J. Phys. Chem. 1996, 100, 17995-18003
17995
Bond Shift Tautomerism of Bibullvalenyl in Solution and in the Solid State. A Carbon-13 NMR Study L. Olivier,† R. Poupko,† H. Zimmermann,‡ and Z. Luz*,† The Weizmann Institute of Science, 76100 RehoVot, Israel, and Max-Planck-Institut fu¨ r Medizinische Forschung, Jahnstrasse 29, 69120 Heidelberg, Germany ReceiVed: June 24, 1996; In Final Form: August 26, 1996X
High-resolution carbon-13 NMR of bibullvalenyl solutions and magic angle spinning (MAS) of solid bibullvalenyl are reported over a wide temperature range and interpreted in terms of the isomeric distribution and the kinetics of the bond shift (Cope) rearrangements. In solution, bibullvalenyl exists predominantly as a mixture of the 3-3, 3-2, and 2-2 isomers, in which the bullvalenyl radicals are linked at the olefinic carbons. Their relative concentrations in the temperature range -50 to -20 °C are 0.67, 0.28, and 0.05, respectively. Above -30 °C bond shift rearrangement results in broadening of the NMR signals. Detailed analysis of these dynamic spectra indicates the occurence of at least three main rearrangement processes: (i) direct interconversion of the isomeric pairs 3-X a 2-X (X ) 2 or 3), (ii) degenerate rearrangement of the 2-X isomers, 2-X a 2*-X (where the asterisk indicates a rearranged bullvalenyl radical), and (iii) a pseudodegenerate rearrangement of the 3-X isomers via the intermediate 1-X, 3-X f [1-X] f 3*-X, and possibly also via the intermediate 4-X. In the solid state, bibullvalenyl crystallizes entirely as isomer 3-3, with the two bullvalenyl radicals most probably in crystallographically unrelated sites. Above room temperature the MAS spectra exhibit selective line broadening due to the Cope rearrangement. Detailed analysis shows that the pathway for the reaction involves the isomer 1-3, which serves as a transient intermediate in the reaction. It is likely that at higher temperatures additional pathways involving the isomers 4-3 and/or 2-3 also contribute to the line broadening in the solid state.
Introduction The bond shift tautomerism (Cope rearrangement) of bullvalene1-3 and its monosubstituted derivatives (bullvalenylX)4-9 has been extensively studied in solution and more recently, for some members of this family (X ) F, SC2H5, CN, COOH, Br, I), also in the solid state.7,10-16 In solution the monosubstituted bullvalenes exist as mixtures of isomers rapidly interconverting into each other via the Cope rearrangement, while in the solid state they crystallize as single isomers, usually as the one most abundant in solution. Thus fluorobullvalene15 crystallizes as isomer 4; cyanobullvalene,16 ethylthiobullvalene,7 and bullvalenecarboxylic acid16 as isomers 3; and bromo- and iodobullvalene17 as isomers 2. (We label the isomers according to the substitution site using the numbering system as given in the bottom of Figure 1.) These compounds crystallize in welldefined lattices, although the latter two compounds exhibit orientational disorder in otherwise ordered crystals.17 It was therefore surprising to discover that not only unsubstituted bullvalene but also its monosubstituted derivatives undergo Cope rearrangement in the solid state. This was unexpected, since the bond shift rearrangement in monosubstituted bullvalenes usually leads to interconversion between different isomers, as is shown by the seven-step cycle of Figure 1. According to this cycle isomer 4, for example, can only transform to isomer 1 by the Cope rearrangement, isomer 1 can revert to isomer 4 or transform to isomer 3, etc. Only isomer 2 can undergo a one-step degenerate rearrangement. To explain the occurrence of the Cope rearrangement in the solid state where only species such as isomer 4 or 3 exist, it was necessary to assume that the †
The Weizmann Institute of Science. Max-Planck-Institut fu¨r Medizinische Forschung. X Abstract published in AdVance ACS Abstracts, October 1, 1996. ‡
S0022-3654(96)01865-5 CCC: $12.00
Figure 1. Bond shift isomerization cycle of monosubstituted bullvalenes. The substituent, which for bibullvalenyl is another bullvalenyl radical, is indicated by X and the isomers are labeled according to the substitution site as indicated at the bottom of the figure.
