The Theory of Raman Spectroscopy

I n the previous column (1) we discussed two additional phenomena arising from the interaction of light with matter. One was Rayleigh scattering, a two-photon process having a net effect of changing the direction of, or scattering, light, while keeping its frequency constant. Because of this, Rayleigh scattering is a form of elastic scattering. The other was Raman scattering, a twophoton process having net effects of scattering photons but changing their frequency. This changing in frequency — characteristic of inelastic scattering — provides a basis for a form of spectroscopy. (We did not consider some other forms of scattering, like Brillouin or Mie scattering. Perhaps we’ll discuss those in a future column.) What causes the scattering of a photon? It turns out that the key property of a molecule scattering a photon is the molecule’s polarizability. The polarizability, , represents the ability of an applied electric field, E, to induce a dipole moment, in, in an atom or molecule: