Gas-Phase Kinetics and Activation Parameters for Thermal [1,5] Hydrogen Shifts Interconverting MonodeuteriumLabeled 1,3-Cycloheptadienes
SCHEME 1
John E. Baldwin* and Anuradha S. Raghavan
SCHEME 2
Department of Chemistry, Syracuse University, Syracuse, New York 13244
[email protected] Received July 19, 2004
Abstract: The kinetics of thermal equilibrations among monodeuterium-labeled 1,3-cycloheptadienes in the gas phase followed from 154 to 190 °C provide activation parameters for the [1,5] shift of a single hydrogen: Ea ) (27.5 ( 0.9) kcal/mol and log A ) 9.9 ( 0.4. These activation parameters imply a comparatively low Ea barrier balanced by demandingly specific geometric constraints, for ∆Sq (170 °C) ) -16 e.u.
Thermally induced [1,5] hydrogen shifts in suitable conjugated dienes were recognized only in the 1960s, though earlier examples of such molecular rearrangements soon became apparent retrospectively.1-4 With the advent of orbital symmetry theory applied to sigmatropic reactions,5 such isomerizations were accorded fresh attention. Appropriately labeled acyclic dienes were studied closely to test whether the stereochemical dictates of theory were indeed observed. Experimental studies conclusively demonstrated that [1,5] sigmatropic hydrogen shifts in simple acyclic systems do take place in a suprafacial fashion,6 just as required by theory. Cyclic dienes constrained geometrically to suprafacial hydrogen migrations rearrange through [1,5] hydrogen shifts with activation energies indicative of a very large energy of concert.7 Thus, such prototypical sigmatropic thermal rearrangements take place without mechanistic ambiguities. One cannot reasonably conjecture that these reactions take place through a stepwise process. Accordingly, the [1,5] hydrogen shifts exhibited by cyclic dienes provide an excellent opportunity for delving more deeply into issues associated with modulated geometrical constraints, correlative variations in transition structure geometries, and changes in the activation parameters defined by experiment and by theory.8,9 The present study followed the isomerizations interconverting the four monodeuterium-labeled 1,3-cyclohep(1) Roth, W. R. Chimia 1966, 20, 229-236. (2) Spangler, C. W. Chem. Rev. 1976, 76, 187-217. (3) Hasselmann, D. Stereoselective Synthesis; G. Thieme: Stuttgart, 1996; Vol. E21, pp 4421-4463. (4) For a recent extensive gathering of references on [1,5] hydrogen shifts, see: Alabugin, I. V.; Manoharan, M.; Breiner, B.; Lewis, F. D. J. Am. Chem. Soc. 2003, 125, 9329-9342. (5) Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87, 2511-2513. (6) Roth, W. R.; Ko¨nig, J.; Stein, K.Chem. Ber. 1970, 103, 426-439. (7) Compare: Doering, W. von E.; Roth, W. R.; Breuckmann, R.; Figge, L.; Lennartz, H. W.; Fessner, W. D.; Prinzbach, H. Chem. Ber. 1988, 121, 1-9.
