Editing Rotamer

{{Short description|Various molecular structures formed only by rotation about single bonds}}
[[File:Gauche-eclipsed interconversion.svg|thumb|300px|Rotation about single bond of [[butane]] to interconvert one conformation to another.  The ''gauche'' conformation on the right is a conformer, while the ''eclipsed'' conformation on the left is a transition state between conformers. Above: Newman projection; below: depiction of spatial orientation.]]

In [[chemistry]], '''rotamers''' are chemical species that differ from one another primarily due to rotations about one or more [[single bond]]s. Various arrangements of [[atom]]s in a [[molecule]] that differ by rotation about single bonds can also be referred to as '''conformations'''.  Conformers/rotamers differ little in their energies, so they are almost never separable in a practical sense. Rotations about single bonds are subject to small energy barriers.<ref>{{cite journal |title=free rotation (hindered rotation, restricted rotation) |url=https://goldbook.iupac.org/terms/view/F02520 |website=IUPAC Gold Book|doi=10.1351/goldbook.F02520 |doi-access=free }}</ref> When the time scale for interconversion is long enough for isolation of individual rotamers (usually arbitrarily defined as a [[half-life]] of interconversion of 1000 seconds or longer), the species are termed '''atropisomers''' (''see:'' [[atropisomer]]ism).<ref name=":0">{{Cite journal|last=Moss|first=GP|date=1996-01-01|title=Basic terminology of stereochemistry (IUPAC Recommendations 1996)|journal=Pure and Applied Chemistry|volume=68|issue=12|pages=2193–2222|doi=10.1351/pac199668122193|s2cid=98272391|issn=1365-3075|doi-access=free}}</ref><ref>Ōki, Michinori (1983) Recent Advances in Atropisomerism, in ''Topics in Stereochemistry'', Vol. 14 (N. L. Allinger, E. L. Eliel and S. H. Wilen, Eds.), Hoboken, NJ:John Wiley & Sons, pp. 1–82; ''published online in 2007'', DOI: 10.1002/9780470147238.ch1, see [http://onlinelibrary.wiley.com/doi/10.1002/9780470147238.ch1/summary] and [http://onlinelibrary.wiley.com/store/10.1002/9780470147238.fmatter/asset/fmatter.pdf?v=1&t=hwclipn7&s=be733dd54229cc5689e4f5e17777dcb94458748b]{{Dead link|date=July 2019|bot=InternetArchiveBot|fix-attempted=yes}}, accessed 12 June 2014.</ref><ref name=bookatrop>{{cite book|last=Alkorta|first=Ibon|author2=Jose Elguero |author3=Christian Roussel |author4=Nicolas Vanthuyne |author5=Patrick Piras |title=Atropisomerism and Axial Chirality in Heteroaromatic Compounds|series=Advances in Heterocyclic Chemistry|year=2012|doi= 10.1016/B978-0-12-396530-1.00001-2|volume=105 |pages=1–188|isbn=9780123965301|hdl=10261/62060}}</ref> The [[Ring flip|ring-flip]] of substituted [[cyclohexane]]s constitutes a common form of conformers.<ref>{{cite web|last=Hunt|first=Ian|title=Stereochemistry|url=http://www.chem.ucalgary.ca/courses/350/Carey5th/Ch07/ch7-1.html|work=University of Calgary|access-date=28 October 2013}}</ref>

The study of the energetics of bond rotation is referred to as '''conformational analysis'''.<ref name=dougherty>{{cite book|last=Anslyn|first=Eric|title=Modern Physical Organic Chemistry|url=https://archive.org/details/modernphysicalor00ansl|url-access=limited|year=2006|publisher=University Science|isbn=978-1891389313|page=[https://archive.org/details/modernphysicalor00ansl/page/n122 95]|author2=Dennis Dougherty}}</ref> In some cases, conformational analysis can be used to predict and explain product selectivity, mechanisms, and rates of reactions.<ref name="nobel lect">{{cite journal|last=Barton|first=Derek|title=The Principles of Conformational Analysis.|url=https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1969/barton-lecture.html|journal=Nobel Media AB 2013|year=1970|volume=169|issue=3945|pages=539–44|publisher=Elsevier Publishing Co.|doi=10.1126/science.169.3945.539|access-date=10 November 2013|pmid=17746022|bibcode=1970Sci...169..539B|url-access=subscription}}</ref> Conformational analysis also plays an important role in rational, structure-based [[drug design]].

