Gas phase thermal reactions of exo-8-cyclopropyl-bicyclo[4.2.0]oct-2-ene (1-exo).

The title compound 1-exo (with minor amounts of its C8 epimer 1-endo) was prepared by Wolff-Kishner reduction of the cycloadduct of 1,3-cyclohexadiene and cyclopropylketene. The [1,3]-migration product 2-endo was synthesized by efficient selective cyclopropanation of endo-5-vinylbicyclo[2.2.2]oct-2-ene at the exocyclic π-bond. Gas phase thermal reactions of 1-exo afforded C8 epimerization to 1-endo, [1,3]- migrations to 2-exo and 2-endo, direct fragmentation to cyclohexadiene and vinylcyclopropane, and CPC rearrangement in the following relative kinetic order: kep > k13 > kf > kCPC.

Thermal isomerizations of cis,anti,cis-tricyclo[7.4.0.0(2,8)]tridec-10-ene.

cis,anti,cis-Tricyclo[7.4.0.0(2,8)]tridec-10-ene (13TCT) undergoes [1,3] sigmatropic rearrangements at 315 °C in the gas phase to the si product 1 and to the sr product 2 with si/sr = 2.1. The dominant thermal isomerization process, however, is epimerization at C8 to afford product 3. That stereomutation at C8 occurs 50% faster than the si and sr shifts combined.

On the stereochemical characteristic of the thermal reactions of vinylcyclobutane.

This Perspective outlines the stereochemical and mechanistic complexities inherent in the thermal reactions converting vinylcyclobutane to cyclohexene, butadiene, and ethylene. The structural isomerization and the fragmentation processes seem, at first sight, to be obvious and simple. When considered more carefully and investigated with the aid of deuterium-labeled stereochemically well-defined vinylcyclobutane derivatives there emerges a complex kinetic situation traced by 56 structure-to-structure transformations and 12 independent kinetic parameters. Experimental determinations of stereochemical details of stereomutations and [1,3] carbon sigmatropic shifts are now being pursued and will in time contribute to gaining relevant evidence casting light on the reaction dynamics involved as flexible short-lived diradical intermediates trace the paths leading from one d(2)-labeled vinylcyclobutane starting material to a mixture of 16 structures.

Quantitative analyses of mixtures of 2-deuterio-1-vinylcyclobutanes.

Making distinctions between two stereoisomers characterized by diastereotopic deuterium atoms can ordinarily be achieved using standard NMR spectroscopic methods. Mixtures of stereoisomers having both diastereotopic and enantiotopic deuterium labels, however, may be difficult to analyze quantitatively. The present work introduces a simple way to gain quantitative analyses of mixtures of the four stereoisomeric 2-deuterio-1-vinylcyclobutanes, an essential prerequisite to establishing the stereochemical characteristics of the thermal stereomutations of vinylcyclobutane and its structural isomerizations to cyclohexene. The unconventional NMR method introduced and validated in this work will likely prove convenient and generally applicable to related stereochemical investigations.

Quantitative analyses of stereoisomeric 3,4-d2-cyclohexenes in the presence of 3,6-d2-cyclohexenes.

The challenging analytical problem posed by mixtures of the four isomeric 3,4-d(2)-cyclohexenes and the three isomeric 3,6-d(2)-cyclohexenes has been solved through a novel one-dimensional NMR spectroscopic method dependent on recording (13)C resonances while broadband decoupling both proton and deuteron nuclei. Upfield deuterium perturbations of (13)C chemical shifts in chair conformationally locked cyclohexane derivatives readily secured from a mixture of the seven deuterium-labeled cyclohexenes allow quantitative analytical assessments of the four possible 3,4-d(2)-cyclohexenes in the mixture. This analytical capability is an essential prerequisite for uncovering the relative participations of the four possible stereochemical paths followed by the thermal structural isomerizations of vinylcyclobutane to cyclohexene. The unconventional NMR method validated in this work will likely prove invaluable in related stereochemical investigations.

Vicinal deuterium perturbations on hydrogen NMR chemical shifts in cyclohexanes.

The substitution of a deuterium for a hydrogen is known to perturb the NMR chemical shift of a neighboring hydrogen atom. The magnitude of such a perturbation may depend on the specifics of bonding and stereochemical relationships within a molecule. For deuterium-labeled cyclohexanes held in a chair conformation at -80 degrees C or lower, all four possible perturbations of H by D as H-C-C-H is changed to D-C-C-H have been determined experimentally, and the variations seen, ranging from 6.9 to 10.4 ppb, have been calculated from theory and computational methods. The predominant physical origins of the NMR chemical shift perturbations in deuterium-labeled cyclohexanes have been identified and quantified. The trends defined by the Delta delta perturbation values obtained through spectroscopic experiments and by theory agree satisfactorily. They do not match the variations typically observed in vicinal J(H-H) coupling constants as a function of dihedral angles.