tadienes. Scheme 1 depicts the four isotopomers and provides rate constants for interconversions labeled by subscripts and in terms of the rate constant k for migration of a single hydrogen times an integer appropriate to the number of hydrogen atoms that might migrate to form the given product. The kinetic study required a substrate labeled with but a single deuterium. Any one of the isotopomers 1-4, or a mixture of two or more well away from equilibrium, would suffice. A mixture of isomers 1 and 2 was prepared through the synthetic sequence shown in Scheme 2. 2-Cyclohepten-1-one (5) was reduced with NaBD4 and CeCl3 in methanol to form 6.10 Dehydration using NaI and CeCl3 in acetonitrile11 took place as expected through both 1,2- and 1,4-elimination to provide a mixture of 1 and 2. After a conventional workup and simple Kugelrohr distillation at reduced pressure, the 92.1 MHz 2H NMR spectrum of the dienes showed incompletely resolved vinylic deuterium absorptions. No deuterium signals for isomers 3 or 4 were in evidence. The 600 MHz 1H NMR spectrum for unlabeled cycloheptadiene shows multiplets for vinyl hydrogens at δ 5.85 and 5.80. The lower-field multiplet is due to C1-H and C4-H, based on the careful analysis of NMR spin-spin coupling constants in 1,3cycloheptadiene reported by Crews.12 Purification of the monodeuterium-labeled cycloheptadienes by preparative GC gave a clean sample homogeneous by capillary GC analysis, but by 2H NMR it proved to be a mixture of all four isomers. Some thermal rearrangement in the injection port of the preparative GC system was deemed to be the likely culprit responsible for the scrambling. The integrated intensities were consistent with 80.3% {1 + 2}, 15.4% 3 at δ 2.35, and 4.3% 4 at δ 1.84. A less precise estimation of the initial mole percent concentrations of isomers 1 (45%) and 2 (35%) was made from the partially resolved vinylic deuterium multiplets. Fortunately, the lack of precision in this estimate turned out to have little consequence for data reduction, as demonstrated through sensitivity analysis calculations. (8) Baldwin, J. E.; Lee, T. W.; Leber, P. A. J. Org. Chem. 2001, 66, 5269-5271. (9) Hess, B. A., Jr.; Baldwin, J. E. J. Org. Chem. 2002, 67, 60256033. (10) Sabitha, G.; Babu, R. S.; Rajkumar, M.; Srividya, R.; Yadav, J. S. Org. Lett. 2001, 3, 1149-1151. (11) Bartoli, G.; Bellucci M. C.; Petrini, M.; Marcantoni, E.; Sambri, L.; Torregiani, E. Org. Lett. 2000, 2, 1791-1793. (12) Crews, P. Chem. Commun. 1971, 583-584. 10.1021/jo040238w CCC: $27.50 © 2004 American Chemical Society
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Published on Web 10/15/2004
TABLE 1. Rate Constants for the [1,5] Shift of a Single Hydrogen in cis-1,3-Cycloheptadiene T (°C)
rate constant k
154.1 169.7 180.0 189.9
(4.15 ( 0.39) × 10-5 s-1 (1.63 ( 0.17) × 10-4 s-1 (2.49 ( 0.26) × 10-4 s-1 (5.50 ( 0.65) × 10-4 s-1
Samples of the GC-purified mixture of monodeuteriumlabeled 1,3-cycloheptadienes diluted with 2,2-dimethylbutane were injected into an evacuated static reactor attached to a vacuum line and heated at defined temperatures for specific reaction times. Product mixtures were isolated and analyzed by 2H NMR. The kinetic data are provided in Table S1, Supporting Information. The relative concentrations of 1 and 2 were estimated together. The analysis required to find rate constant k from relative concentration data at any one temperature has been detailed elsewhere.13 The differential equations corresponding to the kinetic situation summarized in Scheme 1 may be solved with the aid of some matrix algebra14 to provide expressions for {1 + 2}, 3, and 4 as functions of time, the initial relative concentrations, and the single unknown k, as summarized in eqs 1-3, wherein x ) exp(-1.172kt), y ) exp(-5kt), and z ) exp(-6.828kt).13