==Types==
{{Quote box|width = 25% |title = [[International Union of Pure and Applied Chemistry|IUPAC]] definition |quote = '''rotamer''': One of a set of conformers arising from restricted rotation about one single bond.<ref name=GoldBookR05407>{{cite journal |title=rotamer |journal=Gold Book |date=2014 |publisher=IUPAC |ref=Gold Book R05407 |doi=10.1351/goldbook.R05407 |doi-access=free }}</ref>}}
[[File:Butane conformations and relative energies.svg|thumb|400x400px|Relative conformation energy diagram of butane as a function of dihedral angle.<ref>{{Cite book|title=Organic chemistry|last=J|first=McMurry|date=2012|publisher=Brooks/Cole|isbn=9780840054449|edition=8|location=Belmont, CA|pages=98}}</ref> A: antiperiplanar, anti or trans. B: synclinal or gauche. C: anticlinal or eclipsed. D: synperiplanar or cis.<ref name=":0" />]]
Rotating their carbon–carbon bonds, the molecules ethane and propane have three local energy minima.  They are structurally and energetically equivalent, and are called the ''staggered conformers''.  For each molecule, the three substituents emanating from each carbon–carbon bond are staggered, with each H–C–C–H [[dihedral angle]] (and H–C–C–CH<sub>3</sub> dihedral angle in the case of propane) equal to 60° (or approximately equal to 60° in the case of propane).  The three eclipsed conformations, in which the dihedral angles are zero, are transition states (energy maxima) connecting two equivalent energy minima, the staggered conformers. {{citation needed|date=January 2025}}

The butane molecule is the simplest molecule for which single bond rotations result in two types of nonequivalent structures, known as the ''anti''- and ''gauche-''conformers (see figure).

For example, butane has three conformers relating to its two methyl (CH<sub>3</sub>) groups: two ''gauche'' conformers, which have the methyls ±60° apart and are [[enantiomer]]ic, and an ''anti'' conformer, where the four carbon centres are coplanar and the substituents are 180° apart (refer to free energy diagram of butane). The energy separation between gauche and anti is 0.9&nbsp;kcal/mol associated with the [[Strain (chemistry)|strain]] energy of the gauche conformer. The anti conformer is, therefore, the most stable (≈&nbsp;0&nbsp;kcal/mol). The three eclipsed conformations with dihedral angles of 0°, 120°, and 240° are transition states between conformers.<ref name="dougherty" /> Note that the two eclipsed conformations have distinct energies: at 0° the two methyl groups are eclipsed, resulting in higher energy (≈&nbsp;5&nbsp;kcal/mol) than at 120°, where the methyl groups are eclipsed with hydrogens (≈&nbsp;3.5&nbsp;kcal/mol).<ref>{{cite web|last=Bauld|first=Nathan|title=Butane Conformational Analysis|url=http://research.cm.utexas.edu/nbauld/teach/butane.html|work=University of Texas|access-date=28 October 2013}}</ref>

===Mathematical analysis===
A rough approximate function can illustrate the main features of the conformational analysis for unbranched linear alkanes with rotation around a central C–C bond (C1–C2 in ethane, C2–C3 in butane, C3–C4 in hexane, etc.).<ref>{{Cite journal |last=Bixon |first=M. |last2=Lifson |first2=S. |date=1967-01-01 |title=Potential functions and conformations in cycloalkanes |url=https://linkinghub.elsevier.com/retrieve/pii/0040402067850233 |journal=Tetrahedron |volume=23 |issue=2 |pages=769–784 |doi=10.1016/0040-4020(67)85023-3 |issn=0040-4020|url-access=subscription }}</ref> The members of this series have the general formula C<sub>''2n''</sub>H''<sub>4n+2</sub>'' with the index ''n = 1, 2, 3,'' etc. It can be assumed that the [[Ring strain|angle strain]] is negligible in alkanes since the bond angles are all near the tetrahedral ideal. The [[Energy profile (chemistry)|energy profile]] is thus periodic with <math>2\pi/3</math> (120°) [[Periodic function|periodicity]] due to the threefold [[Molecular symmetry|symmetry]] of sp<sup>3</sup>-hybridized carbon atoms. This suggests a [[Sine and cosine|sinusoidal]] potential energy function <math>V(\theta, k)</math>, typically modelled using a [[Fourier series]] truncated to the dominant terms:<ref>{{Cite journal |last=Pitzer |first=Kenneth S. |date=1951-01-01 |title=Potential energies for rotation about single bonds |url=https://pubs.rsc.org/en/content/articlelanding/1951/df/df9511000066/unauth |journal=Discussions of the Faraday Society |language=en |volume=10 |issue=0 |pages=66–73 |doi=10.1039/DF9511000066 |issn=0366-9033|url-access=subscription }}</ref>  

