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WIREs Comput Mol Sci
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Hyperconjugation

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Abstract This review outlines the ubiquitous nature of hyperconjugative interactions and their role in the structure and reactivity of organic molecules. After defining the common hyperconjugative patterns, we discuss the main factors controlling the magnitude of hyperconjugative effects, including orbital symmetry, energy gap, electronegativity, and polarizibility. The danger of underestimating the magnitude of hyperconjugative interactions are illustrated by a number of spectroscopic, conformational, and structural effects. Through the use of advanced computational techniques, the true role of hyperconjugative effects, as it pertains to their influence on stereoelectronics, conformational equilibria, and reactivities relative to other electronic effects, continue to be uncovered. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 109–141 DOI: 10.1002/wcms.6 This article is categorized under: Structure and Mechanism > Molecular Structures

Natural bond orbital energies (in a.u., 1 a.u. = 627.5 kcal/mol) of axial and equatorial lone pairs in oxa‐, thia‐, selena‐, and azacyclohexane calculated at the B3LYP/6–31G** level.

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Comparison of acceptor ability (natural bond orbital Edel energies in kcal/mol) of CX bonds in different directions.

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Top: Correlation of energy of vicinal NBO σCH → σ*CX interaction, Edel with electronegativity of element X in substituted ethanes, CH3CH2X. Bottom: Correlation of energy of σ*CX orbitals with electronegativity of element X in substituted ethanes, CH3CH2X.

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A schematic representation of three possible homoanomeric interactions in six‐membered saturated heterocycles: (a) the W‐effect, (b) the Plough (the ‘Big Dipper’) effect, and (c) the ‘mirror image’ of the Plough effect. Differences in hybridization are neglected.

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Intermolecular positive hyperconjugation in the transition state for an SE2 process with retention of configuration. M is an electrofuge, R is an alkyl group, and E is the electrophilic site in the reagent EX.126

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Left: Hyperconjugative stabilization of H‐bonded complexes. Right: The analogy of F ⋅⋅⋅ He ⋅ ⋅⋅HY+ fragmentation of FHeH ⋅ ⋅ ⋅ Y complexes with an SN2 reaction.

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Top: The antiperiplanar stereoelectronic preference for vicinal conjugation and hyperconjugation. Bottom: Key hyperconjugative interactions between σCH and σ*CH orbitals (Reprinted with permission from Refs 59 to 61).

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The significant stabilization of a δ‐cyclohexyl cation by a series of equatorial substituents via double hyperconjugation.

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Comparison of normal and extended positive hyperconjugation.

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Effects of neutral hyperconjugation on the direct nuclear magnetic resonance coupling constants.

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Absolute (data below the structures) and relative (data near the arrows) gas phase hydride ion affinities for selected carbocations. All energies are in kcal/mol.96

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Positive hyperconjugation in a cation and a neutral molecule.

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Spectroscopic effects associated with negative hyperconjugation.

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Selected patterns of intra‐ and intermolecular negative hyperconjugation.

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Contributing resonance structures for positive, negative, and neutral hyperconjugation.

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Comparison of contributing resonance structures in sacrificial and isovalent hyperconjugation.

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Top: Definitions of the lone pair (nσ and nπ) delocalization effect (σ‐ or π‐LP effect), the antiperiplanar hyperconjugation effect (the AP effect) and the synperiplanar hyperconjugation effect (the SP effect) within the natural bond orbital framework for cis‐1,2‐dihaloethenes (X = F, Cl, or Br). Bottom: Comparison of hyperconjugative interactions involving CF bonds in (a) cis‐ and (b) trans‐1,2‐difluoroethenes. (B) The interaction is greater for the antiperiplanar interaction in the cis isomer (Reprinted with permission from Ref 275).

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(Left) Four‐electron destabilizing interaction expressed in terms of nonorthogonal “unperturbed” orbitals (for which there is no imaginable Hermitian perturbation theory). (Middle) Four‐electron nonstabilizing interaction expressed in terms of orthogonalized unperturbed orbitals (for which there exists a valid Hermitian). (Right) Four‐electron stabilizing interaction for a proper three‐term description of orbital energies in terms of Löwdin‐orthogonalized basis orbitals (Reprinted with permission from Refs 59 to 61).

