 So as we're beginning to understand what happens for infrared spectroscopy for polyatomic molecules, let's consider another example, still a triatomic molecule, H2O, a molecule with three atoms, but unlike CO2, H2O is a nonlinear molecule. So if we want to know what the infrared spectrum looks like, and I can show you what that looks like over here if I pull up the spectrum for water, it again has the same qualitative features as we've seen for diatomic molecules. The general shape of these bands is a central fundamental vibrational frequency, plus some or minus some smaller amounts for the rotational energy. And we see that there's two separate bands here. One thing we notice is that these peaks have now gotten a little bit messier, not quite as clear and well-defined as they were for diatomic molecules. In order to understand what those peaks come from, we can again count the number of degrees of freedom for translational, rotational, vibrational motion. It's still a triatomic molecule, so we should still have nine degrees of freedom total, three of which are translational, but because this is a nonlinear molecule, the molecule can rotate around the z-axis or around the x-axis or in fact around the y-axis. There's three different ways that it can rotate, and that leaves three vibrational modes in order to add up to nine. So unlike a linear molecule, this nonlinear water molecule only has three vibrational motions rather than four. If we categorize what those vibrational motions are, there's again a symmetric stretch, an asymmetric stretch, and a bending mode. The difference with a linear triatomic molecule being now there's only one distinct bending mode. If we draw cartoons of what these look like, the symmetric stretch involves lengthening the two OH bonds at the same time, the oxygen will have to move down slightly to keep the center of mass where it is. The asymmetric stretch is going to involve lengthening one of them and shortening the other. So if I lengthen this hydrogen at the same time as I shorten this hydrogen, the hydrogens in general have moved to the right, so the oxygen is going to have to move to the left to keep the center of mass stationary, so that's going to involve shortening this bond while I lengthen that bond. And then the bending motion is going to involve the hydrogens moving towards each other and the oxygen moving slightly to keep the center of mass fixed. So that's a description of the three different vibrational modes for water. If I tell you what the frequencies are, we can give these numbers. Traditionally we call this symmetric stretch mode number one, the bending mode is mode number two, and the asymmetric stretch is mode number three. In wave numbers the vibrational frequencies are 3657 wave numbers for the symmetric stretch. That's a relatively high frequency because the hydrogens are so light, the reduced mass is very small, so that makes the vibrational frequencies relatively high. The asymmetric stretch also involves hydrogen motion, so it's also a very high vibrational frequency, 3756 wave numbers, and the bending motion, 1595 wave numbers. So if we use that information to try to interpret this spectrum, what we see is that 1595 is roughly here, so this band comes from the bending motion, which we've called nu sub two. 3650 and 3750 are close enough to each other that they're both buried inside this band over here, so both nu three and nu one are centered at roughly the same place. So I have one band of vibrational peaks centered roughly here, one band shifted slightly a little bit, so those two bands overlapping each other make this portion of the spectrum a little less obviously this double peaked vibrational band shape that we got used to for diatomic molecules, and that's part of the reason this spectrum is a little bit more messy and more complicated than it is for a diatomic. And it brings up this point that relatively commonly there might be an overlap between two different vibrational frequencies which are not exactly the same, they differ by as much as a hundred wave numbers, but the width of these bands is also measured in several hundred wave numbers, so overlapping these two peaks makes them more complicated. So that's helped us understand a little bit about the details of the water infrared spectrum. Things, water itself will get even more interesting when we consider not just the vibrational peaks but also the effect of some non-idealities when we start to include details like the overtones of these particular peaks. So that's what we'll look at next.