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The rearrangement of (-)-/3-caryophyllene (1) with sulfuric acid in ether has been reinvestigated. In the early stage, a multitude of products is formed. Of these, fourteen hydrocarbons (3, 4, 6-17) and four alcohols (5, 18-20) were obtained pure. From the very beginning, the tricycloundecenes 15-17 accumulate quickly. This indicates that a previously unknown rearrangement of 1 by protonation of the exocyclic double bond followed by transannular ring closure is a main reaction, and that the conformation ß is involved. Three hydrocarbons (3, 4, 8) and three alcohols (5,18,19) proved to be stable. They are the main components in the late stage. A complete rearrangement scheme followed from a force field analysis using MMP2. First, all conformations up to 4 kcal above the global minimum of each product and each carbenium ion necessary for its formation were detected automatically using the search program HUNTER. Second, the conformation favoring a specific transformation was searched for. For transannular cyclizations, the conformation with the shortest distance between the atoms to be bound and, for ring openings and 1,2-shifts, the conformation with the smallest dihedral angle between the empty p-orbital and the bond to be broken were selected. In all cases, the selection criteria proved valid: The stereochemistry of the conformations selected matched the stereochemistry of the products observed. On the basis of the results presented, a fully automated search program for favorable rearrangement paths may be developed.

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A conformational search procedure (HUNTER), in combination with the MM3(92) program, was used for the exploration of the conformational hypersurface of alkyl-substituted cyclohexanes and for the calculation of their chair/twist-boat (TB) energy gap. The systems studied were conformationally unconstrained polyalkylcyclohexanes (alkyl = methyl, ethyl, isopropyl, and tert-butyl) possessing either geminal and/or vicinal arrangements of the alkyl groups, but differing in the number of alkyl substituents and in their relative disposition (i.e., cis or trans). The calculations indicate that in 1,1,3,3,5,5-hexaisopropylcyclohexane the TB is the lowest energy form. Modification of the cis,trans relationship of vicinal alkyl groups changes the chair/TB energy gap, and in the minimum energy conformation of cis,trans,trans-1,2,3,4-tetraisopropylcyclohexane (23c) and cis,syn,cis-1,2,4,5-tetraisopropylcyclohexane (31c) the cyclohexyl ring adopts a TB conformation. The tetrasubstituted systems cis,syn,cis-1,2-diisopropyl-3,4-dimethylcyclohexane (46), cis,syn,cis-1,4-diisopropyl-2,5-dimethyl-cyclohexane (47), and cis,trans,trans-1,2-diisopropyl-3,4-dimethylcyclohexane (41) are the least crowded monocyclic unconstrained cyclohexanes found in which the TB conformation is of lower energy than the chair form. The present study indicates that two methyls and two isopropyl substituents are sufficient for stabilizing the TB form of a cyclohexyl ring relative to the chair form.

The pseudohelical hydrocarbons (R)-6, (S)-7, and (R)-8 and the helical hydrocarbon (P)-9, formally derived from the helical hydrocarbon (P)-4 by stepwise replacement of each of the four-membered rings by a five-membered ring, have been prepared. Their optical rotations vary systematically, both in magnitude and sign. Of the extremes, (P)-4 represents the usual case of a right-handed dextrorotatory helix, while (P)-9 represents the unusual case of a right-handed levorotatory helix. To rationalize these facts, DFT calculations of the rotatory power of (P)-helices of three-, four-, and five-membered rings have been performed. The results show a very good agreement with the experimental data for the rigid helices of three-membered rings and always show the correct sign and order of magnitude for the flexible helices of four- and five-membered rings for which Boltzmann-averaged optical rotations of up to six conformers had to be used. Within the conformers of the latter, a set of large dihedral angles for the bonds of the inner sphere correspond to a high specific rotation, and a set of small dihedral angles correspond to a low specific rotation. As a consequence, the Boltzmann-averaged values markedly depend on the geometry and weight of the conformers involved.