Flexing analysis of ethane internal rotation energetics

Abstract

A flexing analysis of the ethane barrier energy in terms of structural (ΔEstruct), steric exchange (ΔEsteric), and hyperconjugative charge-transfer (ΔEdeloc) energy contributions has been carried out using natural bond orbitals. No evidence is found for the view that the ethane staggered equilibrium geometry or the C–C bond expansion that accompanies rotation results from steric exchange repulsion interactions. The analysis shows that ΔEstruct and ΔEdeloc have very different stereoelectronic dependencies, but that the ΔEsteric and ΔEdeloc dependencies are antagonistic. All of their contributions are strongly affected by the C–C bond expansion, with the result that the barrier mechanism cannot be understood without taking into account their different relaxation dependencies. Neglect of C–C expansion leaves the charge-transfer interactions paramount by subduing the steric and structural contributions. These interactions are found to be an important determinant for the expansion. The strong expansion dependence found for ΔEstruct is largely controlled by weakening of the C–C bond, and to a lesser extent by concomitant strengthening of the C–H bonds. Most of this dependence can be mimicked by C–C expansion in the absence of methyl torsion indicating that C–C bond weakening does not arise from the symmetry change accompanying ethane torsion.

The Case for Steric Repulsion Causing the Staggered Conformation of Ethane

“…It turns out that it is very important to take carefully into account the effect of geometry changes during rotation around the CÀC bond, notably the CÀC bond stretching when going towards the eclipsed conformation, as indeed already stressed by England and Gordon [14] and Goodman and coworkers. [15] We will see that the interpretation of the barrier as caused by steric repulsion between vicinal C À H bonds is fully corroborated by this analysis, and we conclude it is perfectly valid for organic chemists to adhere to this view. We comment on the possible source of the difference between our analysis and the NBO one.…”

“…So the NBO scheme introduces a reference state (the Lewis determinant) which is destabilized compared to the Hartree-Fock determinant, and puts considerable emphasis on the s* orbitals of the model, as is evident from the energy lowering coming from their admixing. In the present case we note, from the detailed analysis by Goodman et al, [15] that when we perform a rigid rotation of staggered ethane to eclipsed ethane, keeping the C-C separation and the CH 3 conformation fixed, the energy E Lewis of the Lewis determinant becomes more favorable by 2.68 kcal mol À1 (step I in table III of ref. [15]).…”

“…In the present case we note, from the detailed analysis by Goodman et al, [15] that when we perform a rigid rotation of staggered ethane to eclipsed ethane, keeping the C-C separation and the CH 3 conformation fixed, the energy E Lewis of the Lewis determinant becomes more favorable by 2.68 kcal mol À1 (step I in table III of ref. [15]). We would expect at least some steric hindrance effect, and it is unfortunate that a wavefunction that is supposed to correspond to the Lewis structure, does not exhibit the expected steric repulsion between electron pairs when rotating towards a more sterically crowded conformation.…”

The Magnitude of Hyperconjugation in Ethane: A Perspective from Ab Initio Valence Bond Theory

“…This leads to the counter-intuitive result that the eclipsed conformation is more stable than the staggered conformation by 11.3 kJ mol À1 . [22] Bickelhaupt and Baerends rationalized the exceptionally large hyperconjugative delocalization energy as a result of the construction of the Lewis determinant wavefunction for the localized reference state from the occupied NBOs, [9] which is overly destabilized relative to the Hartree-Fock determinant. [13] Clearly, the concept and significance of steric hindrance and hyperconjugation in rationalizing the cause of the rotational barrier in ethane depend on the method used to derive the wavefunction of the localized reference state.…”

Origin of methyl torsional barrier in 1-methyl-2-(1H)-pyridone

“…Based on theoretical investigations, a new mechanism involving * and * hyperconjugation in the lowest unoccupied molecular orbital was proposed to explain the variation of torsional barrier in substituted toluenes, such as fluorotoluene, cresol etc. Barrier energy partitioning 11 in terms of structural, steric, and hyperconjugative charge transfer during methyl rotation allowed deeper understanding of this problem. However, the role of dominant interactions causing the barrier even in case of the simple textbook molecule Ethane 12 is still under scrutiny.…”