Decaheliceneor: introducing the sheep horn effect.
It will take a while|
to read in all the applets on this page.
An experimental challenge: will this molecule racemize easily?
Helicenes are benzologues of phenanthrene.
With four or more rings (tetrahelicene, or  for short, pentahelicene , etc.) the compounds exist in two helical, enantiomeric forms, with C2 symmetry.
Racemization experiments, carried out in the seventies, gave surprising results (see table). Not only did racemization occur at lower temperatures than expected from hardware models; the barriers even showed a tendency to level off for a higher number of rings:
|Click on number to
load structure in applet.
In the nineties, more than twenty years after the measurements, three groups, remarkably close in space and time but independently performed calculations on the racemization process for the compounds  to , published in two papers:
A preliminary web poster
at the ECCC1
(November 1994!) showed an animation of the racemization of octahelicene.
The racemization is animated on the left.
The calculations confirm that for  to  the racemization occurs
via a symmetric transition state (TS).
For  this TS is flat. In the larger compounds this is obviously not possible and the TS adopts a kind of saddle shape, with Cs symmetry (mirror plane).
The TS for nonahelicene  racemization is shown on the right.
What about the higher helicenes?Decahelicene, to the best of my knowledge, has not been measured; and it was not included in the calculations cited above.
On the one hand, the model presented here suggests that  could have a barrier lower than that of nonahelicene.
On the other hand, larger values of n, the number of rings, introduce a new complication. In the Cs structure, the end rings bend inside and approach the central part of the molecule, as can be seen in a side view on the right. The red H atoms get close the rings in the centre. It reminds me of the horns of a certain type of sheep.
Calculations suggest that the  Cs structure with the mirror plane is relatively stable indeed, even to such an extent that it becomes an intermediate, a local minimum, 33.7 kcal above the helical ground state. A difference which is in between that of hexa- and heptahelicene! (Also calculated with AM1, which underestimates the experimental barrier. Grimme (ref. 2) showed that DFT calculations are the most accurate for this type of structures.)
This result implies that the actual transition state, the maximum in the
racemization path, is asymmetric.
The potential energy surface around the Cs structure appears to be
with respect to the dihedral angles
defined along the inner rim of the helix. |
On its way from Cs to helix the structure passes through a conformation that resembles the TS (+ an extra benzene ring) and subsequently the TS (+ a naphthalene unit attached to one end, structure on the left).
Up to this point, the energy is still rising!
Closer inspection reveals that this increase in energy is caused by the 'sheep horn' effect: the 'extra' naphthalene unit is not flat anymore, but is forced outwards so as to avoid the central bridge. So while in the pure TS the energy falls when one end of the molecule rotates underneath the other end on its way to the helix, in the TS this is compensated for by the strain in the other end of the molecule.
By approximation (what an AM1 calculation is anyway) the  transition state
(left, in green) is some 5.9
kcal above the symmetric Cs structure (above, right, in yellow), and the
calculated racemization barrier is
39.6 kcal/mol. This is much higher than calculated for  and .
Energy diagrams can be found on a separate page.
So, a question for the experimentalists, what is the 'real' value?
And, synthetic chemists, think of the nice structures you can make if you can trap the relatively stable intermediate and connect (photochemically?) the two end rings, lying side by side . . .
In the mean time we'll have to continue our calculations using better, more laborious methods.
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