| ECCC-3 Contents Page | THEOCHEM Home Page | Elsevier Chemistry Home Page |
The twisting along the major axis of a series of linear polycyclic aromatic hydrocarbons has been studied using AM1 semi-empirical calculations. Polycyclic aromatic hydrocarbons (PAH) containing only six-membered rings are shown to be easier to twist along their long axis when compared to similar PAH containing embedded cyclopentene rings (CPAH). The difference in the energies is evident even at very low twist angles and becomes more pronounced as the twist angle approaches 90 degrees. The calculations were done by defining sets of parallel dihedrals along the long axis of the PAH and CPAH and driving the dihedrals symmetrically while allowing for a full geometry optimization of the rest of the molecule.
The text for this paper is in HTML. Molecules are displayed in a number of different formats. Line drawings are from ChemOffice and have been saved as *.PICT files and then translated (using GraphicConverter) into *.gif files and embedded in the HTML document. Structures are provided as *.pdb files, viewable by using RASMOL as a helper application. If you have the Chime plug-in installed and defined to interpret the MIME type chemical/x-pdb then you can view the *.pdb files directly with your browser. The distortions investigated are easiest to see in "ball and stick" or "space filling" models. Animations were prepared from *.gif files generated from graphic convertor using original structures obtained from CAChe,MacSpartan or Chem3D, and assembled into an animation by GifBuilder. (you need Netscape Navigator 2.0 or better to see these animations on a www page) If the large image just below the title is slowly rotating then your browser is reading the gifbuilder document correctly. A number of hotlinks are included to point interested readers in the direction of useful related material available at the time of this work, the stability of these links is, alas, outside the control of the authors. Whenever possible, traditional references have been provided.
Interest in the physical and chemical properties of polycyclic aromatic hydrocarbons (PAH) has increased due, among other things, to questions regarding their carcinogenicity. (1) PAH and CPAH are common pollutants (2) and are formed in almost all incomplete hydrocarbon combustion reactions including the burning of coal, fuel oil, diesal fuel, wood fires and tobacco smoke (3). PAH containing embedded cyclopentene rings (CPAH) are intriguing because the introduction of the cyclopentene rings increases angle strain. (4) Also, if the cyclopentene ring is surrounded by other rings, it will cause the CPAH to distort from planar geometry as exemplified by corannulene. The discovery and intense investigation (5) of the fullerenes, which are CPAH, has increased interest in the smaller CPAH. CPAH may also serve as rational synthetic intermediates along the path to fullerenes as illustrated by the work of Scott and Biederman.(6) Some examples of well known small CPAH include fluoranthene, corannulene and acenaphthylene. In previous work we have investigated the physical properties of CPAH using computational and spectroscopic techniques.(7)
Conformational distortions of PAH and CPAH are of interest because the increased energy of strained systems may make them more potent carcinogens (8) and they are useful as models for the limits of aromaticity as investigated extensively by Herndon and others. (9) In this paper we investigate the twisting motions of a series of PAH and closely related CPAH and compare their energies. Our hypothesis is that the increased angle strain in CPAH due to the inclusion of five-membered rings will result in a concomittant increase in the energy needed for torsional distortion of the CPAH. The exact geometric distortions that occur as the PAH and CPAH are twisted are hard to quantify but the overall energy and minimized structures should reflect clearly the underlying tradeoffs between angle, bond length and torsional distortions. If correct, consistently higher torsional energies for closely related CPAH vs. PAH will be observed.
Table 1 assigns a number, gives a structural diagram, and a name (if known) for each of the compounds studied. The numbers represent a simple graphical method for describing the number of rings in each layer and are arbitrary. The series of compounds was chosen as a progression from small, difficult to twist compounds, up to large, relatively easy to twist compounds with successive sets being similar PAH and CPAH. An example is shown in Figure 1.
On the left is a CPAH and on the right a closely related PAH. Dihedral angles were defined along the major axis of each molecule as shown. The two dihedrals used for the PAH are highlighted. It was necessary to define two dihedrals because, as an artifact of how the dihedrals were defined, the molecules would sometimes roll up into a "U" shape. Paracyclene (121a) is unusual for two reasons. First, it was necessary to twist along a diagonal axis and second, it is a paratropic molecule.
The compounds investigated were chosen primarily on the basis of molecular similarity. Some have not been made, and some (such as compound 1112111 and paracyclene) are known or likely to be quite unstable. The heats of formation values plotted in the graphs were determined using the AM1 (10) semi-empirical force field as implemented by the CAChe (11) molecular modeling system on a Centris 650. Except for constraining the dihedrals, as explained in the introduction, the molecules were geometry optimized. In a few cases, AM1 calculations were performed using MacSpartan (PowerPC 8500) or Spartan (IBM RS6000) (12) and the results were within 0.05%, as would be expected since the underlying AM1 code is essentially identical.
