# Rotamer A **rotamer** is one of the conformational isomers, or *conformers*, of a [[Molecule|molecule]]: a spatial arrangement that differs from the others only by rotation about one or more single bonds, so that the conformers interconvert without any [[Chemical_bond|chemical bond]] being broken. Conformational isomerism is the branch of [[Stereochemistry|stereochemistry]] that deals with these arrangements, their energies and their populations. Because the barriers to rotation about a C–C single bond are usually only a few kilojoules per mole, conformers interconvert billions of times a second at room temperature and cannot be bottled separately; what is observed is a population-weighted average, and the population follows the [[Boltzmann_distribution|Boltzmann distribution]] over the torsional energy. In the microsim below the reader turns the dihedral angle φ of butane about its C2–C3 bond from 0° to 360° while the 3D molecule and its [[Newman_projection|Newman projection]] rotate together; a torsional-energy curve marks the eclipsed conformer at 0° (about 19 kJ/mol), the gauche conformers at 60° and 300° (about 3.8 kJ/mol) and the anti conformer at 180° (0 kJ/mol), and a readout answers, through `p_anti = 1 / (1 + 2·exp(−ΔE/RT))`, what fraction of butane is anti at the [[Temperature|temperature]] the reader sets.[^openstax-oc3] On Wikitube's [[PORTAL_Chemistry|Chemistry]] flagship this is the main article for the Part XIII — Practice section *Organic chemistry: conformations* (row K60), the [[Organic_chemistry|organic chemistry]] entry between the coordination complexes of the inorganic row and the enzyme kinetics of the biochemistry row. ## Types Rotation about a single bond gives two limiting classes of conformer. In a *staggered* conformer the bonds on the front [[Carbon|carbon]] of a Newman projection bisect the angles between the bonds on the back carbon, 60° apart; in an *eclipsed* conformer they lie directly in front of them.[^openstax-oc3] For ethane, the simplest case, all staggered conformers are equivalent and all eclipsed ones are equivalent, and the difference between them is the rotational barrier of 12 kJ/mol, a number first inferred in 1936 by Kemp and Pitzer from the measured [[Entropy|entropy]] of ethane, which was too small for a freely rotating molecule.[^openstax-oc3][^kemp-pitzer] Once the two carbons carry different groups, the staggered conformers stop being equivalent. The Klyne–Prelog names describe the relationship of two chosen groups across the bond by the dihedral angle between them: synperiplanar near 0°, synclinal (gauche) near ±60°, anticlinal near ±120° and antiperiplanar (anti) near 180°.[^klyne-prelog] Ring molecules add their own vocabulary: cyclohexane adopts a chair, in which every bond is staggered, or the higher-energy twist-boat and boat forms, and a chair "flips" to a second chair in which axial and equatorial substituents exchange places.[^openstax-oc4] ### Mathematical analysis Torsional energy is periodic in the dihedral angle, so the natural description is a Fourier series in φ. Ethane needs a single three-fold term, `V(φ) = (V3/2)·(1 + cos 3φ)`, with V3 = 12 kJ/mol, and the six equal minima and maxima follow at once.[^openstax-oc3] Butane about its central bond needs a one-fold and a two-fold term as well, `V(φ) = ½·[V1·(1 + cos φ) + V2·(1 − cos 2φ) + V3·(1 + cos 3φ)]`, with the anti conformer at 180° taken as zero. Fitting the four stationary values the sim displays (19, 3.8, 16 and 0 kJ/mol at 0°, 60°, 120° and 180°) gives V1 = 4.53, V2 = 0.53 and V3 = 14.47 kJ/mol, and the resulting curve reproduces all four exactly; its gauche minimum falls at 61°, not 60°, because a three-term series is not obliged to put its extrema on the symmetry angles (fit computed for this article). The curve drawn in the microsim is this ILLUSTRATIVE display fit through the six tabulated stationary points, not a measured potential, and it is used only to interpolate between them. [[Molecular_mechanics|Molecular mechanics]] force fields use exactly this functional form for every rotatable bond, with parameters fitted to experiment and to [[Computational_chemistry|quantum-chemical]] calculations, and the [[Potential_energy|potential energy]] of a whole molecule is then summed over all its torsions. ## Equilibrium of conformers Two conformers in rapid exchange are in [[Chemical_equilibrium|chemical equilibrium]], with an [[Equilibrium_constant|equilibrium constant]] `K = [B]/[A] = exp(−ΔG°/RT)`, where ΔG° is the [[Gibbs_free_energy|Gibbs free energy]] difference between them.