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.     

Ab initio study on the mechanism of cycloaddition reaction of ketene with methylenimine: A new reaction scheme

The cycloaddition reaction of ketene and methylenimine, leading to 2-azetidinone, has been studied theoretically by RHF /3-21G and IRC. This reaction is believed to be nonsynchronous and concerted, taking place through a twisted transition state. Four π orbitals are involved in this reaction, which is a “2 × [1 + 1]”-type cycloaddition. In the course of the reaction, rotation of the methylene group instead of oxygen in ketene was ascertained. The activated barrier is calculated to be 33.9 kcal/mol. © 1992 John Wiley & Sons, Inc.     

The ozonolysis of acetylene--a quantum chemical investigation.

The ozonolysis of acetylene was investigated using CCSD(T), CASPT2, and B3LYP-DFT in connection with a 6-311+G(2d,2p) basis set. The reaction is initiated by the formation of a van der Waals complex followed by a [4pi + 2pi] cycloaddition between ozone and acetylene (activation enthalpy DeltaH(a)(298) = 9.6 kcal/mol; experiment, 10.2 kcal/mol), yielding 1,2,3-trioxolene, which rapidly opens to alpha-ketocarbonyl oxide 5. Alternatively, an O atom can be transferred from ozone to acetylene (DeltaH(a)(298) = 15.6 kcal/mol), thus leading to formyl carbene, which can rearrange to oxirene or ketene. The key compound in the ozonolysis of acetylene is 5 because it is the starting point for the isomerization to the corresponding dioxirane 19 (DeltaH(a)(298) = 16.9 kcal/mol), for the cyclization to trioxabicyclo[2.1.0]pentane 10 (DeltaH(a)(298) = 19.5 kcal/mol), for the formation of hydroperoxy ketene 15 (DeltaH(a)(298) = 20.6 kcal/mol), and for the rearrangement to dioxetanone 9 (DeltaH(a)(298) = 23.6 kcal/mol). Compounds 19, 10, 15, and 9 rearrange or decompose with barriers between 13 and 16 kcal/mol to yield as major products formanhydride, glyoxal, formaldehyde, formic acid, and (to a minor extent) glyoxylic acid. Hence, the ozonolysis of acetylene possesses a very complicated reaction mechanism that deserves intensive experimental studies.     

Theoretical study on reactions of nitroethylene with the Si(100)-2 x 1 surface

Possible reaction pathways of nitroethylene with the Si(100)-2 x 1 surface have been investigated by unrestricted density functional theory. The facile occurrence of the studied reactions was demonstrated by the low activation energies of the rate-determining steps (1.07-5.23 kcal/mol). It was found that the [4 + 2] cycloaddition reaction of nitroethylene is most kinetically favorable. The isomerization reactions of the addition products were also investigated. The [3 + 2] cycloaddition product may further undergo a rearrangement by overcoming a 12.37 kcal/mol activation energy barrier into an isomer, with an oxygen atom of the nitryl group inserted between two silicon atoms of the Si(100) surface.     

Cycloaddition of benzene on Si(100) and its surface conversions

A comprehensive ab initio study of the adsorption of benzene on the silicon(100) surface is presented. Five potential candidates ([2+2] adduct, [4+2] adduct, two tetra-sigma-bonded structures, and one radical-like structure) for the reaction product are examined to determine the lowest energy adsorption configuration. A [4+2] butterfly structure is determined to be the global minimum (-29.0 kcal/mol), although one of the two tetra-sigma-bonded structures (-26.7 kcal/mol) is similar in energy to it. Multireference perturbation theory suggests that the [4+2] addition mechanism of benzene on Si(100) is very similar to the usual Diels-Alder reaction (i.e., small or zero activation barrier), even though benzene adsorption entails the loss of benzene aromaticity during the reaction. On the other hand, the [2+2] cycloaddition mechanism is shown to require a relatively high activation barrier (17.8 kcal/mol), in which the initial step is to form a (relatively strongly bound) van der Waals complex (-8.9 kcal/mol). However, the net activation barrier relative to reactants is only 8.9 kcal/mol. Careful examination of the interconversion reactions among the reaction products indicates that the two tetra-sigma-bonded structures (that are energetically comparable to the [4+2] product) can be derived from the [2+2] adduct with activation barriers of 15.5 and 21.4 kcal/mol. However, unlike the previous theoretical predictions, it is found that the conversion of the [4+2] product to the tetra-sigma-bonded structures entails huge barriers (>37.0 kcal/mol) and is unlikely to occur. This suggests that the [4+2] product is not only thermodynamically the most stable configuration (lowest energy product) but also kinetically very stable (large barriers with respect to the isomerization to other products).     