<math>V(\theta, k) = \sum_{k=0}^{\infty} \frac{V_k(n)}{2} [1 - \cos(k\theta)]</math>

Here:

* <math>\theta</math> is the [[dihedral angle]] in degrees,
* <math>V_k(n)</math> are coefficients representing the amplitude of the <math>n</math>th [[harmonic]], corresponding to various energy barriers due to torsional influences and asymmetry in [[Steric effects|steric interactions]]. 
* The factor of <math>\tfrac{1}{2}</math> and the form <math>[1 - \cos(k\theta)]</math> ensure energy minima at staggered conformations and energy maxima at eclipsed conformations.

For alkanes, the dominant term is usually <math>k=3</math>, reflecting the threefold rotational symmetry. Higher terms may be included for precision where steric effects vary. The primary contribution comes from torsional strain due to alkyl groups eclipsing, captured by the <math>\cos(3\theta)</math> term. Steric interactions rise with the size of substituents (H– for ethane, CH<sub>3</sub>– for butane, C<sub>2</sub>H<sub>5</sub>– for hexane, etc.), taken into account by the <math>\cos(\theta)</math> term <math>(k=1)</math>. The number of carbon atoms clearly influences the size of substituents on the central C–C bond. In general, for unbranched linear alkanes with even-numbered chains, there will be two C''<sub>n-1</sub>''H''<sub>2n-1</sub>'' group substituents.

A parameterization using energy values derived from rotational spectroscopy data and theoretical calculations<ref>{{Cite journal |last=Dragojlovic |first=Veljko |date=September 2015 |title=Conformational analysis of cycloalkanes |url=http://link.springer.com/10.1007/s40828-015-0014-0 |journal=ChemTexts |language=en |volume=1 |issue=3 |doi=10.1007/s40828-015-0014-0 |issn=2199-3793}}</ref> gives the following simplified equation:

<math>V(\theta, n) = 0.25 (n-1) [1 - \cos(\theta)] + [1.45 + 0.05 (n-1)] [1 - \cos(3\theta)]</math>

Here <math>V(\theta, n)</math> is given in kcal/mol and <math>k=1,3</math>. This function largely neglects angle strain and long-range interactions for the <math>n</math> members of the series.
[[File:Approximate_potential_function_for_the_conformational_analysis_of_unbranched_linear_alkanes_with_even-numbered_chains.png|thumb|Approximate potential function using a truncated Fourier series for the conformational analysis of unbranched linear alkanes with even-numbered chains.]]
While simple molecules can be described by these types of conformations, more complex molecules require the use of the [[Klyne–Prelog system]] to describe the conformers.<ref name="dougherty" />

More specific examples of conformations are detailed elsewhere:
* Ring conformation
** [[Cyclohexane conformation]]s, including with chair and boat conformations among others.
** [[Cycloalkane]] conformations, including medium rings and [[macrocycles]]
** [[Carbohydrate conformation]], which includes cyclohexane conformations as well as other details.
* [[Allylic strain]] – energetics related to rotation about the single bond between an sp<sup>2</sup> carbon and an sp<sup>3</sup> carbon.
* [[Atropisomerism]] – due to restricted rotation about a bond.
* [[Folding (chemistry)|Folding]], including the secondary and tertiary structure of biopolymers (nucleic acids and proteins).<ref name="Rotamers21stCentury">{{Cite journal | last1 = Dunbrack | first1 = R. | title = Rotamer Libraries in the 21st Century | doi = 10.1016/S0959-440X(02)00344-5 | journal = Current Opinion in Structural Biology | volume = 12 | issue = 4 | pages = 431–440 | year = 2002 | pmid = 12163064}}</ref>
* [[Akamptisomerism]] – due to restricted inversion of a bond angle.

==Equilibrium of conformers==
[[File:Equillibrium conformers.jpg|thumb|250px|Equilibrium distribution of two conformers at various temperatures given the free energy of their interconversion.]]
Conformers generally exist in a [[dynamic equilibrium]]<ref name="eq conformer">{{cite web|last=Bruzik|first=Karol|title=Chapter 6: Conformation|url=http://tigger.uic.edu/~kbruzik/text/chapter6.htm|archive-url=https://archive.today/20131111153747/http://tigger.uic.edu/~kbruzik/text/chapter6.htm|url-status=dead|archive-date=11 November 2013|work=University of Illinois at Chicago|access-date=10 November 2013}}</ref>

