Re‐examining the Mechanisms of Competing Pericyclic Reactions of 1,3,7‐Octatriene

DFT (both B3LYP and M06‐2X), CASSCF, and CASPT2 calculations were used to investigate competing [3, 3] and [3, 5] sigmatropic shifts and intramolecular [4+2] cycloaddition of 1,3,7‐octatriene. In accord with previous results on 1,5‐hexadiene, CASSCF calculations found both stepwise and concerted pathways for the [3, 3] rearrangement. For the competing [3, 5] sigmatropic rearrangement, CASSCF and CASPT2 calculations revealed three stepwise pathways with similar barriers. UB3LYP and UM06‐2X calculations predicted a different potential energy landscape: no stepwise [3, 3] pathway, only two competing [3, 5] sigmatropic shifts, and an intramolecular Diels–Alder cycloaddition/homolytic ring‐opening pathway. Significant lowering of barriers for all rearrangements was predicted for some 1,3,7‐octatrienes with substituents at the 4‐ and 7‐positions.     

A cornucopia of cycloadducts: theoretical predictions of the mechanisms and products of the reactions of cyclopentadiene with cycloheptatriene

The potential cycloaddition reactions between cyclopentadiene and cycloheptatriene have been explored theoretically. B3LYP/6-31G was used to locate the transition states, intermediates, and products for concerted pathways and stepwise pathways passing through diradical intermediates. Interconversions of various cycloadducts through sigmatropic shifts were also explored. CASPT2/6-31G single point calculations were employed to obtain independent activation energy estimates. MM3 was also used to compute reaction energetics. Several bispericyclic cycloadditions in which two cycloadducts are linked by a sigmatropic shift have been identified. B3LYP predicts, in line with frontier molecular orbital predictions, that the [6+4] cycloaddition is the favored concerted pathway, but an alternative [4+2] pathway is very close in energy. By contrast, CASPT2 predicts that a [4+2] cycloaddition is the preferred pathway. B3LYP predicts that the lowest energy path to many of the cycloadducts will involve diradical intermediates, whereas CASPT2 predicts that each of the products of orbital symmetry allowed reactions will be reached most readily by closed shell processes-concerted cycloadditions and sigmatropic shift rearrangements of cycloadducts.     

Mechanism of the forbidden [3s,5s]-sigmatropic shift: orbital symmetry influences stepwise mechanisms involving diradical intermediates

The mechanisms of [3s,5s]-sigmatropic shifts of octa-1,3,7-triene and 7-methylenenona-1,3,8-triene have been elaborated using B3LYP and BPW91 density functional theory and CASPT2 methods. These orbital symmetry forbidden rearrangements are stepwise, involving diradical intermediates. A comparison with several [3,3]-sigmatropic shifts of substituted hexadienes and of [5,5]-sigmatropic shifts that are allowed, but nevertheless follow stepwise paths, shows that the activation barrier for the disallowed [3,5] shift is significantly larger than that for the stepwise reactions that are orbital symmetry allowed. Cyclic diradicals that have an aromatic circuit of electrons including the two radical centers and conjugated pi or sigma bonds are stabilized as compared to cyclic diradicals with an antiaromatic circuit of electrons. This applies to the transition states leading to and from the diradicals and influences the activation energies of stepwise sigmatropic shifts. The magnitudes of these effects are small but will have a significant influence on the rates of competing processes. This series of calculations has been used to assess the relative capabilities of the two functionals. We find that BPW91 underestimates the endothermicity of diradical formation and the barrier to diradical formation whereas B3LYP overestimates these quantities.     

Quantum mechanical inspection of the Diels-Alder approach to biaryls mechanism

The Diels-Alder reaction of substituted cyclohexadienes with substituted phenylacetylenes offers an attractive alternative for the synthesis of biaryl compounds via a two-step cycloaddition/cycloelimination pathway. Quantum mechanical calculations using B3LYP and M06-2X density functional methods for the reaction of 2-chloro-6-nitrophenylacetylene with 1-carbomethoxy-cyclohexadiene show the reaction proceeds by a stepwise diradical [4+2] cycloaddition followed by concerted [2+4] cycloelimination of ethylene. [2+2] cycloadducts are also the result of stepwise addition. [2+2] cycloadducts isomerize to [4+2] cycloadducts via diradical pathways, which involve the same diradical intermediate in cycloaddition. There is also a competitive conrotatory ring opening followed by trans-cis double bond isomerization pathway of the [4.2.0] bicycle (the [2+2] cycloadduct) to give the cis,cis,cis-1,3,5-cyclooctatriene.     

