Lecture 13: Raman Spectroscopy

Before going to Raman spectroscopy, we mention one point regarding rotational and vibrational spectroscopy. The spectroscopy that we had de- scribed were pure rotational and pure vibrational spectroscopy. It is also possible to have a combination of both. We could have a vibrational spec- trum where the rotational transitions are also observed. This is the case for high resolution vibrational spectroscopy. In this case, a molecule in a vibra- tional state v and rotational state J makes a transition such that ∆v = ±1. The final state can have rotational state J + 1(called R branch) or J − 1 called P branch of the spectrum. The Q branch corresponds to final state with ∆J = 0. This is forbidden for linear molecules. Though the analysis of vibrational-rotational spectrum is not very complicated, we will not discuss it in this course. We have noticed that both IR and rotational spectroscopy cannot give us information about homonuclear diatomic molecules. Raman Spectroscopy is an alternative to absorption spectroscopy which can give us information about homonuclear diatomic molecules. In Raman Spectroscopy, the inten- sity of scattered light is detected as opposed to the intensity of transmitted light. When light falls on a sample, a small part of it gets scattered in differ- ent directions. By scattering, we mean that the molecules absorb the light and emit light by going to a different state. The scattered light can have the same frequency as the incident light, or it can have higher or lower frequency. The Raman spectrum consists of lines due to these scattered light rays. The scattered light with the same frequency is referred to as Rayleigh scattering. The scattered light with lower frequency(energy) is referred to as Stokes lines in the spectrum and that with higher frequency is referred to as anti-Stokes lines in the spectrum. Usually, only a small fraction (about 1 per million) of the incident light is scattered, so we need a very sensitive technique for Raman scattering. In addition, the frequency shifts are also very small as we shall see below,

1 so nowadays, a laser light source is used. The original Raman effect was discovered using focussed sunlight or mercury arc lamps. The discovery of this effect led to C.V.Raman’s Nobel prize in Physics in 1930. Raman spec- troscopy is right now one of the most widely used methods of analysis of all materials. If the frequency of incident light is ν and that of scattered light is ν0, then by energy conservation, we have

0 Ei + hν = Ef + hν where Ei and Ef are the energies of the initial and final states of the molecule. Thus, in scattering the light at a different frequency, the molecule goes from an initial state to a final state. Now, we can write

0 h(ν − ν) = h∆ν = hc∆¯ν = Ei − Ef Thus, the incident light frequency need not match the difference in energies, but it is the difference between the frequencies of the incident and scattered light that needs to match. Thus, any frequency of light can be used. Indeed there is both Rotational and Vibrational Raman spectroscopy. In Rotational Raman spectroscopy, the change in frequency of light is related to the dif- ference in rotational energy levels. In vibrational Raman spectroscopy, this change is related to the difference in vibrational energy levels. Let us consider Rotational Raman spectroscopy. In this case, the con- dition for observation of Raman spectrum is that the polarizability of the molecule should change as the molecule rotates in an electric field. Thus all molecules except a class of molecules called spherical rotors (e.g. CH4, SF6) show Raman spectroscopy. For diatomic molecules, the specific selec- tion rule is given by ∆J = 0, ±2. The ∆J = 0 corresponds to Rayleigh line, the ∆J = 2 corresponds to the Stokes line and the ∆J = −2 corresponds to the Anti-Stokes line. When ∆J = 2, the final state has a higher rotational energy so the wavenumber of the scattered light is smaller. When ∆J = −2, the final state has lower rotational energy so the wavenumber of scattered light is larger. For the Stokes lines for the transition from J to J + 2, we have E − E nu¯ 0 =nu ¯ + i f =nu ¯ +B¯(J(J+1)−(J+2)(J+3)) =nu ¯ −4BJ¯ −6B¯ =nu ¯ −2B¯(2J+3) hc Thus the difference in wavenumbers corresponds to 6B¯, 10 B¯, 14B¯, ...

2 For the Anti-Stokes lines for the transition from J + 2 to J, we have exactly the same case, but now the wavenumber of the final state is higher. The lines appear at wavenumbers 6B¯, 10 B¯, 14B¯, ...higher than the incident wavenumber. For vibrational Raman spectroscopy, the gross selection rule is that the polarizability of the molecule should change as it vibrates. The specific selec- tion rule for vibrational Raman spectroscopy is ∆v = ±1, where the ∆v = 1 corresponds to Stokes lines and the ∆v = −1 corresponds to Anti-Stokes lines.

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