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.     

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.     

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.     

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.     

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.     

Reaction mechanism and chemoselectivity of intermolecular cycloaddition reactions between phenyl-substituted cyclopropenone ketal and methyl vinyl ketone

In this paper, the mechanisms of the intermolecular [3+2] and [1+2] cycloaddition reactions of 1,1/1,3-dipolar π-delocalized singlet vinylcarbenes, which is obtained from cyclopropenone, with an electron-deficient C═O or C═C dipolarophile, to generate five-membered ring products are first disclosed by the density functional theory (DFT). Four reaction pathways, including two concerted [3+2] cycloaddition reaction pathways and two stepwise reaction pathways (an initial [1+2] cycloaddition and then a rearrangement from the [1+2] cycloadducts to the final [3+2] cycloadducts), are investigated at the B3LYP/6-31G(d,p) level of theory. The calculated results reveal that, in contrast to the concerted C═O [3+2] cycloaddition reaction pathway, which is 7.1 kcal/mol more energetically preferred compared with its stepwise reaction pathway, the C═C dipolarophile favors undergoing [1+2] cycloaddition rather than concerted [3+2] cycloaddition (difference of 5.3 kcal/mol). The lowest free energy barrier of the C═O concerted [3+2] cycloaddition reaction pathway shows that it predominates all other reaction pathways. This observation is consistent with the finding that the C═O [3 + 2] cycloadduct is the main product under experimental conditions. In addition, natural bond orbital second-order perturbation charge analyses are carried out to explain the preferred chemoselectivity of C═O to the C═C dipolarophile and the origins of cis-stereoselectivity for C═C [1+2] cycloaddition. Solvent effects are further considered at the B3LYP/6-31G(d,p) level in the solvents CH(3)CN, DMF, THF, CH(2)Cl(2), toluene, and benzene using the PCM model. The results indicate that the relative reaction trends and the main products are insensitive to the polarity of the reaction solvent.     

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.     

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.     

Understanding the nature of the molecular mechanisms associated with the competitive Lewis acid catalyzed [4+2] and [4+3] cycloadditions between arylidenoxazolone systems and cyclopentadiene: a DFT analysis

The molecular mechanisms of the reactions between aryliden-5(4H)-oxazolone 1, and cyclopentadiene (Cp), in presence of Lewis acid (LA) catalyst to obtain the corresponding [4+2] and [4+3] cycloadducts are examined through density functional theory (DFT) calculations at the B3LYP/6-31G* level. The activation effect of LA catalyst can be reached by two ways, that is, interaction of LA either with carbonyl or carboxyl oxygen atoms of 1 to render [4+2] or [4+3] cycloadducts. The endo and exo [4+2] cycloadducts are formed through a highly asynchronous concerted mechanism associated to a Michael-type addition of Cp to the beta-conjugated position of alpha,beta-unsaturated carbonyl framework of 1. Coordination of LA catalyst to the carboxyl oxygen yields a highly functionalized compound, 3, through a domino reaction. For this process, the first reaction is a stepwise [4+3] cycloaddition which is initiated by a Friedel-Crafts-type addition of the electrophilically activated carbonyl group of 1 to Cp and subsequent cyclization of the corresponding zwitterionic intermediate to yield the corresponding [4+3] cycloadduct. The next rearrangement is the nucleophilic trapping of this cycloadduct by a second molecule of Cp to yield the final adduct 3. A new reaction pathway for the [4+3] cycloadditions emerges from the present study.     