reaction proceeds via closed, multistep, subcycles involving other isomers as short-lived intermediates in the reaction.15,16 Magic angle spinning (MAS) carbon-13 NMR turned out to be an excellent tool for investigating the mechanisms of such rearrangement processes in the solid state. In the slow exchange regime they can be studied by (rotor-synchronized) two© 1996 American Chemical Society
17996 J. Phys. Chem., Vol. 100, No. 45, 1996
Figure 2. Formulas and notation for the bibullvalenyl isomers observed experimentally.
dimensional (2D) exchange techniques,12,18,19 while at faster rates by a quantitative analysis of the experimental line shapes.13,20 In the present work we extend our earlier studies of the Cope rearrangement in monosubstituted bullvalenes to bivullvalenyl, a dimer molecule in which two bullvalenyl radicals are linked via a single covalent bond. This compound differs from the other monosubstituted bullvalenes in that, rather than just four, it can exist as 10 isomers, depending on the linking sites in the two subunits. The proton NMR spectrum of bibullvalenyl in solution was studied a quarter of a century ago by Oth et al.8 The resolution of the proton spectrum was not sufficient to directly identify the isomers in solution. However, from the relative NMR intensities of the olefinic and aliphatic protons at low temperatures (-50 °C) they were able to deduce that the dominant species in solution are those where the two radicals are linked via their olefinic carbons, i.e. isomers 3-3, 3-2, and 2-2 (see Figure 2 for the definition of the isomeric species). On heating to room temperature and above, the proton NMR peaks were found to undergo line broadening, coalescence, and eventually merge into a single line, indicating that the three isomers rapidly interconvert via the Cope rearrangement. We have now studied the corresponding carbon-13 spectra of bibullvalenyl in solution, confirming the earlier assignment of Oth et al. and deriving quantitative values for the equilibrium constants between the species and for the kinetic parameters of their interconversion. More importantly, we have extended the measurements to carbon-13 NMR in solid bibullvalenyl. We identified the isomer that crystallizes in the solid state and detected a Cope rearrangement in this state. By a detailed analysis of the dynamic MAS spectrum we identified the mechanism of this rearrangement and determined its rate parameters. Experimental Section Bibullvalenyl was prepared from bromobullvalene via the Grignard intermediate, bullvalenylmagnesium bromide, as described in ref 8. Carbon-13 solution NMR spectra were recorded at 125.7 MHz on a Bruker AM500 spectrometer. The solvent used was CD2Cl2. Carbon-13 MAS spectra of solid samples were measured at 75.46 MHz on a Bruker CXP300 spectrometer, using a Doty variable temperature magic angle spinning probe. Details of the experimental conditions are given in the appropriate figure captions. Results and Discussion 1. The Low-Temperature Carbon-13 Spectrum and the Isomeric Equilibria in Solution. A high-resolution carbon-
Olivier et al. 13 NMR spectrum of a bibullvalenyl solution (4.3 wt %) in CD2Cl2 at -50 °C is shown in Figure 3. Various fractions of the spectra are inserted at an expanded scale and higher gain. For each of these fractions one can roughly identify three types of peaks: very strong, intermediate, and very weak ones. We have performed a series of experiments on this solution including proton-carbon correlation, 2D exchange, and proton undercoupled carbon-13 spectroscopy. These experiments allowed us to unequivocally identify all peaks in the spectra in terms of just three species, i.e. the 3-3, 3-2, and 2-2 isomers. The peak assignment is given in Figure 3. In our notation the substitution site is on wing C, while wings A and B remain unsubstituted, and in solutions they are equivalent. The peaks of the symmetric 3-3 and 2-2 isomers are doubly degenerate because of the equivalence of dimers’ components. Each of these isomers gives rise to seven peaks, which we label 1AB(4), 2AB(4), 3AB(4), 1C(2), 2C(2), 3C(2), and 4(2), where the numbers in parentheses correspond to their relative intensities and 1AB refers to 1A and 1B, etc. The superscripts on the labels identify the isomers, 3-3 or 2-2. For the asymmetric 3-2 isomer the peaks due to the two bullvalenyl radicals are not degenerate. We distinguish between them by the superscript 3-2 (if the carbon belongs to the 3-bullvalenyl