Editing Rotamer (section)

==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>