Raman scattering

21/02/1928View on timeline

C.V. Raman, in full Sir Chandrasekhara Venkata Raman, Indian physicist whose work was influential in the growth of science in India. Studying the scattering of light in various substances, in 1928 he found that when a transparent substance is illuminated by a beam of light of one frequency, a small portion of the light emerges at right angles to the original direction, and some of this light is of different frequencies than that of the incident light. These so-called Raman frequencies are the energies associated with transitions between different rotational and vibrational states in the scattering material.

Raman effect, change in the wavelength of light that occurs when a light beam is deflected by molecules. When a beam of light traverses a dust-free, transparent sample of a chemical compound, a small fraction of the light emerges in directions other than that of the incident (incoming) beam. Most of this scattered light is of unchanged wavelength. A small part, however, has wavelengths different from that of the incident light; its presence is a result of the Raman effect.

The Raman effect was first reported by C. V. Raman and K. S. Krishnan, and independently by Grigory Landsberg and Leonid Mandelstam, on 21 February 1928 (that is why in the former Soviet Union the priority of Raman was always disputed; thus in Russian scientific literature this effect is usually referred to as "combination scattering" or "combinatory scattering").

Raman scattering is perhaps most easily understandable if the incident light is considered as consisting of particles, or photons (with energy proportional to frequency), that strike the molecules of the sample. Most of the encounters are elastic, and the photons are scattered with unchanged energy and frequency. On some occasions, however, the molecule takes up energy from or gives up energy to the photons, which are thereby scattered with diminished or increased energy, hence with lower or higher frequency. The frequency shifts are thus measures of the amounts of energy involved in the transition between initial and final states of the scattering molecule.

The Raman effect is feeble; for a liquid compound the intensity of the affected light may be only 1/100,000 of that incident beam. The pattern of the Raman lines is characteristic of the particular molecular species, and its intensity is proportional to the number of scattering molecules in the path of the light. Thus, Raman spectra are used in qualitative and quantitative analysis.

The energies corresponding to the Raman frequency shifts are found to be the energies associated with transitions between different rotational and vibrational states of the scattering molecule. Pure rotational shifts are small and difficult to observe, except for those of simple gaseous molecules. In liquids, rotational motions are hindered, and discrete rotational Raman lines are not found. Most Raman work is concerned with vibrational transitions, which give larger shifts observable for gases, liquids, and solids. Gases have low molecular concentration at ordinary pressures and therefore produce very faint Raman effects; thus liquids and solids are more frequently studied.

Degrees of freedom

For any given chemical compound, there are a total of 3N degrees of freedom, where N is the number of atoms in the compound. This number arises from the ability of each atom in a molecule to move in three different directions (x, y, and z). When dealing with molecules, it is more common to consider the movement of the molecule as a whole. Consequently, the 3N degrees of freedom are partitioned into molecular translational, rotational, and vibrational motion. Three of the degrees of freedom correspond to translational motion of the molecule as a whole (along each of the three spatial dimensions). Similarly, three degrees of freedom correspond to rotations of the molecule about the x, y, and z-axes. Linear molecules only have two rotations because rotations along the bond axis do not change the positions of the atoms in the molecule. The remaining degrees of freedom correspond to molecular vibrational modes. These modes include stretching and bending motions of the chemical bonds of the molecule. For a linear molecule, the number of vibrational modes is:

3N – 3 – 2 = 3N – 5

Molecular vibrations and infrared radiation

The frequencies of molecular vibrations range from less than 10¹² to approximately 10¹⁴ Hz. These frequencies correspond to radiation in the infrared (IR) region of the electromagnetic spectrum. At any given instant, each molecule in a sample has a certain amount of vibrational energy. However, the amount of vibrational energy that a molecule has continually changes due to collisions and other interactions with other molecules in the sample.

At room temperature, most of the molecules will be in the lowest energy state, which is known as the ground state. A few molecules will be in higher energy states, which are known as excited states. The fraction of molecules occupying a given vibrational mode at a given temperature can be calculated using the Boltzmann distribution. Performing such a calculation shows that, for relatively low temperatures (such as those used for most routine spectroscopy), most of the molecules occupy the ground vibrational state. Such a molecule can be excited to a higher vibrational mode through the direct absorption of a photon of the appropriate energy. This is the mechanism by which IR spectroscopy operates: infrared radiation is passed through the sample, and the intensity of the transmitted light is compared with that of the incident light. A reduction in intensity at a given wavelength of light indicates the absorption of energy by a vibrational transition. The energy, E, of a photon is

E= hν

where h is Planck's constant and v is the frequency of the radiation. Thus, the energy required for such a transition may be calculated if the frequency of the incident radiation is known.

Raman scattering

It is also possible to observe molecular vibrations by an inelastic scattering process. In inelastic (Raman) scattering, an absorbed photon is re-emitted with lower energy; the difference in energy between the incident photons and scattered photons corresponds to the energy required to excite a molecule to a higher vibrational mode.

Typically, in Raman spectroscopy high intensity laser radiation with wavelengths in either the visible or near-infrared regions of the spectrum is passed through a sample. Photons from the laser beam produce an oscillating polarization in the molecules, exciting them to a virtual energy state. The oscillating polarization of the molecule can couple with other possible polarizations of the molecule, including vibrational and electronic excitations. If the polarization in the molecule does not couple to these other possible polarizations, then it will not change the vibrational state that the molecule started in and the scattered photon will have the same energy as the original photon. This type of scattering is known as Rayleigh scattering.

When the polarization in the molecules couples to a vibrational state that is higher in energy than the state they started in, then the original photon and the scattered photon differ in energy by the amount required to vibrationally excite the molecule. In perturbation theory, the Raman effect corresponds to the absorption and subsequent emission of a photon via an intermediate quantum state of a material. The intermediate state can be either a "real", i.e. stationary state, or a virtual state.

Stokes and anti-Stokes

The Raman interaction leads to two possible outcomes:

the material absorbs energy and the emitted photon has a lower energy than the absorbed photon. This outcome is labeled Stokes Raman scattering in honor of George Stokes who showed in 1852 that fluorescence is due to light emission at longer wavelength (now known to correspond to lower energy) than the absorbed incident light.

the material loses energy and the emitted photon has a higher energy than the absorbed photon. This outcome is labeled anti-Stokes Raman scattering.

The energy difference between the absorbed and emitted photon corresponds to the energy difference between two resonant states of the material and is independent of the absolute energy of the photon.

The spectrum of the scattered photons is termed the Raman spectrum. It shows the intensity of the scattered light as a function of its frequency difference Δν to the incident photons. The locations of corresponding Stokes and anti-Stokes peaks form a symmetric pattern around Δν=0. The frequency shifts are symmetric because they correspond to the energy difference between the same upper and lower resonant states. The intensities of the pairs of features will typically differ, though. They depend on the populations of the initial states of the material, which in turn depend on the temperature. In thermodynamic equilibrium, the lower state will be more populated than the upper state. Therefore, the rate of transitions from the more populated lower state to the upper state (Stokes transitions) will be higher than in the opposite direction (anti-Stokes transitions). Correspondingly, Stokes scattering peaks are stronger than anti-Stokes scattering peaks. Their ratio depends on the temperature, and can therefore be exploited to measure it.