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Rotamer

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In chemistry, rotamers are chemical species that differ from one another primarily due to rotations about one or more single bonds. Various arrangements of atoms in a molecule that differ by rotation about single bonds can also be referred to as different conformations. Conformers/rotamers differ little in their energies, so they are almost never separable in a practical sense.[citation needed] Rotations about single bonds are subject to small energy barriers.[1][failed verification] 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: atropisomerism).[2][3][4] The ring-flip of substituted cyclohexanes constitutes a common form of conformers.[5]

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.

The study of the energetics of bond rotation is referred to as conformational analysis.[6] In some cases, conformational analysis can be used to predict and explain product selectivity, mechanisms, and rates of reactions.[7] Conformational analysis also plays an important role in rational, structure-based drug design.

Types

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IUPAC definition

rotamer: One of a set of conformers arising from restricted rotation about one single bond.[8]

 
Relative conformation energy diagram of butane as a function of dihedral angle.[9] A: antiperiplanar, anti or trans. B: synclinal or gauche. C: anticlinal or eclipsed. D: synperiplanar or cis.[2]

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–CH3 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.

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 (CH3) groups: two gauche conformers, which have the methyls ±60° apart and are enantiomeric, 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 difference between gauche and anti is 0.9 kcal/mol associated with the strain energy of the gauche conformer. The anti conformer is, therefore, the most stable (≈ 0 kcal/mol). The three eclipsed conformations with dihedral angles of 0°, 120°, and 240° are transition states between conformers.[6] Note that the two eclipsed conformations have different energies: at 0° the two methyl groups are eclipsed, resulting in higher energy (≈ 5 kcal/mol) than at 120°, where the methyl groups are eclipsed with hydrogens (≈ 3.5 kcal/mol).[10]

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 different conformers.[6]

More specific examples of conformations are detailed elsewhere:


Equilibrium of conformers

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Equilibrium distribution of two conformers at different temperatures given the free energy of their interconversion.

Conformers generally exist in a dynamic equilibrium[12]

Three isotherms are given in the diagram depicting the equilibrium distribution of two conformers at different temperatures. At a free energy difference of 0 kcal/mol, this 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 ΔG° for the transformation of butane from the gauche conformer to the anti conformer is −0.47 kcal/mol at 298 K.[13] 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 < 1). Even for highly unfavorable changes (large positive ΔG°), the equilibrium constant between two conformers can be increased by increasing the temperature, so that the amount of the less stable conformer present at equilibrium increases (although it always remains the minor conformer).

Population distribution of conformers

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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 different conformers follows a Boltzmann distribution:[14]

 

The left hand side is the proportion of conformer i in an equilibrating mixture of M conformers in thermodynamic equilibrium. On the right side, Ek (k = 1, 2, ..., M) is the energy of conformer k, R is the molar ideal gas constant (approximately equal to 8.314 J/(mol·K) or 1.987 cal/(mol·K)), and T is the absolute temperature. The denominator of the right side is the partition function.

Factors contributing to the free energy of conformers

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The effects of electrostatic and 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.[15][16]

 
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 values, 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.[17]

Observation of conformers

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The short timescale of interconversion precludes the separation of conformer in most cases. Atropisomers are conformational isomers which can be separated due to restricted rotation.[18] The equilibrium between conformational isomers can be observed using a variety of spectroscopic techniques.

Protein folding also generates conformers which can be observed. The Karplus equation relates the dihedral angle of 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 molecules.[19] Protein side chains exhibit rotamers, whose distribution is determined by their steric interaction with different conformations of the backbone.[20] This is evident from statistical analysis of the conformations of protein side chains in the Backbone-dependent rotamer library.

Spectroscopy

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Conformational dynamics can be monitored by variable temperature NMR spectroscopy. The technique applies to barriers of 8–14 kcal/mol, and species exhibiting such dynamics are often called "fluxional". For example, in cyclohexane derivatives, the two chair conformers interconvert rapidly at room temperature. The ring-flip proceeds at a rates of approximately 105 ring-flips/sec, with an overall energy barrier of 10 kcal/mol (42 kJ/mol). This barrier precludes separation at ambient temperatures.[21] However, at low temperatures below the coalescence point one can directly monitor the equilibrium by NMR spectroscopy and by dynamic, temperature dependent NMR spectroscopy the barrier interconversion.[22]

Besides NMR spectroscopy, IR spectroscopy is used to measure conformer ratios. For the axial and equatorial conformer of bromocyclohexane, νCBr differs by almost 50 cm−1.[21]

Conformation-dependent reactions

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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. 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 nucleophilic substitution is possible if all conformers and their relative stability ruled by their strain is taken into account.[23]

One example where the rotamers become significant is elimination reactions, which involve the simultaneous removal of a proton and a leaving group from vicinal or antiperiplanar positions under the influence of a base.