half) or 2-3 (if it is in the 2-bullvalenyl half). For example, 1C3-2 refers to the 1C carbon in the 3-bullvalenyl radical of the 3-2 isomer. The 1C carbon in the 2-bullvalenyl half of the same isomer is labeled 1C2-3. Note the strong chemical shift difference between the aliphatic carbons 1AB, 1C, and 4, which lie in the range 20-35 ppm, and the olefinic carbons, 2AB, 3AB, 2C, and 3C, in the range 120-145 ppm. The chemical shifts for all the carbons are summarized in Table 1. Peak intensity measurements over the temperature range -50 to -20 °C, where the exchange broadening is small, allowed us to determine the relative concentrations of the three isomers. These were nealy constant at the indicated range with the following equilibrium ratios:
3-3:3-2:2-2 ) 0.67:0.28:0.05 We note that the signals at 140 ppm, which correspond to the carbons linking the two bullvalenyl radicals, are significantly weaker than the corresponding other carbons. This is due to the fact that they have no directly bound protons and therefore experience much weaker NOE enhancement. 2. The Carbon-13 Dynamic Spectra and the Mechanisms of the Cope Rearrangement in Solution. As the temperature of the bibullvalenyl solution is raised to above -30 °C, line broadening sets in the carbon-13 spectrum. Examples of such exchange-broadened spectra are shown in the left column of Figure 4. This broadening is due to the Cope rearrangement, which interchanges the various isomers. In the present section we will attempt to identify the rearrangement mechanisms responsible for the line broadening and determine their rate parameters. The first mechanisms that come to mind and which were actually detected by preliminary 2D exchange spectroscopy are the rearrangement reactions that interchange between the 3-X and 2-X isomers, where X ) 2 or 3, i.e. a
b
}2-3 and 3-2{\ }2-2 3-3{\ a′ b′ with a and b the rate constants for the indicated processes and 3-3 a′ ) aK2-3
3-2 b′ ) bK2-2
the rate constants for the corresponding reverse reactions.
NMR of Bibullvalenyl in Solution and in the Solid State
J. Phys. Chem., Vol. 100, No. 45, 1996 17997
Figure 3. High-resolution, proton-decoupled, carbon-13 NMR spectrum of a 4.3 wt % solution of bibullvalenyl in CD2Cl2 at -50 °C. Recycle time, 3 s. Number of scans, 240. Various fractions of the spectrum at a ×4 expanded scale are inserted. The asterisk corresponds to an impurity peak.
TABLE 1: Carbon-13 Chemical Shifts (in ppm Relative to TMS) for the Bullvalenyl Isomers in Solution and in the Solid State solutiona
1AB 1C 4
solidd
3-3
3-2b
2-3c
2-2
20.90 20.22 33.86
20.65 20.18 33.64
20.33 21.99 30.31
20.33 22.09 30.31
e δiso
f δxx
f δyy
22.33 20.93 37.48
f δzz
∆g 80 35 40
2AB 127.77 127.41 126.93 127.66
127.31 61.4 20.4 -81.8 70 128.30
3AB 127.44 127.56 127.81 127.66
128.30 64.6 21.6 -86.2 70 129.46
2C
120.95 120.26 141.06 142.70
119.11 45.0 36.4 -81.4 35 119.65
3C
143.24 145.16 122.20 121.70 146.50 66.0 20.0 -86.0 40
Measured in a 4.3 wt % solution in CD2Cl2 at -50 °C. b The numbers refer to the 3-bullvalenyl component. c The numbers refer to the 2-bullvalenyl component. d The entries refer to the 3-3 isomer. e The doubling of the peaks due to carbons 2AB, 3AB, and 2C is apparently due to crystallographic inequivalence of the two bullvalenyl radicals in the dimer. f The principal directions correspond respectively to x, perpendicular to the double bond in the plane of the wing; y, along the double bond; z, perpendicular to the wing plane. g Full line width (in Hz) at half-maximum intensity used in the simulations. a
The K’s are equilibrium constants: 3-3 K2-3 )
[3-3] [2-3]
3-2 K2-2 )
[3-2] [2-2]
We assume that the rearrangement in both halves of the molecule occur independently and the rate constants refer to a particular bullvalenyl radical (not the whole dimer). In principle a rearrangement reaction in which both bullvalenyls rearrange simultaneously (e.g. 3-3 f 2-2) could also occur, but we consider such a mechanism unlikely. To derive rate constants for the isomerization reactions, we need to compare the
