An experimental challenge: will this molecule racemize easily?

Helicenes are benzologues of phenanthrene.
With four or more rings (tetrahelicene, or [4] for short, pentahelicene [5], 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:

Racemization barriers (kcal/mol)

Click on number to load structure in applet.	[4]	[5]	[6]	[7]	[8]	[9]	[10]
Experimental results
Grac	--	24.1	36.2	41.7	42.4	43.5	?
Hrac	--	22.9	35.0	40.5	41.0	41.7	?
Computational results
DFT-BLYP (ref. 2)	3.5	22.7	35.2	--	41.5	--	?
AM1 (ref. 1)	7.6	22.9	31.4	34.7	34.9	34.0	39.6?

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 [4] to [9], published in two papers:

Ref. 1: R.H. Janke, G. Haufe, E.-U. Würthwein, and J.H. Borkent (Münster, Nijmegen),

J.Amer.Chem.Soc. 118 (25) 6031 (1996)

Ref. 2: S. Grimme and S.D. Peyerimhoff (Bonn),

Chemical Physics 204 (2/3) 411 (1996)

	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 [4] to [9] the racemization occurs via a symmetric transition state (TS). For [4] 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 [9] racemization is shown on the right.

This model explains why the energy barrier is not simply rising with an increasing number of rings.
In the ground state, the helical forms with C₂ symmetry, the strain increases regularly with every extra ring that is added.
In the C_s structures, this strain is more severe and the barriers increase going from [4} to [7].
In the [7] TS however, the end rings are almost parallel to each other. One or two extra rings added are hardly distorted and less extra strain is introduced. See the [9] TS above.
So one would expect the barrier to decrease rather than increase for a higher number of rings, as is actually found in the calculations for [8] and [9] (not in the experiment, however no error is given for these measurements).

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 [10] 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 [10] C_s 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 rather flat 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 [9]TS (+ an extra benzene ring) and subsequently the [8]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 [8]TS the energy falls when one end of the molecule rotates underneath the other end on its way to the helix, in the [10]TS this is compensated for by the strain in the other end of the molecule.

By approximation (what an AM1 calculation is anyway) the [10] transition state (left, in green) is some 5.9 kcal above the symmetric C_s structure (above, right, in yellow), and the calculated racemization barrier is 39.6 kcal/mol. This is much higher than calculated for [8] and [9].
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. And, now we are at it, take dodecahelicene, or, the [26] TS structure, or extrapolating even further, cut the coiled part out of your telephone cord.....