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A possible way to estimate hyperconjugation in propene through a bond separation reaction.

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(a) Description of the vicinal σCH → σ*CH interaction in ethane in terms of resonance theory (‘double bond/no bond resonance’). (b) Energy lowering due to hyperconjugative interaction between σCH and σ*CX orbitals. (c) Natural bond orbital plots illustrating overlap of vicinal σCH and σ*CH orbitals in ethane.

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The gauche effect for a 1,2‐disubstituted ethanes.

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(a) Energy lowering due to hyperconjugative interaction between n(Y) and σ*XH orbitals in XH ⋅ ⋅ ⋅ Y complex. (b) Natural bond orbital plots illustrating the overlap of the σ*CH of fluoroform and the n(O) orbital of the oxygen atom in water in the fluoroform/water complex and (c) description of the hyperconjugative n(O) → σ*CH interaction in this complex in terms of resonance theory illustrating effective charge transfer from H‐bond acceptor (water) to H‐bond donor (fluoroform).

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Bonds involved in the main hyperconjugative interactions which influence the conformational equilibrium of methylcyclohexane (Reprinted with permission from Ref 208).

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Dominating antiperiplanar negative hyperconjugative interactions involved in endo‐ and exo‐anomeric effects.

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Second‐order perturbation natural bond orbital energies in kcal/mol for important hyperconjugative interactions in axial and equatorial cyclohexyl cations (B3LYP/6–31G**).

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Axial and equatorial ‘hyperconjomers’ of cyclohexyl cations.

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The difference between eclipsed and staggered conformers of propene and natural bond orbital‐derived rotational potential energy surface without certain hyperconjugation interactions (reprinted with permission from Ref 206).

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(a) Conventional equations for the evaluation of hyperconjugation.202 (b) Revised bond separation energy values for alkene and alkyne hyperconjugation, corrected for protobranching.51

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Comparison of the G3(MP2) calculated enthalpies of formation ΔHf298 (‘G3’) and experimental hydrogenation ΔHhyd (‘expt’) in kcal/mol of butenes and butynes. According to these estimates, the conjugation energy of 1,3‐butadiene (right) is 3.9 ± 0.1 kcal/mol, but for 1,3‐butadiyne (left), it is zero.

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σ‐Homoaromaticity (two‐electron system a) and antiaromaticity (four‐electron system b) in six‐membered heterocycles.

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Molecular orbital symmetry effects on hyperconjugation efficiency in cyclic systems.

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Examples of stereoselective cyclobutene and oxacyclobutene ring openings.

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Correlation of CCl distance with the natural bond orbital (NBO) energies of n(N)→σ*CCl interaction and the NBO charge at Cl during the process of CCl bond stretching in 3‐chloropiperidine.

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The most important transition state stabilizing hyperconjugative interactions for axial and equatorial nucleophilic addition to cyclohexanone according to the Cieplak's model.

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Left: Changes in HOMO and LUMO upon stretching and twisting of the central σ‐bond. Right: Dominant hyperconjugative interactions that control outward rotation of a donor substituent and inward rotation of an acceptor substituent. In the first case, the key interaction is negative hyperconjugation between the transition state (TS) HOMO (a stretched and twisted σ‐orbital) with a substituent empty p‐orbital (same topology is important for an acceptor σ*‐ or a π*‐orbital). In the second case, the key interaction is positive hyperconjugation between the TS LUMO (a stretched and twisted σ*‐orbital) with a substituent filled p‐orbital (same topology is important for a donor σ‐ or a π‐orbital).

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Two correlations between the differences in stabilization energies of δ‐XHn substituents in the equatorial and axial cyclohexyl cations (Figure 12) and electronegativity of X. (a) The left plot corresponds to the general correlation. (b) The right plot gives separate correlations for each row. Calculations were performed at the B3LYP/6–31G** (B3LYP/6–311++G**) level (Reprinted with permission from Refs 118 and 119).

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Three isodesmic equations used to calculate substituent stabilization energies [SEax(top), SEeq(middle), and ΔSEeq‐ax(bottom)] in the equatorial and axial cyclohexyl cations.

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