Henry Rzepa's Blog

In an earlier post, I re-visited the conformational analysis of cyclohexane by looking at the vibrations of the entirely planar form (of D_6h symmetry). The method also gave interesting results for the larger cyclo-octane ring. How about a larger leap into the unknown?

Let us proceed as follows. One fun game to play in chemistry is to invoke iso-electronic substitutions. In this case, we can subtitute a nitrogen and a boron atom for a pair of carbons. Thrice invoked, it leads to a molecule known as cyclotriborazane.

This species is in fact very well known, and a crystal-structure was determined some time ago (DOI: 10.1021/ja00786a022). It is worth considering some of its properties.

1. The species is crystalline, and sublimes rather than melts. Contrast this with the iso-electronic cyclohexane, which melts at around 6C (itself a surprisingly high value).
2. The parent H₃BNH₃ also has a very high melting point of > 100C, which is attributed to an extensive array of so-called dihydrogen bonds in the crystal lattice, in which a positively charged hydrogen deriving from an NH is attracted to a negatively charged hydrogen deriving from a BH. Such dihydrogen bonds have been shown to be quite strong due to this electrostatic interaction, and are responsible for the extraordinary elevation of the melting point compared to the iso-electronic ethane.
3. The chair form of cyclotriborazane aligns the three hydrogens shown in either blue or red in the axial positions. The three red hydrogens might be expected to be all negatively charged, and the three blue ones positively charged. So in the chair conformation, might we expected the electrostatic repulsions between either the blue or the red hydrogens to destabilize these axial positions, and hence perhaps even destabilize the chair conformation itself?

The crystal structure however shows clearly that the chair is still the favoured conformation. Equally intriguing, one might expect the three blue hydrogens to stack up to attract electrostatically to the three red hydrogens. But you can see from the crystal packing if you activate the model below that this does not happen!

What of the vibrational analysis, conducted as it was for cyclohexane itself (DOI: 10042/to-4170). Well, just as before, for the planar geometry, three imaginary modes are calculated (A₂“, E”) and just as before, they distort the geometry in the direction of a chair (C_s symmetry), a C₂-disymmetric twist boat (with a predicted optical rotation of -54°) and a boat respectively (the latter, as before, being a transition state connecting the two C₂-enantiomers).

But here we get a surprise! According to the B3LYP/6-311G(d,p) model, the final resting energy for the chair is almost the same (indeed 0.2 kcal/mol higher in free energy) as the twist-boat. Perhaps that blue/red repulsion did have an effect after all! If you look at the calculated structure, you can indeed see that the blue/red hydrogens are splayed-out, avoiding each other!

This is one of those molecules where one might have expected surprises. In the end, it is surprising at how similar cyclotriborazane is to its iso-electronic cousin cyclohexane.

Tags: chair, conformational analysis, final resting energy, free energy, Interesting chemistry

This entry was posted on Sunday, February 14th, 2010 at 1:03 pm and is filed under Interesting chemistry. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.