Inchemistry,rotamers are chemical species that differ from one another primarily due to rotations about onesingle bond. Various arrangements ofatoms in amolecule that differ by rotation about single bonds can also be referred to asconformations. Conformations, which representlocal minima on thepotential energy surface, are calledconformers.[1] Conformers can differ from one another due to rotation of multiple bonds; rotamers are a subset of conformers.[2] Conformers/rotamers usually 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.[3] When the time scale for interconversion is long enough for isolation of individual rotamers (usually arbitrarily defined as ahalf-life of interconversion of 1000 seconds or longer), the species are termedatropisomers.[4][5][6] Thering-flip of substitutedcyclohexanes constitutes a common form of conformers.[7]
The study of the energetics of bond rotation is referred to asconformational analysis.[8] In some cases, conformational analysis can be used to predict and explain product selectivity, mechanisms, and rates of reactions.[9] Conformational analysis also plays an important role in rational, structure-baseddrug design.
rotamer: One of a set of conformers arising from restricted rotation about one single bond.[10]
Rotating their carbon–carbon bonds, the molecules ethane and propane have three local energy minima. They are structurally and energetically equivalent, and are called thestaggered conformers. For each molecule, the three substituents emanating from each carbon–carbon bond are staggered, with each H–C–C–Hdihedral 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.[citation needed]
The butane molecule is the simplest molecule for which single bond rotations result in two types of nonequivalent structures, known as theanti- andgauche-conformers (see figure).
For example, butane has three conformers relating to its two methyl (CH3) groups: twogauche conformers, which have the methyls ±60° apart and areenantiomeric, and ananti 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 kcal/mol associated with thestrain 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.[8] Note that the two eclipsed conformations have distinct 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).[12]
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.).[13] The members of this series have the general formula C2nH4n+2 with the indexn = 1, 2, 3, etc. It can be assumed that theangle strain is negligible in alkanes since the bond angles are all near the tetrahedral ideal. Theenergy profile is thus periodic with (120°)periodicity due to the threefoldsymmetry of sp3-hybridized carbon atoms. This suggests asinusoidal potential energy function, typically modelled using aFourier series truncated to the dominant terms:[14]
Here:
For alkanes, the dominant term is usually, 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 term. Steric interactions rise with the size of substituents (H– for ethane, CH3– for butane, C2H5– for hexane, etc.), taken into account by the term. 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 Cn-1H2n-1 group substituents.
A parameterization using energy values derived from rotational spectroscopy data and theoretical calculations[15] gives the following simplified equation:
Here is given in kcal/mol and. This function largely neglects angle strain and long-range interactions for the members of the series.
While simple molecules can be described by these types of conformations, more complex molecules require the use of theKlyne–Prelog system to describe the conformers.[8]
More specific examples of conformations are detailed elsewhere:
Conformers generally exist in adynamic equilibrium[17]
Three isotherms are given in the diagram depicting the equilibrium distribution of two conformers at various temperatures. At a free energy difference of 0 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 ΔG° for the transformation of butane from thegauche conformer to theanti conformer is −0.47 kcal/mol at 298 K.[18] This gives an equilibrium constant is about 2.2 in favor of theanti conformer, or a 31:69 mixture ofgauche: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).
The fractional population distribution of various conformers follows aBoltzmann distribution:[19]
The left hand side is the proportion of conformeri in an equilibrating mixture ofM conformers in thermodynamic equilibrium. On the right side,Ek (k = 1, 2, ...,M) is the energy of conformerk,R is the molar ideal gas constant (approximately equal to 8.314 J/(mol·K) or 1.987 cal/(mol·K)), andT is theabsolute temperature. The denominator of the right side is the partition function.