Three isotherms are given in the diagram depicting the equilibrium distribution of two conformers at various temperatures. At a free energy difference of 0&nbsp;kcal/mol, this analysis gives an equilibrium constant of 1, meaning that two conformers exist in a 1:1 ratio. The two have equal free energy; neither is more stable, so neither predominates compared to the other. A negative difference in free energy means that a conformer interconverts to a thermodynamically more stable conformation, thus the equilibrium constant will always be greater than 1. For example, the Δ''G°'' for the transformation of butane from the ''gauche'' conformer to the ''anti'' conformer is −0.47&nbsp;kcal/mol at 298 K.<ref>The standard enthalpy change Δ''H''° from ''gauche'' to ''anti'' is –0.88 kcal/mol.  However, because there are ''two'' possible ''gauche'' forms, there is a statistical factor that needs to be taken into account as an entropic term.  Thus, Δ''G''° =  Δ''H''° – ''T''Δ''S° ='' Δ''H° + RT'' ln 2 ''='' –0.88 kcal/mol + 0.41 kcal/mol = –0.47 kcal/mol, at 298 K.</ref> This gives an equilibrium constant is about 2.2 in favor of the ''anti'' conformer, or a 31:69 mixture of ''gauche'':''anti'' conformers at equilibrium. Conversely, a positive difference in free energy means the conformer already is the more stable one, so the interconversion is an unfavorable equilibrium (''K''&nbsp;<&nbsp;1).

===Population distribution of conformers===
[[Image:2ConfBoltzmannDist.png|right|thumb|350px|Boltzmann distribution % of lowest energy conformation in a two component equilibrating system at various temperatures (°C, color) and energy difference in kcal/mol (''x''-axis)]]
The fractional population distribution of various conformers follows a [[Boltzmann distribution]]:<ref name="boltz dist">{{cite web|last=Rzepa|first=Henry|title=Conformational Analysis|url=http://www.ch.ic.ac.uk/local/organic/conf/c1_definitions.html|work=Imperial College London|access-date=11 November 2013}}</ref>
:<math> \frac{N_i}{N_\text{total}} = \frac {e^{-E_i/RT}} {\sum_{k=1}^M e^{-E_k/RT}}. </math>

The left hand side is the proportion of conformer ''i'' in an equilibrating mixture of ''M'' conformers in thermodynamic equilibrium. On the right side, ''E''<sub>''k''</sub> (''k'' = 1, 2, ..., ''M'') is the energy of conformer ''k'', ''R'' is the molar ideal gas constant (approximately equal to 8.314&nbsp;J/(mol·K) or 1.987 cal/(mol·K)), and ''T'' is the [[Absolute Temperature|absolute temperature]]. The denominator of the right side is the partition function.

===Factors contributing to the free energy of conformers===
The effects of [[electrostatics|electrostatic]] and [[steric effects|steric]] interactions of the substituents as well as orbital interactions such as [[hyperconjugation]] are responsible for the relative stability of conformers and their transition states. The contributions of these factors vary depending on the nature of the substituents and may either contribute positively or negatively to the energy barrier. Computational studies of small molecules such as ethane suggest that electrostatic effects make the greatest contribution to the energy barrier; however, the barrier is traditionally attributed primarily to steric interactions.<ref>{{cite journal|last=Liu|first=Shubin|title=Origin and Nature of Bond Rotation Barriers: A Unified View|journal=The Journal of Physical Chemistry A|date=7 February 2013|volume=117|issue=5|pages=962–965|doi=10.1021/jp312521z|pmid=23327680|bibcode=2013JPCA..117..962L}}</ref><ref>{{cite book|last=Carey|first=Francis A.|title=Organic chemistry|url=https://archive.org/details/organicchemistry00care_486|url-access=limited|year=2011|publisher=McGraw-Hill|location=New York|isbn=978-0-07-340261-1|page=[https://archive.org/details/organicchemistry00care_486/page/n139 105]|edition=8th}}</ref>
[[File:Contributions to Rotational Energy Barrier.png|center|thumb|450px|Contributions to rotational energy barrier]]
In the case of cyclic systems, the steric effect and contribution to the free energy can be approximated by [[A value]]s, which measure the energy difference when a substituent on cyclohexane in the axial as compared to the equatorial position. In large (>14 atom) rings, there are many accessible low-energy conformations which correspond to the strain-free diamond lattice.<ref>{{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 |page=14 |bibcode=2015ChTxt...1...14D |s2cid=94348487 }}</ref>

