1. Bredt's rule violations. For various values of x, y, and z in the generalized structure shown, calculate the strain energy. How does the double bond's geometry differ from that of an unstrained alkene? The [2.2.1] (shown), [2.2.2], [3.2.2], and [3.3.1] cases are of interest. Adamantene (shown) is a special case; there are a few recent reports of its transient existence. Do calculations on these (and other of your choosing).
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[Warner, P. M. Chem. Rev. 1989, 89, 1067 and references therein; see also Luef, W.; Keese, R. Top. Stereochem. 1991, 20, 231.]
32. Carbon crystals exist in several allotropic forms. Three of these are based on repeating units of adamantane (C10H16), iceane (C12H18), and BC-8 (C14H20) whose structures are shown below. Calculate the strain energies of these three "monomeric" units. Then, try extending these units (e.g., from adamantane to diadamantane and triamantane) to see how the strain energy changes; do similar calculations on extensions of the iceane and BC-8 units.
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[Johnston, R. L.; Hoffmann, R. J. Am. Chem. Soc. 1989, 111, 810;
Laqua, G.; Musso, H.; Boland, W.; Ahlrichs, R. ibid. 1990, 112, 7391.]
40. Adamantane (1)
is a rigid molecule consisting of four cyclohexanes in chair conformations;
make a model if you don't see this. An alkyl substituent (as in 2)
is, therefore, axial in one six-membered ring, equatorial in another. Do
MM calculations to see how the geometry and heat of formation vary as R
changes from methyl to ethyl to isopropyl to tert-butyl; compare
these numbers with those from axial-alkyl-cyclohexane and equatorial-alkyl-cyclohexane
along the same series of alkyl groups. Then, for compound 3, compute
the energy difference between the isomer shown (R = methyl through tert-butyl)
and the epimer with R oriented away from the axial methyl. Compare your
calculated geometries with those reported for 2, R = t-Bu
and 3, R = t-Bu (see article).
[Duddeck, H.; Rosenbaum, D. J. Org. Chem. 1991, 56, 1707.]
110. Calculate the
energies, bond angles, bond distances, etc. for adamantane (shown to the
right), diadamantane (C14H20), triamantane (C18H24),
isotetramantane (C22H28), cyclohexamantane (C26H30),
and "super-adamantane" (C35H36); see the
article for the structures of these hydrocarbons. Compare your results
with those found by other versions of MM and by various quantum mechanical
methods, as listed in the tables of the cited reference.
[Shen, M.; Schaefer, H. F., III; Liang, C.; Lii, J.-H.; Allinger, N. L.; Schleyer, P. von R. J. Am. Chem. Soc. 1992, 114, 497.]
160. This exercise
is concerned with the staggered conformations of heptane [CH3(CH2)5CH3].
By specifying whether the conformations are gauche (g) or transoid
(t) at each of the four four-carbon fragments (C1 to
C4, C2 to C5, C3 to C6,
and C4 to C7), one can easily describe all of the
conformations. For example, the conformation with all transoid interactions
would be called tttt. A clever way of generating these conformations
is to imagine them as superimposed on an adamantyl-like framework. For
example, C1 to C7 (in the diagram), after discarding
all of the unnumbered carbons and putting in the H's, is the g-ttg-
conformation (the sign - or + is used to differentiate two different types
of gauche interactions). Do the calculation (energy and dihedral angles)
on this conformation; then rotate about the C2-C3
and/or C5-C6 bonds to generate the other conformations
that have "tt" in the middle. Similarly, carbons 1, 2,
3, 4, 5, VI, VII represent the g-tg+g+ conformation, and it can
then be used to generate all that have "tg+" in the middle;
finally, I, II, 3, 4, 5, VI, VII give all having "g+g+"
in the center. This may sound complicated, but it is all clearly delineated
in the cited article (fear not, it's auf Englisch, meine Kinder).
You should also calculate the energies of the much higher-energy staggered
conformations that have "g-g+" in the middle.
[Hoffmann, R. W.; Sander, T.; Brumm, M. Chem. Ber. 1992, 125, 2319.]
198.
Prof. Alan Marchand of North Texas State University has described a synthesis
of (E)- and (Z)-1,2-di(1-adamantyl)ethene. One of the interests in these
compounds is the large steric repulsion of the Z-isomer. Compute the heats
of hydrogenation of both stereoisomers as well as of their structural isomer,
the 1,1-disubstituted ethene. Compare your results with those for the di-tert-butylethene
compounds, as given in Chem. 550 lecture.
215. van der Waals
forces can not only be destabilizing but stabilizing if the distance between
the groups is correct. Consider the series of compounds to the right; in
all of them, R1 is the bulky (essentially spherical) 1-adamantyl
group. First, do MMX calculations on the parent phenyl compound (R2
= H) to determine whether or not the conformation shown, with the tertiary
C-H coplanar with the benzene ring, is preferred. Then do calculations
on the other three compounds (R2 = Me, t-Bu, 1-Ad) in
their two possible conformations (the one with the C-H anti to R2,
the one with it syn) to determine if having the bulky groups closer to
one another is actually preferred; compare your answers with the calculated
and experimental results in the cited reference.
[Anderson, J. E.; Bru-Capdeville, V.; Kirsch, P. A.; Lomas, J. S. J. Chem. Soc., Chem. Commun. 1994, 1077.]
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