The delocalised nature of hyperconjugation

Question

I have always thought I understood hyperconjugation well until recently, in my post on Regioselectivity of bromination of alkenes, I began to question my understanding of this concept. Hyperconjugation is essentially an MO concept which can be generalised to include any sort of intramolcular orbital interaction between one set of occupied molecular or atomic orbitals with another such set of unoccupied orbitals, belonging to adjacent atoms or groups of atoms in a molecule. A most excellent introduction to this concept can be found here. This is not the IUPAC definition, but anyway, the emphasis of my question is not on the definition so there is no point being pedantic here. This term is most commonly evoked to explain the mechanism by which alkyl groups "donate" electron density to stabilise carbocations.

I am aware that there have already been multiple posts, with good answers, on this concept:

• What is hyperconjugation?
• Stabilisation of carbocations through hyperconjugation
• Inductive effect and hyperconjugation - one elephant, different parts?
• Hyperconjugation involving other bonds

In my post which discusses the nucleophilic attack on the cyclic bromonium ion intermediate, I was enlightened by Martin through one of his comments:

I am certain there is hyperconjugation, as there already was hyperconjugation in a substituted alkene. There probably is always something to which we refer to as hyperconjugation. You are thinking in localised orbitals, which is only one viewpoint...

Just like he said, my conception of hyperconjugation had always been how Ron frequently describes it as - a localised phenomena. Specifically, in the context of stabilising carbocations, I see it as an interaction between a $\sigma$ bonding MO of the $\ce {C-H}$ or $\ce {C-C}$ bond with the empty p orbital of the carbocation. However, this comment made me think about the delocalised nature of these interactions. MO theory is supposed to be based heavily on delocalised interactions, yet we are considering rather localised interactions here. Well, it is not as localised as a 2-centre 2-electron bond, but still it is a rather localised picture. I would not like to contend this. But... I would just like to pose the following related questions below:

If hyperconjugation should be more seen as a more delocalised phenomena, would distance and geometry play such important factors? Please take note of my examples below and pay attention to them as you attempt a response at my question.

For example, if I have a tert-butyl group bonded to a carbocationic centre, would there also be (significant enough) hyperconjugative interactions between the $\ce {C-H}$ $\sigma$ bonding MOs with the empty p orbital of the carbon atom. Note that by looking at the more localised picture, such as that given by Ron, we would likely only expect the $\ce {C-C}$ bonds to be significant hyperconjugative donors. Additionally, specifically, in my case of the bromonium ion, would there be significant hyperconjugative interactions between the bonding MOs of the $\ce {C-C}$ and $\ce {C-H}$ bonds of the adjacent alkyl groups with the low-energy $\ce {C-Br}$ $\sigma$* LUMO?

Any help is much appreciated!

Answer 1

I'll try to answer your question through the exemples you give us.

Where are the electrons ?

If you look at the hybridized orbitals making the C-H and the C-C bonds, you can see that the more the bond is polarized, the worse electron donor you have. It's quite understandable since if the bond is polarized, the electron density will be closer to the heteroatom but further to the carbocation that needs stabilization.

Usually the donor ability goes in this order increasingly: C-F < C-O < C-N < C-H < C-C

Hyperconjugation from C-C to carbocation

Following the "rule" stated before, the stabilization of a carbocation will be best with an adjacent C-C bond. And this is in accordence with what we learn in school since the more alkyl groups nearby, the more stable is the carbacation. Not only because of the increased overall electron density (donor inductive effect) but also because of the hyperconjugation. This is also the base of some reactivity (1,2-C-C bond migration)

Hyperconjugation in the bromonium case

We can easely extend the thing we just saw for the exemple of a bromonium intermediate. In fact it is important to dissociate the cases of the bromonium and the transition state for the bromonium openning.

The bromonium has two bonds with a carbon atom. One could expect the opening reaction to occur in competition between these two sites. We can see that the C-Br bond (Scheme 2, left) can be aligned with a C-C bond, so if we take a look at the molecular orbitals, we will see that this filled sigma C-C bond can interact with the empty C-Br sigma*. Thus creating a destabilization of the C-Br bond (filling a anti-bonding molecular orbital destabilizes the bond) trough an hyperconjugation intercation. But if we look at the second C-Br bond (right) we see that there are no such interaction since there are no filled molecular orbital which can interact with the sigma* of the C-Br bond.

In term of reactivity, the destabilization of the left-hand C-Br bond will favor the breaking of this bond instead of the other one.

