Strain Energy

7. In the second issue of Angew. Chem., Int. Ed. Engl. in 1987, the synthesis of this compound is reported. How strained is it? What about the corresponding compound with a central four-membered ring? What about a central eight-membered ring? Compare these to the permethylated cyclohexane, cyclobutane, and cyclooctane.

13. Propellanes are tricyclo[x.y.z.0] molecules. How strained are the [2.2.2.0] and related [2.y.z.0] compounds?

26. Calculate the strain energy of pyramidalized alkenes, such as those shown to the right.

73. The asteranes (p. 93) are also beautifully symmetrical molecules. Shown here are triasterane and hexaasterane. Your task is to do MM calculations on the energies and geometries of tri-, tetra-, penta-, and hexaasterane. Discuss the variations in strain energy as the ring size changes; explain clearly why hexaasterane is not the least strained of the series.

74. Israelane and Helvetane (p. 87) [Why are these names used?] are (CH)₂₄ molecules. Do MM calculations on both of them. What you will discover is that although these structures are aesthetically pleasing, they are disasters chemically. The latter structure has not only the strain of the four-membered rings but also has four H's from the "front" 12-membered ring and four more from the "rear" ring pointing toward one another; nevertheless, it minimizes to a structure not too different from that shown. Israelane, on the other hand, has six H's on the "front" and six more on the "rear" ring, all pointing to the center; neither RMM nor JEB has managed to get a minimized structure whose geometry is close to that shown. Try the MM procedure on israelane, and see what you get. Then, try various "tricks" to hold the ring system in this geometry; for example, connect the interior carbons to an added single carbon or to the carbons of added three-membered or six-membered rings; be creative!

75. The name triblattane (p. 269) is derived from the German word for "leaf" and is used to describe the distorted bicyclo[2.2.2]octane nucleus which results when various short chains are introduced. The exercise, here, is to calculate the energy and geometry of the parent compound; pay special attention to the dihedral angle C₁- C₂-C₃-C₄. Then do calculations on three molecules with just one bridge; let m = 2, 1, and 0. Then do calculations on three molecules with two bridges; let m = p = 2, 1, and 0. Finally, do calculations on three molecules with three bridges; let m = p = n = 2, 1, and 0; the last compound is the beautifully symmetrical "cubane." Discuss the strain energy and the variation in the dihedral angle as the number and length of the bridges are changed.

76. Problem 75 was concerned with the increasing strain of a bicyclic octane as bridges of ever-shorter length were incorporated into it. The present problem starts with an analogous molecule, but with two cyclopropane rings instead of the two bridgehead carbons. Models (and MM) suggest that unlike bicyclo[2.2.2]octane itself, there is already significant twist in the parent structure, the one with no bridges; models also suggest the cyclopropane rings are not quite orthogonal and also that introduction of the bridges does not lead to a large increase in strain. Do MM calculations on the energy, geometry, and dihedral angles for the parent compound; for the singly-bridged compounds with m = 1 or 0; for the doubly- bridged compounds with m = p = 1 or 0; and for the triply-bridged compounds with m = p = n = 1 or 0. This last compound, a wonderfully symmetrical structure, is identical to the first bis-peristylane of the next problem.

77. Problem 72 asked for an analysis of the [n]-peristylanes from n = 3 through 5. One can also imagine a set of bis-[n]- peristylanes for which structures are shown for n = 3 (two perspectives) and n = 6. Do MM calculations on the complete set from n = 3 through n = 6; discuss the large variation in strain energy (and the principal reasons for it) along this series; as in Problem 73, note that the n = 6 compound is not the least strained. Also note that n = 3 is identical to the last compound calculated in Problem 76 and that n = 5 is identical to dodecahedrane from Problem 72.

78. There are five possible "Platonic solids," polyhedra in which all faces are identical rings. Three of these are the tetrahedron, cube, and dodecahedron, all of which have been "built" in the form of saturated organic molecules: tetrahedrane (C₄H₄), cubane (C₈H₈, Problem 75), and dodecahedrane (C₂₀H₂₀, Problems 72 and 77). The other two cannot be "built" as organic structures, either because they would require five bonds to carbon or because they would require inverted sp³-hybridized carbons. There are, however, many other molecules which are nearly spherical, which have symmetry almost as high as the Platonic solids, but which contain two (or more) different-sized rings (rather than all rings the same). Any one of the following five sections will constitute a reasonable MM problem set for solution.

A. Do MM calculations on compounds 1 and 2 which consist of three- and six- membered rings. The latter, despite its lovely shape, is a very strained molecule (make a model!); perhaps the best way to do its MM structure is first to enter compound 3; minimize it; replace one of the five CH groups by a C₃H₃ group; minimize; and continue the process so that eventually all five CH groups of 3 are replaced by the three-membered rings needed for 2. Report the MM structures and energies for 1, for 3, for each of the cyclopropane-substituted materials, and finally for 2. You'll note that introduction of the first cyclopropane raises the energy somewhat; introducing the second, third, and fourth raises it a little; and introducing the final one leads to a large increase.

B. Do MM calculations on this set of compounds which consists of molecules containing various combinations of three-, four-, five-, and six-membered rings. Note that the first two structures have, respectively, two and one inverted sp³-hybridized carbons; note, also, that the third compound is geometrically constrained to have planar four-membered rings. As a result, the first set of three structures is much more strained than the second set of three.