experimental spectra with simulated line shapes calculated with an appropriate kinetic matrix and associated population vector. Such a matrix is shown in Table 2, with the rows and columns labeling the carbon atoms as defined in Figure 3. These were ordered in seven groups of four peaks, which interchange by the 3-X a 2-X rearrangement. If these processes, represented by the rate constants a, a′, b, and b′, were the only ones to take place, the kinetic matrix would factorize into seven 4 × 4 blocks, and the dynamic spectra would, in the fast exchange limit, merge into seven bands. Each group of four peaks will undergo broadening, coalescence, and eventually narrowing to a single line, with the maximum broadening of each band depending on the chemical shift spread within the group. Thus, the first and third groups in the kinetic matrix, which involve aliphatic and olefinic carbons, are associated with a wide chemical shift spread, while the spread in the other groups, which involve either aliphatic or olefinic carbons, is relatively small. Referring to Figure 4, we note that the group of peaks at 120 ppm, corresponding to the penultimate block in the exchange matrix, indeed first coalesces and then starts to narrow. However, above room temperature it begins to broaden again. A plot of the overall width (at half-maximum intensity) of this band versus the temperature is shown in Figure 5. The dashed line in the figure shows the calculated line width if the 3-X a 2-X processes were the only rearrangement mechanisms. It is thus clear that we need to consider additional exchange mechanisms that result in permutation of atoms between different groups. A most likely mechanism that can bring about such permutations is the degenerate rearrangement of the 2-bullvalenyl radical, as indicated at the top of the seven-step cycle in Figure 1. In our case it only applied to the 2-X isomers, c
d
2*-3 and 2-2a 2*-2 2-3a c d where the asterisk indicates a rearranged 2-bullvalenyl radical, and c and d are rate constants. The effects of these processes
17998 J. Phys. Chem., Vol. 100, No. 45, 1996
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Figure 4. (Left) Carbon-13 spectra of the same solution as in Figure 3 as function of temperature as indicated. Recycle time, 3 s. The number of scans was gradually increased from 1600 at -20 °C to 10 000 at 55 °C. (Right) Simulated dynamic spectra calculated with the indicated rate constants. In both columns the central part of the spectrum between 45 and 95 ppm, where no peaks (except for the solvent CD2Cl2) are observed, was deleted.
are included in the kinetic matrix of Table 2. When these rates were included in the simulation of the dynamic line shapes, the fit with the experimental spectra was considerably improved; in particular it accounted for the rebroadening of some of the bands as observed experimentally (see Figure 5). However, this alone was found insufficient to reproduce the behavior of the dynamic spectra at higher temperatures (above about 30 °C). To improve the fit, additional mechanisms had to be assumed. Such mechanisms must involve isomeric species not observed in the experimental spectra. The interconversion cycle of Figure 1 allows several such mechanisms to be considered, but the most likely ones are those that involve the isomers 1-X (i.e., 1-3 and 1-2) as transient intermediates, as indicated by the square brackets in the following cycles: k1
k1-1
k2
k2-1
3-3{\ }[1-3]{\ }3*-3 and 3-2{\ }[1-2]{\ }3*-2 -1 -1 k k k1
k2
1
2
The overall rate constants for these processes are indicated as f and g in Table 2, where
k1-1
1 1 f ) k1 -1 ) k1 and g ) k2 2 2 2k1 In practice, to reduce the number of adjustable parameters, we assumed that a ) b, c ) d, and f ) g. This amounts to assuming that the rearrangement within a bullvalenyl radical is the same whether it is bound to X ) 2 or X ) 3. These rate constants are per bullvalenyl radical. The overall rates of rearrangement of the symmetric isomers are therefore twice as fast. Examples of spectra simulated to fit the experimental results are shown in the right column of Figure 4 along with the rate constants a, c, and f used in the calculations. The
agreement is quite satisfactory and certainly reproduces the main features of the dynamic spectra. It could probably further be improved by including additional rearrangement mechanisms, for example involving the 4-X isomers as intermediates and assuming the equilibrium constants to be temperature dependent. The large number of parameters would, however, render the problem an intractable one. Rate constants used to simulate the spectra under the above restrictions are plotted in Figure 6 as a function of the reciprocal absolute temperature. For the 3-3 f 2-3 process (a) there are sufficient data to derive reliable Arrhenius kinetic parameters,