One-bond, two-bond, and three-bond mechanisms in thermal deazetizations of 2,3-diazabicyclo[2.2.2]oct-2-enes, trans-azomethane, and 2,3-diazabicyclo[2.2.1]hept-2-ene

The thermal deazetizations of a series of substituted 2,3-diazabicyclo[2.2.2]oct-2-enes and some simpler model systems have been studied using the UB3LYP/6-31G(d) and CASPT2 methods, with a variety of active spaces. A fused cyclopropane exerts unique control on the mechanism and rate of deazetization. When the Walsh sigma-orbitals are appropriately aligned in an exo orientation, a pericyclic three-bond cleavage occurs. For an endo-fused cyclopropane, sequential one-bond cleavages occur to take advantage of orbital overlap with the Walsh orbitals. In systems lacking strongly directing substituents, concerted two-bond cleavage pathways to form diradical intermediates have a small enthalpic advantage (DeltaH(0K)++) over sequential one-bond cleavage pathways. However, the one-bond mechanism has an entropic advantage over the two-bond; consequently, at 400-500 K where decomposition occurs, one-bond and two-bond diradical cleavages both occur simultaneously. The thermal decompositions of trans-azomethane and 2,3-diazabicyclo[2.2.1]hept-2-ene are also studied, and the results are compared to extensive computational studies in the literature. Comparisons of UB3LYP, CASSCF, and CASPT2 surfaces for these reactions are made.     

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.     

A DFT study for the regioselective 1,3-dipolar cycloadditions of nitrile N-oxides toward alkynylboronates

The mechanism for the 1,3-dipolar cycloaddition of benzonitrile oxide toward ethynyl and propynylboronate has been studied by using density functional theory (DFT) at B3LYP/6-31G* level. These cycloadditions are concerted [3+2] processes. The presence of the two oxygens on the boronic ester precludes the participation of the boron atom on [3+3] processes. The two regioisomeric channels associated to the formation of the isoxazoles bearing the boronic ester unit on the 4- or 5-positions have been characterized. The B3LYP/6-31G* activation parameters are in acceptable agreement with the experiments, allowing to explain the factors controlling these regioselective cycloadditions.     

The reaction of cyclopentyne with ethene: concerted vs stepwise mechanism?

The cycloaddition of cyclopentyne with ethene was examined using (U)B3LYP and CASSCF methods to discern the reaction mechanism. (U)B3LYP/6-31G* and (U)B3LYP/6-311+G* slightly favor the concerted pathway, whereas CASSCF(4,4)/6-31G* and CASCF(6,6)/6-31G* favor the diradical pathway. MRMP2 using the CASSCF(4,4) wave function also favors the diradical mechanism. In the context of a diradical pathway, the experimentally observed complete retention of stereochemistry for this reaction is understood in terms of stereochemical control resulting from dynamic effects.     

Concerted vs stepwise mechanism in 1,3-dipolar cycloaddition of nitrone to ethene, cyclobutadiene, and benzocyclobutadiene. A computational study

The problem of competition between concerted and stepwise diradical mechanisms in 1,3-dipolar cycloadditions was addressed by studying the reaction between nitrone and ethene with DFT (R(U)B3LYP/6-31G) and post HF methods. According to calculations this reaction should take place via the concerted cycloaddition path. The stepwise process is a viable but not competitive alternative. The R(U)B3LYP/6-31G study was extended to the reaction of the same 1, 3-dipole with cyclobutadiene and benzocyclobutadiene. The very reactive antiaromatic cyclobutadiene has an electronic structure that is particularly disposed to promote stepwise diradical pathways. Calculations suggest that its reaction with nitrone represents a borderline case in which the stepwise process can compete with the concerted one on similar footing. Attenuation of the antiaromatic character of the dipolarophile, i.e., on passing from cyclobutadiene to benzocyclobutadiene, causes the concerted 1,3-dipolar cycloaddition to become once again prevalent over the two-step path. Thus, our results suggest that, in 1,3-dipolar cycloadditions that involve normal dipolarophiles, the concerted path (Huisgen's mechanism) should clearly overwhelm its stepwise diradical (Firestone's mechanism) counterpart.     