C. A compound much in the news lately is "buckminsterfullerene" or "buckyball," a form of carbon having the formula C₆₀ and consisting of fused five- and six- membered rings in a nearly spherical array. Its saturated version, C₆₀H₆₀ ("soccerane"), consisting of 12 regular pentagons and 20 regular hexagons, has never been made. Because that structure has too many atoms for an MMX calculation, you should do MM calculations on two smaller molecules (shown) which contain 12 pentagons but only three or two hexagons; the second of these is also found in Problem 77.

D. Do MM calculations on this set of structures which contain four-membered rings in combination with rings of varying sizes. The third compound is also found in Part B; the fourth compound is also calculated (although not shown) in Problem 77.

E. Replacement of any one of the CH groups of cubane by a C₃H₃ unit generates a compound called "lampane." From lampane, replacement of one or another of the three different CH groups by a C₃H₃ unit gives three different C₁₂H₁₂ compounds. Compute the MM energy and structure of these five compounds.

80. One can imagine the triple intramolecular [2 + 2] cycloaddition shown here, giving a saturated molecule which is drawn with deliberately ridiculous-looking long bonds. Do MM calculations on this cyclized compound, C₂₁H₁₈, and on the analogous compounds which one would get from the quadruple and pentuple cyclization of related compounds with a central four- or five-membered ring; these will have formulas C₂₈H₂₄ and C₃₅H₃₀, respectively.

101. Hexaprismane (1) is a highly strained molecule, but various derivatives such as seco-[6]-prismane (2), homo-[6]-prismane (3), and various bis-homo-[6]-prismanes (such as 1,3-bishomo compound 4) have been made. Do MM calculations on the geometry and energy of these structures and structures related to them. Alternatively, one could do calculations on the heptaprismane and its various seco-, homo-, and bishomo-derivatives.

140. Tritwistatriene, a beautifully symmetrical molecule, at 350 ·C gives a mixture of four isomeric products, all (CH)14. Compute the heats of formation and strain energies of the starting material and of its four reaction products; compare your results with those obtained by MM3 calculations reported in the reference. [Mechanisms for the formation of these products are described in the article.]

151. Shown to the right are naphthalene and perylene (a "double" naphthalene). Compute the structures and energies of these two molecules and of the derivatives in which two-carbon bridges, either as -CH₂-CH₂- or -CH=CH-, are connected to naphthalene at C₁ and C₈ or at C₁-C₈ and C₄-C₅; similarly for positions C₁-C₁₂ and C₆-C₇ of perylene. Compare the increase in strain with numbers reported in the reference.

190. In principle, removal of one, two, and then three moles of H₂ from the trimethyltriphenylene derivative shown here can lead to the interesting molecule called sumanene (from the Hindi word for sunflower). This system with fused five- and six-membered rings resembles a structural fragment of buckministerfullerene (C₆₀). Do MMX calculations on the four molecules; comment on their shape (planar vs. bowl- shaped); compare the increase in strain energy for each dehydrogenation step with the values in the literature reference.

211. The beautifully bowl- shaped molecule "Pinakene", C₂₈H₁₄, is a fragment of C₇₀ (one of the fullerenes). A possible synthetic route (reminiscent of that in Problem No. 190) involves removal of one mole of H₂ from the tetramethyl-dibenzonaphthacene (shown) followed by removal of three more. The strain energy increases with each removal of a hydrogen molecule and creation of a five-membered ring. Do MMX calculations on the tetramethyl compound, on pinakene, and on the three intermediate structures. Compare your answers with those in the cited reference. Compare the shape of pinakene calculated by MMX with that in the article.

248. The "triangulanes" are an interesting class of molecules. They are made up of repeating units of spiropentane (C₅H₈, to the right). Do MMX calculations on cyclopropane, spiropentane (also called [2]-triangulane), and the various [3]-, [4]-, and [5]-triangulanes shown. Compare your determination of the "incremental strain energy" with the calculated and experimental values in the cited article. Although not mentioned by the authors, there are two diastereomers (one meso, one chiral) possible for [5]-triangulene; do calculations on both of them.

265. A recent article has the intriguing title "Flexible backbone segments with a marked conformational preference." Consider, first, the case of 2,4-dimethylpentane. It exists nearly 100% as an equal mixture of conformations A and B, interconverting by rotation about the C₂-C₃ and C₄-C₃ bonds; the other staggered conformations (C, D, and E) all suffer from at least one severe CH₃/CH₃ interaction. Calculate the energies and structures of conformations A, C, D, and E. Because A and B are of equal energy, this molecule is "bi- conformational" (i.e., it populates two equally energetic conformations). So is dicyclohexylmethane (1) whose energy and structure you should calculate. [Use molecular models; use your framework from A to set up the best conformation of 1; be sure to choose the chairs that have the bridging CH₂ group equatorial on both rings.] On the other hand, chiral bis-acetal 2 and, especially, methyl-substituted 3 are "mono-conformational" in that one of the conformations resembling A or B is much more stable than the other. Do MMX calculations on the two conformations for 2 and 3; determine energies and structures; compare your results with those reported.

266. A recent article is concerned with the preparation and X-Ray crystal structure of the stereoisomeric 1,2,3- tricyclohexylcyclohexanes (R = C₆H₁₁). Do MMX calculations on the three isomers. Compare your results for heats of formation and dihedral angles with the experimental and computed values in the cited article.

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