Aa ) 1.3 × 1014 s-1, ∆Ea ) 15.2 kcal mol-1 The results for the 2-X f 2*-X rearrangement (c) appear to lie on the same Arrhenius curve as a, while those for 3-X f [1-X] f 3*-X (f) are about a factor of 5 slower (at corresponding temperatures). As may be seen in Figure 6, at different temperatures the dynamic spectra are differently sensitive to the various rate constants. Thus, below 0 °C the spectra are essentially determined by the rate parameter a, while at higher temperatures they are more sensitive to c and f. The latter could in fact only be determined in a relatively narrow temperature range. The estimated accuracy of ∆Ea is (15%. Its value falls within the range of the ∆E’s determined for other monosubstituted bullvalenes.9 Before proceeding to the solid state results for bivullvalenyl a note concerning the group of peaks for the 3C and 2C carbons around 143 ppm (last group in Table 2), which correspond to the atoms linking the two bullvalenyl radicals, is in order. It was already indicated that because of their less efficient NOE enhancement, the intensities of these signals are lower than for the other carbons. This group of peaks does not mix with any of the rest of the carbons in the spectrum and should therefore
TABLE 2: Kinetic Matrix Used in the Simulation of the Carbon-13 Dynamic Spectra of Bibullvalenyl in Solution (Entries Are Rate Constants As Defined in the Text)
NMR of Bibullvalenyl in Solution and in the Solid State J. Phys. Chem., Vol. 100, No. 45, 1996 17999
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Figure 5. Full line width at half-maximum intensity of the band around 120 ppm as a function of temperature. The dashed curve gives the calculated width of the band if the 3-X a 2-X processes were the only rearrangement mechanism with rate equations, a ) b ) 1.3 × 1014 exp(15.2/RT) s-1 (where R is in kcal‚mol-1).
Figure 6. Arrhenius plots of the rate constants used in the simulation of the dynamic spectra in bibullvalenyl solutions (a, c, f) and in solid bibullvalenyl (k).
yield a sharp intense signal once its coalescence temperature is surpassed (as shown by the simulated spectra in Figure 4). In fact, although it remains isolated, it appears broader than expected from the simulations. It is possible that the extra broadening of this peak is due to exchange with the 1-X and possibly 4-X species. When their concentration is increased, as would be expected at higher temperatures, they may cause rebroadening of the 143 ppm peak. It is however impossible to check this possibility because the peaks associated with these species should be excessively broad. 3. The Low-Temperature Carbon-13 MAS Spectrum of Solid Bibullvalenyl. In Figure 7 is shown a room temperature carbon-13 MAS spectrum of bibullvalenyl. From the number of center bands in the spectrum it becomes immediately clear that the compound crystallizes as a single isomer. The structure of the spectrum around 37 and 146 ppm, corresponding to the bridgehead carbons 4 and the olefinic bridging carbons of wing C, is particularly simple and indicates that the isomer is a symmetric one. Comparison of the actual chemical shifts with those in solution allows the identification of the isomer in the solid state as 3-3 bibullvalenyl. This assignment is further supported by the dynamic spectra discussed below. It is also consistent with the fact that the 3-3 isomer is the most abundant
Olivier et al. species in solution. On the basis of this identification we assign the various peaks as indicated in the spectrum of Figure 7. It may be noted in this spectrum that some of the peaks exhibit a small splitting. Note in particular the peaks due to carbons 2C and 2AB/3AB. We believe that this peak doubling reflects crystallographic inequivalence. Most likely the bullvalenyl radicals in the dimer are not related by a crystallographic symmetry element, but it could also be due to the fact that there are more than one type of molecule in the unit cell. As the crystal structure of solid bibullvalenyl is not known, we cannot distinguish between the two alternatives. The isotropic chemical shifts in the solid state are summarized in Table 1 along with those for the bibullvalenyl solution. There are two entries for those carbons for which a splitting in the MAS spectrum was observed. 