimentalist, but I know that if you shine object or element you know what kind of frequencies now they are books available that this line corresponds to this emission or absorption this you can compare yeah. So, in a simple way yeah I think that we I know that this is water I have this is a pure water according to me or this is somebody told me oh this is mineral pure water I know its emission and absorption spectrum that we have of course, we it is not the beginning of the world that I do not know the spectrum or absorption or emission of this water and I know what is present in the water. So, if I see I can compare a new object or new material or compound I take a emission and absorption spectrum of that new compound or something there must be I have some idea about it contains nitrogen it contains hydrogen it contains this or that because there are I think there are signature lines of each yeah. So, you can compare and you have an idea then the different thing I am sorry let me so, I think according to I am not very good in this thing, but according to me that due to rotational and vibrational level in a compound a symmetric and asymmetric stretch can change few things. So, I know that is a kind of signature. So, you know okay something you mixed in it okay yeah okay how I will refer to Amberto because he is spectroscopist. So, tell me how you differentiate between two lines whether it is rotational because first is the energy corresponding energy. If that line lies in visible region of its range of frequency or it is absorbed in the visible part of electromagnetic spectrum I know that it will be electronic transition. If it is in the microwave region of that because I know the frequency of microwave region its limits its boundary if line lies there it means it was a micro yeah okay if there is no shop order yeah please. But I think according to me which I understand is it should be if there is only the rotational transition it should lie in the microwave region of that electromagnetic part. So, you know that this emission line or this the part which is absorbed by this electromagnetic spectrum which is missing is in microwave region and of course, for complicated when there will be a microwave absorption there will be infrared absorption there will be but I am sure in this period we live in there are many datas because I saw in my university because I know my professor he used to compare everything okay these lines are this these lines are this yeah yeah now there are very bad yeah yeah because this data I I never worked in a spectroscopy lab but I saw one of my friend has a they have so big huge books or all the time they may have something and then they are comparing with that and then they also I saw that they fit it okay this is the curve fitting this is this line to a good approximation this is how I think things evolve and it is now okay so these are vibrational and rotational so the wave number spectrum line is given by the term value of the two states you can calculate the spectrum line by the difference of the term value of the two states you can calculate that a change in vibrational quantum the number V is accompanied by a change in rotational limit according to the selection rule this thing because if 0 as I mentioned earlier delta j is equal to 0 it is a change in vibrational level okay so the complete set of rotational transition between two is known as a band and these are we have we have q branch r branch and the p branch as I showed you before there is that okay these are it's a change of vibrational level but r branch and p branch is for a delta j minus one and r branch is for delta j plus one okay i'm done so we will yeah please we will do politics tomorrow questions yeah questions comments yeah please