Substituent Effects on Site Selectivity (C=C vs C=N) in Heterocumulene-Heterodiene [4 + 2] Cycloadditions: Density Functional and Semiempirical AM1 Molecular Orbital Calculations

The effect of substituents on the site selectivity (C=C vs C=N) in the [4 + 2] cycloaddition between heterocumulenes (ketene imines) 2a-g with heterodienes (acroleines 9a-n and 4-acylfuran-2,3-diones 1a-d) is treated by semiempirical AM1 molecular orbital and density functional calculations using Becke's three-parameter hybrid method (B3LYP/6-31G). For some reactions calculations were also done at the B3LYP/6-31+G level of theory. For reaction of the oxa 1,3-dienes with ketene imines unsubstituted at the terminal carbon invariably addition across the C=C heterocumulene double bond has a lower activation energy than addition across the C=N double bond. Substitution of methyl or especially phenyl groups at the ketene imine C-terminus leads to a reversal of the respective activation energies. Incorporation of the oxa 1,3-diene system into the heterocyclic dione 1 substantially enhances the reactivity ( approximately 10 kcal mol(-1) lower activation energies) as compared to similarly substituted acroleins. At the DFT level of theory all reactions are found to proceed via a concerted asynchronous mechanism.     

2+3] Cycloaddition of ethylene to transition metal oxo compounds. analysis of density functional results by marcus theory.

Density functional results on the [2+3] cycloaddition of ethylene to various transition metal complexes MO(3)(q) and LMO(3)(q) (q = -1, 0, 1) with M = Mo, W, Mn, Tc, Re, and Os and various ligands L = Cp, CH(3), Cl, and O show that the corresponding activation barriers DeltaE(double dagger) depend in quadratic fashion on the reaction energies DeltaE(0) as predicted by Marcus theory. A thermoneutral reaction is characterized by the intrinsic reaction barrier DeltaE(0) of 25.1 kcal/mol. Both ethylene [2+3] cycloaddition to an oxo complex and the corresponding homolytic M-O bond dissociation are controlled by the reducibility of the transition metal center. Indeed, from the easily calculated M-O bond dissociation energy of the oxo complex one can predict the reaction energy DeltaE(0) and hence, by Marcus theory, the corresponding activation barrier DeltaE. This allows a systematic representation of more than 25 barriers of [2+3] cycloaddition reactions that range from 5 to 70 kcal/mol.     

Ab initio studies on the mechanism of the cycloaddition reaction between ketene and allene

The mechanism of the cycloaddition reaction between ketene and allene to form methylene–cyclobutanones has been studied theoretically by HF /3–21G and MP2 /3–21G . These two reactions are believed to be unsynchronous and concerted, taking place through the twisted transition states. Four orbitals are mainly involved in each reaction, which is a “2 × [1 + 1]”-type cycloaddition. The activated barrier for the two reactions are 27.2 and 27.1 kcal/mol, respectively, at the level of MP 2/6–31G * based on the MP 2/3–21G geometries, i.e., these two reactions are compatible. © 1994 John Wiley & Sons, Inc.     

Understanding the participation of quadricyclane as nucleophile in polar [2sigma + 2sigma + 2pi] cycloadditions toward electrophilic pi molecules

The formal [2sigma + 2sigma + 2pi] cycloaddition of quadricyclane, 1, with dimethyl azodicarboxylate, 2, in water has been studied using DFT methods at the B3LYP/6-31G** and MPWB1K/6-31G** levels. In the gas phase, the reaction of 1 with 2 has a two-stage mechanism with a large polar character and an activation barrier of 23.2 kcal/mol. Inclusion of water through a combined discrete-continuum model changes the mechanism to a two-step model where the first nucleophilic attack of 1 to 2 is the rate-limiting step with an activation barrier of 14.7 kcal/mol. Analysis of the electronic structure of the transition state structures points out the large zwitterionic character of these species. A DFT analysis of the global electrophilicity and nucleophilicity of the reagents provides a sound explanation about the participation of 1 as a nucleophile in these cycloadditions. This behavior is reinforced by a further study of the reaction of 1 with 1,1-dicyanoethylene.     

An ab initio study on the allene-isocyanic acid and ketene-vinylimine [2 + 2] cycloaddition reaction paths

The reaction paths of [2 + 2] cycloadditions of allene (H2C=C=CH2) to isocyanic acid (HN=C=O) and ketene (H2C=C=O) to vinylimine (H2C=C=NH), leading to all the possible 14 four-membered ring molecules, were investigated by the MP2/aug-cc-pVDZ method. In the two considered reactions, the 2-azetidinone (beta-lactam) ring compounds were predicted to be the most stable thermodynamically in the absence of an environment. Although 4-methylene-2-azetidinone is the most stable product of the ketene-vinylimine cycloaddition, its activation barrier is higher than that for 4-methylene-2-iminooxetane by ca. 6 kcal/mol. Therefore, the latter product can be obtained owing to kinetic control. The activation barriers in the allene-isocyanic acid reactions are quite high, 50-70 kcal/mol, whereas in the course of the ketene-vinylimine cycloaddition they are equal to ca. 30-55 kcal/mol. All the reactions studied were found to be concerted and mostly asynchronous. Simulation of the solvent environment (toluene, tetrahydrofuran, acetonitrile, and water) by using Tomasi's polarized continuum model with the integral equation formalism (IEF-PCM) method showed the allene-isocyanic reactions remained concerted, yet the activation barriers were somewhat higher than those in the gas phase, whereas the ketene-vinylimine reactions became stepwise. The larger the solvent dielectric constant, the lower the activation barriers found. The lowest-energy pathways in the gas phase and in solvent were confirmed by intrinsic reaction coordinate (IRC) calculations. The atoms in molecules (AIM) analysis of the electron density distribution in the transition-state (TS) structures allowed us to distinguish pericyclic from pseudopericyclic from nonplanar-pseudopericyclic types of reactions.     