A computational investigation on the sequential rearrangement mechanism of 2-allyl-2,4,5-hexatrienaldehyde involving [1,5]-hydrogen migration and 8pi-electrocyclization

The sequential rearrangement reaction mechanism of the 2-allyl-2,4,5-hexatrienaldehyde has been studied at the unrestricted Becke three-parameter hybrid functional combined with Lee-Yang-Parr correlation functional (UB3LYP)/6-31G**, Complete Active Space Self-Consistent Field (CAS (8,8))/6-31G**, Configuration Interaction with Single and Double Excitations (CISD)//UB3LYP/6-31G** and the second-order perturbation theory based on the CASSCF reference wave function (CASPT2)//CAS(8,8)/6-31G** levels. Two pathways have been found to be involved for this reaction. The first pathway includes four processes of the rotation of the C3--C4 single bond, the stepwise [2 + 2] cycloaddition, the [1,5]-hydrogen migration, and the ring opening isomerization, while the second pathway undergoes only two processes of the [1,5]-hydrogen migration and the 8pi-electrocyclization. The calculation results indicate that the second pathway is favorable, in good agreement with the recent experimental observation. The whole reaction is stepwise and strong exothermic.     

Transition states for the dimerization of 1,3-cyclohexadiene: a DFT, CASPT2, and CBS-QB3 quantum mechanical investigation

Quantum mechanical calculations using restricted and unrestricted B3LYP density functional theory, CASPT2, and CBS-QB3 methods for the dimerization of 1,3-cyclohexadiene (1) reveal several highly competitive concerted and stepwise reaction pathways leading to [4 + 2] and [2 + 2] cycloadducts, as well as a novel [6 + 4] ene product. The transition state for endo-[4 + 2] cycloaddition (endo-2TS, DeltaH(double dagger)(B3LYP(0K)) = 28.7 kcal/mol and DeltaH(double dagger)(CBS-QB3(0K)) = 19.0 kcal/mol) is not bis-pericyclic, leading to nondegenerate primary and secondary orbital interactions. However, the C(s) symmetric second-order saddle point on the B3LYP energy surface is only 0.3 kcal/mol above endo-2TS. The activation enthalpy for the concerted exo-[4 + 2] cycloaddition (exo-2TS, DeltaH(double dagger)(B3LYP(0K)) = 30.1 kcal/mol and DeltaH(double dagger)(CBS-QB3(0K)) = 21.1 kcal/mol) is 1.4 kcal/mol higher than that of the endo transition state. Stepwise pathways involving diallyl radicals are formed via two different C-C forming transition states (rac-5TS and meso-5TS) and are predicted to be competitive with the concerted cycloaddition. Transition states were located for cyclization from intermediate rac-5 leading to the endo-[4 + 2] (endo-2) and exo-[2 + 2] (anti-3) cycloadducts. Only the endo-[2 + 2] (syn-3) transition state was located for cyclization of intermediate meso-5. The novel [6 + 4] "concerted" ene transition state (threo-4TS, DeltaH(double dagger)(UB3LYP(0K)) = 28.3 kcal/mol) is found to be unstable with respect to an unrestricted calculation. This diradicaloid transition state closely resembles the cyclohexadiallyl radical rather than the linked cyclohexadienyl radical. Several [3,3] sigmatropic rearrangement transition states were also located and have activation enthalpies between 27 and 31 kcal/mol.     

Acyclic or long-bond intermediate in the electron-transfer-catalyzed dimerization of 4-methoxystyrene

The electron-transfer-catalyzed dimerization of 4-methoxystyrene has long been a prototypical reaction for the study of radical cation reactivity. The different possible pathways were explored at the B3LYP/6-31G level of theory. Both [2 + 2] and [4 + 2] cycloadditions proceed via a stepwise pathway, diverging at an acyclic intermediate and interconnected by a vinylcyclobutane-type rearrangement. The experimentally observed stereoselectivity of the cycloaddition was traced to relatively high barriers for isomerization, while the previously described "long-bond" intermediate could not be located at the higher level of theory. CPCM calculations show that the highly exothermic [4 + 2] pathway becomes kinetically more favorable in condensed phase. Time-dependent density functional theory calculations indicate that the different possible intermediates have very similar absorption spectra, making the unambiguous assignment of the experimentally observed transient absorption of 500 nm to a given species difficult.     