==Observation of conformers==
The short timescale of interconversion precludes the separation of conformer in most cases. [[Atropisomer]]s are conformational isomers which can be separated due to restricted rotation.<ref>{{cite book|last=McNaught|title=IUPAC Compendium of Chemical Terminology|year=1997|publisher=Blackwell Scientific Publications|location=Oxford|isbn=978-0967855097|chapter-url=http://goldbook.iupac.org/A00511.html|doi=10.1351/goldbook.A00511|chapter=Atropisomers}}</ref> The equilibrium between conformational isomers can be observed using a variety of [[spectroscopy|spectroscopic techniques]].<ref>{{March6th|page=195-196}}</ref>

[[Protein folding]] also generates conformers which can be observed. The [[Karplus equation]] relates the dihedral angle of [[Vicinal (chemistry)|vicinal]] protons to their [[J-coupling]] constants as measured by NMR. The equation aids in the elucidation of protein folding as well as the conformations of other rigid [[Aliphatic compound|aliphatic]] molecules.<ref>{{cite web|last=Dalton|first=Louisa|title=Karplus Equation|url=http://pubs.acs.org/cen/science/8151/8151karplus.html|work=Chemical and Engineering News|publisher=American Chemical Society|access-date=2013-10-27}}</ref> Protein side chains exhibit rotamers, whose distribution is determined by their steric interaction with different conformations of the backbone. This effect is evident from statistical analysis of the conformations of protein side chains in the [[Backbone-dependent rotamer library]].<ref>{{cite journal |last1=Dunbrack |first1=R. L. |last2=Cohen |first2=F. E. |title=Bayesian statistical analysis of protein side-chain rotamer preferences. |journal=Protein Science |date=1997 |volume=6 |issue=8 |pages=1661–1681 |doi=10.1002/pro.5560060807 |pmid=9260279 |pmc=2143774 |issn=0961-8368}}</ref>

===Spectroscopy===
Conformational dynamics can be monitored by variable temperature [[NMR]] spectroscopy. The technique applies to barriers of 8–14&nbsp;kcal/mol, and species exhibiting such dynamics are often called "[[Fluxional molecule|fluxional]]". For example, in [[Cyclohexane|cyclohexane derivatives]], the two chair conformers interconvert rapidly at room temperature. The ring-flip proceeds at a rates of approximately 10<sup>5</sup>&nbsp;ring-flips/sec, with an overall energy barrier of 10 kcal/mol (42 kJ/mol).  This barrier precludes separation at ambient temperatures.<ref name="eliel"/> However, at low temperatures below the [[Coalescence (chemistry)|coalescence]] point one can directly monitor the equilibrium by NMR spectroscopy and by dynamic, temperature dependent NMR spectroscopy the barrier interconversion.<ref>{{Cite journal|last1=Jensen|first1=Frederick R.|last2=Bushweller|first2=C. Hackett|date=1969-06-01|title=Separation of conformers. II. Axial and equatorial isomers of chlorocyclohexane and trideuteriomethoxycyclohexane|journal=Journal of the American Chemical Society|volume=91|issue=12|pages=3223–3225|doi=10.1021/ja01040a022|bibcode=1969JAChS..91.3223J |issn=0002-7863}}</ref>

Besides NMR spectroscopy, [[IR spectroscopy]] is used to measure conformer ratios. For the axial and equatorial conformer of bromocyclohexane, ν<sub>CBr</sub> differs by almost 50&nbsp;cm<sup>−1</sup>.<ref name="eliel">{{cite book|last1=Eliel|first1= E. L.|last2= Wilen|first2= S. H.|last3= Mander|first3= L. N. |title=Stereochemistry Of Organic Compounds|publisher= J. Wiley and Sons|date= 1994 |isbn=978-0-471-01670-0}}</ref>

==Conformation-dependent reactions==
Reaction rates are highly dependent on the conformation of the reactants. In many cases the dominant product arises from the reaction of the ''less prevalent'' conformer, by virtue of the [[Curtin–Hammett principle|Curtin-Hammett principle]]. This is typical for situations where the conformational equilibration is much faster than reaction to form the product. The dependence of a reaction on the stereochemical orientation is therefore usually only visible in [[Configurational analysis]], in which a particular conformation is locked by substituents. Prediction of rates  of many reactions involving the transition between sp2 and sp3 states, such as ketone reduction, alcohol oxidation or [[SN2 reaction|nucleophilic substitution]] is possible if all conformers and their relative stability ruled by their [[Strain (chemistry)|strain]] is taken into account.<ref>Schneider, H.-J.; Schmidt, G.; Thomas F. J. Am. Chem. Soc., 1983, 105, 3556.
https://pubs.acs.org/doi/pdf/10.1021/ja00349a031</ref>

One example where the rotamers become significant is  [[elimination reaction]]s, which involve the simultaneous removal of a proton and a [[leaving group]] from vicinal or ''anti''periplanar positions under the influence of a base.