Molecular rearrangements through thermal [1,3] carbon shifts.

Molecular rearrangements through thermal [1,3] carbon shifts, such as vinylcyclopropane-to-cyclopentene and vinylcyclobutane-to-cyclohexene isomerizations, were recognized and exemplified repeatedly from 1960-1964. Serious mechanistic studies of these and related rearrangements over the past 40 years have provided ample grounds for interpreting them as processes taking place by way of conformationally flexible but not statistically equilibrated diradical intermediates. Orbital symmetry theory fails to account for the stereochemical characteristics of [1,3] carbon shifts. For sigmatropic reactions of this class the theory can no longer be retained as a valid basis for mechanistic interpretations, or even as a serious contender for consideration as a mechanistic possibility.

Thermal chemistry of bicyclo[4.2.0]oct-2-enes.

At 300 degrees C, bicyclo[4.2.0]oct-2-ene (1) isomerizes to bicyclo[2.2.2]oct-2-ene (2) via a formal [1,3] sigmatropic carbon migration. Deuterium labels at C7 and C8 were employed to probe for two-centered stereomutation resulting from C1-C6 cleavage and for one-centered stereomutation resulting from C1-C8 cleavage, respectively. In addition, deuterium labeling allowed for the elucidation of the stereochemical preference of the [1,3] migration of 1 to 2. The two possible [1,3] carbon shift outcomes reflect a slight preference for migration with inversion rather than retention of stereochemistry; the si/sr product ratio is approximately 1.4. One-centered stereomutation is the dominant process in the thermal manifold of 1, with lesser amounts of fragmentation and [1,3] carbon migration processes being observed. All of these observations are consistent with a long-lived, conformationally promiscuous diradical intermediate.

Thermal [1,5] hydrogen sigmatropic shifts in cis,cis-1,3-cyclononadienes probed by gas-phase kinetic studies and density functional theory calculations.

The kinetics of gas-phase thermal [1,5] hydrogen shifts interconverting the five isomeric mono-deuterium-labeled cis,cis-1,3-cyclononadienes have been followed at four temperatures from 240 to 287 degrees C. The activation parameters found were Ea = 37.1 +/- 0.8 kcal/mol, log A = 11.6 +/- 0.3, DeltaH++ = 36.0 +/- 0.8 kcal/mol, and DeltaS++ = -9.0 +/- 0.3 eu. Density functional theory based calculations have provided geometries and energies for the ground-state cyclononadiene conformational isomers, for the transition states linking one to another, and for the transition states for [1,5] hydrogen shifts responsible for isomerizations among the five labeled dienes. A generalized formulation of the Winstein-Holness equation is presented and applied to the complex system, one that involves 11 ground-state conformers, 10 transition states separating them, and five transition states for [1,5] hydrogen shifts. The value for the empirical Ea derived from calculated mole fractions of ground-state conformers and calculated energies for specific ground-state conformers and [1,5] hydrogen shift transition structures was 37.5 kcal/mol, in excellent agreement with the experimentally obtained activation energy. The significance of conformational options in various ground states and transition structures for the [1,5] hydrogen shifts is considerable, an inference that may well have general applicability.

Thermal reactions of 7-d- and 8-d-bicyclo[4.2.0]oct-2-enes.

The gas phase thermal reactions exhibited by bicyclo[4.2.0]oct-2-ene and 7-d and 8-d analogues at 300 degrees C have been followed kinetically through GC and 2H NMR spectroscopic analyses. In contrast to the pattern of transformations exhibited by bicyclo[3.2.0]hept-2-ene and deuterium-labeled analogues, no reactions initiated by C1-C6 bond cleavage are seen, epimerization at C8 is much faster than [1,3] shifts leading to bicyclo[2.2.2]oct-2-ene, and the ratio of rate constants for [1,3] carbon migration with inversion versus migration with retention is approximately 1.4. Homolysis of C1-C8 to give a conformationally flexible diradical intermediate having a relatively long lifetime and multiple options for further reaction (re-formation of C1-C8 with or without net epimerization, fragmentation to 1,3-cyclohexadiene and ethylene, migration to the original C3 with inversion or retention) accords well with the observations. Clearly, orbital symmetry control does not govern stereochemistry for the [1,3] sigmatropic carbon shifts.

