Thank you for another fantastic post!

Ref. 259 in my recent “tutorial review” on hyperconjugation (10.1002/wcms.6/pdf) reports another NBO analysis of this interesting problem.

For the last four years, I have been assigning NBO analysis of difluoroethane to my graduate class as one of the computational homework assignments. Students enjoy doing the the detective work and connecting NBO analysis of stereoelectronic interactions described in your post with the conformational equilibria. I will make sure to include dichloroethane as well next year!

]]>The two values for gauche and trans difluoroethane are 74.1 and 73.8 kcal/mol, whilst those for dichloroethane are 69.8 and 68.4 kcal/mol. In other words, the gauche isomer of dichloroethane has a greater steric effect than that of difluoroethane. This is pretty much what I said above (phew!), but its nice to have some numbers to attach to that statement.

]]>You have created a very helpful web site, keep up the great posts!

]]>This is one of those areas where the *full story* is complicated. Firstly, it is worth pointing out that an orbital picture of a molecule, and one based on charges and dipoles are related. In the limit, analyzing the charges needs a summation of the charge, the dipole, the quadrupole, the octupole and the hexadecapole distributions. The electron distribution predicted by such a summation is the same as that predicted by molecular (or other equivalent) orbital theories. But whereas the MO approach is in effect already summed, the dipole moment alone is only part of the multipole story. So inspecting just the dipole moment of a molecule as you can see, is quite an incomplete story (although it is likely to be a major contribution to the summation).

Looking at the (localized) molecular orbital analysis of difluoroethane, one can partition this into pairs of interacting filled and empty (localized) MOs, the so-called NBO approach. With gauche difluoroethane, one can identify six such terms, which together add to e.g. 16.6 kcal/mol, some 3 kcal greater than the equivalent sum of the orbitals of the antiperiplanar difluoroethane. It turns out that in the equivalent dichloroethane, the gauche interactions sum to 24.9 and the antiperiplanar to 21.9. So its clear that looking just at this specific interaction in the molecule, the so-called stereoelectronic interaction, both difluoro and dichloroethane should be gauche. Clearly, something else must be involved, since dichloroethane is experimentally antiperiplanar. A calculation of the total energy (which takes into account all the interactions in the molecules) does indeed show this conformation to be about 1 kcal/mol lower in free energy.

The NBO terms above show the interaction between a filled and an empty orbital. But there is another, the so called bond-bond, or electron pair repulsions involving (approximately) four rather than two electrons. We know this by the rather more familiar term of steric repulsions, and this can be reduced to inspecting the non-bonded distances between atoms, via the sum of their van der Waals radii. It turns out that in gauche difluoroethane, the non-bonded F…F contact is a little larger than the van der Waals radii sum, whereas in dichloroethane, it’s a little shorter. Whether it’s this that makes the dichloroethane different from the difluoroisomer needs further investigation.

As I said at the start, this is a complicated story. Some stories in chemistry are dominated by a few terms (in Mathematics, we would call this a strongly convergent series), but others may involve a fine balance between a greater number of terms (a weakly, or even poorly convergent series). I suspect its the luck of the draw which one gets. Clearly, in chemistry we constantly strive to find strongly convergent explanations of phenomena. I suspect the difluoro/dichloroethane phenomenon is probably weakly convergent than we would like! But that simply means we have to find another summation that converges more strongly!

]]>It seems also likely that another effect is responsible for gauche populations of n-alkenes, the non-bonded van der Waals dispersion attraction (worth about 0.13 kcal/mol for two argon atoms, it soon adds up for larger molecules).

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