 Okay, so at the level that we can understand infrared spectroscopy, it turns out we can answer a pretty fundamental question about water, namely why water is blue. So I can hear some of you telling me that water is not blue. You might be drinking water out of a bottle at your elbow or have recently poured water out of the tap and you'll tell me that water is clear, not blue, but it depends how much water you're looking at when you ask whether water has a color or not. So if I bring up some illustrations just to be able to talk about the color of water, these pictures will show us that depending on how much water we're talking about the color in fact does change. A small amount of water like a glass of water does look clear, hopefully, if your water is good quality. But if you have enough water to fill a bathtub, it begins to take on a slightly bluish tint and a swimming pool has enough water to really begin to look blue and of course the ocean isn't clear at all. It's quite blue, at least if you're in an area where there's not much muddy sediment clouding up the water. So water is in fact blue in large quantities, although it looks clear at smaller quantities. And the reason for this boils down to the details of the infrared spectrum. So if I take these pictures away and put up the infrared spectrum for water, we've already seen that water absorbs light at several different frequencies, at bands which are roughly 3650 wave numbers, 3657 for the symmetric stretch, 1595 inverse centimeters for the bending mode, and 3756 inverse centimeters for the asymmetric stretch. Just as a reminder, symmetric stretch, bending mode, asymmetric stretch. We've seen the bending mode absorbs around here, so this absorption is nu sub two, here's nu sub one and nu sub three, a little above 3500 wave numbers. These peaks, however, water also absorbs at frequencies of 5000 in some wave numbers, a little above 7000 wave numbers. And what those are, are the overtones. Water can, in addition to these fundamental vibrational frequencies, because water, the vibrational modes in water are not perfectly harmonic, and harmonicity means the selection rules that we derive from the harmonic oscillator don't perfectly apply. So the absorption is a little weaker, but the molecule can absorb light at frequencies of nu, not nu three, but nu one and nu two combined, nu three and nu two combined. What that means is the molecule is simultaneously increasing by one quantum number in its symmetric stretch and by one quantum number in its bend. It's exciting both of those motions at the same time. That costs an amount of energy equivalent to the energy of the bending mode plus the energy of the stretching mode, whichever vibrational mode nu one or nu three is being increased. So that 1500 plus about 3500 adds up to a little above 5000 wave numbers. So this would be the overtones associated with combining these two frequencies. Can also absorb at twice the symmetric stretch frequency or twice the asymmetric stretch frequency. So that would be these peaks over here, which are about twice the energy of the peaks at 3500. Those peaks are weaker because although these overtones don't technically violate the selection rules because the vibrational motions are anharmonic, they're still weaker than the fundamental vibrational modes. What that means is further overtones further out at higher frequencies also absorb a little bit of light. So if I replace this spectrum with one at a wider range of frequencies and the other thing I've done here is I've changed from a linear scale to a log scale. So again we see if I label these, this is the nu two peak. The second peak is either nu one or nu three, symmetric or anti-symmetric stretches. Those are the ones that are about 3500 wave numbers or so. Here's a non-ideal overtone, nu one plus nu two or nu three plus nu two. The ones that are double the symmetric and anti-symmetric stretch, that's this collection of peaks here, twice nu one or twice nu three. Those are at a little above 7000 wave numbers. On the log scale, notice on the log scale each line on the scale is decreasing by a factor of 100. So these next few peaks that we can talk about, those are roughly 100 times weaker in intensity than the fundamental vibrational peaks. So those are beginning to be quite minor peaks. But those would be, we won't label them all, but this one here, those would be the second overtones for the symmetric and anti-symmetric stretch that show up at three times the fundamental vibrational frequency. Here we've got four times the fundamental vibrational frequencies for the symmetric and anti-symmetric stretch and so on. So there's overtones all the way out, the higher the overtone, the less intense the peak is. So by the time we're out here, we're absorbing light with an intensity of maybe one millionth the intensity of the fundamental vibrational frequencies. So what that means is water is pretty good at absorbing infrared light. As I move to higher and higher frequencies, however, toward the visible portion of the spectrum, it gets less good at absorbing that light. The intensity is smaller. In fact, if I overlay on this graph the wavelengths or colors of the visible portion of the spectrum, you can see that by the time we get up to a little above 14,000 wave numbers or so, we've entered the visible portion of the spectrum. So there is some, in this region, there isn't in fact some weak absorption in the red, the orange, into the yellow, even a little bit of the green parts of the spectrum are being absorbed by water not from its fundamental vibrational frequencies, but from these weakly absorbing fourth, fifth, sixth overtone frequencies. So what that means is if I have a large enough body of water that the photon can pass through quite a bit of the water, some of those photons, a small number of those photons will be absorbed. But if I pass through enough molecules to eventually absorb most of the red, orange, yellow, green parts of the spectrum, then the part of the light that's left over after that absorption is blue. The overtones, there are no overtones or at least none with any significant absorption out beyond the blue portion of the spectrum. So the reason water looks blue, even though water should only be absorbing in the infrared, if it's a harmonic oscillator, is because the bonds are not perfectly harmonic. That non-ideality, that anharmonicity, causes the overtones to weakly absorb in the red side of the visible spectrum. So it turns out the spectroscopy of water is quite complex, but it gives rise to this perfectly ordinary everyday phenomenon. This spectrum is complicated enough already, even for a triatomic molecule like water. As we move on to larger, more polyatomic molecules, we'll see that the spectrum gets more complicated still, and that's what we'll do next.