Henry Rzepa's Blog

In the previous post, I showed how modelling of unbranched alkenes depended on dispersion forces. When these are included, a bent (single-hairpin) form of C₅₈H₁₁₈ becomes lower in free energy than the fully extended linear form. Here I try to optimise these dispersion forces by adding further folds to see what happens.

I had noted a small kink in the bent single-hairpin form (above, red circle). What about making a full bend at that point? Such forms have been previously investigated using OPLS-AA mechanics[1], with the finding that such a triple-hairpin conformation (below) was 9.7 kcal/mol higher in energy than the single hairpin (above). OK, its got eight gauche-turns more (four per bend, and which do cost energy), but it also has three rather than just one row of close dispersion-stabilising contacts to compensate. Using quantum rather than molecular mechanics (B3LYP+D3/TZVP), I found that this triple-hairpin folded form was 3.2 kcal/mol higher in free energy than the single hairpin.[2]

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One folded at a slightly different point (below) was in fact higher 4.7 kcal/mol in energy that the single hairpin,[3] indicating that there is an optimum position for the bend.

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I was convinced better folds could be found. So how about this double-hairpin, but in three dimensions to form a prism so that each chain has just as many contacts as the triple-hairpin, but is achieved with two-fewer gauche-turns? Its free energy[4] is 1.6 2.5 kcal/mol lower than the single-hairpin. It did not feature in the previous report[1] and hence represents a new lowest-energy folding (the colour indicates three ribbons of attractive non-covalent interactions, using the NCI technique). I would point out that such “manual” searching for better folds is not really sustainable; a statistical method would normally be used (MD or Monte-Carlo).

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A similarly folded version of the triple-hairpin can be made (below), with more opportunity for five rows of close dispersion contacts. This time however, the free energy is 1.9 kcal/mol higher than the single hairpin[5] (but the position of the fold does need to be optimised and perhaps a better one can be found). This result does imply that there is an optimum balance between the energy penalty of creating four gauche-turns per fold and the additional energy stabilisation of the dispersion. Perhaps the triple hair-pin above is close to that optimum?

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Unfortunately no crystal structures for the higher linear alkanes have been reported that would give us a reality check on any of these models. Can it really be that difficult to crystallise such molecules?

References

1. L.L. Thomas, T.J. Christakis, and W.L. Jorgensen, "Conformation of Alkanes in the Gas Phase and Pure Liquids", The Journal of Physical Chemistry B, vol. 110, pp. 21198-21204, 2006. http://dx.doi.org/10.1021/jp064811m
2. Henry S. Rzepa., "Gaussian Job Archive for C58H118", 2014. http://dx.doi.org/10.6084/m9.figshare.988335
3. Henry S. Rzepa., "Gaussian Job Archive for C58H118", 2014. http://dx.doi.org/10.6084/m9.figshare.988334
4. Henry S. Rzepa., "Gaussian Job Archive for C58H118", 2014. http://dx.doi.org/10.6084/m9.figshare.988771
5. Henry S. Rzepa., "Gaussian Job Archive for C58H118", 2014. http://dx.doi.org/10.6084/m9.figshare.988333