Synthesis of unsymmetrical substituted 1,4-dihydropyridines through thermal and microwave assisted [4+2] cycloadditions of 1-azadienes and allenic esters

Thermal and microwave assisted [4+2] cycloadditions of 1,4-diaryl-1-aza-1,3-butadienes with allenic esters lead to cycloadducts, which after a 1,3-H shift afford variedly substituted unsymmetrical 2-alkyl-1,4-diaryl-3-ethoxycarbonyl-1,4-dihydropyridines in high yields. Reactions carried out under microwave irradiation are cleaner and give higher yields with much shortened reaction times. Density functional theory (DFT) at the B3LYP/6-31G* level has been used to calculate geometric features of the reactants, barrier for s-trans to s-cis and reverse isomerization of azadienes (5a-d, 10a-e), dihedral angles between N(1), C(2), C(3), and C(4) atoms of azadienes along with various indices such as chemical hardness (eta), chemical potential (micro), global electrophilicity (omega), and the difference in global electrophilicity (Deltaomega) between the reacting pairs and Fukui functions (f (+) and f(-)). The results revealed that s-trans is the predominant conformation of azadienes at ambient temperature and the barrier for conversion of the s-trans rotamer of 1-azadienes to s-cis may be the major factor influencing the chemoselectivity, i.e., [4+2] verses [2+2] cycloaddition. The regiochemistry of the observed cycloadditions is collated with the obtained local electrophilicity indices (Fukui functions). Transition states for the formation of both [4+2] and [2+2] cycloadducts as located at the PM3 level indicate that the transition state for the formation of [4+2] cycloadducts has lower energy, again supporting the earlier conclusion that preferred formation of [4+2] cycloaaducts at higher temperature may be a consequence of barrier for s-trans to s-cis transformation of 1-azadienes.     

A theoretical study of the reaction of alkynylboranes with butadiene: competition between cycloaddition and alkynylboration

The reactions of alkynyldihaloboranes and alkynyldialkylboranes with butadiene have been explored by using DFT methods at the B3LYP level with the 6-31G basis set. Transition structures for the concerted [4+2] cycloaddition have been found for the alkynylborane derivatives. Along with these, another reactive pathway has been found for the cycloaddition process with transition structures of high [4+3] character. The transition structures for the 1,4-alkynylboration processes have also been found. The geometries computed for the cycloaddition transition structure with high [4+3] character and the 1,4-alkynylboration transition structures are surprisingly similar though leading to different products. IRC calculations suggest that the [4+3] cycloaddition and alkynylboration pathways are associated by a zwitterionic structure.     

1,3-Dipolar cycloadditions of electrophilically activated benzonitrile N-oxides. Polar cycloaddition versus oxime formation

The reactions of electrophilically activated benzonitrile N-oxides (BNOs) toward 3-methylenephthalimidines (MPIs) have been studied using density functional theory (DFT) at the B3LYP/6-31G* level. For these reactions, two different channels allowing the formation of the [3 + 2] cycloadducts and two isomeric (E)- and (Z)-oximes have been characterized. The 1,3-dipolar cycloadditions take place along concerted but highly asynchronous transition states, while formation of the oximes is achieved through a stepwise mechanism involving zwitterionic intermediates. Both reactions are initiated by the nucleophilic attack of the methylene carbon of the MPIs to the carbon atom of the electrophilically activated BNOs. The analysis based on the natural bond orbital (NBO) and the topological analysis of the electron localization function (ELF) at the transition structures and intermediates explains correctly the polar nature of these reactions. Solvent effects considered by the PCM model allow explaining the low incidence of the solvent polarity on the rate and composition of the reactions.     

Mechanistic twist of the [8+2] cycloadditions of dienylisobenzofurans and dimethyl acetylenedicarboxylate: stepwise [8+2] versus [4+2]/[1,5]-vinyl shift mechanisms revealed through a theoretical and experimental study