4. The Temperature Dependent Spectra and the Cope Rearrangement in Solid Bibullvalenyl. As the temperature of the solid bibullvalenyl sample is raised to above room temperature, its MAS carbon-13 spectra exhibit changes that clearly reflect the occurrence of a dynamic process. Examples of such spectra are shown in the left column of Figure 8. It may be noted that there is a very conspicuous line broadening for some of the peaks, while others remain relatively sharp. In particular the peaks associated with the carbons of wing C (1C, 2C, and 3C) appear not to change, while those of wings A and B and carbon 4 gradually broaden with increasing temperature. This selective broadening rules out spin diffusion as a broadening mechanism and indicates that bond rearrangement leading to permutation between carbon atoms takes place in the solid state. The interpretation of these spectra in terms of the Cope rearrangement is more subtle than in solution. Referring to Figure 1 we note that a single rearrangement step in one of the bullvalenyl radicals will transform the 3-3 isomer to either the 2-3 or the 1-3 isomer, which are not observed in the NMR spectrum of the bibullvalenyl crystals. We therefore need to assume that the rearrangement involves a cycle of two or more bond shift steps with one or several isomers as transient intermediates. To identify the actual pathway of the reaction, we must consider the various possible cycles and check which of them are consistent with the experimental results. As for the solution spectra, we assume that the two halves of the bibullvalenyl dimer rearrange independently. We consider first the cycle 3-3 f [2-3] f 3-3, where as before the square brackets indicate a short-lived transient intermediate,
This formula can be expressed in terms of the following diagram: 1A 2A 3A
1B 2B 3B 4
1C 2C {3C}
f
1A 2A 3A
1C 1B 2B 3B
2C {3C} 4
f
1A 2A 3A
1B 2B 3B 4
1C 2C {3C}
where the columns represent the wings of the bullvalenyl cage, the isolated number the bridgehead atom, and the curly brackets the bridging site to the second half of the dimer. Comparing the last and first diagrams, it may be seen that in
NMR of Bibullvalenyl in Solution and in the Solid State
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this cycle each atom reverts to its original site in the diagram. Hence it does not lead to permutation between carbon atoms and can therefore not be responsible for the observed line broadening. On the other hand, the cycle 3-3 f [1-3] f 3*-3 can lead to permutation between the carbons, as may be seen in the following diagram: 1A 2A 3A
1B 2B 3B 4
1C 2C {3C}
f
1A 2A 3A
1B 2B 3B 4
1C 2C {3C}
f
1B 1A 2A
2B 3B 4 3A
1C 2C {3C}
This process can also be represented by the permutation cycle (1A, 2A, 3A, 4, 3B, 2B, 1B) (1C) (2C) ({3C}). To construct the corresponding kinetic matrix, we also need to consider the equivalent reverse cycle, represented by the diagram 1A 2A 3A
1B 2B 3B 4
1C 2C {3C}
f
2A 3A 4
1A 1B 2B 3B
1C 2C {3C}
f
2A 3A 4
1A 1B 2B 3B
1C 2C {3C}
which corresponds to the inverse permutation of the previous cycle (1A, 1B, 2B, 3B, 4, 3A, 2A) (1C) (2C) ({3C}). We note that in both cycles atoms 1C, 2C, and 3C remain invariant, while all other carbons undergo permutation. These pathways are thus consistent with the experimental results. Using similar diagrams we can check the other possible cycles,16 3-3 f [2-3] f [2*3] f 3*-3; 3-3 f [2-3] f [2*-3] f [2**-3] f 3**-3; and 3-3 f [1-3] f [4-3] f [1*-3] f 3*-3. All of these cycles involve, however, permutation of either one or both of the carbons 1C and 2C and can therefore be ruled out. We are thus left with 3-3 f [1-3] f 3*-3 as the only cycle consistent with the experiments. Assuming that the two pathways of the 3-3 f [1-3] f 3*-3 mechanism are equally probable and that the two bullvalenyl radicals behave similarly in solid bibullvalenyl, their permutation schemes lead to a single kinetic matrix kK, where k is the rate constant for the reaction and
To derive rate constants for the rearrangement reaction in solid bibullvalenyl, we have computed a series of dynamic spectra using the above kinetic matrix and compared them with the experimental results. Examples of such calculated spectra are shown in the right-hand side of Figure 8. For these computations we considered the spectra as superpositions of two components, a dynamic one, comprising the signals due to the carbons of wings A and B and carbon 4, and a static component due to carbons 1C, 2C, and 3C. The subspectrum due to the latter carbons was computed with their sidebands using the
Figure 7. Carbon-13 MAS spectrum of bibullvalenyl at room temperature. Spinning rate, VR ) 3.8 kHz; number of scans, 200; recycle time, 5 min.
