The geometry of cyclo-octatetraenes differs fundamentally from the lower homologue benzene in exhibiting slow (nuclear) valence bond isomerism rather than rapid (electronic) bond-equalising resonance. In 1992 Anderson and Kirsch[1] exploited this property to describe a simple molecular balance for estimating how two alkyl substituents on the ring might interact via the (currently very topical) mechanism of dispersion (induced-dipole-induced-dipole) attractions. These electron correlation effects are exceptionally difficult to model using formal quantum mechanics and are nowadays normally replaced by more empirical functions such as Grimme's D3BJ correction.[2] Here I explore aspects of how the small molecule below might be used to investigate the accuracy of such estimates of dispersion energies.
The concentration of the two forms shown above can be readily estimated by NMR spectroscopy (the barrier is slow enough to allow peaks for both isomers to be integrated). This shows that the 1,6 form is present in greater concentrations than the 1,4 form, equivalent to a difference in free energy ΔΔG298 of 0.39 kcal/mol in favour of the former. Why is this? Because, it is claimed, in the 1,6 isomer the two t-butyl groups are close enough to experience mutual dispersion attractions not experienced by the 1,4 form. This can be illustrated using the NCI display below for the two forms.
Method | Equilibrium constant, 298K | ΔΔE | ΔΔH298 | ΔΔS298 | ΔΔG298 | Source |
---|---|---|---|---|---|---|
Experiment | 1.93 | – | 1.14 | -2.5 | 0.387 | [1] |
B3LYP/Def2-TZVPP/CDCl3 (no dispersion) | 1.906‡ | 0.05 | 0.00 | +1.3‡ | 0.382‡ | [3],[4] |
B3LYP/Def2-TZVPP/CDCl3 (gd3bj dispersion) | 8.36 | 0.75 | 0.66 | +2.0 | 1.25 | [5],[6] |
‡This contains a contribution of RTLn 2 (= 0.410 kcal/mol = 1.04 in ΔS), where 2 is the symmetry number for a species with C2 rotational symmetry, to the 1,4-isomer only.
The interpretation of these results, as is often found, is non-trivial.
So we may conclude that whereas the dispersion uncorrected method gets the right answer for the equilibrium constant for probably the wrong reasons, inclusion of a dispersion correction would get the right answer were it not for the error in the entropy. Agreement with experiment would be obtained if the calculated entropy difference were to be -0.9 kcal/mol K-1 instead of +2.0. Thus the 1,6 isomer has the two t-butyl groups weakly interacting (red circle above), which intuition tends to suggest would reduce the entropy (reduce the disorder) of the system and not increase it.
At least in this relatively small molecule, we now have a handle for estimating these sorts of effects in terms of variables such as the basis set used, the energy Hamiltonian (e.g. type of functional etc) and of course the dispersion correction.
In the mid to late 1990s as the Web developed, it was becoming more obvious…
I have written a few times about the so-called "anomeric effect", which relates to stereoelectronic…
The recent release of the DataCite Data Citation corpus, which has the stated aim of…
Following on from my template exploration of the Wilkinson hydrogenation catalyst, I now repeat this…
In the late 1980s, as I recollected here the equipment needed for real time molecular…
On 24th January 1984, the Macintosh computer was released, as all the media are informing…