Efficient syntheses of four stable-isotope labeled (1R)-menthyl (1S,2S)-(+)-2-phenylcyclopropanecarboxylates.

Many carbenoid cyclopropanation reactions promoted by chiral catalysts give product mixtures reflecting impressive diastereo- and enantioselectivities. Few provide a single chiral product efficiently. This limitation has been overcome in cyclopropanations of styrene and isotopically labeled styrenes with alpha-diazoacetates. Convenient syntheses on a 20 g scale of each of four chiral isotopically labeled (1R)-menthyl (1S,2S)-2-phenylcyclopropanecarboxylates (the 1-d-3-(13)C, 1,(3S)-d2, 1,2,(3S)-d3, and 1,3,3-d3 isotopomers) of better than 99% ee have been realized.

Thermal isomerizations of 2-d-1-(E)-propenylcyclobutanes to 4-d-3-methylcyclohexenes.

Racemic trans-2-d-1-(E)-propenylcyclobutane at 276 degrees C in the gas phase fragments to give ethylenes and pentadienes, equilibrates with its cis isomer, and rearranges to mixtures of 4-d- and 6-d-3-methylcyclohexenes through [1,3] carbon shifts. The time-dependent distributions of deuterium-labeled isomers of propenylcyclobutanes and 3-methylcyclohexenes reveal a significant secondary deuterium kinetic isotope effect favoring C1-C4 over C1-C2 bond breaking (kH/kD = 1.16 +/- 0.02) and a 72:28 preference for structural isomerizations giving (si + ar) rather than (sr + ai) products through conformationally flexible short-lived diradical intermediates.

Thermal isomerization of cis,anti,cis-tricyclo[6.3.0.0(2,7)]undec-3-ene to endo-tricyclo[5.2.2.0(2,6)]undec-8-ene.

[reaction: see text] The gas-phase thermal isomerization of cis,anti,cis-tricyclo[6.3.0.0(2,7)]undec-3-ene (1) to endo-tricyclo[5.2.2.0(2,6)]undec-8-ene (2) at 315 degrees C occurs cleanly through a symmetry-forbidden [1,3] suprafacial,retention (sr) pathway.

Thermal isomerizations of 1-(13)c-2,2,3,3-d(4)-cyclopropane to isotopically labeled trimethylene diradicals, 1-propylidenes, and propenes.

The gas-phase thermal isomerizations of 1-13C-2,2,3,3-d4-cyclopropane lead to isotopically labeled propenes characteristic of both the traditional reaction mechanism involving a trimethylene diradical intermediate and a previously predicted, but never observed, path involving rate-limiting conversion of the cyclopropane to singlet 1-propylidenes, followed by a [1,2]-deuterium shift. The isomerizations give mixtures of both 1-13C-2,3,3,3-d4-propene and 1-13C-1,2,3,3-d4-propene, products characteristic of the two mechanisms that are clearly observable by 13C{1H} NMR spectroscopy.

Gas-phase kinetics and activation parameters for thermal 1,5-hydrogen shifts interconverting monodeuterium-labeled 1,3-cyclohexadienes.

Thermal equilibrations among the three possible monodeuterium-labeled 1,3-cyclohexadienes have been followed in the gas phase at temperatures from 254 to 284 degrees C. The temperature-dependent rate constants for the 1,5-shift of a single hydrogen lead to the activation parameters E(a) = (40.1 +/- 0.8) kcal/mol, log A = (12.1 +/- 0.3), and DeltaS = -(6.3 +/- 1.3) e.u. These activation parameters are reconciled with experimental values reported earlier for reactions starting with 1,4-d(2)-cyclohexadiene.

Gas-phase kinetics and activation parameters for thermal [1,5] hydrogen shifts interconverting monodeuterium- labeled 1,3-cycloheptadienes.

The kinetics of thermal equilibrations among monodeuterium-labeled 1,3-cycloheptadienes in the gas phase followed from 154 to 190 degrees C provide activation parameters for the [1,5] shift of a single hydrogen: E(a) = (27.5 +/- 0.9) kcal/mol and log A = 9.7 [corrected] +/- 0.4. These activation parameters imply a comparatively low E(a) barrier balanced by demandingly specific geometric constraints, for DeltaS (170 degrees C) = -17 [corrected] e.u.