Herzfeld-Berger formalism.21 The dynamic component of the spectrum was calculated using the Floquet formalism, as described in refs 20, 13, and 15. We neglected the anisotropic chemical shifts of the aliphatic carbons 1A, 1B, 1C, and 4 since in our spectra they did not give any measurable spinning sidebands, while for the olefinic carbons we used the chemical shift tensors shown in Table 1. They were determined from the corresponding spinning sideband intensities at room temperature. Experimentally at most two pairs of spinning sidebands were observed for each olefinic carbon at the spinning frequency used in our measurements (VR ) 3.8 kHz). To ensure convergence of the calculations, we computed five such pairs for each exchanging olefinic carbon. Thus the total size of the Floquet matrix (for the dynamic component) was 11 × 4 + 2 ) 46 where we considered the 1A and 1B carbons as a single atom of double intensity. A typical computation time for a single dynamic spectrum was 5 h on a Digital Alpha 3000/800 computer. In superposing the two spectral components, the relative intensity of the invariant peaks was slightly attenuated relative to the dynamic part in order to account for the reduction in the efficiency of the cross polarization of dynamically broadened carbons. Examples of simulated spectra are shown in the right column of Figure 8. The attenuation factors in the spectra shown in this figure are 0.83 for the bottom trace, 0.67 for the next two, and 0.5 for the top two traces. By fitting the simulated line shapes to the experimental spectra, values for the rearrangement rate constant, k, in solid bibullvalenyl could be derived. The results are included in Figure 6, together with those for the rearrangement rate constants in solution. The kinetic parameters derived for the rearrangement process are A ) 1.1 × 1013 s-1, ∆E ) 15.7 kcal mol-1. They are similar to those determined for two other monosubstituted bullvalenes (cyanobullvalene and bullvalenecarboxylic acid), which also crystallize as the 3-isomer and were shown to undergo Cope rearrangement in the solid state via the 1-isomer.16 This solid state process may be compared with the f-rearrangement in solution, where it was found to be about 5-fold faster at comparable temperatures (see Figure 6). Finally we wish to remark on the experimental hightemperature spectra in Figure 8. It may be seen that in these spectra the peaks associated with carbons 1C and 2C broaden slightly compared to their width at room temperature and to the width of the carbon 3C peak, which appears to remain sharp. This broadening is almost certainly due to the setting-in of other rearrangement pathways, which we excluded under the assumption that the peaks due to the wing C carbon remain invariant.
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Figure 8. (Left) Carbon-13 MAS spectra of bibullvalenyl at different temperatures as indicated. Experimental conditions as in Figure 7. (Right) Simulated spectra calculated as described in the text for the indicated rate constants.