{1 + 2} ) 40.0 + 38.6x + 0.86y + 0.84z
(1)
3 ) 40.0 - 22.6x + 0.85y - 2.83z
(2)
4 ) 20.0 - 16.0x - 1.71y + 2.00z
(3)
The value of k appropriate to each set of data was first estimated using a least-squares best-fit program.15 The relative concentration data and the theory-based singlevariable expressions given by eqs 1-3 gave three nearly equal values of k at each temperature. The best value was found by optimizing the match between all data points at a given temperature and theory-based calculated relative concentrations to minimize the estimated variance, σ2C ) Σ(Ci(obsd) - Ci(calcd))/(n - 1).16 One of the kinetic runs (180.0 °C, 43,200 s) extended to more than 15 half-lives. The observed distribution of isomers (40.2% {1 + 2}, 39.5% 3, 20.3% 4) matched the equilibrium proportions (40, 40, and 20%) quite well, a confirmation of the adequacy of the 2H NMR data acquisition parameters utilized and the reliability of the integrations. Overall, the average difference between observed and calculated relative concentrations, Ci(obsd) - Ci(calcd), was 0.9%. The rate constants and estimated uncertainties (taken to be ( 2σk) are summarized in Table 1. The sample kinetic plot shown in Figure 1 shows data from kinetic runs at 189.9 °C and theory-based functions with k ) 5.50 × 10-4 s-1. Figure 2 portrays the Arrhenius plot based on these temperatures and rate constants. The activation parameters and estimated (13) Baldwin, J. E.; Leber, P. A.; Lee, T. W. J. Chem. Ed. 2001, 78, 1394-1399. (14) LinearAlgebra, Maple 6.01; Waterloo Maple, Inc.: Waterloo, ON, Canada. (15) DeltaGraph Pro 3, Version 3.0.1; Deltapoint, Inc.: Monterey, CA. (16) Perrin, C. L. Mathematics for Chemists; Wiley-Interscience: New York, 1970; pp 152-159.
FIGURE 1. Time-dependent mole percent proportions of
monodeuterium-labeled cis-1,3-cycloheptadiene isomers {1 + 2}, 3, and 4 at 189.9 °C. The theoretical functions drawn are based on the functions of eqs 1-3 and rate constant k ) 5.50 × 10-4 s-1.
FIGURE 2. Arrhenius plot of ln(k) versus (1/T), with T (K). The slope and intercept are -13.85 × 103 and +22.25, respectively.
uncertainties found are Ea ) 27.5 ( 0.9 kcal/mol and log A ) 9.7 ( 0.4.17 These kinetic findings cannot be compared directly with other experimental work, for no earlier study has followed the thermal equilibrations of monodeuteriumlabeled 1,3-cycloheptadienes. The most similar investigation may be a study of thermal structural interconversions of the isomeric monomethyl-substituted 1,3-cycloheptadienes.18 At equilibrium at 120-160 °C, the fourisomer set was dominated by the 2-methyl and 1-methyl structures (37.6% 7, 57.7% 8), and the kinetic situation was approximated by a simple two-component, reversible equilibrium model. The activation parameters derived for the 7 to 8 reaction were Ea ) 29.5 ( 1.5 kcal/mol and log A ) 11.4. For the reverse conversion, 8 to 7, they were (17) Benson, S. W.; O’Neal, H. E. Kinetic Data on Gas-Phase Unimolecular Reactions; National Bureau of Standards: Washington, DC, 1970; p 9. (18) Mironov, V. A.; Chizhov, O. S.; Kimel’feld, Ya. M.; Akhrem, A. A. Tetrahedron Lett. 1969, 499-500.
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found to be Ea ) 28.6 ( 1.5 kcal/mol and log A ) 10.8.18 Since the forward and reverse reactions may take place through transfer of either of two hydrogen atoms, the two log A factors would need to be reduced by 0.3 to put them on a per-hydrogen-shift basis. Thus, the [1,5] shift of one hydrogen in 7 or in 8 takes place with Ea ≈ 29 ( 1.5 kcal/ mol and log A ≈ 10.8, values in fair qualitative agreement with the activation parameters reported in the present work for equilibrations among the monodeuteriumlabeled 1,3-cycloheptadienes.
