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Cyclohexane conformation
(section)
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==Principal conformers== The different conformations are called "conformers", a blend of the words "conformation" and "isomer". ===Chair conformation<span class="anchor" id="Axial"></span><span class="anchor" id="Equatorial"></span>=== The chair conformation is the most stable conformer. At {{cvt|25|°C|K|0|order=flip}}, 99.99% of all molecules in a cyclohexane solution adopt this conformation. The C–C ring of the chair conformation has the same shape as the 6-membered rings in the [[diamond cubic]] lattice.<ref name=Dragojlovic>{{cite journal |doi=10.1007/s40828-015-0014-0 |url=https://link.springer.com/content/pdf/10.1007/s40828-015-0014-0.pdf |title=Conformational analysis of cycloalkanes |year=2015 |last1=Dragojlovic |first1=Veljko |journal=Chemtexts |volume=1 |issue=3 |pages=1–30 |bibcode=2015ChTxt...1...14D |s2cid=94348487 }}</ref>{{rp|p=16}} This can be modeled as follows. Consider a carbon atom to be a point with four half-bonds sticking out towards the vertices of a [[tetrahedron]]. Place it on a flat surface with one half-bond pointing straight up. Looking from directly above, the other three half-bonds will appear to point outwards towards the vertices of an [[equilateral triangle]], so the bonds will appear to have an angle of 120° between them. Arrange six such atoms above the surface so that these 120° angles form a regular hexagon. Reflecting three of the atoms to be below the surface yields the desired geometry. All carbon centers are equivalent. They alternate between two parallel planes, one containing C1, C3 and C5, and the other containing C2, C4, and C6. The chair conformation is left unchanged after a rotation of 120° about the symmetry axis perpendicular to these planes, as well as after a rotation of 60° followed by a reflection in the midpoint plane, resulting in a [[symmetry group]] of [[Molecular symmetry#Common point groups|''D''<sub>3d</sub>]]. While all C–C bonds are tilted relative to the plane, diametrically opposite bonds (such as C1–C2 and C4–C5) are parallel to each other. Six of the twelve C–H bonds are '''axial''', pointing upwards or downwards almost parallel to the symmetry axis. The other six C–H bonds are '''equatorial''', oriented radially outwards with an upwards or downwards tilt. Each carbon center has one axial C–H bond (pointed alternately upwards or downwards) and one equatorial C–H bond (tilted alternately downwards or upwards), enabling each X–C–C–Y unit to adopt a [[staggered conformation]] with minimal [[Strain (chemistry)#Torsional strain|torsional strain]]. In this model, the [[dihedral angle#In stereochemistry|dihedral angle]]s for series of four carbon atoms going around the ring alternate between exactly +60° (''gauche<sup>+</sup>'') and −60° (''gauche<sup>−</sup>'').<ref name=Dragojlovic/>{{rp|p=10}} The chair conformation cannot be deformed without changing bond angles or lengths. It can be represented as two linked chains, C1–C2–C3–C4 and C1–C6–C5–C4, each mirroring the other, with opposite dihedral angles. The C1–C4 distance depends on the absolute value of this dihedral angle, so in a rigid model, changing one angle requires changing the other angle. If both dihedral angles change while remaining opposites of each other, it is not possible to maintain the correct C–C–C bond angles at C1 and C4. The chair geometry is often preserved when the hydrogen atoms are replaced by [[halogen]]s or other simple [[functional group|group]]s. However, when these hydrogens are substituted for a larger group, additional strain may occur due to '''diaxial interactions''' between pairs of substituents occupying the same-orientation axial position, which are typically repulsive due to steric crowding.<ref>{{Cite web |title=Illustrated Glossary of Organic Chemistry - Diaxial interaction (1,3-diaxial interaction) |url=http://www.chem.ucla.edu/~harding/IGOC/D/diaxial_interaction.html |access-date=2022-11-18 |website=www.chem.ucla.edu}}</ref> ===Boat and twist-boat conformations=== The boat conformations have higher energy than the chair conformations. The interaction between the two '''flagpole''' hydrogens, in particular, generates [[steric strain]]. Torsional strain also exists between the C2–C3 and C5–C6 bonds (carbon number 1 is one of the two on a mirror plane), which are [[eclipsed]] — that is, these two bonds are parallel one to the other across a mirror plane. Because of this strain, the boat configuration is unstable (i.e. is not a local energy minimum). The [[molecular symmetry]] is ''C''<sub>2v</sub>. The boat conformations spontaneously distorts to twist-boat conformations. Here the [[Symmetry group|symmetry]] is ''D''<sub>2</sub>, a purely rotational point group with three twofold axes. This conformation can be derived from the boat conformation by applying a slight twist to the molecule so as to remove eclipsing of two pairs of methylene groups. The twist-boat conformation is chiral, existing in right-handed and left-handed versions. The concentration of the twist-boat conformation at room temperature is less than 0.1%, but at {{convert|1073|K|C|0}} it can reach 30%. Rapid cooling of a sample of cyclohexane from {{convert|1073|K|C|0}} to {{convert|40|K|C|0}} will freeze in a large concentration of twist-boat conformation, which will then slowly convert to the chair conformation upon heating.<ref>{{Cite journal|title = Spectroscopic detection of the twist-boat conformation of cyclohexane. Direct measurement of the free energy difference between the chair and the twist-boat|journal = [[J. Am. Chem. Soc.]]|date = 1975-05-01|pages = 3244–3246|volume = 97|issue = 11|doi = 10.1021/ja00844a068|first1 = M.|last1 = Squillacote|first2 = R. S.|last2 = Sheridan|first3 = O. L.|last3 = Chapman|first4 = F. A. L.|last4 = Anet| bibcode=1975JAChS..97.3244S }}</ref>
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