 
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.[24] Adjacent substituents on a cyclohexane ring can achieve antiperiplanarity only when they occupy trans diaxial positions (that is, both are in axial position, one going up and one going down).

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).[25] 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.

 
Thermodynamically unfavored conformation of trans-4-tert-butylcyclohexyl chloride where the t-Bu group is in the axial position exerting 7-atom interactions.
 
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.

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 twisted boat conformation. The strain in cyclic structures is usually characterized by deviations from ideal bond angles (Baeyer strain), ideal torsional angles (Pitzer strain) or transannular (Prelog) interactions.

Alkane stereochemistry

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Conformations of Ethane

Alkane conformers arise from rotation around sp3 hybridised carbon–carbon sigma bonds. 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.

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.

In the example of staggered ethane in Newman projection, a hydrogen atom on one carbon atom has a 60° torsional angle or torsion angle[26] 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 kJ/mol than the eclipsed conformation, which is the energy maximum for ethane. In the eclipsed conformation the torsional angle is minimised.

 
staggered conformation left, eclipsed conformation right in Newman projection
   

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).

 
anti vs gauche conformations
   

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 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:[27]

  • Gauche, conformer – 3.8 kJ/mol
  • Eclipsed H and CH3 – 16 kJ/mol
  • Eclipsed CH3 and CH3 – 19 kJ/mol.

The eclipsed methyl groups exert a greater steric strain because of their greater electron density compared to lone hydrogen atoms.

 
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.[28][29][30] In the staggered conformation, one C-H 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.[31] A valence bond theory study also emphasizes the importance of steric effects.[32]

Nomenclature

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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:[26]

 
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 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[33]
  • a torsion angle between 90° and 150° or −90° and −150° is called anticlinal (ac)
  • a torsion angle between ±150° and 180° is called antiperiplanar (ap), also called anti- or trans- conformation

Torsional strain or "Pitzer strain" refers to resistance to twisting about a bond.

Special cases

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In n-pentane, the terminal methyl groups experience additional pentane interference.

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.[34]

See also

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Wikiquote has quotations related to Rotamer.