Toward an understanding of the mechanisms of the intramolecular

The molecular mechanism for the intramolecular [5 + 2] cycloaddition reaction of beta-silyloxy-gamma-pyrones bearing tethered alkenes has been characterized using ab initio methods. A comparative study for this sort of cycloaddition carried out at different computational levels points out that the B3LYP/6-31G calculations give similar barriers to those obtained with the MP3/6-31G level. Analysis of the energetic results shows that the reaction takes place along a stepwise process: first, the migration of the neighboring silyl group to the carbonyl group of the gamma-pyrone takes place to give a weak oxidopyrylium ylide intermediate, which by a subsequent concerted intramolecular [5 + 2] cycloaddition affords the final cycloadduct. The cycloaddition process is very stereoselective due to the constraints imposed by the tether. The [5 + 2] cycloaddition reaction has a large barrier, and the presence of the silyloxy group and the intramolecular character of the process are necessary to ensure the thermodynamic and kinetic feasibility of these cycloadditions.     

Theoretical investigation of the stereoselective stepwise cope rearrangement of a 3-vinylmethylenecyclobutane

The potential energy surface of the rearrangement of 3-vinylmethylenecyclobutane to 4-methylenecyclohexene has been studied computationally using density functional theory (B3LYP) and complete active space ab initio methods (CASSCF and CASPT2). The parent reaction is nonconcerted and occurs through several parallel diradical pathways. Transition structures and diradical intermediates are highly comparable in energy, with no deep potential energy well on the potential energy surface. In the substituted system, stereoelectronic effects of the trialkylsiloxy group regulate torquoselectivity in the bond-breaking processes and this, combined with low barriers to cyclization, leads to a stepwise Cope rearrangement that is, nevertheless, stereoselective.     

Reaction of a complexed phosphinidene with 2,4,6-tri-tert-butyl-1,3,5-triphosphabenzene

The terminal phosphinidene complex PhPW(CO)5 reacts with 2,4,6-tri-tert-butyl-1,3,5-triphosphabenzene to give two unexpected multicyclic organophosphorus compounds. One of them results from an initial 1,2-addition, followed by an intramolecular rearrangement. B3LYP/6-31G* calculations on simplified parent systems suggest that the reaction follows a unique concerted reaction pathway. The second, and major, product is a tetraphosphaquadricyclane derivative, which presumably results from an intramolecular [2+2] cycloaddition of an intermediate tetraphosphanorbornadiene complex. Single-crystal X-ray structures are presented for both products.     

A density functional theory study clarifying the reactions of conjugated ketenes with formaldimine. A plethora of pericyclic and pseudopericyclic pathways

The reactions of vinylketene (1a), imidoylketene (1b), and formylketene (1c) with formaldimine (2) were studied at the B3LYP/6-31G* level. For the cycloadditions of these conjugated ketenes with 2, several possible pathways to both [4 + 2] and [2 + 2] products were examined. The lowest energy [2 + 2] pathways are, in most cases, calculated to be stepwise, forming the products via rate-determining conrotatory electrocyclization of zwitterionic intermediates. However, concerted transition structures analogous to the ketene plus ethene [2 + 2] cycloaddition reaction were also located; the existence of multiple transition states offers a resolution to a long-standing controversy regarding the mechanism of ketene plus imine cycloadditions. Both stepwise and concerted [4 + 2] pathways were calculated for 2b and for 2c; both these pathways are pseudopericyclic. The inherently low barriers associated with pseudopericyclic transition states provide an explanation of the experimental preference for [4 + 2] cycloadditions of alpha-oxoketenes and predict [4 + 2] cycloadditions should also be favored for imidoylketenes. For a vinylketene constrained to a Z-geometry, the concerted [4 + 2] cycloaddition is also predicted to be the lowest energy pathway. An explanation is offered for the unusual thermal equilibration from a six-membered ring (3d) to a four-membered ring (4d) observed by Sato et al. Transition structures for facile pseudopericyclic 1,3- and 1,5-hydrogen shifts in the zwitterions were also calculated.     

The 1deltag dioxygen ene reaction with propene: a density functional and multireference perturbation theory mechanistic study

