Editing Raman scattering (section)

===Molecular vibrations===
{{main|Molecular vibration}}
Raman scattering generally gives information about vibrations within a molecule. In the case of gases, information about rotational energy can also be gleaned.<ref name="Weber">{{Cite book|title=Handbook of Vibrational Spectroscopy|last=Weber|first=Alfons|publisher=Wiley|year=2002|isbn=0471988472|volume=1|location=Chichester|chapter=Raman Spectroscopy of Gases}}</ref> For solids, [[phonon]] modes may also be observed.<ref name="Everall">{{Cite book|title=Handbook of Vibrational Spectroscopy|last=Everall|first=Neil J.| publisher=Wiley| year=2002|isbn=0471988472|volume=1| location=Chichester|chapter=Raman Spectroscopy of the Condensed Phase}}</ref> The basics of [[Infrared spectroscopy|infrared absorption]] regarding molecular vibrations apply to Raman scattering although the [[selection rules]] are different.

====Degrees of freedom====
{{main|Degrees of freedom (physics and chemistry)}}
For any given molecule, there are a total of 3{{mvar|N}} [[Degrees of freedom (physics and chemistry)|degrees of freedom]], where {{mvar|N}} is the number of [[atom]]s. This number arises from the ability of each atom in a molecule to move in three dimensions.<ref name=Laidler>[[Keith J. Laidler]] and John H. Meiser, ''Physical Chemistry'' (Benjamin/Cummings 1982), pp.646-7 {{ISBN|0-8053-5682-7}}</ref> When dealing with molecules, it is more common to consider the movement of the molecule as a whole. Consequently, the 3{{mvar|N}} degrees of freedom are partitioned into molecular translational, [[rotational motion|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 <math>x</math>, <math>y</math>, and <math>z</math>-axes. [[Linear molecular geometry|Linear molecule]]s 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 bond]]s of the molecule. For a linear molecule, the number of vibrational modes is 3{{mvar|N}}-5, whereas for a non-linear molecule the number of vibrational modes is 3{{mvar|N}}-6.<ref name=Laidler/>

====Vibrational energy====
{{main|Quantum harmonic oscillator}}
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
:<math>E_n = h \left( n + {1 \over 2 } \right)\nu=h\left( n + {1 \over 2 } \right) {1\over {2 \pi}} \sqrt{k \over m} \!</math>,
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 <math>E=h \nu={h\over {2 \pi}} \sqrt{k \over m}</math>

The energy range for vibrations is in the range of approximately 5 to 3500&nbsp;cm<sup>−1</sup>. 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 [[Sir George Stokes, 1st Baronet|George Stokes]] in 1852, with light emission at [[Stokes line|longer wavelength]] (now known to correspond to lower energy) than the absorbed incident light. Conceptually similar effects can be caused by [[Inelastic neutron scattering|neutrons]] or [[High resolution electron energy loss spectroscopy|electrons]] rather than light.<ref>{{Cite journal|last1=Krivanek|first1=O. L.|last2=Dellby|first2=N.|last3=Hachtel|first3=J. A.|last4=Idrobo|first4=J. -C.|last5=Hotz|first5=M. T.|last6=Plotkin-Swing|first6=B.|last7=Bacon|first7=N. J.|last8=Bleloch|first8=A. L.|last9=Corbin|first9=G. J.|date=2019-08-01|title=Progress in ultrahigh energy resolution EELS|journal=Ultramicroscopy|series=75th Birthday of Christian Colliex, 85th Birthday of Archie Howie, and 75th Birthday of Hannes Lichte / PICO 2019 - Fifth Conference on Frontiers of Aberration Corrected Electron Microscopy|volume=203|pages=60–67|doi=10.1016/j.ultramic.2018.12.006|pmid=30577954|osti=1530104|issn=0304-3991|doi-access=free}}</ref> An increase in photon energy which leaves the molecule in a lower vibrational energy state is called anti-Stokes scattering.