[^openstax-oc3] The size of the barrier decides how fast the equilibrium is reached, the size of ΔG° decides where it lies, and the two are independent: a 12 kJ/mol barrier is crossed on the order of 10¹⁰ times per second at room temperature by the Eyring estimate `(kB·T/h)·exp(−ΔG‡/RT)`, while a 45 kJ/mol cyclohexane ring flip is crossed about 10⁵ times per second (both computed here as illustrations), yet neither barrier says anything about which side is favoured.[^openstax-oc4] ### Population distribution of conformers The microsim's readout is the population of the anti conformer of butane. Three staggered conformers matter: one anti at 180° and two gauche at 60° and 300°, each gauche lying ΔE = 3.8 kJ/mol above anti.[^openstax-oc3] If the entropy difference between the conformers is taken as nothing but this two-fold degeneracy, the Boltzmann ratio for each gauche conformer is `exp(−ΔE/RT)` and the anti fraction is `p_anti = 1 / (1 + 2·exp(−ΔE/RT))`. At 298 K, with RT = 2.48 kJ/mol, the exponential is 0.216, so p_anti = 1/1.432 = 0.70: roughly 70 % of butane molecules are anti and 30 % gauche, 15 % in each mirror-image gauche form.[^openstax-oc3] Cooling sharpens the preference and heating blurs it, which is what the temperature control shows: p_anti is 0.83 at 200 K, 0.61 at 400 K and 0.56 at 500 K (computed here from the same ΔE), and it tends to 1/3 as the thermal energy swamps the 3.8 kJ/mol gap. The eclipsed conformers hardly appear in the population at any of these temperatures because 16 and 19 kJ/mol are six to eight times RT; they matter as barriers, not as residents. The same [[Statistical_mechanics|statistical mechanics]], summed over every torsion, gives the conformational [[Partition_function_(statistical_mechanics)|partition function]] that fixes the average shape of a flexible molecule. ### Factors contributing to the free energy of conformers Two kinds of strain set the energies in the butane profile. *Torsional strain* is the cost of eclipsing bonds: in the OpenStax accounting each eclipsed H/H pair costs 4.0 kJ/mol, each eclipsed H/CH₃ pair 6.0 kJ/mol and each eclipsed CH₃/CH₃ pair 11 kJ/mol, so the 0° conformer of butane carries 11 + 4.0 + 4.0 = 19 kJ/mol and the 120° conformer 6.0 + 6.0 + 4.0 = 16 kJ/mol.[^openstax-oc3] *Steric strain* is the repulsion of groups forced too close together even in a staggered arrangement: the gauche conformer of butane pays 3.8 kJ/mol for the proximity of its two methyl groups, and this "gauche-butane interaction" reappears throughout conformational analysis, for instance as the 1,3-diaxial interactions that cost an axial methyl group on cyclohexane 7.6 kJ/mol relative to equatorial.[^openstax-oc4] The same additive terms are the six-term energy table the microsim carries.[^tru-ch9] Beyond these, the [[Enthalpy|enthalpy]] of a conformer is shifted by [[Hydrogen_bond|hydrogen bonds]] and [[Dipole|dipole]]–dipole interactions between substituents, by [[Van_der_Waals_force|van der Waals]] attraction between chains, and by the solvent, which stabilises the more polar conformer; and the entropy term is shifted by symmetry, as the two-fold degeneracy of gauche butane shows, and by how loosely each conformer vibrates in its well. ## Observation of conformers Whether a conformer can be observed as a separate species depends on the ratio of its lifetime to the timescale of the measurement. Barriers of a few kilojoules per mole give lifetimes of picoseconds, so most methods see an average; barriers near 100 kJ/mol give lifetimes of hours at room temperature by the same Eyring estimate, and the conformers become separable atropisomers, the point at which conformational isomerism shades into configurational [[Chirality_(chemistry)|chirality]].