This study aims to determine whether a balance between concerted and non-concerted pathways exists, and in particular to ascertain the possible role of diradical/zwitterion or peroxirane intermediates. Three non-concerted pathways, via 1) diradical or 2) peroxirane intermediates, and 3) by means of hydrogen-abstraction/radical recoupling, plus one concerted pathway (4), are explored. The intermediates and transition structures (TS) are optimized at the DFT(MPW1K), DFT(B3LYP) and CASSCF levels of theory. The latter optimizations are followed by multireference perturbative CASPT2 energy calculations. (1) The polar diradical forms from the separate reactants by surmounting a barrier (deltaE(++)(MPW1K)=12, deltaE++(B3LYP)=14, and deltaE(++)(CASPT2)=16 kcal mol(-1) and can back-dissociate through the same TS, with barriers of 11 (MPW1K) and 8 kcal mol(-1) (B3LYP and CASPT2). The diradical to hydroperoxide transformation is easy at all levels (deltaE(++)(MPW1K)<4, deltaE(++)(B3LYP)=1 and deltaE(++)(CASPT2)=1 kcal mol(-1)). (2) Peroxirane is attainable only by passing through the diradical intermediate, and not directly, due to the nature of the critical points involved. It is located higher in energy than the diradical by 12 kcal mol(-1), at all theory levels. The energy barrier for the diradical to cis-peroxirane transformation (deltaE(++)=14-16 kcal mol(-1)) is much higher than that for the diradical transformation to the hydroperoxide. In addition, peroxirane can very easily back-transform to the diradical (deltaE(++)<3 kcal mol(-1)). Not only the energetics, but also the qualitative features of the energy hypersurface, prevent a pathway connecting the peroxirane to the hydroperoxide at all levels of theory. (3) The last two-step pathway (hydrogen-abstraction by (1)O(2), followed by HOO-allyl radical coupling) is not competitive with the diradical mechanism. (4) A concerted pathway is carefully investigated, and deemed an artifact of restricted DFT calculations. Finally, the possible ene/[pi2+pi2] competition is discussed.     

Experimental and theoretical evidences of 2-aza-Cope rearrangement of nitrones

Both the intramolecular cycloaddition of diastereomeric homochiral N-alkenyl nitrones and the corresponding theoretical calculations using DFT and ab initio methods provided evidences of a thermal [3,3] sigmatropic rearrangement of the nitrones with a complete chirality transfer.     

Thermal [1,3] sigmatropic rearrangements of bicyclic and tricyclic vinylcyclobutanes: a gray zone between the concerted and stepwise extremes

Four typical thermal [1,3] sigmatropic rearrangements of bicyclic and tricyclic vinylcyclobutanes and one fancied analogous reaction (R2 in Scheme 1) were examined using CASSCF, CASPT2 and CAS+1+2 methods to discern the reaction mechanisms. Computed results indicate that it is difficult to simply designate these reactions as traditional single-step concerted or stepwise mechanisms, but a situation locating between these two extremes seems to be reasonable. The extent the reaction exhibits as a single-step concerted or stepwise path is much dependent on the geometrical constraints of reactant. For example, the system with three-member ring will tend to behave like a single-step concerted process, where only one rotation movement around C–C bond could be found when the bridged C–C is broken. However, the species with four-member ring will be much closer to the stepwise mechanism involving diradical varieties, because there are two different rotation movements exist when the bridged C–C is broken. Our calculation will also rationalize that only suprafacial retention product could be yielded for the thermal [1,3] sigmatropic rearrangement of tricyclic vinylcyclobutane.     

黄嘌呤异构体质子转移异构化反应机理的理论研究

采用量子化学密度泛函B3LYP/6-31G(d,p)和M06-2X/6-311++G(d,p)方法对黄嘌呤两种酮式异构体X(1,3,7)与X(1,3,9)间质子转移引起的互变异构反应机理进行了计算研究,获得了异构化反应过程的反应焓﹑活化吉布斯自由能和质子转移反应的速率常数等参数。水相计算采用极化连续(PCM)模型。结果表明,由于可能的氢迁移顺序差异,分子内由X(1,3,7)向X(1,3,9)异构化可能共有16条反应通道,涉及11个中间体和20个过渡态,其主反应通道速控步骤的活化吉布斯自由能为183.10k J/mol,速率常数为5.17×10-20s-1,其余各通道速控步骤活化吉布斯自由能均较高,而且整体水溶剂效应不利于质子转移的发生。     

Palladium-catalyzed [3 + 2] intramolecular cycloaddition of alk-5-enylidenecyclopropanes

Readily accessible alk-5-enylidenecyclopropanes undergo [3 + 2] intramolecular cycloaddition reactions upon treatment with appropriate palladium complexes. The method allows the rapid and efficient assembly of a variety of bicyclo[3.3.0]octane systems with up to three stereocenters. Preliminary theoretical calculations uncovered previously unsuspected mechanistic possibilities based on either a concerted pallada-ene-like rearrangement or a stepwise process involving zwitterionic intermediates.     