References

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  1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (1996) "Free rotation (hindered rotation, restricted rotation)". doi:10.1351/goldbook.F02520
  2. ^ a b Moss, GP (1996-01-01). "Basic terminology of stereochemistry (IUPAC Recommendations 1996)". Pure and Applied Chemistry. 68 (12): 2193–2222. doi:10.1351/pac199668122193. ISSN 1365-3075. S2CID 98272391.
  3. ^ 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 [1] and [2][permanent dead link‍], accessed 12 June 2014.
  4. ^ Alkorta, Ibon; Jose Elguero; Christian Roussel; Nicolas Vanthuyne; Patrick Piras (2012). Atropisomerism and Axial Chirality in Heteroaromatic Compounds. Advances in Heterocyclic Chemistry. Vol. 105. pp. 1–188. doi:10.1016/B978-0-12-396530-1.00001-2. hdl:10261/62060. ISBN 9780123965301.
  5. ^ Hunt, Ian. "Stereochemistry". University of Calgary. Retrieved 28 October 2013.
  6. ^ a b c Anslyn, Eric; Dennis Dougherty (2006). Modern Physical Organic Chemistry. University Science. p. 95. ISBN 978-1891389313.
  7. ^ Barton, Derek (1970). "The Principles of Conformational Analysis". Nobel Media AB 2013. 169 (3945). Elsevier Publishing Co.: 539–44. Bibcode:1970Sci...169..539B. doi:10.1126/science.169.3945.539. PMID 17746022. Retrieved 10 November 2013.
  8. ^ "rotamer". Gold Book. IUPAC. 2014. doi:10.1351/goldbook.R05407.
  9. ^ J, McMurry (2012). Organic chemistry (8 ed.). Belmont, CA: Brooks/Cole. p. 98. ISBN 9780840054449.
  10. ^ Bauld, Nathan. "Butane Conformational Analysis". University of Texas. Retrieved 28 October 2013.
  11. ^ Dunbrack, R. (2002). "Rotamer Libraries in the 21st Century". Current Opinion in Structural Biology. 12 (4): 431–440. doi:10.1016/S0959-440X(02)00344-5. PMID 12163064.
  12. ^ Bruzik, Karol. "Chapter 6: Conformation". University of Illinois at Chicago. Archived from the original on 11 November 2013. Retrieved 10 November 2013.
  13. ^ The standard enthalpy change ΔH° 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, ΔG° = ΔH° – TΔS° = ΔH° RT ln 2 = –0.88 kcal/mol 0.41 kcal/mol = –0.47 kcal/mol, at 298 K.
  14. ^ Rzepa, Henry. "Conformational Analysis". Imperial College London. Retrieved 11 November 2013.
  15. ^ Liu, Shubin (7 February 2013). "Origin and Nature of Bond Rotation Barriers: A Unified View". The Journal of Physical Chemistry A. 117 (5): 962–965. Bibcode:2013JPCA..117..962L. doi:10.1021/jp312521z. PMID 23327680.
  16. ^ Carey, Francis A. (2011). Organic chemistry (8th ed.). New York: McGraw-Hill. p. 105. ISBN 978-0-07-340261-1.
  17. ^ Dragojlovic, Veljko (2015). "Conformational analysis of cycloalkanes" (PDF). Chemtexts. 1 (3): 14. Bibcode:2015ChTxt...1...14D. doi:10.1007/s40828-015-0014-0. S2CID 94348487.
  18. ^ McNaught (1997). "Atropisomers". IUPAC Compendium of Chemical Terminology. Oxford: Blackwell Scientific Publications. doi:10.1351/goldbook.A00511. ISBN 978-0967855097.
  19. ^ Dalton, Louisa. "Karplus Equation". Chemical and Engineering News. American Chemical Society. Retrieved 2013-10-27.
  20. ^ Dunbrack, R. L.; Cohen, F. E. (1997). "Bayesian statistical analysis of protein side-chain rotamer preferences". Protein Science. 6 (8): 1661–1681. doi:10.1002/pro.5560060807. ISSN 0961-8368. PMC 2143774. PMID 9260279.
  21. ^ a b Eliel, E. L.; Wilen, S. H.; Mander, L. N. (1994). Stereochemistry Of Organic Compounds. J. Wiley and Sons. ISBN 978-0-471-01670-0.
  22. ^ Jensen, Frederick R.; Bushweller, C. Hackett (1969-06-01). "Separation of conformers. II. Axial and equatorial isomers of chlorocyclohexane and trideuteriomethoxycyclohexane". Journal of the American Chemical Society. 91 (12): 3223–3225. Bibcode:1969JAChS..91.3223J. doi:10.1021/ja01040a022. ISSN 0002-7863.
  23. ^ Schneider, H.-J.; Schmidt, G.; Thomas F. J. Am. Chem. Soc., 1983, 105, 3556. https://pubs.acs.org/doi/pdf/10.1021/ja00349a031
  24. ^ Rzepa, Henry S. (2014). "Cycloalkanes". Imperial College London.
  25. ^ Dougherty, Eric V. Anslyn; Dennis, A. (2006). Modern Physical Organic Chemistry (Dodr. ed.). Sausalito, CA: University Science Books. p. 104. ISBN 978-1-891389-31-3.
  26. ^ a b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "torsion angle". doi:10.1351/goldbook.T06406
  27. ^ McMurry, J.E. (2003). Organic Chemistry (6 ed.). Brooks Cole. ISBN 978-0534000134.
  28. ^ Pophristic, Vojislava; Goodman, Lionel (2001). "Hyperconjugation not steric repulsion leads to the staggered structure of ethane". Nature. 411 (6837): 565–568. Bibcode:2001Natur.411..565P. doi:10.1038/35079036. ISSN 1476-4687. PMID 11385566.
  29. ^ Weinhold, Frank (2001). "A new twist on molecular shape". Nature. 411 (6837). Springer Science and Business Media LLC: 539–541. doi:10.1038/35079225. ISSN 0028-0836. PMID 11385553.
  30. ^ Weinhold, Frank (2003-09-15). "Rebuttal to the Bickelhaupt–Baerends Case for Steric Repulsion Causing the Staggered Conformation of Ethane". Angewandte Chemie International Edition. 42 (35): 4188–4194. doi:10.1002/anie.200351777. ISSN 1433-7851.
  31. ^ Bickelhaupt, F. Matthias; Baerends, Evert Jan (2003-09-15). "The Case for Steric Repulsion Causing the Staggered Conformation of Ethane". Angewandte Chemie (in German). 115 (35): 4315–4320. Bibcode:2003AngCh.115.4315B. doi:10.1002/ange.200350947. ISSN 0044-8249.
  32. ^ Mo, Yirong; Wu, Wei; Song, Lingchun; Lin, Menghai; Zhang, Qianer; Gao, Jiali (2004-03-30). "The Magnitude of Hyperconjugation in Ethane: A Perspective from Ab Initio Valence Bond Theory". Angewandte Chemie International Edition. 43 (15). Wiley: 1986–1990. doi:10.1002/anie.200352931. ISSN 1433-7851. PMID 15065281.
  33. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "gauche". doi:10.1351/goldbook.G02593
  34. ^ 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; Graphical abstract
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