Alright. So let's talk more about this harmonic oscillator. And I'm going to skip [COUGH] fairly quickly through this, when you're talking about the vibrations of atoms, you have to invoke quantum mechanics, because just, atoms are small, and they need to be treated using quantum mechanics. And you can work out what quantum mechanics means it the classic, we'll call it classical system, you can actually be able to have any energy for that bond. You should be able to stretch it out, sort of diatomic stretch it out, and have any value of the energy. But what quantum mechanics tells us is that's not allowed, and you only have discrete energies. So, what quantum mechanics does is it gets you the energy for these. So this is all you need to remember, that the energy for each of the levels in this diatomic oscillator when you treat it quantum mechanically is Ev is equal to (v + 1/2)hv, all right? That's the energy that comes out. This is when you solve equation for this system, these are the energies that come out. Where v is entry value zero, one, two, three, and so forth. All right. That's all you need to know about that. And then, another thing about spectroscopy is that you have selection rules. And you can only have selection rules, you can only have changes delta v going from plus or minus one. So usually we have absorption. So you can have that going to that. That's allowed. And this one going to two is allowed. But you can't have say zero going to two. It's not allowed. So what this means then is that you have this, kind of a ladder of energy levels. And you have, if you work out the distance between these, is pretty much all the all the same. If you could get transition between these levels, different levels, then you'd just get a line in the same place. But again, you don't need to really get too involved in this. Usually molecules exist mainly In the lowest vibrational state. So you're just mainly talking about, what kind of spectroscopy we're talking about, you're talking about transitions from the ground state, vehicle zero to V equals one. Right, okay. So, you have a molecule and so you have a gap. You have the correct gap. What determines whether that molecule will absorb the infrared radiation? Now you might think if we talk about spectrocity of the ground stage and you have the excited stage, first excited stage. And then if the energy comes along and it's the same energy, you would predict that you would get a transition from the ground stage to the excited state if the energy is matched that is one condition. But there is also another condition of vibration spectroscopy and that you must have what you call an oscillating dipole, or a change in the dipole moment of the molecule before it's absorbed the infrared radiation. So, this comes from the fact, if we go back to the first lecture, we had a, in we showed the electro-magnetic field, and it was an oscillating electric field, and then perpendicular to it you had a magnetic field, so you had an oscillating electric field so the molecule won't absorb it. In addition to having the right energy gap, unless it has an oscillating electric field as well. And this, we'll see in a minute, this oscillating electric field in vibrations can occur from what we call a change in the dipole moment. So the basic fact is that If the mode, the vibration mode of the molecule doesn't involve a change in a dipole of the molecule, it won't absorb any infrared radiation, so you won't see an infrared band for that vibration. If it has to change in the dipole moment, then it will absorb it. So the photon, well, we'll cover that. So heteronuclear diatomics, when we're talking about heteronuclear diatomics, I'm talking about H CL. And you know that Cl is more electronegative than the hydrogen, so it'll pull the electron density towards it. So, when you stretch that molecule, you change the dipole. But because the dipole is the product of the charge by the distance apart, so if you change the distance, you'll change the dipole. And this then generates what we call an oscillating electric field. So that, when the electromagnetic radiation comes in, it can interact with the molecule, and it'll absorb that energy. So here is just an example of a diatomic like a heteronuclear molecule like HCL, so you got delta plus and delta minus, and then you stretch it out, so you change the dipole or if you compress the bond, like we show here, you change the dipole as well. Because the dipole, as I say, as opposed to a charge might have just slightly changed distance. Then you're going to change at dipole. So when the HCl molecule stretches, it creates an oscillating dipole. Electromagnet frequency in the infrared region comes in and they can absorb it. It won't absorb it, as we see in other molecules, if it hasn't got an oscillating that. So, what I'm saying here, the infrared and all if you like all, homonuclear diatomics. And that where you have two atoms that are the same. So you have hydrogen, nitrogen, and chlorine. So they don't have a dipole mole. You should know that doctrine. You have two molecules. Hydrogen, there's no dipole moment in hydrogen. You do have the same electronegativity. They both share the electron density equally. So therefore you will not observe any infrared spectrum for these types of molecules. Okay, they vibrate in the infrared range. So they