There are two mechanisms that could cause this extra broadening, i.e. 3-X f [2-X] f [2*-X] f 3*-X and 3-X f [1-X] f [4-X] f [1-X] f 3*-X. The experimental data are however insufficient to distinguish between these two alternatives. From the width of the 1C and 2C peaks relative to that of 3C we estimate the rate of this extra mechanism as 300 s-1 at 100 °C. Summary and Conclusions We have confirmed that bibullvalenyl in solution exists predominantly as the 3-3, 3-2, and 2-2 isomers, in which the bullvalenyl radicals are linked via olefinic carbons. Analysis of the carbon-13 spectra showed that the relative abundance of these isomers is in the order 3-3 > 3-2 > 2-2. The preference for olefinic substitution in bullvalene derivatives, in particular in site 3, is apparently quite general for the bullvalene molecule. There is actually only one known exception to this rule, i.e. fluorobullvallene, in which the 4-isomer dominates the isomeric equilibrium.5 The different isomers interconvert in solution on the NMR time scale. Quantitative analysis of the spectral line shapes indicates that there are at least three dominant bond shift mechanisms responsible for their interconversion; one of them involves the 1-X isomers (X ) 3, 2), which must therefore also exist in solution, although at a concentration too low to observe by NMR. The results suggest that the 4-X isomers may also be present. The X-ray structure of bibullvalenyl has so far not been determined. The solid state NMR data suggest, however, that it crystallizes entirely as the 3-3 isomer, and it appears that the two bullvalenyl radicals in the dimer are not crystallographically related. Despite the fact that only one isomer is present in the crystalline state, the molecules undergo thermally activated bond shift rearrangement. Such a rearrangement can only take place via short-lived intermediate species. We have
determined from the dynamic carbon-13 MAS spectra that these intermediates include predominantly the 1-3 isomer and only to a lesser extent the 4-3 isomer. It is important to emphasize, however, that we cannot rule out a rearrangement cycle involving the 2-3 isomer as an intermediate, via the cycle 3-3 f [2-3] f 3-3. This pathway does not lead to permutation of carbon atoms in the bullvalenyl cage and therefore cannot be detected by NMR. In fact, since the 2-3 isomer is second in importance among the isomers in solution, we believe that this cycle does occur, perhaps even at a faster rate than the 3-3 f [1-3] f 3*-3 cycle. Acknowledgment. This research was supported by Grant No. 92-0094/5862 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel, and by the Minerva Foundation, Munich, Germany. References and Notes (1) Schro¨der, G.; Oth, J. F. M. Angew. Chem. 1967, 458, 79. (2) Oth, J. F. M.; Mu¨llen, K.; Gilles, J.-M.; Schro¨der, G. HelV. Chim. Acta 1974, 57, 1415. (3) Poupko, R.; Zimmermann, H.; Luz, Z. J. Chem. Phys. 1984, 106, 5391. (4) Oth, J. F. M.; Merenyi, R.; Nielsen, J.; Schro¨der, G. Chem. Ber. 1965, 98, 3385. (5) Oth, J. F. M.; Merenyi, R.; Ro¨ttele, H.; Schro¨der, G. Tetrahedron Lett. 1968, 3941. (6) Hoogzand, C.; Nielsen, J.; Oth, J. F. M. Tetrahedron Lett. 1970, 2287. (7) Luger, P.; Roth, K., J. Chem. Soc., Perkin Trans. 2 1989, 649. (8) Oth, J. F. M.; Machens, E.; Ro¨ttele, H.; Schro¨der, G. Liebigs Ann. Chem. 1971, 745, 112. (9) Poupko, R.; Zimmermann, H.; Mu¨ller, K.; Luz, Z. J. Am. Chem. Soc. 1996, 118, 7995. (10) Meier, B. H.; Earl, W. L. J. Am. Chem. Soc. 1985, 107, 5553. (11) Schlick, S.; Luz, Z.; Poupko, R.; Zimmermann, H. J. Am. Chem. Soc. 1992, 114, 4315. (12) Titmann, J. J.; Luz, Z.; Spiess, H. W. J. Am. Chem. Soc. 1992, 114, 3765.
NMR of Bibullvalenyl in Solution and in the Solid State (13) Luz, Z.; Poupko, R.; Alexander, S. J. Chem. Phys. 1993, 99, 7544. (14) Mu¨ller, A.; Haeberlen, U.; Zimmermann, H.; Poupko, R.; Luz, Z., Mol. Phys. 1994, 81, 1239. (15) Mu¨ller, K.; Zimmermann, H.; Krieger, C.; Poupko, R.; Luz, Z. J. Am. Chem. Soc. 1996, 118, 8006. (16) Poupko, R.; Mu¨ller, K.; Zimmermann, H.; Krieger, C.; Luz, Z. J. Am. Chem. Soc. 1996, 118, 8015. (17) Unpublished results from this laboratory.
J. Phys. Chem., Vol. 100, No. 45, 1996 18003 (18) de Jong, A. F.; Kentgens, A. P. M.; Veeman, W. S. Chem. Phys. Lett. 1984, 109, 337. (19) Hagemeyer, A.; Schmidt-Rohr, K.; Spiess, H. W. AdV. Magn. Reson. 1989, 13, 85. (20) Schmidt, A. J.; Vega, S. J. Chem. Phys. 1987, 87, 6895. (21) Herzfeld, J.; Berger, A. E. J. Chem. Phys. 1980, 73, 6021.
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