In the Classroom
Cyclohexane: Boat Form Revisited Ronald R. Sauers Department of Chemistry, Rutgers, the State University, New Brunswick, NJ 08903;
[email protected] Almost without exception, modern textbooks of first-level organic chemistry and at least one advanced organic text present an outdated description of the structure and properties of the boat form of cyclohexane. Typically, it is described as a transition state between twist boat forms as a result of destabilizing ethane-like eclipsing interactions between adjacent C–H bonds and a repulsive steric interaction between the flagpole (1) hydrogens. In this context, a H…H bond distance between the flagpole hydrogen atoms of 1.8–1.83 Å is frequently cited, which would be expected to induce severe steric congestion given the van der Waals radius of hydrogen, 1.11–1.2 Å (2). Although a recent article in this Journal correctly points out that boat forms are not required transition states for chair–chair interconversions, a statement is made that “all carbons in boat conformations are tetrahedral with normal bond angles and bond lengths” (3). These arguments are flawed on several counts. The widely quoted value of 1.8 Å has apparently been taken from an early paper by Hassel (4 ), who derived it from a model of the boat conformer with fixed C–C–C angles of 109.5 Å. In addition, the use of spherical van der Waals radii for hydrogen may be inappropriate for evaluation of intramolecular atomic contact distances. These values are based on intermolecular contacts determined from crystal packing measurements and may be inappropriate to evaluate H…H interactions within molecules.1 Lastly, “eclipsing” strain should refer to all of the butane-like C—H and C—C interactions not simply eclipsed “ethane” C–H bonds. While it is not possible to probe the structure of this conformer experimentally because it is a transition state, modern computational methods can provide accurate structural information by any one of several methodologies, for example molecular mechanics or electronic structure methods (5). Full geometric optimization (Cs symmetry) of the boat conformer was carried out via a density functional calculation at the B3LYP/6-311++G(2d,p) level (6, 7). A significantly different representation (Figs. 1, 2) was obtained in which the fully relaxed structure flexed outward at the flagpole carbons to a separation of 2.74 Å vs 2.57 Å in the “ideal” model. At the same time, the flagpole H...H interaction was effectively relieved at an interatomic separation of 2.35 Å. A similar structure is obtained via MM3 methods and the structural changes can be attributed to differences in the “hardness” of the nonbonded and bending potential energy functions (8). It is clear from the geometric parameters described in Figure 2 that there are significant bond angle distortions from pure sp3 hydbridization, for example, the H–C–H angles of 106.0° and internal C–C–C angles of 112.6°. In summary, the destabilization commonly attributed to flagpole H...H interactions is minimal and it is likely that the repulsive interactions between the flagpole carbon atoms are much more severe given the traditional van der Waals radius of carbon (1.68 Å). This factor and the eclipsed butane interactions are the most likely sources of strain in the cyclohexane boat conformer. 332
Figure 1. Top view and side view of space-filling representations for calculated structure of boat conformer of cyclohexane. Van der Waals radii used are C: 1.60 Å, H: 1.05 Å. H
H
H
2.353Å
H
H
H 1.556Å
H
H
111.5°
112.6°
H
106.0°
C
C
1.535Å
H
H
H C
2.736Å
C
H
H
H
H
H
H H
H
106.0°
H
H
H
H
Figure 2. Geometric parameters for the B3LYP/6-31G(d) calculated structure for the boat conformer of cyclohexane.
Note 1. Allinger’s MM3 program uses a value of 1.62 Å for the van der Waals radius of hydrogen (8). In the derivation of this parameter a distinction was made between the distance of closest approach in crystallographic measurements and traditional van der Waals radii. The effects of anisotropy of C–H bonds on non-bonded H…H interactions were taken into account by basing H:H distance measurements on interaction centers located at 92.3% of the calculated C–H bond lengths. In this context, use of the MM3 force field gave rise to a boat conformer with H…H separation of 2.36 Å and van der Waals energy 0.28 kcal/mol. The flagpole C…C energy was found to be 0.95 kcal/ mol at a separation of 2.72 Å. Although the absolute values of these energies are dependent on the force field, the relative values are significant (9). It should also be pointed out that the density functional results refer to a vibrationless state at 0 K, but MM3 is parameterized to fit experimental data and includes averaging of vibrational motions.
Literature Cited 1. Lyle, G.; Lyle, R. E. J. Chem. Educ. 1973, 50, 655. 2. Chauvin, R. J. Am. Chem. Soc. 1992, 96, 9194–9197. 3. Leventis, N.; Hanna, S. B.; Sotiriou-Leventis, C. J. Chem. Educ. 1997, 74, 813–814. 4. Hassel, O.; Ottar, B. Acta Chem. Scand. 1947, 1, 929–943. 5. Ferguson, D. M.; Gould, I. R.; Glauser, W. A.; Schroeder, S.; Kollman, P. A. J. Comput. Chem. 1992, 13, 525–532. 6. The optimization used Gaussian94 Revision B.1 and default convergence criteria: Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; AlLaham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian, Inc.: Pittsburgh, PA, 1995. 7. Becke’s three-parameter hybrid method using the LYP correlation functional: Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. 8. Lii, J.-H.; Allinger, N. L. J. Am. Chem. Soc. 1989, 111, 8576–8582. 9. Lipkowitz, K. B. J. Chem. Educ. 1995, 72, 1070–1075.
Journal of Chemical Education • Vol. 77 No. 3 March 2000 • JChemEd.chem.wisc.edu
