Editing Rotamer (section)

===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.