Visualizing the Racemization of Octahelicene

AM1 calculations on the racemization reaction coordinate

J.H. Borkent, CMBI (formerly called CAOS/CAMM Center), P.O.Box 9010, 6500 GL Nijmegen, The Netherlands

Note: There are two versions of this document. The one you are reading now will be updated regularly, and expanded as our work in this field continues (see bottom).
The second version is the one submitted to the ECCC conference in 1994, which will be published on CD-ROM later in 1995. After applying the referees comments that paper will not be changed anymore.

Introduction: Hexa- and higher helicenes consist of two enantiomeric, helical forms: the M and the P conformation. Hexa- and octahelicene possess a C2 axis along the central C-C bond.
Their thermal racemization has been studied in the seventies:
Martin, R.H. and Marchant, M.J., Tetrahedron 30, 347 (1974)
For octahelicene the following data were obtained (temp. 270° C):

For hexahelicene a transition state (TS) with mirror symmetry was proposed by Lindner: Lindner, H.J., Tetrahedron 31, 281 (1975)
Apart from referring to 'the many degrees of freedom', there was no clear picture of how the racemization actually occurred; hardware models lack the required flexibility.

Experimental: AM1 calculations were performed on a Silicon Graphics Indigo, using AMPAC 4.5/5.0 and its Graphical User Interface.
From IRC calculations, starting from both sides of the TS, 34 structures were selected. They are presented below , from the M conformer #01, via the TS #18 (see below), to the P conformer #34, in two fashions:
1. in the form of an mpeg movie, for which you need (obviously) an mpeg player;
2. as a hyperactive molecule in the multiple XYZ format, for which you need a plugin (like Chime) or an external molecule viewer.
A few crucial structures are presented as gif files.

Results and Discussion: A symmetrical structure can be constructed by imposing mirror symmetry on just two torsions in the inner rim of the helix, indicated in yellow in the figure below. It was characterized as a transition state for the racemization. A FORCE calculation gives one negative force constant. Minimizations starting from structures with slightly distorted symmetry result in either of the two helical conformations.

TS seen from front

A GRID calculation with the two torsions as variables shows in a rather flat energy surface, with a saddle point at 36.85, -36.85. Large changes in the geometry (one end going up, the other end going down) are possible within a few kcal/mol.
The energy profile for the racemization path is presented below.

reaction profile

The presentations:
1. Click here for the mpeg visualization of a full reaction path from one helix to the other.
2. You can also load the structures as a multiple XYZ file with 34 frames into your molecule viewer and inspect them from different angles.

The result can be interpreted in two ways:
The racemization can be described in terms of the six torsion angles along the inner rim of the helix.
In the TS (#18) the values reflect the mirror symmetry: 14 58 37 -37 -58 -14. Starting from the center of the molecule, the negative values approach zero and become positive one by one:
In #22 the torsion number 4 is close to zero: 5 41 59 -3 -58 -28. Note how the 'opposite' torsion angle (3) increases from +37 to 59 degrees to make this possible.
In #30 the next one, numbered 5 in the plot crosses the zero line: 15 21 37 51 1.5 -34. Again the neighbouring torsion (4) increases to more than 50 degrees.
Now one end of the helix can pass underneath the opposite end and the last torsion, number 6, becomes positive. In the P helix the values are: 15 27 28 28 27 15.

Treated as a mechanical model, the racemization can be described in terms of a moving 'hinge', a fold clearly visible in the center of the TS, along the central radial C-C bond. Going from the TS to the helix, this hinge moves from the center outwards. In structure #22 the adjacent ring is flat, in #26 the hinge has reached the next radial C-C bond. After this stage, one end of the helix fits underneath the opposite end and the structure changes rapidly: in structures #30 and #31 the next ring and bond serve as hinge. In #34 the helical form is obtained.

[Exercise: Now cut the helical part from your telephone cord and invert it, applying the descriptions given above!]

Similar calculations have been performed for 1,16-dimethylhexahelicene, in an attempt to explain the deviating thermodynamic data.
Borkent, J.H. and Laarhoven, W.H., Tetrahedron 34, 2565 (1978)

The larger entropy contribution (-54 J/mol.deg) suggests a different TS. Not the symmetrical structure, but the one in which one methyl group is more or less stuck underneath the opposite end of the helix. The entropy term associated with the hindered rotation of the methyl group possibly raises the energy above that of the symmetrical structure, which becomes an intermediate then.
This was the subject of a poster presented at the First European Conference on Computational Chemistry, Nancy May 23-27, 1994.
It is known that the semi-empirical methods underestimate the steric hindrance caused by hydrogen atoms (methyl groups), so it is not surprising that the hypothesis could not be confirmed by AM1 calculations. Suggestions of ways to tackle this problem are welcome.
After this poster was published, it turned out that two more groups were working on this subject. Our cooperation with a group in Munster, Germany, resulted in a 'real' publication:
R.H. Janke, G. Haufe, E.-U. Würthwein, and J.H. Borkent, J.Amer.Chem.Soc. 118 (25) 6031 (1996)

At about the same time a group in Bonn, Germany published DFT calculations on a number of helicenes and their transition states:
S. Grimme and S.D. Peyerimhoff, Chemical Physics 204 (2/3) 411 (1996)
DFT energies show a better match with experimental results than our AM1 calculations.

In 1996 I submitted the special case of decahelicene as "Molecule of the month" December. Here you can find .pdb files of the helicenes [4] to [10].
Last update: February 9, 2001 by borkent@cmbi.kun.nl