Table 1 contains line drawings and links to the data tables for all the compounds studied. Each data table includes a *.gif file of the flat structure for the compound. The first column gives the twist angle, the second column is the calculated heat of formation and the third column contains a link, for most of the compounds, to a *.pdb file for a conformation with a given twist angle. The angle refered too is the overall twist along the length of a molecule. Zero is flat and 90 degrees represents a total twist of 90 degrees for the whole molecule. The lowest energy conformers for the CPAH were always flat. The flat conformers for the PAH contained slight ortho hydrogen interactions that distorted them minimally from planarity so that they were frequently slightly higher in energy than the close by minimally twisted conformers.
Figure 2 shows a plot of dihedral angle vs. the relative heat of formation for the CPAH 21112 (acenapth [1,2-k] fluoranthene) and 21212 (terrylene). Note that the energy differences have been normalized for each compound (ie the difference between the energy of each successive higher energy conformer and the lowest energy conformer has been plotted instead of the actual heat of formation). As expected, the energy rises smoothly as the compounds are distorted from planarity. It is clear that the energy needed to twist the CPAH increases more rapidly with respect to the twisting energy for the closely related PAH. Figure 3 and Figure 4 give the twist angle vs. Hf energy for the CPAH and PAH respectively. The same trend is observed for the entire set of compounds, the CPAH are consistently more difficult to distort along the longitudinal axis than similar PAH. Figure 5 is an animation of the data set for the first eight compounds being built sequentially from the compound with the highest energy for twisting down to the lowest. A closeup view of the twisting data for the first eight compounds between zero and 40 degrees is shown in Figure 6. Compound 211121112 appears to have somewhat anomalous energies for twisting but, in reality, it is just that a considerably shorter PAH, 212 (perylene), has comparable but slightly flatter twist energies. When compared to quaterrylene, which is not on the graph, it is not unusual.
Figure 7 is an animation of the twisting of compound 211121112, the largest CPAH compound studied, along with an animation of its most distorted conformer rotating around the y axis of the screen. It is clear from the animation that the twisting distortion is spread fairly evenly across the entire compound. However, close inspection of many of the compounds studied indicates a slight preference for less twisting in "naphthylene" units and more twisting in the connecting five or six membered rings. This can be seen by slowly rotating one of the longer molecules while viewing it along its edge. Adjacent "naphthylene" hydrogens are twisted less than those that are close, but separated by a bridging ring. At low twist angels, this is may be due simply to "ortho" interactions. One way to investigate this further was to tie the naphtylene units together, this was done for the quaterrylene structure, giving bis-corannulene. It is indeed more difficult to twist the bis-corannulene when compared to the closely related quatterrylene. A 40 degree twist of bis-corannulene raises its energy 2.06 kcal/mol above the lowest energy conformer wheras at 40 degrees the quaterrylene conformer is only 0.27 kcal/mol higher. An AM1 frequency calculation was done on a subset of the compounds studied and the lowest or second lowest energy vibration observed corresponds closely to the longitudinal twisting modeled in this paper. Here is an animation of this low energy vibration, generated from MacSpartan AM1 calculations, for compound 21212. And the corresponding low energy vibration for 21112 is shown here. The actual vibrational motion is much smoother, what is shown is simply a series of screen snapshots of the vibration output.
AM1 calculations can clearly distinguish between the energies for twisting of the various PAH and CPAH. Similar CPAH always required more energy for twisting than the PAH. Contrary to common ideas about PAH, for the larger PAH and CPAH significant twisting distortions can occur with very low energies. For example compound 21112 can distort 50 degrees along its major axis with a concomittant rise in energy of only 10.2 kcal/mol. Likewise, the closely related PAH, 21212, takes a mere 2.31 kcal/mol for the same 50 degree twist and can twist 80 degrees for 10 kcal/mol. Quaterrylene needs only 7 kcal/mol to twist 90 degrees!
One problem that is not resolved from this work is that the PAH and CPAH are similar, not identical. The differences observed may be due not to the presence of the cyclopentene rings but instead to the fact that the CPAH are, on average, slightly shorter than the corresponding PAH and contain fewer atoms and bonds to distribute the torsional energy amongst. For example, the distance from C1 to C6 (as defined in Figure 1) in 21112 is 11.115 angstroms and the distance from C1 to C6 in 21212 is 11.668 angstroms. However, this is unlikely since the clearly shorter perrylene is easier to twist than the considerable longer acenapth [1,2-k] fluoranthene. Further work is in progress to correlate the results obtained with fluerescene data for PAH and to evaluate fully the orbital perturbations which occur upon torsional distortion.
LKS would like to thank the Dreyfus Foundation for funds used to purchase the CAChe system and Ben Plummer for showing me how interesting hydrocarbons can be!