Recently, it was reported that both dienylfurans and dienylisobenzofurans could react with dimethyl acetylenedicarboxylate (DMAD) to give [8+2] cycloadducts. Understanding these [8+2] reactions will aid the design of additional [8+2] reactions, which have the potential for the synthesis of 10-membered and larger carbocycles. The present Article is aimed to understand the detailed mechanisms of the originally reported [8+2] cycloaddition reaction between dienylisobenzofurans and alkynes at the molecular level through the joint forces of computation and experiment. Density functional theory calculations at the (U)B3LYP/6-31+G(d) level suggest that the concerted [8+2] pathway between dienylisobenzofurans and alkynes is not favored. A stepwise reaction pathway involving formation of a zwitterionic intermediate for the [8+2] reactions between dienylisobenzofurans that contain electron-donating methoxy groups present in their diene moieties and DMAD has been predicted computationally. This pathway is in competition with a Diels-Alder [4+2] reaction between the furan moieties of dienylisobenzofurans and DMAD. When there is no electron-donating group present in the diene moieties of dienylisobenzofurans, the [8+2] reaction occurs through an alternative mechanism involving a [4+2] reaction between the furan moiety of the tetraene and DMAD, followed by a [1,5]-vinyl shift. This computationally predicted novel mechanism was supported experimentally.     

Addition reactions of nitrones on the reconstructed C(1 0 0)-2 × 1 surfaces

In this paper, the reactions of nitrone, N-methyl nitrone, N-phenyl nitrone and their hydroxylamine tautomers (vinyl-hydroxylamine, N-methyl-vinyl-hydroxylamine and N-phenyl-vinyl-hydroxylamine) on the reconstructed C(1 0 0)-2 × 1 surface have been investigated using hybrid density functional theory (B3LYP), Møller–Plesset second-order perturbation (MP2) and multi-configuration complete-active-space self-consistent-field (CASSCF) methods. The calculations showed that all the nitrones can react with the surface “dimer” via facile 1,3-dipolar cycloaddition with small activation barriers (less than 12.0 kJ/mol at B3LYP/6-31g(d) level). The [2+2] cycloaddition of hydroxylamine tautomers on the C(1 0 0) surface follows a diradical mechanism. Hydroxylamine tautomers first form diradical intermediates with the reconstructed C(1 0 0)-2 × 1 surface by overcoming a large activation barrier of 50–60 kJ/mol (B3LYP), then generate [2+2] cycloaddition products via diradical transition states with negligible activation barriers. The surface reactions result in hydroxyl or amino-terminated diamond surfaces, which offers new opportunity for further modifications.     

Dynamic effects on the periselectivity, rate, isotope effects, and mechanism of cycloadditions of ketenes with cyclopentadiene

The cycloadditions of cyclopentadiene with diphenylketene and dichloroketene are studied by a combination of kinetic and product studies, kinetic isotope effects, standard theoretical calculations, and trajectory calculations. In contrast to recent reports, the reaction of cyclopentadiene with diphenylketene affords both [4 + 2] and [2 + 2] cycloadducts directly. This is surprising, since there is only one low-energy transition structure for adduct formation in mPW1K calculations, but quasiclassical trajectories started from this single transition structure afford both [4 + 2] and [2 + 2] products. The dichloroketene reaction is finely balanced between [4 + 2] and [2 + 2] cycloaddition modes in mPW1K calculations, as the minimum-energy path (MEP) leads to different products depending on the basis set. The MEP is misleading in predicting a single product, as trajectory studies for the dichloroketene reaction predict that both [4 + 2] and [2 + 2] products should be formed. The periselectivity does not reflect transition state orbital interactions. The (13)C isotope effects for the dichloroketene reaction are well-predicted from the mPW1K/6-31+G** transition structure. However, the isotope effects for the diphenylketene reaction are not predictable from the cycloaddition transition structure and transition state theory. The isotope effects also appear inconsistent with kinetic observations, but the trajectory studies evince that nonstatistical recrossing can reconcile the apparently contradictory observations. B3LYP calculations predict a shallow intermediate on the energy surface, but trajectory studies suggest that the differing B3LYP and mPW1K surfaces do not result in qualitatively differing mechanisms. Overall, an understanding of the products, rates, selectivities, isotope effects, and mechanism in these reactions requires the explicit consideration of dynamic trajectories.