Why nature eschews the concerted [2 + 2 + 2] cycloaddition of a nonconjugated cyanodiyne. Computational study of a pyridine synthesis involving an ene-Diels-Alder-bimolecular hydrogen-transfer mechanism

An intramolecular formal metal-free intramolecular [2 + 2 + 2] cycloaddition for the formation of pyridines has been investigated with M06-2X and B3LYP density functional methods, and compared to the experimentally established three-step mechanism that involves ene reaction-Diels-Alder reaction-hydrogen transfer. The ene reaction of two alkynes is the rate-determining step. This is considerably easier than other possible mechanisms, such as those involving an ene reaction of an alkyne with a nitrile, a one-step [2 + 2 + 2] cycloaddition, or a 1,4-diradical mechanism. The relative facilities of these processes are analyzed with the distortion-interaction model. A bimolecular hydrogen-transfer mechanism involving a radical-pair intermediate is proposed rather than a concerted intramolecular 1,5-hydrogen shift for the last step in the mechanism.     

Thermolysis of 2-methyloxetane: a computational study

Thermal fragmentation of 2-methyloxetane (2MO), which yields two different sets of products by virtue of ring asymmetry, was studied theoretically by using DFT, MPn and CASPT2//CASSCF methods. At the MPn and DFT theoretical levels, only concerted transition states were located on the ground state potential energy surface (PES). The CASSCF approach leads to different stepwise pathways for the two fragmentation modes, with biradical as intermediates, in addition to the concerted paths, with a very shallow PES for the asynchronous region in which intermediates becomes unstable under CASPT2//CASSCF calculations. Nevertheless, activation barriers thus calculated were quite consistent with experimental values. The reaction pathway that experimentally renders the main set of products was calculated as the lowest-energy path for the fragmentation of the 2-methyloxetane heterocycle, and this evolves with an initial cleavage of the C–O bond of the oxetane ring.     

Mechanism of the ring-chain rearrangement in phosphiranes: hydrogen versus halogen migration

Ab initio quantum chemical calculations including HF, MP2, CCSD(T), CASSCF(10,10)/CASPT2, and B3LYP methods with the 6-31G(d,p) basis set were used to probe the mechanism of the ring-chain rearrangement of halogeno-phosphiranes. It is confirmed that the lowest energy interconversion between C-halogenated-(X)-phosphiranes and vinylphosphines, with X = H, F, Cl, and Br, is a one-step process in which the C-P bond cleavage and X-sigmatropic migration from C to P occur in a concerted manner in a single transition structure. The migration of a hydrogen from CH(H) is slightly favored over that of CX(H), and thus, the cleavage of the C(X)-P bond is preferred. The energy barrier for the whole process involving hydrogen migration in the parent phosphirane is calculated to be about 45 +/- 5 kcal/mol. The migratory aptitude of the atoms X in the uncomplexed species is found as follows: H > Br > Cl > F, either in the gaseous phase or in aqueous and DMSO solutions. The solvation enthalpies that were estimated using a polarizable continuum model (PCM) are rather small and do not modify the relative ordering of the energy barriers. Such a trend is at variance with recent experimental findings on metal-phosphinidene complexes in which only halogen migration was observed. This might arise from a peculiar effect of the metal fragments W(CO)(5) used in the experimental studies to stabilize the phosphorus species that induce a quite different mechanism. Calculations of the (31)P chemical shifts using the GIAO/B3LYP/6-311+G(d,p) method show a remarkable correlation between the delta(31)P(X) chemical shifts of X-phosphiranes and those of X-phosphines (XCH(2)PH(2)), suggesting that the large beta substituent effect is not inherent to the small rings.     

Rearrangement and hydrogen scrambling pathways of the toluene radical cation: a computational study

A computational study is undertaken to provide a unified picture for various rearrangement reactions and hydrogen scrambling pathways of the toluene radical cation (1). The geometries are optimized with the BHandHLYP density functional, and the energies are computed with the ab initio CCSD(T) method, in conjunction with the 6-311+G(d,p) basis set. In particular, four channels have been located, which may account for hydrogen scrambling, as they are found to have overall barriers lower than the observed threshold for hydrogen dissociation. These are a stepwise norcaradiene walk involved in the Hoffman mechanism, a rearrangement of 1 to the methylenecyclohexadiene radical cation (5) by successive [1,2]-H shifts via isotoluene radical cations, a series of [1,2]-H shifts in the cycloheptatriene radical cation (4), and a concerted norcaradiene walk. In addition, we have also investigated other pathways such as the suggested Dewar-Landman mechanism, which proceeds through 5, via two consecutive [1,2]-H shifts. This pathway is, however, found to be inactive as it involves too high reaction barriers. Moreover, a novel rearrangement pathway that connects 5 to the norcaradiene radical cation (3) has also been located in this work.