[^eliel] In the solid state the question is moot: [[X-ray_crystallography|X-ray crystallography]] sees whichever conformer packed into the crystal, which is often, but not always, the one favoured in solution. ### Spectroscopy [[Nuclear_magnetic_resonance|Nuclear magnetic resonance]] is the workhorse. At room temperature the exchange between conformers is fast on the NMR timescale, so each nucleus shows one averaged signal; on cooling, the exchange slows until the signals of the individual conformers decoalesce, and the temperature at which they do so gives the barrier. Even in the averaged regime the three-bond coupling constant ³J between vicinal protons depends on the dihedral angle through the Karplus relation, `³J(φ) ≈ A·cos²φ + B·cos φ + C`, large near 0° and 180° and small near 90°, so a measured coupling reports the population-weighted average of cos²φ.[^karplus1959] Vibrational [[Spectroscopy|spectroscopy]] is faster than any rotation, so [[Infrared_spectroscopy|infrared]] and Raman spectra show separate bands for separate conformers even at room temperature; the way the intensity ratio of two such bands changes with temperature gives the enthalpy difference between the conformers through the [[Van_'t_Hoff_equation|van 't Hoff equation]]. In the gas phase, microwave rotational spectra and electron diffraction resolve the geometry of each conformer directly, which is how the gauche and anti forms of butane were characterised.[^eliel] ## Conformation-dependent reactions A reaction that requires a particular geometry runs through a particular conformer, and the product ratio is not simply the conformer ratio. The Curtin–Hammett principle states that when conformers interconvert much faster than they react, the product distribution is set by the difference between the free energies of the two transition states, not by the populations of the ground-state conformers; a minor conformer can give the major product if its barrier is lower.[^seeman1983] The elimination reaction E2 is the textbook case: it needs the leaving group and the β-hydrogen antiperiplanar, so a substituted cyclohexane reacts only from the chair in which the leaving group is axial, and a compound whose stable chair has the leaving group equatorial reacts slowly because it must first flip.[^openstax-oc4] The [[Reaction_rate|rate]] of such a reaction therefore carries a conformational term, and the [[Activation_energy|activation energy]] measured by an Arrhenius plot includes the free energy needed to reach the reactive conformer. ## Alkane stereochemistry Alkanes have no functional groups and no stereocenters, so their entire stereochemistry is conformational, and butane is the molecule on which it is taught. The microsim shows butane end-on along its C2–C3 bond, exactly as a Newman projection does: the front carbon carries one methyl group and two hydrogens, the back carbon the same, and the dihedral angle φ between the two methyl groups is the single control. As φ runs from 0° to 360° the molecule passes through six stationary points, alternately eclipsed and staggered: eclipsed with the methyls superimposed at 0°, gauche at 60°, eclipsed with each methyl over a hydrogen at 120°, anti at 180°, and then the mirror images of the last three at 240° and 300°.[^openstax-oc3] The energy curve above the molecule carries the six values from the additive table, 19, 3.8, 16, 0, 16 and 3.8 kJ/mol, and a marker rides the curve as the molecule turns, so the reader sees the two methyl groups clash at the 19 kJ/mol maximum and settle at maximum separation in the 0 kJ/mol anti minimum.[^tru-ch9] The Boltzmann readout in the corner converts the curve into a population at the chosen temperature. Longer alkanes repeat the pattern bond by bond: an all-anti chain is the extended zig-zag drawn in every [[Ball-and-stick_model|ball-and-stick model]], each gauche kink costs about 3.8 kJ/mol, and the conformational freedom of a long chain is why a [[Polymer|polymer]] such as polyethylene is a random coil in the melt and an extended zig-zag in the crystal. ### Nomenclature The Newman projection, introduced by Melvin Newman in 1955, looks straight down the bond of interest: the front carbon is the point where three bonds meet, the back carbon is a circle, and the dihedral angle is read directly as the angle between a front bond and a back bond.