 If you look up at the sky you'll notice that it's blue, although at sunset and sunrise that tends to turn a bit more orange. That brightness and colour is sunlight, but it's white that's been scattered, it's flown over us, hit the molecules in the atmosphere and then bounce back down again. Now this is due to something called Rayleigh scattering or Elastic scattering, and it's a slightly different concept to what we've discussed previously which is all about absorption. So it's known as Rayleigh scattering after Lord Rayleigh, who did a lot of work in the 19th century on this sort of phenomena, and Elastic scattering because the energy is conserved after that bounce. The frequency or wavelength of light doesn't change. But some molecules do interact with that light and do change its wavelength, and that forms the basis of the next topic we're going to discuss, which is Raman spectroscopy. Raman spectroscopy is named after Nobel Prize winning Indian physicist Chandra Shakara Raman. Recall that in absorption infrared spectroscopy, the dipole of the molecule must change during the vibration. This leaves some vibrations and even some molecules completely silent in IR spectroscopy. We just don't see a transition. In Raman spectroscopy, the gross selection rule is that polarizability must change. And generally speaking, for molecules with centres of symmetry, this means that any vibration that is invisible in infrared absorption is visible in Raman, and any vibration that isn't visible in Raman is visible in absorption. Polarizability is something you may not have come across before, but it's a measure of how polarisable a molecule is, or in overly simplistic words, how squishy the molecule's electron cloud is. Now, that can be a little bit difficult to understand or visualise for more complicated molecules, but it should make a bit of sense for, say, a really simplistic, homonuclear diatomic molecule. Now, these should not be infrared active. No matter how long this bond is, no matter how much it vibrates, the electrons are experiencing identical poles in each direction. But how easy it is to move the electrons within that will change. An electron in the middle, for instance, will be more easily pulled apart when the bond is long, but more closely attached to both when the bond is short. So, further away from the nuclear eye at longer wavelengths, this electron can be pushed around a lot more easily. We can quantify polarisability, how easily the electrons can be pushed around, as a proportionality constant that relates to the strength of the electric field that's applied to the molecule and the strength of the dipole moment that's produced. Of course, the electric field from light oscillates, so we can replace E with a time-dependent sine wave. And if polarisability also changes with the frequency of a vibration, we can also replace that term with a time-dependent version. Putting these two together and with a little mathematical transformation gives us a dipole that consists of three terms. One where the energy isn't modified, which corresponds to elastic Rayleigh scattering, and two where the energy increases or decreases, called stokes or anti-stokes scattering. That maths isn't essential to memorise, but it is nice to see the theory and the practice line up nicely because that part of the equation that isn't modified is the Rayleigh scattering that we see in the sky because that's elastic, it hasn't modified the energy at all the energy has been conserved. The quantum mechanical interpretation of this effect involves electronic excitation to any arbitrarily high energy level. In a spectroscopic context, this is usually done with a laser. If the molecule decays back to the ground state by emitting a photon, the photon will be of the same energy but released in any direction, therefore scattered. But the molecule doesn't need to decay back to the ground state or even start at the ground state. Therefore, these emitted or scattered photons will differ from the incoming light by a fixed amount. If we measured the scattered photons, we would find a strong central band representing the elastic Rayleigh scattering and side bands corresponding to stokes and anti-stokes scattering. These frequencies have been altered by vibrational modes that we can't always see in absorption spectroscopy. That's all there is to say on the theory of Raman spectroscopy right now. There is also a rotational analog that will affect molecules that don't have that permanent dipole required for a rotational spectrum to work. But that's a rarer technique. It's not in use very much now, so we're going to skip it. Just remember the basics. If there is a dipole that changes during a vibration, that's going to be active in the infrared. But that polarising ability change during a vibration, that can be picked up by a Raman spectrum through light scattering. And through a combination of both infrared and Raman, we can begin to see all of the vibrations in a molecule.