Answer 2

Though your question is written in a slightly confusing fashion and seems to assume a simplistic view of the concept of hyperconjugation, I will try to answer to "If hyperconjugation should be more seen as a more delocalized phenomenon, would distance and geometry play such important factors?". IT DEPENDS on the specific case. However, from fundamental principles, distance and geometry are the critical factors in all types of interactions involving charge transfer, including hyperconjugation, irrespective of the magnitude of the interaction in a particular case.^[1] Delocalization of electrons itself is caused both by distance and geometrical factors. Orbital sizes are defined finitely; thus correct donor-acceptor distances are crucial for orbitals to be able to overlap or hybridize. In most cases, a proper orbital distance (assuming an adequate symmetry, see below) is proportional to the stabilization energy that is achieved, with the concomitant delocalization of the electron or electrons (double hyperconjugation).^[2] Of course, geometry (topology, technically) is just as crucial, because if the donor and acceptor orbitals are not allowed to overlap in space by symmetry, then no 'hyperconjugative stabilization' is likely to occur (perhaps other types of factors, stabilizing in some cases, such as exchange repulsions from the periphery, and/or Coulombic factors, could, directly or indirectly, create the illusory picture that the system is somehow stabilized hyperconjugatively, even though no geometrically correct orbital matching was even there. This all, adds to the complexity of dissecting energy contributions accurately, even for 'simple' molecular systems). Going back to the dynamic nature of hyperconjugation, and to your question on the importance of the degree of localization or delocalization in defining the mere concept, it was found that hyperconjugative and not steric reasons are behind the preference of ethane to adopt a staggered conformation over an eclipsed one;^[3] it was found explicitly that vicinal hyperconjugation (σCH–σCH*) and not geminal hyperconjugation (σCC–σCC*) factors lead to the staggered equilibrium structure of ethane. On the other hand, and as a contrasting example, it is geminal hyperconjugation which is linked to the low ring strain of cyclopropane, and not vicinal.^[4] The views expressed in ref. 3 are, however, disputed by Bickelhaupt and Baerends.^[5] Based on these two examples, it seems as if tight, or strained hydrocarbon species in space, and hindered small systems, display a more "localized" type of hyperconjugation, semantically speaking, hence favoring geminal hyperconjugation, whereas relaxed systems may prefer vicinal hyperconjugation. These are just two basic examples I could pick out from the literature and which you can use with those you already asked and were answered by Gwendal to increase your intuition about the phenomenon, but eventually, you will realize that these stabilizing interactions are not detectable quantities, and thus it is impossible to define them or generalize cases wholly from basic concepts or from hardcore quantum chemical methods, at the moment. Keep in mind that hyperconjugation is a highly controversial topic, all the way from the days of Mulliken and Dewar.^[6–8] A comprehensive review may help out.^[9]

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References

1. Solà, M. Why Aromaticity Is a Suspicious Concept? Why? Front. Chem. 2017, 5, 22. DOI: 10.3389/fchem.2017.00022.

2. Wu, J. I.; Schleyer, P. v. R. Hyperconjugation in hydrocarbons: Not just a “mild sort of conjugation”. Pure Appl. Chem. 2013, 85 (5), 921–940. DOI: 10.1351/PAC-CON-13-01-03.

3. Pophristic, V.; Goodman, L. Hyperconjugation not steric repulsion leads to the staggered structure of ethane. Nature 2001, 411 (6837), 565–568. DOI: 10.1038/35079036.

4. Inagaki, S.; Ishitani, Y.; Kakefu, T. Geminal Delocalization of .sigma.-Electrons and Ring Strains. J. Am. Chem. Soc. 1994, 116 (13), 5954–5958. DOI: 10.1021/ja00092a052.

5. Bickelhaupt, F. M.; Baerends, E. J. The Case for Steric Repulsion Causing the Staggered Conformation of Ethane. Angew. Chem. Int. Ed. 2003, 42 (35), 4183–4188. DOI: 10.1002/anie.200350947.

6. Mulliken, R. S. Intensities of Electronic Transitions in Molecular Spectra IV. Cyclic Dienes and Hyperconjugation. J. Chem. Phys. 1939, 7 (5), 339–352. DOI: 10.1063/1.1750446.

7. Mulliken, R. S.; Rieke, C. A.; Brown, W. G. Hyperconjugation. J. Am. Chem. Soc. 1941, 63 (1), 41–56. DOI: 10.1021/ja01846a008.

8. Dewar, M.; Schmeising, H. A re-evaluation of conjugation and hyperconjugation: The effects of changes in hybridisation on carbon bonds. Tetrahedron 1959, 5 (2-3), 166–178. DOI: 10.1016/0040-4020(59)80102-2.

9. Alabugin, I. V.; Gilmore, K. M.; Peterson, P. W. Hyperconjugation. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2011, 1 (1), 109–141. DOI: 10.1002/wcms.6.