Deuterium kinetic isotope effects and mechanism of the thermal isomerization of bicyclo[4.2.0]oct-7-ene to 1,3-cyclooctadiene.

The thermal conversion of cis-bicyclo[4.2.0]oct-7-ene to cis,cis-1,3-cyclooctadiene might involve a direct disrotatory ring opening, or it might possibly take place by way of cis,trans-1,3-cyclooctadiene. This cis,trans-diene might possibly form the more stable cis,cis isomer through a [1,5] hydrogen shift or a trans-to-cis isomerization about the trans double bond. Deuterium kinetic isotope effect determinations for the isomerizations of 2,2,5,5-d(4)-bicyclo[4.2.0]oct-7-ene and 7,8-d(2)-bicyclo[4.2.0]oct-7-ene rule out these two alternatives because the observed effects are much smaller than would be anticipated for these mechanisms: k(H)/k(D)(d(4)) at 250 degrees C is 1.17 (1.04 per D), and k(H)/k(D)(d(2)) at 238 degrees C is 1.20 (1.10 per D). The direct disrotatory ring opening route remains the preferred mechanism.

Markov-chain Monte Carlo approach to the design of multilayer thin-film optical coatings.

We reconsider the problem of locating the globally optimal solution of a multilayer-optical-coating design problem, within some predetermined space of parameters, with the aim of obtaining a robust technique that requires a minimum of user intervention. The approach we adopt centers on exploring the space of the parameters of interest by using a Markov-chain Monte Carlo sampling algorithm. This technique enables one to locate the global optimum automatically with high confidence and without the need for a good starting design. It also allows the trivial inclusion of prior constraints on the variables and provides a natural means for investigating the robustness of the optimal solution.

Thermal disrotatory electrocyclic isomerization of cis-bicyclo[4.2.0]oct-7-ene to cis,cis-1,3-cyclooctadiene.

[reaction: see text] The ratio of observed rate constants, k/k', for thermal isomerizations of cis-bicyclo[4.2.0]oct-7-ene and its 2,2,5,5-d(4) analogue to cis,cis-1,3-cyclooctadienes at 250 degrees C is 1.17, indicative of a secondary, not a primary, deuterium kinetic isotope effect. The reaction does not occur through a [1,5] hydrogen shift from the transient cis,trans-1,3-cyclooctadiene intermediate to form the observed cis,cis-diene product.

Thermal stereomutations and stereochemically elucidated [1,3]-carbon sigmatropic shifts of 1-(E)-propenyl-2-methylcyclobutanes giving 3,4-dimethylcyclohexenes.

The thermal stereomutations and [1,3] carbon sigmatropic shifts shown by (+)-(1S,2S)-trans-1-(E)-propenyl-2-methylcyclobutane and by (-)-(1S,2R)-cis-1-(E)-propenyl-2-methylcyclobutane in the gas phase at 275 degrees C leading to 3,4-dimethylcyclohexenes have been followed. The reaction-time-dependent data for concentrations and enantiomeric excess values for substrates and [1,3] shift products have been deconvoluted to afford rate constants for the discrete isomerization processes. Both trans and cis substrates react through four stereochemically distinct [1,3] carbon shift paths. For one enantiomer of the trans reactant the relative rate constants are k(si) = 58%, k(ar) = 5%, k(sr) = 33%, and k(ai) = 4%. For a single enantiomer of the cis reactant, k'(si) = 18%, k'(ar) = 11%, k'(sr) = 51%, and k'(ai) = 20%. A trans starting material reacts through orbital symmetry allowed suprafacial,inversion and antarafacial,retention paths to give trans-3,4-dimethylcyclohexenes 63% of the time. A cis isomer reacts to give the more stable trans-3,4-dimethylcyclohexenes through orbital symmetry-forbidden suprafacial,retention and antarafacial,inversionpaths 71% of the time. The [1,3] carbon sigmatropic shifts are not controlled by orbital symmetry constraints. They seem more plausible rationalized as proceeding through diradical intermediates having some conformational flexibility after formation and before encountering an exit channel. The distribution of stereochemical outcomes may well be conditioned by dynamic effects. The thermal stereomutations of the 1-(E)-propenyl-2-methylcyclobutanes take place primarily through one-center epimerizations. For the trans substrate, the relative importance of the three distinction rate constants are k(2) = 48%, k(1) = 34%, and k(12) = 18%. For the cis isomer, k'(2) = 44%, k'(1) = 32%, and k'(12) = 24%. These patterns are reminiscent of ones determined for stereomutations in 1,2-disubstitued cyclopropanes.