Editing Infrared spectroscopy (section)

===Number of vibrational modes===
In order for a vibrational mode in a sample to be "IR active", it must be associated with changes in the molecular dipole moment. A permanent dipole is not necessary, as the rule requires only a ''change'' in dipole moment.<ref>{{cite book| first1 = Peter | last1 = Atkins | first2 = Julio | last2 = de Paula | name-list-style = vanc |title=Physical Chemistry|date=2002|publisher=W.H.Freeman|location=New York|isbn=0-7167-3539-3|pages=513|edition=7th}}|quote=the electric dipole moment of the molecule must change when the atoms are displaced relative to one another</ref>

A molecule can vibrate in many ways, and each way is called a '''vibrational mode'''. For molecules with N number of atoms, geometrically [[Linear molecular geometry|linear molecules]] have 3''N''&nbsp;–&nbsp;5 degrees of vibrational modes, whereas [[Molecular geometry|nonlinear molecules]] have 3''N''&nbsp;–&nbsp;6 degrees of vibrational modes (also called vibrational degrees of freedom). As examples linear [[carbon dioxide]] (CO<sub>2</sub>) has 3&nbsp;×&nbsp;3&nbsp;–&nbsp;5&nbsp;=&nbsp;4, while non-linear [[Water (molecule)|water (H<sub>2</sub>O)]], has only 3&nbsp;×&nbsp;3&nbsp;–&nbsp;6&nbsp;=&nbsp;3.<ref>{{cite book|title=Physical Chemistry, 5th Edition|first1= Peter|last1=Atkins|publisher=Freeman|year=1994|page = 577}}</ref>

[[File:Co2 vibrations.svg|thumb|right|[[#Number of vibrational modes|Stretching and bending oscillations]] of the CO<sub>2</sub> carbon dioxide molecule. Upper left: symmetric stretching. Upper right: antisymmetric stretching. Lower line: degenerate pair of bending modes.]]

Simple [[diatomic molecule]]s have only one bond and only one vibrational band. If the molecule is symmetrical, e.g. N<sub>2</sub>, the band is not observed in the IR spectrum, but only in the [[Raman spectrum]]. Asymmetrical diatomic molecules, e.g. carbon monoxide ([[Carbon monoxide|CO]]), absorb in the IR spectrum. More complex molecules have many bonds, and their vibrational spectra are correspondingly more complex, i.e. big molecules have many peaks in their IR spectra.

The atoms in a CH<sub>2</sub>X<sub>2</sub> group, commonly found in [[organic compound]]s and where X can represent any other atom, can vibrate in nine different ways. Six of these vibrations involve only the [[Methylene group|CH<sub>2</sub>]] portion: two '''stretching''' modes (ν): '''symmetric''' (ν<sub>s</sub>) and '''antisymmetric''' (ν<sub>as</sub>); and four '''bending''' modes: '''scissoring''' (δ), '''rocking''' (ρ), '''wagging''' (ω) and '''twisting''' (τ), as shown below. Structures that do not have the two additional X groups attached have fewer modes because some modes are defined by specific relationships to those other attached groups. For example, in water, the rocking, wagging, and twisting modes do not exist because these types of motions of the H atoms represent simple rotation of the whole molecule rather than vibrations within it. In case of more complex molecules, '''out-of-plane''' (γ) vibrational modes can be also present.<ref>{{cite book| first1 = Bernhard | last1 = Schrader | name-list-style = vanc |title=Infrared and Raman Spectroscopy: Methods and Applications|date=1995|publisher=VCH, Weinheim|location=New York|isbn=978-3-527-26446-9|pages=787}}</ref>

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{| class="wikitable"
|-
! {{diagonal split header|<br />Direction|Symmetry}}
! Symmetric
! Antisymmetric
|- style="text-align: center;"
! Radial
| [[Image:Symmetrical stretching.gif]]<br />Symmetric stretching (ν<sub>s</sub>)
| [[Image:Asymmetrical stretching.gif]]<br />Antisymmetric stretching (ν<sub>as</sub>)
|- style="text-align: center;"
! Latitudinal
| [[Image:Scissoring.gif]]<br />Scissoring (δ)
| [[Image:Modo rotacao.gif]]<br />Rocking (ρ)
|- style="text-align: center;"
! Longitudinal
| [[Image:Wagging.gif]]<br />Wagging (ω)
| [[Image:Twisting.gif]]<br />Twisting (τ)
|}

These figures do not represent the "[[recoil]]" of the [[Carbon|C]] atoms, which, though necessarily present to balance the overall movements of the molecule, are much smaller than the movements of the lighter [[Hydrogen|H]] atoms.

The simplest and most important or ''fundamental'' IR bands arise from the excitations of normal modes, the simplest distortions of the molecule, from the [[ground state]] with [[Molecular vibration#Quantum mechanics|vibrational quantum number]] ''v'' = 0 to the first [[excited state]] with vibrational quantum number ''v'' = 1. In some cases, [[overtone band]]s are observed. An overtone band arises from the absorption of a photon leading to a direct transition from the ground state to the second excited vibrational state (''v'' = 2). Such a band appears at approximately twice the energy of the fundamental band for the same normal mode. Some excitations, so-called ''combination modes'', involve simultaneous excitation of more than one normal mode. The phenomenon of [[Fermi resonance]] can arise when two modes are similar in energy; Fermi resonance results in an unexpected shift in energy and intensity of the bands etc.{{citation needed|date=October 2019}}