The effects ofelectrostatic andsteric interactions of the substituents as well as orbital interactions such ashyperconjugation 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.[20][21]
In the case of cyclic systems, the steric effect and contribution to the free energy can be approximated byA 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.[22]
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.[23] The equilibrium between conformational isomers can be observed using a variety ofspectroscopic techniques.[24]
Protein folding also generates conformers which can be observed. TheKarplus equation relates the dihedral angle ofvicinal protons to theirJ-coupling constants as measured by NMR. The equation aids in the elucidation of protein folding as well as the conformations of other rigidaliphatic molecules.[25] 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 theBackbone-dependent rotamer library.[26]
Conformational dynamics can be monitored by variable temperatureNMR spectroscopy. The technique applies to barriers of 8–14 kcal/mol, and species exhibiting such dynamics are often called "fluxional". For example, incyclohexane 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.[27] However, at low temperatures below thecoalescence point one can directly monitor the equilibrium by NMR spectroscopy and by dynamic, temperature dependent NMR spectroscopy the barrier interconversion.[28]
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.[27]
Reaction rates are highly dependent on the conformation of the reactants. In many cases the dominant product arises from the reaction of theless prevalent conformer, by virtue of theCurtin-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 inconfigurational 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 ornucleophilic substitution is possible if all conformers and their relative stability ruled by theirstrain is taken into account.[29]
One example where the rotamers become significant iselimination reactions, which involve the simultaneous removal of a proton and aleaving group from vicinal orantiperiplanar positions under the influence of a base.
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.[30] Adjacentsubstituents on a cyclohexane ring can achieve antiperiplanarity only when they occupy transdiaxial positions (that is, both are in axial position, one going up and one going down).[citation needed]
One consequence of this analysis is thattrans-4-tert-butylcyclohexyl chloride cannot easily eliminate but instead undergoes substitution (see diagram below) because the most stable conformation has the bulkyt-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 thet-Bu group in the axial position, which is higher in energy by more than 5 kcal/mol (seeA value).[31] As a result, thet-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 thet-Bu group is in the favorable equatorial position.
-4-chlorocyclohexane.svg)
-4-chlorocyclohexane.svg)
The repulsion between an axialt-butyl group and hydrogen atoms in the 1,3-diaxial position is so strong that the cyclohexane ring will revert to atwisted boat conformation. The strain in cyclic structures is usually characterized by deviations from idealbond angles (Baeyer strain), idealtorsional angles (Pitzer strain) ortransannular (Prelog) interactions.
Alkane conformers arise from rotation aroundsp3 hybridised carbon–carbonsigma 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 forhyperconjugation is proposed by a competing theory.[citation needed]
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 ofasymmetric induction and the ability to predict thestereochemistry of reactions controlled by steric effects.[citation needed]
In the example of staggeredethane inNewman projection, a hydrogen atom on one carbon atom has a 60°torsional angle ortorsion angle[32] with respect to the nearest hydrogen atom on the other carbon so thatsteric hindrance is minimised. The staggered conformation is more stable by 12.5kJ/mol than theeclipsed conformation, which is the energy maximum for ethane. In the eclipsed conformation the torsional angle is minimised.
Inbutane, the two staggered conformations are no longer equivalent and represent two distinct conformers:theanti-conformation (left-most, below) and thegauche conformation (right-most, below).
Both conformations are free of torsional strain, but, in the gauche conformation, the twomethyl 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 anenergy barrier results.
A measure of thepotential energy stored in butane conformers with greater steric hindrance than the 'anti'-conformer ground state is given by these values:[33]
The eclipsedmethyl groups exert a greater steric strain because of their greaterelectron density compared to lonehydrogen atoms.
The textbook explanation for the existence of the energy maximum for an eclipsed conformation in ethane issteric hindrance, but, with a C-Cbond length of 154 pm and aVan 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 onhyperconjugation as analyzed within the Natural Bond Orbital framework.[34][35][36] In the staggered conformation, one C-Hsigmabonding orbital donates electron density to theantibonding 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 quantitativemolecular orbital theory shows that 2-orbital-4-electron (steric) repulsions are dominant over hyperconjugation.[37] Avalence bond theory study also emphasizes the importance of steric effects.[38]
Naming alkanes per standards listed in theIUPAC Gold Book is done according to theKlyne–Prelog system for specifying angles (called either torsional ordihedral angles) between substituents around a single bond:[32]
Torsional strain or "Pitzer strain" refers to resistance to twisting about a bond.
Inn-pentane, the terminalmethyl groups experience additionalpentane interference.[citation needed]
Replacing hydrogen byfluorine inpolytetrafluoroethylene changes the stereochemistry from the zigzag geometry to that of ahelix due to electrostatic repulsion of the fluorine atoms in the 1,3 positions. Evidence for the helix structure in the crystalline state is derived fromX-ray crystallography and fromNMR spectroscopy andcircular dichroism in solution.[40]
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