Steric hindrance of an unbonded electron pair

Question

This question is half inspired by this question, and half inspired by the structure of molecules like hydrazine and hydrogen peroxide.

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When I was looking at the aforementioned molecules, I started trying to reason as to why the lowest energy conformation of these molecules are what they are.

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In hydrazine, the lowest energy conformation is not the one in which the unbonded electron pairs are anti-periplanar. This makes me think that hydrogen have a greater steric hindrance than unbonded electron pairs do.

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In hydrogen peroxide, however, the lowest energy conformation is not the one in which the hydrogen are anti-periplanar. This contradicts what I reasoned form the structure of hydrazine.

Being confused by this, I tried a different approach—what about the cyclohexyl carbanion? Surely using $\Delta G = -RT \ln{K_\mathrm{eq}}$ the relative steric hindrance of an unbonded electron pair and a hydrogen atom could be determined. What I became unsure about, however, was how rapid inversion might affect this, and additionally whether or not there even is even any data regarding the major and minor confirmations of the cyclohexyl carbanion (because I am unsure if it even exists in such a way that this can even be measured).

So am I flawed in my reasonings? Does the equilibrium data for the cyclohexyl carbanion exist?

Answer 1

Since I just covered this material in depth in my physical organic chemistry class, I figured I'd write up an answer.

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Electronegative elements lower the energies of all molecular orbitals to which they contribute, of which their low-lying $\sigma ^{*}$ orbitals are of particular importance. Electronegative atom lone pair MOs, which have little bonding character and are also (relatively) high-lying in energy, are very close in energy and will donate their electrons to the low lying empty orbitals, producing a stabilizing interaction. Molecular conformations are in part shaped by these interactions, which is known as the donor-acceptor effect.

Hydrogen peroxide is a classic example of this effect. In addition to sterics predicting that the hydrogens be anti-periplanar, this conformation also minimizes the molecule's net dipole (another stabilizing effect), yet its most stable conformation adopts anti-clinal geometry. This can essentially be thought of as a compromise between between sterics and dipole minimization, and the donor-acceptor effect:

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The $\sigma ^{*} (\ce{O-H})$ is an excellent acceptor, and oxygen's highest energy unbonded pair is one of the strongest donating. The lower energy lone pair occupies a $\sigma\text{-out}$ orbital, and the higher energy lone pair occupies a pure $\mathrm{p}$ orbital. The mixing of this orbital with the $\sigma ^{*} (\ce{O-H})$ orbital favors a $90º$ dihedral angle, but due to steric and dipole effects, the actual angle is $\approx 120º$.

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In hydrazine, the $- 2.5 \ \mathrm{kcal \ mol^{-1}}^{[1]}$ preference for the two $\mathrm{n}(\ce{N})$ orbitals being syn-clinal over anti-periplanar is also explained by the donor-acceptor effect. When the $\mathrm{n}(\ce{N})$ are syn-clinal, they are each eclipsed by the $\sigma ^{*} (\ce{N-H})$ orbitals, and orbital mixing occurs. The effects of this are further seen in the $\ce{N-N}$ bond length difference between the two conformations: $1.448\ \mathrm{Å}$ in the syn structure and $1.489\ \mathrm{Å}$ in the anti structure. The shortening of the bond length in the syn structure is a direct result of the multiple bond character introduced by the $\mathrm{n}(\ce{N}) \rightarrow \sigma ^{*} (\ce{N-H})$ interactions$^{[1]}$.

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_{$^{[1]}$ Wilcox, C.; Bauer, S. Journal of Molecular Structure: THEOCHEM 2003, 625 (1-3), 1–8.}