Ab Initio Calculations on Spiropentane Stereomutations Lead to a Reinterpretation of the Experimental Results

Abstract

The potential energy surfaces for stereomutation of spiropentane (1) and cis-and trans-1,2-dimethylspiropentanes (4 and 7) have been explored, using ab initio methods. In diradicals 2, 5, and 6, which are formed by cleavage of the peripheral bond between C-1 and C-2 in the spiropentanes, the weakly electrondonating cyclopropane ring results in the lowest energy pathway for stereomutation of all three being computed to be conrotatory. A larger preference for double over single rotation is computed in 4 than in 7, in agreement with the experimental results reported in 1980 by Gajewski and Chang. However, in contrast to the assumption made by these authors, our calculations find that the s-cis-methyl conformation in diradical 6 is lower in energy than the s-trans-methyl conformation in diradical 5, and moreover, 6 is statistically favored over 5 by a factor of 2. Thus, double rotation is both computed and found to be preferred by more in the stereomutation of 4 than of 7 because 4 undergoes conrotatory opening to 6, the lower energy diradical. A long-range attraction between the s-cis methyl group at C-1 and the nonbonding p-π AO at C-3 in 6 is shown to contribute to stabilizing this diradical.The first study of the stereomutation of spiropentane (1) was published 30 years ago. 1 Gilbert reported that, upon heating, cis-1,2-2 H 2 -spiropentane isomerizes to trans-1,2-2 H 2 -spiropentane, prior to undergoing structural rearrangement. 2 Subsequently, Gajewski and Burka pyrolyzed the proximal, medial, and distal stereoisomers of 1,4-dimethylspiropentanes, 3 and from the kinetics of interconversion that they observed, they concluded that fission of a peripheral bond, to form diradical 2, is preferred to cleavage of a radial bond, to form diradical 3. Stereomutation of 1 by exclusive formation of 1,1-dimethylenecyclopropane (2) is supported by the results of additional experiments by Gajewski. 4 Gajewski and Chang (G&C) investigated the pyrolyses of syn-4,4-2 H 2 -cis-1,2-dimethylspiropentane (4-2 H 2 ) and of optically active trans-1,2-dimethylspiropentane (7) at 290°C. 5a Coupled rotation was found to be slightly favored over monorotation in both spiropentanes.G&C based their assignment of the mode of coupled rotation that is preferred on the experimental finding that double rotation is favored over monorotation by a factor of 3.6 in the pyrolysis of 4-2 H 2 and by a factor of only 1.4 in the pyrolysis of 7. On the basis of the experimental results in the pyrolyses of other hydrocarbons, G&C assumed that "outward" rotation of a methyl group in 4 and 7 is sterically less demanding than "inward" rotation. Therefore, they expected formation of diradical 5 to provide a lower energy pathway for double rotation than formation of diradical 6. This assumption, together with the modes of coupled rotation that connect 4 and 7 to 5 and 6 (shown in Figure 1), resulted in G&C interpreting the experimental ratios of single to double rotation in 4 and 7 as indicating that disrotation is preferred to conrotation in the stereomutati...

Ab Initio Calculations on the Formation and Rearrangement of Spiropentane

“…The calculations of Johnson et al found a very small (0.1 kcal/mol) preference for monorotation. They calculated 43 an overall activation enthalpy of 51.3 kcal/mol, in excellent agreement with the experimental value of 50.9 ( 1.0 kcal/mol. 44 The stereomutation reaction turns out to provide a very severe test for the single-reference computational models, as shown in Table 1.…”

“…The calculations of Johnson et al found a very small (0.1 kcal/mol) preference for monorotation. They calculated an overall activation enthalpy of 51.3 kcal/mol, in excellent agreement with the experimental value of 50.9 ± 1.0 kcal/mol …”

“…The stereomutation of spiropentane has been thoroughly analyzed by Johnson and coworkers using a CASPT2 computational model. 43 Experimentally, it is known that spiropentane-cis-1,2-d 2 interconverts with the trans isomer and that this takes place faster than isomerization to methylenecyclobutane. 44 However, this observation does not reveal the details of how the stereomutation occurs.…”

Notable Effect of an Electron-Withdrawing Group at C3 on the Selective Formation of Alkylidenecyclobutanes in the Thermal Denitrogenation of 4-Spirocyclopropane-1-pyrazolines. Nonstatistical Dynamics Effects in the Denitrogenation Reactions

“…The adequacy of the DFT calculations for such denitrogenation reactions can be judged by the comparison of the calculated results with the experimental facts, for example, product distribution and activation energy that were determined by Bergman and co-worker. High-level ab initio calculations with configuration interaction, that is, CASPT2 method, were also reported for the reactivity of the diradical DR1 by Borden and co-workers …”

Photochemical Ring Opening of 7-Benzoyl- and 7-Methoxycarbonyldibenzonorcaradienes. Competing 1,2-Hydrogen Shift and Cyclization Reactions of 1,3-Diradicals

“…The rotation around the central σ-bond in 1,3-diradicals, which leads to cis − trans isomerization of cyclopropanes, is a fast process for sterically unhindered systems, k rot ≈ 10 12 s -1 . , We have conducted semiempirical calculations on diradical 3b and found no significant steric barrier for rotation in that system . This result suggests that rotation in diradical 3b can be considered virtually free.…”