Editing Rotational spectroscopy (section)

===Classification of molecular rotors===
In [[quantum mechanics]] the free rotation of a molecule is [[angular momentum quantization|quantized]], so that the [[rotational energy]] and the [[angular momentum]] can take only certain fixed values, which are related simply to the [[moment of inertia]], <math> I </math>, of the molecule. For any molecule, there are three moments of inertia: <math>I_A</math>, <math>I_B</math> and <math>I_C</math> about three mutually orthogonal axes ''A'', ''B'', and ''C'' with the origin at the [[center of mass]] of the system. The general convention, used in this article, is to define the axes such that <math>I_A \leq I_B \leq I_C</math>, with axis <math>A</math> corresponding to the smallest moment of inertia. Some authors, however, define the <math>A</math> axis as the molecular [[molecular symmetry#Elements|rotation axis]] of highest order.

The particular pattern of [[energy level]]s (and, hence, of transitions in the rotational spectrum) for a molecule is determined by its symmetry. A convenient way to look at the molecules is to divide them into four different classes, based on the symmetry of their structure. These are

{{glossary}}
{{term|Spherical tops (spherical rotors)}}{{defn|
All three moments of inertia are equal to each other: <math>I_A = I_B = I_C</math>. Examples of spherical tops include [[Allotropes of phosphorus#White phosphorus|phosphorus tetramer ({{chem|P|4}})]], [[Carbon tetrachloride|carbon tetrachloride ({{chem|CCl|4}})]] and other tetrahalides, [[methane|methane ({{chem|CH|4}})]], [[silane|silane, ({{chem|SiH|4}})]], [[Sulfur hexafluoride|sulfur hexafluoride ({{chem|SF|6}})]] and other hexahalides. The molecules all belong to the cubic [[molecular point group|point group]]s T<sub>d</sub> or O<sub>h</sub>.
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{{term|Linear molecules}}{{defn|
For a linear molecule the moments of inertia are related by <math>I_A \ll I_B = I_C </math>. For most purposes, <math>I_A</math> can be taken to be zero. Examples of linear molecules include [[Oxygen|dioxygen ({{chem|O|2}})]], [[nitrogen|dinitrogen ({{chem|N|2}})]], [[Carbon monoxide|carbon monoxide (CO)]], [[Hydroxyl radical|hydroxy radical (OH)]], [[Carbon dioxide|carbon dioxide (CO<sub>2</sub>)]], [[Hydrogen cyanide|hydrogen cyanide (HCN)]], [[Carbonyl sulfide|carbonyl sulfide (OCS)]], [[Acetylene|acetylene (ethyne (HC≡CH)]] and dihaloethynes. These molecules belong to the point groups C<sub>∞v</sub> or D<sub>∞h</sub>.
}}
{{term|Symmetric tops (symmetric rotors)}}{{defn|
A symmetric top is a molecule in which two moments of inertia are the same, <math>I_A = I_B</math> or <math>I_B = I_C</math>. By definition a symmetric top must have a 3-fold or higher order [[molecular symmetry#Elements|rotation axis]]. As a matter of convenience, spectroscopists divide molecules into two classes of symmetric tops, ''[[Oblate spheroid|Oblate]] symmetric tops'' (saucer or disc shaped) with <math>I_A = I_B < I_C</math> and ''[[Prolate]] symmetric tops'' (rugby football, or cigar shaped) with <math>I_A < I_B = I_C </math>. The spectra look rather different, and are instantly recognizable. Examples of symmetric tops include
; [[Oblate spheroid|Oblate]]: [[Benzene|Benzene, {{chem|C|6|H|6}}]]; [[ammonia|ammonia, {{chem|NH|3}}]]; [[xenon tetrafluoride|xenon tetrafluoride, {{chem|Xe|F|4}}]]
; [[Prolate]]: [[Chloromethane|Chloromethane, {{chem|CH|3|Cl}}]], [[methylacetylene|propyne, {{chem|CH|3|C≡CH}}]]

As a detailed example, ammonia has a moment of inertia {{nowrap|''I''<sub>C</sub> {{=}} 4.4128 × 10<sup>−47</sup> kg m<sup>2</sup>}} about the 3-fold rotation axis, and moments {{nowrap|''I''<sub>A</sub> {{=}} ''I''<sub>B</sub> {{=}} 2.8059 × 10<sup>−47</sup> kg m<sup>2</sup>}} about any axis perpendicular to the C<sub>3</sub> axis. Since the unique moment of inertia is larger than the other two, the molecule is an oblate symmetric top.<ref>Moment of inertia values from {{harvnb|Atkins|de Paula|2006|p=445}}</ref>
}}
{{term|Asymmetric tops (asymmetric rotors)}}{{defn|
The three moments of inertia have different values. Examples of small molecules that are asymmetric tops include [[Water (molecule)|water, {{chem|H|2|O}}]] and [[Nitrogen dioxide|nitrogen dioxide, {{chem|NO|2}}]] whose symmetry axis of highest order is a 2-fold rotation axis. Most large molecules are asymmetric tops.
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{{glossary end}}