have a frequency gap that should be excited. But because they haven't got an oscillating dipole, they won't absorb that. And just here, information that you have to use another technique of measures of vibrations called RAMAN spectroscopy, which we're not going to get into here. And with diatomic software what you've got more complex molecules. Then, remember at the start, we have, addition to stretching, we have different types of stretches, we call sometric, asometric stretches. We have bending, vibrations, and so forth. And what you'll find is, that you have many modes, call these bending and stretching, modes, and they're IR inactive, and the reason they're IR inactive, IR inactive means they don't absorb the infrared frequency. These molds haven't got a dipole change. So, the example, simplest example is CO, and in CO, what we call a symmetric stretch, and here you have the carbon, here you have the two oxygens. And you can see here that I've got CO has or sorry, CO2. This is C, this is O, CO2 here. It's got what we call a symmetric stretch and for a CO2 molecule, you have one dipole this way and you have another dipole this way. So they actually cancel. So it hasn't got a dipole moment, and when you update call a symmetric stretch, when you stretch the two bonds the same side the same way and then let them go back again, the two dipoles still cancel each other. Because they stay the same distance apart for that stretch. And what you saw was that that's inactive, that particular vibrational mode for CO2 is inactive. But you have another stretch, which is called an asymmetric stretch, which means it's not symmetric. And in this case, here you have, again, your equilibrium CO2 molecule. It hasn't got any dipole movement, but now what happens to this one is one of the bonds stretches while the other one compresses. So what's going to happen during this stretch, you can see that this dipole moment now, this one, because this one definitely is going to be different. So the stretch will involve a change in the dipole moment. And because you have a change in the dipole moment for that particular mode, then it becomes active. So you will observe an infrared band for that particular molecule. So that's the idea. So if you want to do more complex molecules then when you're talking about analyzing infrared spectrum. You need to be aware of this. Okay, so here we have, moving on to now more complex cases, here you have the water molecule. And the water molecule has three vibrational modes. And you can see, it's more accomplished. You're moving away from just the diatomics with just one stretch. And here we call the symmetric stretch, and the symmetric stretch is where the two bonds, you can see the two bond lengths are increasing by the sudden mass symetric system, and here you have the wiggle one, the isometric stretch, where one end is stretching and the other end is shorting. That's a isometric stretch. And then what we've got here, there's a bending mode. You can see the molecule is bending between its increase in the HOH angle. So all of these are active, because they all involve a change in the dipole moment. And you can see one thing just to pick up here, we'll talk about this later on, is that the stretchers are quite high in frequency or high in wave number. Whereas the bend is lower, and that's just again common sense. Because you think you're trying to stretch something, it's more difficult to stretch something down, so you have a rod or something you can stretch it out, a rubber band. It's much more difficult to do that than it is to bend. The bending mode is easier to do, so it's got a lower energy dot. Okay, so them other modes of, right. So, what we did there we showed for. >> [COUGH] >> We showed for water, that we showed just three vibrational modes, three ways in which it can vibrate. And what we come on to hear is that, that's a non-linear molecule. So the number of modes a non-linear molecule has vibrational modes is minus three and minus six. So if you got three atoms of water, you've got three by three minus six, so that's going to give you three. So you have just three vibrational modes. If it's a linear molecule, it's 3n-5. So when you have CO2, that's a linear molecule, you would get three by three minus five, so you get four for that. Okay. CH4, another molecule, n is equal to five, so the number five rational mode is non-linear. Is three by five minus six, this minus six here refers to you have other movements of the atoms like translations and rotations. You have three translations and three rotations, so they make up six for a non-linear molecule, whereas in a linear molecule you only have two degrees of rotational freedom. And what this all comes back to for the molecules that we're interested is that IR spectra can be very complex. We've talked about the simple diatomics developed theory, but they can get very complex. So if you have a big molecule like this, just a big fullerene, as a typical one. So, let's see, 60, so the 60 atoms, so there's 174 in total between minus 6 or the 174 vibrational mode for that. So what it means is as you get onto complex molecules, to be able to assign each band, then you have to remember that some of them will be active, some of them will be inactive. So the whole idea from a sign spectrum for infrared gets quite complex and difficult.