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CHAPTER 1 Chemical Bonding and Molecular Structure
Scheme 1.6. AIM Charge Distribution and Strain Energy (kcal/mol) for Cyclic Hydro-
89
TOPIC 1.3 Bonding in Cyclopropane and Other Small Ring Compounds
X2 X
X
X X
X X
X+ X
+
X+
+ +
The bridgehead C–H bond in tricyclo[1.1.1]pentane is not quite as strong as the C–H bond in cyclopropane. A value of 104.4 kcal/mol is calculated at the MP3/6-31G∗ level.128The total strain energy is 68 kcal/mol.
H H H
C-H bond strengths at MP3/6-311G* level 107.9 kcal 116.7 kcal 104.4
The alignment of the two bridgehead bonds is such that there is strong interaction between them. As a result of this interaction, there is hyperconjugation between the two bridgehead substituents. For example, the 19F chemical shifts are effected by →∗donation to the C–F∗ orbital.129
X Y X– Y+
[1.1.1]Propellane has a very unusual shape. All four bonds at the bridgehead carbons are directed toward the same side of the nucleus.130 There have been many computational studies of the [1.1.1]propellane molecule. One of the main objectives has been to understand the nature of the bridgehead-bridgehead bond and the extension of the orbital external to the molecule. The distance between the bridgehead carbons in [1.1.1]propellane is calculated to be 159 Å. The molecule has been subjected to AIM analysis. The c value for the bridgehead-bridgehead bond is 0173a3, which indicates a bond order of about 0.7.131 There is a low-temperature X-ray crystal structure of [1.1.1]propellane. Although it is not of high resolution, it does confirm the length of the bridgehead bond as 160 Å.132Higher-resolution structures of related tetracyclic compounds give a similar distance and also show electron density external to the bridgehead carbons.133
1.587 Å 1.585 Å
128 K. B. Wiberg, C. M. Hadad, S. Sieber, and P. v. R. Schleyer,J. Am. Chem. Soc.,114, 5820 (1992).
129 W. Adcock and A. N. Abeywickrema,J. Org. Chem.,47, 2957 (1982); J. A. Koppel, M. Mishima, L. M. Stock, R. W. Taft, and R. D. Topsom,J. Phys. Org. Chem.,6, 685 (1993).
130 L. Hedberg and K. Hedberg,J. Am. Chem. Soc.,107, 7257 (1985).
131 K. B. Wiberg, R. F. W. Bader, and C. D. H. Lau,J. Am. Chem. Soc.,109, 985 (1987); W. Adcock, M. J. Brunger, C. I. Clark, I. E. McCarthy, M. T. Michalewicz, W. von Niessen, E. Weigold, and D. A. Winkler,J. Am. Chem. Soc.,119, 2896 (1997).
132 P. Seiler,Helv. Chim. Acta,73, 1574 (1990).
133 P. Seiler, J. Belzner, U. Bunz, and G. Szeimies,Helv. Chim. Acta,71, 2100 (1988).
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CHAPTER 1 Chemical Bonding and Molecular Structure
Surprisingly, [1.1.1]propellane is somewhat more stable to thermal decomposition than the next larger propellane, [2.1.1]propellane, indicating a reversal in the trend of increased reactivity with increased strain. To understand this observation, it is important to recognized that the energy ofboth the reactant and intermediate influence the rate of unimolecular reactions that lead to decomposition. In the case of propellanes, homolytic rupture of the central bond is expected to be the initial step in decomposition. This bond rupture is very endothermic for [1.1.1]propellane. Because relatively less strain is released in the case of [1.1.1]propellane than in the [2.1.1]- and [2.2.1]-homologs, [1.1.1]propellane is kinetically most stable.134
ΔH=+65kcal/mol +30kcal/mol +5kcal/mol Another manifestation of the relatively small release of strain associated with breaking the central bond comes from MP4/6-31G∗ calculations on the energy of the reverse ring closure.135
H + H
+ 27 kcal/mol
The thermal decomposition of [1.1.1]propellane has been studied both experimen- tally and by computation.136The initial product is 1,2-dimethylenecyclopropane, and theEa is 39.7 kcal/mol. The mechanism of the reactions has been studied using both MO and DFT calculations. The process appears to be close to a concerted process, which is represented in Figure 1.37. DFT computations suggest that structure A is an intermediate,137 slightly more stable than TS1 and TS2. The corresponding MO calculations [CCSD(T)/6-311G(2d,p)] do not find a minimum. However, both methods agree thatA,TS1, andTS2are all close in energy. Note that this reaction isheterolytic and that the diradical is not an intermediate. This implies that there is a smaller barrier for the observed reaction than for homolytic rupture of the central bond. The calculated Ea is substantially less than the bond energy assigned to the bridgehead bond, which implies that bond making proceeds concurrently with bond breaking, as expected for a concerted process.
+
– –
A
TS1 TS2
Visual models, additional information and exercises on Thermal Rearrangement of [1.1.1]Propellane can be found in the Digital Resource available at:
Springer.com/carey-sundberg.
134 K. B. Wiberg,Angew. Chem. Int. Ed. Engl.,25, 312 (1985).
135 W. Adcock, G. T. Binmore, A. R. Krstic, J. C. Walton and J. Wilkie,J. Am. Chem. Soc.,117, 2758 (1995).
136 O. Jarosch, R. Walsh, and G. Szeimies,J. Am. Chem. Soc.,122, 8490 (2000).
137 . Both B3LYP/6-311G(d,p) and B3PW91/D95(d,p) computations were done and the latter were in closer agreement with the CCSD(T)/6-311G(2d,p) results.
91
TOPIC 1.3 Bonding in Cyclopropane and Other Small Ring Compounds 38.7
37.9 40.6
–11.0 0.0
Fig. 1.37. DFT (B3PW91/D95(d,p) representation of the thermal isomerization of [1.1.1]propellane to 1,2-dimethylenecyclopropane. Adapted from O. Jarosch, R. Walsh, and G.
Szeimies,J. Am. Chem. Soc.,122, 8490 (2000).
Both radicals and electrophiles react at the bridgehead bond of [1.1.1]propellane.
The reactivity toward radicals is comparable to that of alkenes, with rates in the range of 106 to 108 M−1s−1, depending on the particular radical.138 For example, [1.1.1]propellane reacts with thiophenol at room temperature.139
PhSH H SPh
+
Reaction with the halogens breaks the bridgehead bond and leads to 1,3- dihalobicyclo[1.1.1]butanes. When halide salts are included, mixed dihalides are formed, suggesting an ionic mechanism.140
+ X2 + X + + Y– X Y
[1.1.1]Propellane and maleic anhydride copolymerize to an alternating copolymer.141
O O
O
O
O O
O O
O O + O
O
Each of these reactions indicates the high reactivity of the bridgehead-bridgehead bond.
138 P. F. McGarry and J. C. Scaiano,Can. J. Chem.76, 1474 (1998).
139 K. B. Wiberg and S. T. Waddell,J. Am. Chem. Soc.,112, 2194 (1990).
140 I. R. Milne and D. K. Taylor,J. Org. Chem.,63, 3769 (1998).
141 J. M. Gosau and A.-D. Schlüter,Chem. Ber.,123, 2449 (1990).
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CHAPTER 1 Chemical Bonding and Molecular Structure
Topic 1.4. Representation of Electron Density by the Laplacian