[^newman1955] A sawhorse projection views the same bond obliquely and shows both carbons. The dihedral or torsion angle itself is defined by four atoms, A–B–C–D, as the angle between the planes ABC and BCD, positive for a clockwise rotation of the front bond onto the back bond. The everyday names *eclipsed*, *staggered*, *gauche* and *anti* and the systematic Klyne–Prelog ranges (syn/anti, periplanar/clinal) describe the same angles at two levels of precision.[^klyne-prelog] ### Special cases Ethane's barrier of 12 kJ/mol has no steric explanation, because hydrogen atoms are too small to clash; it is torsional strain, now attributed mainly to the stabilising overlap of a filled C–H bonding orbital with the empty antibonding orbital of the C–H bond behind it, which is possible only in the staggered form.[^openstax-oc3] Propane's barrier of 14 kJ/mol adds one H/CH₃ eclipsing to the ethane pattern.[^openstax-oc3] Cyclohexane is the special case that organised the field: its chair has all bonds staggered and no torsional strain, it flips between two chairs across a barrier of 45 kJ/mol, and a substituent prefers the equatorial position by an amount, 7.6 kJ/mol for methyl, that comes from two gauche-butane-like 1,3-diaxial interactions.[^openstax-oc4] Molecules with a very hindered bond, such as biaryls with bulky ortho substituents, have rotational barriers high enough that the two rotamers are stable, separable and chiral, the atropisomers already mentioned.[^eliel] ## See also - [[Stereochemistry]] - [[Newman_projection]] - [[Chirality_(chemistry)]] - [[Organic_chemistry]] - [[Boltzmann_distribution]] - [[Molecular_mechanics]] - [[Nuclear_magnetic_resonance]] ## References [^openstax-oc3]: McMurry, John (2023). *Organic Chemistry*. OpenStax. Chapter 3, Organic Compounds: Alkanes and Their Stereochemistry, §3.6 Conformations of Ethane and §3.7 Conformations of Other Alkanes (staggered and eclipsed conformers; the 12 kJ/mol ethane barrier; the 14 kJ/mol propane barrier; eclipsing costs of 4.0, 6.0 and 11 kJ/mol; the 3.8 kJ/mol gauche interaction; the butane profile). https://openstax.org/details/books/organic-chemistry [^openstax-oc4]: McMurry, John (2023). *Organic Chemistry*. OpenStax. Chapter 4, Organic Compounds: Cycloalkanes and Their Stereochemistry, §4.5–4.7 (chair and twist-boat cyclohexane; the 45 kJ/mol ring flip; axial and equatorial positions; 7.6 kJ/mol for an axial methyl group); Chapter 11 for the antiperiplanar requirement of E2. https://openstax.org/details/books/organic-chemistry [^tru-ch9]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter 9, Organic Chemistry III – Conformational Analysis, pp. 519–574 (torsional strain; the butane energy table) (page to pin). https://open.umn.edu/opentextbooks/textbooks/chemical-bonding-and-organic-chemistry [^kemp-pitzer]: Kemp, J. D.; Pitzer, K. S. (1936). "Hindered rotation of the methyl groups in ethane." *Journal of Chemical Physics* 4: 749. [^klyne-prelog]: Klyne, W.; Prelog, V. (1960). "Description of steric relationships across single bonds." *Experientia* 16: 521–523. [^newman1955]: Newman, M. S. (1955). "A notation for the study of certain stereochemical problems." *Journal of Chemical Education* 32 (7): 344–347. [^karplus1959]: Karplus, M. (1959). "Contact electron-spin coupling of nuclear magnetic moments." *Journal of Chemical Physics* 30 (1): 11–15. [^seeman1983]: Seeman, J. I. (1983). "Effect of conformational change on reactivity in organic chemistry. Evaluations, applications, and extensions of Curtin–Hammett/Winstein–Holness kinetics." *Chemical Reviews* 83 (2): 83–134. [^eliel]: Eliel, Ernest L.; Wilen, Samuel H.; Mander, Lewis N. (1994). *Stereochemistry of Organic Compounds*. New York: Wiley (conformational analysis of acyclic and cyclic molecules; atropisomers; physical methods). <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Rotamer.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Rotamer* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Rotamer.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Rotamer.html" data-title="Rotamer"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Rotamer) : [Wikitube](https://en.wikitube.io/wiki/Rotamer) · pinned revision [1369677744](https://en.wikipedia.org/w/index.php?oldid=1369677744) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Chemistry]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Chemistry row K60 · sim pending (matter/Rotamer).*