[[Image:E2 elimination reaction.svg|center|thumb|350px|Base-induced bimolecular dehydrohalogenation (an E2 type reaction mechanism). The optimum geometry for the transition state requires the breaking bonds to be antiperiplanar, as they are in the appropriate staggered conformation]]

The mechanism requires that the departing atoms or groups follow antiparallel trajectories. For open chain substrates this geometric prerequisite is met by at least one of the three staggered conformers. For some cyclic substrates such as cyclohexane, however, an antiparallel arrangement may not be attainable depending on the substituents which might set a conformational lock.<ref>{{cite web|title=Cycloalkanes |url=http://www.ch.ic.ac.uk/local/organic/conf/c1_rings.html|publisher=Imperial College London|access-date=|first =Henry S. |last =Rzepa|date = 2014}}</ref> Adjacent [[substituent]]s on a cyclohexane ring can achieve antiperiplanarity only when they occupy trans [[wikt:diaxial|diaxial]] positions (that is, both are in axial position, one going up and one going down). {{citation needed|date=January 2025}}

One consequence of this analysis is that ''trans''-4-''tert''-butylcyclohexyl chloride cannot easily eliminate but instead undergoes substitution (see diagram below) because the most stable conformation has the bulky ''t''-Bu group in the equatorial position, therefore the chloride group is not antiperiplanar with any vicinal hydrogen (it is gauche to all four). The thermodynamically unfavored conformation has the ''t''-Bu group in the axial position, which is higher in energy by more than 5 kcal/mol (see [[A value]]).<ref name="dougherty a value">{{cite book|last1=Dougherty|first1=Eric V. Anslyn |last2= Dennis|first2= A.|title=Modern Physical Organic Chemistry|url=https://archive.org/details/modernphysicalor00ansl|url-access=limited|year=2006|publisher=University Science Books|location=Sausalito, CA|isbn=978-1-891389-31-3|page=[https://archive.org/details/modernphysicalor00ansl/page/n131 104]|edition=Dodr.}}</ref> As a result, the ''t''-Bu group "locks" the ring in the conformation where it is in the equatorial position and substitution reaction is observed. On the other hand, ''cis''-4-''tert''-butylcyclohexyl chloride undergoes elimination because antiperiplanarity of Cl and H can be achieved when the ''t''-Bu group is in the favorable equatorial position.

{{multiple image
| align = center
| image1 = Seven-atom interaction 1-(tert-butyl)-4-chlorocyclohexane.svg
| width1 = 230
| alt1 =
| caption1 = Thermodynamically unfavored conformation of ''trans''-4-''tert''-butylcyclohexyl chloride where the ''t''-Bu group is in the axial position exerting 7-atom interactions.
| image2 = E2 1-(tert-butyl)-4-chlorocyclohexane.svg
| width2 = 500
| alt2 =
| caption2 = The ''trans'' isomer can attain antiperiplanarity only via the unfavored axial conformer; therefore, it does not eliminate. The ''cis'' isomer is already in the correct geometry in its most stable conformation; therefore, it eliminates easily.
| footer =
}}

The repulsion between an axial ''t''-butyl group and hydrogen atoms in the 1,3-diaxial position is so strong that the cyclohexane ring will revert to a [[cyclohexane conformation|twisted boat]] conformation. The strain in cyclic structures is usually characterized by deviations from ideal [[bond angles]] ([[Baeyer strain]]), ideal [[torsional angle]]s ([[Pitzer strain]]) or [[transannular strain|transannular]] (Prelog) interactions.

==Alkane stereochemistry==
Alkane conformers arise from rotation around [[Sp³ bond|sp<sup>3</sup>]] hybridised carbon–carbon [[sigma bond]]s. The smallest alkane with such a chemical bond, [[ethane]], exists as an infinite number of conformations with respect to rotation around the C–C bond. Two of these are recognised as energy minimum ([[staggered conformation]]) and energy maximum ([[eclipsed conformation]]) forms. The existence of specific conformations is due to hindered rotation around sigma bonds, although a role for [[hyperconjugation]] is proposed by a competing theory. {{citation needed|date=January 2025}}

The importance of energy minima and energy maxima is seen by extension of these concepts to more complex molecules for which stable conformations may be predicted as minimum-energy forms.  The determination of stable conformations has also played a large role in the establishment of the concept of [[asymmetric induction]] and the ability to predict the [[stereochemistry]] of reactions controlled by steric effects. {{citation needed|date=January 2025}}

In the example of staggered [[ethane]] in [[Newman projection]], a hydrogen atom on one carbon atom has a 60° '''torsional angle''' or '''torsion angle'''<ref name = torsion/> with respect to the nearest hydrogen atom on the other carbon so that [[steric hindrance]] is minimised. The staggered conformation is more stable by 12.5 [[joule|kJ]]/[[mole (unit)|mol]] than the [[eclipsed]] conformation, which is the energy maximum for ethane. In the eclipsed conformation the torsional angle is minimised.

