Can cis-trans isomers interconvert?

Question

Can cis-trans isomers interconvert via tunneling ?

Answer 1

Electron tunneling

Tunneling refers to elementary particles moving "through" a potential barrier in the absence of sufficient energy to go "over the barrier". This is roughly equivalent to saying that a particle can occupy two locations and traverse between them even though all paths between those locations have a zero probability of the particle being there.

Some orbitals such as the p-orbital describe a probability density with areas of non-zero probability ("lobes") separated by space with zero probability ("nodes").

When electrons are transferred from one electron carrier to another, the transfer can occur through bonds or through space; the through-space transfer is either based on orbital overlap or on tunneling.

Proton tunneling

Proton tunneling is much slower because the proton is about 2000-times heavier than the electron. Tunneling has been used to explain reactions involving protons that are faster than expected from inspecting the potential energy landscape. This proton tunneling also explains proton transfer in hydrogen bonds.

For formic acid and acetic acid, proton tunneling explains cis-trans isomerism at ultra-low temperatures. Acetic acid, at room temperature, has a cis and a trans conformation.

There is a rotational barrier (which one may explain via resonance involving the carbonyl double bond) which is lower than thermal energy at room temperature [Ref 1]. For related systems like the peptide bond, cis and trans forms are isomers because the rotation barrier is higher.

At ultra-low temperature in a nobel gas matrix, the trans form is dominant and does not convert into the cis form unless you excited the molecule at the right wavelength. This means that the cis and the trans form are isomers with individual properties. Under these conditions, it is possible to enrich the cis form, and to observe the conversion to the trans form in the dark [Ref 2]. The temperature-dependence of the kinetics (and kinetic isotope effects) suggest that this cis-to-trans reaction occurs via tunneling.

Hydride tunneling in enzymes

Many redox reactions involve hydride transfer, e.g. from alcohol to NAD+ in the alcohol dehydrogenase catalyzed reaction. For enzymes, it is typically not possible to measure reactions at ultra-low temperatures; instead, a key experiment is to study the primary and secondary kinetic isotope effect [Ref 3]. From studies of multiple enzymes that catalyze hydride transfer it is evident that tunneling does occur, and the extent of tunneling is modulated by mutations in the active site. The review makes the argument that tunneling is easier to study for hydrogen (i.e. proton, hydrogen radical and hydride) transfer than for electron transfer because in the former case, isotopes (with a different deBroglie wavelength) are available as a probe. While the examples in the review are all redox reactions rather than E/Z isomerization reactions, one could envision the latter based on hydride tunneling as well.

"Double" tunneling

If there are two atoms connected to a double bond (such as in the molecule $\ce{H2C=CDH}$ mentioned in the comments), isomerization through tunneling would be much harder because the hydrogen and the deuterium have to somehow switch position. To avoid a clash, they would have to tunnel simultaneously, and could not both take a path along the saddle point of the potential energy landscape. Therefor, a cis-trans isomerization of $\ce{H2C=CDH}$ seems much less feasible, and there does not seem to be any experimental evidence for it.

References

1. Barriers to rotation adjacent to double bonds. 3. The carbon-oxygen barrier in formic acid, methyl formate, acetic acid, and methyl acetate. The origin of ester and amide resonance. Kenneth B. Wiberg and Keith E. Laidig. Journal of the American Chemical Society 1987 109 (20), 5935-5943. DOI: 10.1021/ja00254a006
2. Rotational isomerism of acetic acid isolated in rare-gas matrices: Effect of medium and isotopic substitution on IR-induced isomerization quantum yield and cis→trans tunneling rate. E. M. S. Macoas, L. Khriachtchev, M. Pettersson, R. Fausto, M. Rasanen J. Chem. Phys. 121, 1331 (2004); DOI:10.1063/1.1760733
3. Tunneling and Dynamics in Enzymatic Hydride Transfer. Zachary D. Nagel and Judith P. Klinman, Chem. Rev. 2006, 106, 3095-3118, DOI:10.1021/cr050301x

Answer 2

Tunneling between atoms may be difficult according to the other answer, but in some environments a scrambling mechanism may work. In the presence of superacid, a bridgehead hydrogen in bicyclic compounds can be removed as a hydride ion, forming a carbocation. Upon re-attachment the hydride ion may return to either of two positions mixing the cis and trans isomers, and eventually equilibrating them. This process is documented for two such hydrocarbons by Olah et al. [1].

From Ref. [1]

Reference

1. George A. Olah, G. K. Surya Prakash, Jean Sommer, Arpad Molnar, Superacid Chemistry (John Wiley & Sons, Mar 26, 2009), p. 533.

Answer 3

Have a look at the literature report by Helen Leung et al. (2013):

We synthesized cis-1,2-difluoroethylene from the dechlorination of 1,2-dichloro-1,2-difluoroethane. The products contain a cis/trans mixture of 1,2-difluoroethylene (...).

Here's the experimental evidence of tunneling using microwave spectroscopy (Leung, 2013, fig. 4a):

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Edit

I think we should strive to use E/Z instead of cis/trans.

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Reference

Leung, H.O., Marshall, M.W., Mueller, J.L., and Amberger, B.K. (2013) "The molecular structure of and interconversion tunneling in the argon-cis-1,2-difluoroethylene complex" J. Chem. Phys. 139:134303. DOI: 10.1063/1.4823494