Conjugation and Structure

28. There are five possible isomers for the bicyclo[3.3.0]octatrienes, of which A is one. Do an MM analysis (including pi calculations) for A and its four isomers; move the pair of double bonds around the left-hand five-membered ring in order to generate the other structures. Similarly, do the complete analysis for the homologous B and its four positional isomers. Comment on the importance of pi-conjugation in stabilizing the various [3.3.0] and [4.3.0] systems.

105A. 1,3-Butadiene is the simplest conjugated hydrocarbon. Calculate the energy and structure (including bond angles, bond lengths, and degree of non-planarity of the diene system) as substituents are introduced; compare your answers with those in the article. Do calculations on the parent; on the three possible monomethyl derivatives; on the 2,3-dimethyl and 2,3-di-t- butyl derivatives; and on the three stereoisomeric 1,2,3,4-tetramethyl compounds (i.e., 3,4- dimethyl-2,4-hexadiene).

162. Experimental work and ab initio calculations on 1,3-cyclohexadiene and on its mono and dibenzo derivatives suggest that the diene ring is non-planar; i.e., steric considerations, apparently, take precedence over conjugation. Do MMX calculations on the preferred conformation (whichever it may be) and then use FXTOR (PCMODEL) to force the molecule to minimize in a non-preferred conformation. Compare your computed energies, angles, and dihedral angles with those in the article.

177. Bicyclo[3.2.0]-1,3-heptadiene, shown to the right, is very unstable and can rearrange via both [1,5] sigmatropic shifts of H and [1,5] sigmatropic shift of a CH₂ group. Compute the heats of formation of the four isomers shown and compare the values with those in the reference. By examining geometric parameters (angles, dihedral angles, bond lengths) and comparing them with the values in the article, try to establish an explanation for the order of stability of these isomers.

225. Detailed molecular mechanics and AM1 semi-empirical calculations have been reported on the various conformations of conjugated 1,3- and unconjugated 1,4- cycloheptadiene. Using MMX, determine the energies, angles, and dihedral angles of these compounds; compare your results with those in the cited article.

227. Two recent papers present detailed experimental and theoretical work on various tert- butyl derivatives of 1,3-butadiene. Either Part A or Part B would constitute a suitable MMX project.

A. Compute the energies and structures of 2-t-butyl- and of 2,3- di-t-butyl-1,3-butadiene (R₃ = t-Bu or R₃ = R₄ = t-Bu). Compare your calculated geometrical parameters with the experimental and calculated values in the first article cited below; pay particular attention to the question of planarity of the conjugated diene and to the dihedral angle between C₁ of the diene and one of the methyl groups; discuss the similarities and discrepancies.

B. A chart of the various t-butyl substituted compounds is found on p 1470 of the second article cited below. It is alleged (p 1476 and Table 10) that most of the mono- and di-substituted compounds have a C₁ to C₄ dihedral angle of 180°; included in this list are R₁ = t-Bu; R₂ = t-Bu; R₁ = R₂ = t-Bu; R₁ = R₅ = t-Bu; R₁ = R₆ = t-Bu; and R₂ = R₅ = t-Bu. All of the others (R₃ = t-Bu; R₁ = R₃ = t-Bu; R₂ = R₃ = t-Bu; R₁ = R₄ = t-Bu; R₂ = R₄ = t-Bu; and R₃ = R₄ = t-Bu) are alleged to have dihedral angles that are as large as 90° for the especially strained cases. Use MMX to determine these dihedral angles; do you agree that only those compounds having t-butyl on an "interior" carbon (position 3 or 4) deviate from an anti, coplanar conformation?

230. A recent article presents experimental data for the relative energies of the E or Z 3- ethylidenecyclohexenes and of the three possible cyclohexadienes having ethyl attached to an sp² carbon (two conjugated, one not; see structures at right). Do MMX calculations on these five isomers and compare the computed energy values with the experimental energies. Discuss and rationalize any differences found.

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