[[File:Staggered and eclipsed.svg|center|338px|staggered conformation left, eclipsed conformation right in [[Newman projection]]]]

<div class="center">[[Image:Ethane-staggered-depth-cue-3D-balls.png|150px]] [[Image:Ethane-eclipsed-depth-cue-3D-balls.png|150px]]</div>

In [[butane]], the two staggered conformations are no longer equivalent and represent two distinct conformers:the '''anti-conformation''' (left-most, below) and the '''gauche conformation''' (right-most, below).

[[File:Anti gauche.svg|center|558px|anti vs gauche conformations]]

<div class="center">[[Image:Butane-anti-side-3D-balls.png|150px]] [[Image:Butane-eclipsed-side-3D-balls.png|150px]] [[Image:Butane-negative-gauche-side-3D-balls.png|150px]]</div>

Both conformations are free of torsional strain, but, in the gauche conformation, the two [[methyl]] groups are in closer proximity than the sum of their van der Waals radii. The interaction between the two methyl groups is repulsive ([[van der Waals strain]]), and an [[activation energy|energy barrier]] results.

A measure of the [[potential energy]] stored in butane conformers with greater steric hindrance than the 'anti'-conformer ground state is given by these values:<ref>{{cite book|title =Organic Chemistry|edition = 6|last1= McMurry|first1= J.E.|publisher= Brooks Cole |year=2003|isbn = 978-0534000134}}</ref>
* Gauche, conformer – 3.8 kJ/mol
* Eclipsed H and CH<sub>3</sub> – 16 kJ/mol
* Eclipsed CH<sub>3</sub> and CH<sub>3</sub> – 19 kJ/mol.
The eclipsed [[methyl group]]s exert a greater steric strain because of their greater [[electron density]] compared to lone [[hydrogen]] atoms.

[[image:Butane conformers.svg|400px|thumb|center|Relative energies of conformations of butane with respect to rotation of the central C-C bond.]]

The textbook explanation for the existence of the energy maximum for an eclipsed conformation in ethane is [[steric hindrance]], but, with a C-C [[bond length]] of 154 pm and a [[Van der Waals radius]] for hydrogen of 120 pm, the hydrogen atoms in ethane are never in each other's way. The question of whether steric hindrance is responsible for the eclipsed energy maximum is a topic of debate to this day. One alternative to the steric hindrance explanation is based on [[hyperconjugation]] as analyzed within the Natural Bond Orbital framework.<ref>{{cite journal | last1=Pophristic | first1=Vojislava | last2=Goodman | first2=Lionel | title=Hyperconjugation not steric repulsion leads to the staggered structure of ethane | journal=Nature | volume=411 | issue=6837 | date=2001 | issn=1476-4687 | doi=10.1038/35079036 | pages=565–568 | pmid=11385566 | bibcode=2001Natur.411..565P | url=http://www.nature.com/nature/journal/v411/n6837/abs/411565a0.html | url-access=subscription }}</ref><ref>{{cite journal | last=Weinhold | first=Frank | title=A new twist on molecular shape | journal=Nature | publisher=Springer Science and Business Media LLC | volume=411 | issue=6837 | year=2001 | issn=0028-0836 | doi=10.1038/35079225 | pages=539–541| pmid=11385553 }}</ref><ref>{{cite journal | last=Weinhold | first=Frank | title=Rebuttal to the Bickelhaupt–Baerends Case for Steric Repulsion Causing the Staggered Conformation of Ethane | journal=Angewandte Chemie International Edition | volume=42 | issue=35 | date=2003-09-15 | issn=1433-7851 | doi=10.1002/anie.200351777 | pages=4188–4194 |url=https://www.researchgate.net/publication/229639507}}</ref> In the staggered conformation, one C-H [[sigma bond|sigma]] [[bonding orbital]] donates electron density to the [[antibonding orbital]] of the other C-H bond.  The energetic stabilization of this effect is maximized when the two orbitals have maximal overlap, occurring in the staggered conformation.  There is no overlap in the eclipsed conformation, leading to a disfavored energy maximum. On the other hand, an analysis within quantitative [[molecular orbital theory]] shows that 2-orbital-4-electron (steric) repulsions are dominant over hyperconjugation.<ref>{{cite journal | last1=Bickelhaupt | first1=F. Matthias | last2=Baerends | first2=Evert Jan | title=The Case for Steric Repulsion Causing the Staggered Conformation of Ethane | journal=Angewandte Chemie | volume=115 | issue=35 | date=2003-09-15 | issn=0044-8249 | doi=10.1002/ange.200350947 | pages=4315–4320 | bibcode=2003AngCh.115.4315B | language=de}}</ref> A [[valence bond theory]] study also emphasizes the importance of steric effects.<ref>{{cite journal | last1=Mo | first1=Yirong | last2=Wu | first2=Wei | last3=Song | first3=Lingchun | last4=Lin | first4=Menghai | last5=Zhang | first5=Qianer | last6=Gao | first6=Jiali | title=The Magnitude of Hyperconjugation in Ethane: A Perspective from Ab Initio Valence Bond Theory | journal=Angewandte Chemie International Edition | publisher=Wiley | volume=43 | issue=15 | date=2004-03-30 | issn=1433-7851 | doi=10.1002/anie.200352931 | pages=1986–1990| pmid=15065281 }}</ref>

