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 (change of light frequency) and a change in the light's direction (momentum). 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 (Rayleigh scattering), such that the scattered photons have the same energy (frequency, wavelength, and therefore color) 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 (about 1 in a million) can be scattered inelastically, with the scattered photons having an energy different (usually lower) 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 (on 16 February 1928) 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 (5 days after Raman and Krishnan). 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 (CCDs). Photodiode arrays and photomultiplier tubes were common prior to the adoption of CCDs.

Theory The following focuses on the theory of normal (non-resonant, spontaneous, vibrational) 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 3N degrees of freedom, where N 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 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 {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle 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-5, whereas for a non-linear molecule the number of vibrational modes is 3N-6.

Vibrational energy

Molecular vibrational energy is known to be quantized and can be modeled using the quantum harmonic oscillator (QHO) approximation or a Dunham expansion when anharmonicity is important. The vibrational energy levels according to the QHO are

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