Calculated Ea values for [1,5] hydrogen shifts in cis1,3-cycloheptadiene, for the 7 to 8 reaction, and the 8 to 7 process found using density functional theory, are 33.7, 32.7, and 33.8 kcal/mol, respectively,9,19 in satisfactory agreement with yet consistently somewhat larger than the experimental values. The [1,5] hydrogen shifts in cycloheptadienes take place with relatively low activation energies and low log A values, just like the [1,5] shifts in cis-1,3-cyclooctadiene (Ea ) 29.0, log A 10.4).8,20 When the geometrical strictures of the ideal transition structure are fully satisfied, the low activation energy path is available and utilized. Other geometrical configurations of the reactant, even many near the proper dispositions of atoms and vibration modes, do not cross the low-energy barrier to form the rearrangement product. Whether tunneling of the shifting hydrogen is an important concomitant of such reactions remains under active debate. Experimental Section 1-Deuterio-2-cycloheptene-1-ol (6). To a stirred solution of 2-cycloheptene-1-one (5; 2.2 g, 20 mmol) in 45 mL of 0.4 M CeCl3‚7H2O in methanol was added NaBD4 (0.8 g, 20 mmol) in portions over a period of 10 min. The reaction mixture was then heated to reflux for about 4 h10 as progress was monitored by capillary GC.
After completion of the reaction, water (15 mL) was added to the reaction mixture, and a conventional workup led to crude deuterium-labeled alcohol; MS (m/z) 113 (M+). 1-d- and 2-d-1,3-Cycloheptadienes (2 and 1). A stirred solution of the deuterium-labeled 2-cycloheptene1-ol (1.69 g, 15 mmol), CeCl3‚7H2O (9.35 g, 25.5 mmol), and NaI (3.75 g, 25 mmol) in acetonitrile (40 mL) was heated at reflux for over 10 h20 and then diluted with pentane, treated with 0.5 N HCl (10 mL), and diluted with ∼15 mL of water. The organic material was isolated, and the deuterium-labeled product was secured by concentration and then Kugelrohr distillation (50 °C, 1 atm; 63% yield). Analysis by 2H NMR at 92.1 MHz showed absorptions for isomers 2 (δ 5.85) and 1 (δ 5.80); isomers 3 and 4 were not in evidence. The 600 MHz 1H NMR spectrum showed signals at δ 5.85 and 5.80 in 55: 45 proportions, consistent with a 35:65 ratio of isomers 2 and 1. The mixture of monodeuterium-labeled cycloheptadienes was purified by preparative GC using a 0.64 cm × 2.3 m β,β′-ODPN column at 56 °C to secure material that was homogeneous by analytical GC. 2H NMR δ 5.78-5.84 (80.3% D, {1 + 2}), 2.35 (s, 15.4% D, 3), 1.84 (s, 4.3% D, 4); the incompletely resolved 2H NMR absorptions for 2 and 1 were estimated to be in a 1:1.3 ratio, or about 35% 2, 45% 1. Gas-Phase Thermal Rearrangements were conducted using a static reactor attached to a vacuum line.21 About 220 µL of a 0.3% solution of monodeuteriumlabeled cycloheptadienes in 2,2-dimethylbutane was used for each kinetic run. Product mixtures were transferred to an NMR tube containing 250-300 µL of degassed chloroform; the tubes were sealed, and the product mixtures were analyzed by 2H NMR (Table S1, Supporting Information).
Acknowledgment. We thank the National Science Foundation for support of this work through CHE0211120, and Professor Philip Crews, University of California, Santa Cruz, for helpful correspondence. Supporting Information Available: Kinetic data, selected 2H NMR spectra, and kinetic plots. This material is available free of charge via the Internet at http://pubs.acs.org. JO040238W
(19) Hess, B. A., Jr. Int. J. Quantum Chem. 2002, 90, 1064-1070. (20) See also: Glass, D. S.; Boikess, R. S.; Winstein, S. Tetrahedron Lett. 1966, 999-1008.
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(21) Baldwin, J. E.; Burrell, R. C. J. Org. Chem. 1999, 64, 35673571.
