Raman scattering
In chemistry and physics, Raman scattering or the Raman effect is the inelastic scattering of photons by matter, meaning that there is both an exchange of energy and a change in the light's direction. Typically this effect involves vibrational energy being gained by a molecule as incident photons from a visible laser are shifted to lower energy. This is called normal Stokes-Raman scattering.
Light has a certain probability of being scattered by a material. When photons are scattered, most of them are elastically scattered, such that the scattered photons have the same energy as the incident photons, but different direction. Rayleigh scattering usually has an intensity in the range 0.1% to 0.01% relative to that of a radiation source. An even smaller fraction of the scattered photons can be scattered inelastically, with the scattered photons having an energy different from those of the incident photons—these are Raman scattered photons. Because of conservation of energy, the material either gains or loses energy in the process.
The effect is exploited by chemists and physicists to gain information about materials for a variety of purposes by performing various forms of Raman spectroscopy. Many other variants of Raman spectroscopy allow rotational energy to be examined, if gas samples are used, and electronic energy levels may be examined if an X-ray source is used, in addition to other possibilities. More complex techniques involving pulsed lasers, multiple laser beams and so on are known.
The Raman effect is named after Indian scientist C. V. Raman, who discovered it in 1928 with assistance from his student K. S. Krishnan. Raman was awarded the 1930 Nobel Prize in Physics for his discovery of Raman scattering.
History
The elastic light scattering phenomena called Rayleigh scattering, in which light retains its energy, was described in the 19th century. The intensity of Rayleigh scattering is about 10−3 to 10−4 compared to the intensity of the exciting source. In 1908, another form of elastic scattering, called Mie scattering was discovered.The inelastic scattering of light was predicted by Adolf Smekal in 1923 and in older German-language literature it has been referred to as the Smekal-Raman-Effekt. In 1922, Indian physicist C. V. Raman published his work on the "Molecular Diffraction of Light", the first of a series of investigations with his collaborators that ultimately led to his discovery of the radiation effect that bears his name. The Raman effect was first reported by Raman and his coworker K. S. Krishnan, and independently by Grigory Landsberg and Leonid Mandelstam, in Moscow on 21 February 1928. In the former Soviet Union, Raman's contribution was always disputed; thus in Russian scientific literature the effect is usually referred to as "combination scattering" or "combinatory scattering". Raman received the Nobel Prize in 1930 for his work on the scattering of light.
In 1998 the Raman effect was designated a National Historic Chemical Landmark by the American Chemical Society in recognition of its significance as a tool for analyzing the composition of liquids, gases, and solids.
Instrumentation
Modern Raman spectroscopy nearly always involves the use of lasers as an exciting light source. Because lasers were not available until more than three decades after the discovery of the effect, Raman and Krishnan used a mercury lamp and photographic plates to record spectra. Early spectra took hours or even days to acquire due to weak light sources, poor sensitivity of the detectors and the weak Raman scattering cross-sections of most materials. The most common modern detectors are charge-coupled devices. Photodiode arrays and photomultiplier tubes were common prior to the adoption of CCDs.Theory
The following focuses on the theory of normal Raman scattering of light by discrete molecules. X-ray Raman spectroscopy is conceptually similar but involves excitation of electronic, rather than vibrational, energy levels.Molecular vibrations
Raman scattering generally gives information about vibrations within a molecule. In the case of gases, information about rotational energy can also be gleaned. For solids, phonon modes may also be observed. The basics of infrared absorption regarding molecular vibrations apply to Raman scattering although the selection rules are different.Degrees of freedom
For any given molecule, there are a total of 3 degrees of freedom, where is the number of atoms. This number arises from the ability of each atom in a molecule to move in three dimensions. When dealing with molecules, it is more common to consider the movement of the molecule as a whole. Consequently, the 3 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. Similarly, three degrees of freedom correspond to rotations of the molecule about the,, and -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 3-5, whereas for a non-linear molecule the number of vibrational modes is 3-6.Vibrational energy
Molecular vibrational energy is known to be quantized and can be modeled using the quantum harmonic oscillator approximation or a Dunham expansion when anharmonicity is important.The vibrational energy levels according to the QHO are
where n is a quantum number. Since the selection rules for Raman and infrared absorption generally dictate that only fundamental vibrations are observed, infrared excitation or Stokes Raman excitation results in an energy change of
The energy range for vibrations is in the range of approximately 5 to 3500 cm−1. The fraction of molecules occupying a given vibrational mode at a given temperature follows a Boltzmann distribution. A molecule can be excited to a higher vibrational mode through the direct absorption of a photon of the appropriate energy, which falls in the terahertz or infrared range. This forms the basis of infrared spectroscopy. Alternatively, the same vibrational excitation can be produced by an inelastic scattering process. This is called Stokes Raman scattering, by analogy with the Stokes shift in fluorescence discovered by George Stokes in 1852, with light emission at longer wavelength than the absorbed incident light. Conceptually similar effects can be caused by neutrons or electrons rather than light. An increase in photon energy which leaves the molecule in a lower vibrational energy state is called anti-Stokes scattering.
Raman scattering
Raman scattering is conceptualized as involving a virtual electronic energy level which corresponds to the energy of the exciting laser photons. Absorption of a photon excites the molecule to the imaginary state and re-emission leads to Raman or Rayleigh scattering. In all three cases the final state has the same electronic energy as the initial state but is higher in vibrational energy in the case of Stokes Raman scattering, lower in the case of anti-Stokes Raman scattering or the same in the case of Rayleigh scattering. Normally this is thought of in terms of wavenumbers, where is the wavenumber of the laser and is the wavenumber of the vibrational transition. Thus Stokes scattering gives a wavenumber of while is given for anti-Stokes. When the exciting laser energy corresponds to an actual electronic excitation of the molecule then the resonance Raman effect occurs.A classical physics based model is able to account for Raman scattering and predicts an increase in the intensity which scales with the fourth-power of the light frequency. Light scattering by a molecule is associated with oscillations of an induced electric dipole. The oscillating electric field component of electromagnetic radiation may bring about an induced dipole in a molecule which follows the alternating electric field which is modulated by the molecular vibrations. Oscillations at the external field frequency are therefore observed along with beat frequencies resulting from the external field and normal mode vibrations.
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, more commonly called a Raman shift. The locations of corresponding Stokes and anti-Stokes peaks form a symmetric pattern around the RayleighΔν=0 line. 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 will be higher than in the opposite direction. 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:
Selection rules
In contrast to IR spectroscopy, where there is a requirement for a change in dipole moment for vibrational excitation to take place, Raman scattering requires a change in polarizability. A Raman transition from one state to another is allowed only if the molecular polarizability of those states is different. For a vibration, this means that the derivative of the polarizability with respect to the normal coordinate associated to the vibration is non-zero:. In general, a normal mode is Raman active if it transforms with the same symmetry of the quadratic forms, which can be verified from the character table of the molecule's point group. As with IR spectroscopy, only fundamental excitations are allowed according to the QHO. There are however many cases where overtones are observed. The rule of mutual exclusion, which states that vibrational modes cannot be both IR and Raman active, applies to certain molecules.The specific selection rules state that the allowed rotational transitions are, where is the rotational state. This generally is only relevant to molecules in the gas phase where the Raman linewidths are small enough for rotational transitions to be resolved.
A selection rule relevant only to ordered solid materials states that only phonons with zero phase angle can be observed by IR and Raman, except when phonon confinement is manifest.