===Nomenclature===
Naming alkanes per standards listed in the [[IUPAC Gold Book]] is done according to the [[Klyne–Prelog system]] for specifying angles (called either torsional or [[dihedral angles]]) between substituents around a single bond:<ref name =torsion>{{GoldBookRef|title=torsion angle|file=T06406| accessdate = 2015-10-29 }}</ref>
[[Image:Synantipericlinal.svg|200px|right|syn/anti peri/clinal]]
* a torsion angle between 0° and ±90° is called '''syn'''  (s)
* a torsion angle between ±90° and 180° is called '''anti''' (a)
* a torsion angle between 30° and 150° or between −30° and −150° is called '''clinal''' (c)
* a torsion angle between 0° and ±30° or ±150° and 180° is called '''periplanar''' (p)
* a torsion angle between 0° and ±30° is called '''[[Anti-periplanar|synperiplanar]]''' (sp), also called '''syn-''' or '''cis-''' conformation
* a torsion angle between 30° to 90° and −30° to −90° is called '''synclinal''' (sc), also called '''gauche''' or '''skew'''<ref name="GoldbookGauche">{{GoldBookRef|title=gauche|file=G02593| accessdate = 2008-02-27 }}</ref> 
* a torsion angle between 90° and 150° or −90° and −150° is called '''anticlinal''' (ac)
* a torsion angle between ±150° and 180° is called '''[[Anti-periplanar|antiperiplanar]]''' (ap), also called '''anti-''' or '''trans-''' conformation
[[Strain (chemistry)#Torsional strain|Torsional strain]] or "Pitzer strain" refers to resistance to twisting about a bond.

===Special cases===
In [[n-pentane|''n''-pentane]], the terminal [[methyl]] groups experience additional [[pentane interference]]. {{citation needed|date=January 2025}}

Replacing hydrogen by [[fluorine]] in [[polytetrafluoroethylene]] changes the stereochemistry from the zigzag geometry to that of a [[helix]] due to electrostatic repulsion of the fluorine atoms in the 1,3 positions. Evidence for the helix structure in the crystalline state is derived from [[X-ray crystallography]] and from [[NMR spectroscopy]] and [[circular dichroism]] in solution.<ref>''Conformational Analysis of Chiral Helical Perfluoroalkyl Chains by VCD'' Kenji Monde, Nobuaki Miura, Mai Hashimoto, Tohru Taniguchi, and Tamotsu Inabe [[J. Am. Chem. Soc.]]; '''2006'''; 128(18) pp 6000–6001; [https://dx.doi.org/10.1021/ja0602041 Graphical abstract]</ref>

==See also==
{{Wikiquote}}
* [[Anomeric effect]]
* [[Backbone-dependent rotamer library]]
* [[Cycloalkane]]
* [[Cyclohexane]]
** [[Cyclohexane conformation]]s.
* [[Gauche effect]]
* [[Klyne–Prelog system]]
* [[Macrocyclic stereocontrol]]
* [[Molecular configuration]]
* [[Molecular modelling]]
* {{slink|Molecular Symmetry|Molecular nonrigidity}}
* [[Steric effects]]
* [[Strain (chemistry)]]

==References==
{{Reflist}}

{{Authority control}}

[[Category:Physical organic chemistry]]
[[Category:Stereochemistry]]