Chemo- and periselectivity in the addition of [OsO2(CH2)2] to ethylene: a theoretical study

Quantum chemical calculations by using density functional theory at the B3LYP level have been carried out to elucidate the reaction course for the addition of ethylene to [OsO2(CH2)2] (1). The calculations predict that the kinetically most favorable reaction proceeds with an activation barrier of 8.1 kcal mol(-1) via [3+2] addition across the O=Os=CH2 moiety. This reaction is -42.4 kcal mol(-1) exothermic. Alternatively, the [3+2] addition to the H2C=Os=CH2 fragment of 1 leads to the most stable addition product 4 (-72.7 kcal mol(-1)), yet this process has a higher activation barrier (13.0 kcal mol(-1)). The [3+2] addition to the O=Os=O fragment yielding 2 is kinetically (27.5 kcal mol(-1)) and thermodynamically (-7.0 kcal mol(-1)) the least favorable [3+2] reaction. The formal [2+2] addition to the Os=O and Os=CH2 double bonds proceeds by initial rearrangement of 1 to the metallaoxirane 1 a. The rearrangement 1-->1 a and the following [2+2] additions have significantly higher activation barriers (>30 kcal mol(-1)) than the [3+2] reactions. Another isomer of 1 is the dioxoosmacyclopropane 1 b, which is 56.2 kcal mol(-1) lower in energy than 1. The activation barrier for the 1-->1 b isomerization is 15.7 kcal mol(-1). The calculations predict that there are no energetically favorable addition reactions of ethylene with 1 b. The isomeric form 1 c containing a peroxo group is too high in energy to be relevant for the reaction course. The accuracy of the B3LYP results is corroborated by high level post-HF CCSD(T) calculations for a subset of species.     

Understanding the electronic reorganization along the nonpolar [3 + 2] cycloaddition reactions of carbonyl ylides

The nonpolar [3 + 2] cycloaddition (32CA) reaction of the carbonyl ylide (CY) 23 with tetramethylethylene (TME) 24 has been studied with DFT methods at the B3LYP/6-31G* level. This cycloaddition reaction, which has a very low activation energy of 4.7 kcal/mol, takes place through a synchronous transition structure. A topological analysis of the ELF along the 32CA reaction provides a new scope of the electronic structure of CY 23 as a pseudodiradical species offering a sound explanation of the high reactivity of this CY in nonpolar reactions. In addition, this analysis points to the nonparticipation of the oxygen lone pairs in the 32CA reaction. This cycloaddition can be seen as a pseudodiradical attack of the terminal carbon atoms of the CY 23 on the π system of TME 24. Therefore, the present study establishes that this 32CA reaction, which is not a pericyclic electron reorganization, may be electronically classified as a [2n + 2π] process.     

A theoretical study of the [4 + 4] dimerization of thioformylketene

[reaction and structure: see text] A theoretical study (B3LYP and G3MP2B3) of the dimerization of thioformylketene (1) was performed. Four pathways-two [4 + 2] pathways with thioformylketene (1), one [4 + 4] pathway with 1, and one [4 + 2] pathway involving 1 and thietone (11)-were considered. Interestingly, the [4 + 4] pathway with 1 had the lowest barrier (3.8 kcal/mol). The geometry of the transition state TS14 is unusual, with the forming bonds in the plane of the ketene. This suggests that the reaction is pseudopericyclic.     

DFT (density functional theory) studies on cycloisomerization of 15–membered triazatriacetylenic macrocycle

The mechanism as well the stereochemistry of cascade cycloisomerization of 15–membered triazatriacetylenic macrocycle was investigated theoretically by using M062X/6–31+G(d,p) and M062X/LANL2DZ calculations. The results showed that the mechanism and outcome of the reaction depended on the absence and presence of a transition metal catalyst. So that, in thermal-induced condition, the reaction had to experience several suprafacial concerted reactions including Ene-reaction (DG^#=35.38 kcal/mol), Diels–Alder cycloaddition (DG^# = 17.16 kcal/mol), and sigmatropic H-shift rearrangement (DG^# = 56.21 kcal/mol) to produce diastereoselective fused cis–tetracyclic aromatic bearing a pyrrole moiety by following kinetic considerations. Also, the [2+2+2] cycloaddition mechanism was neglected in thermal–induced conditions because of high activation free Gibbs energy (DG^# = 63.90 kcal/mol). In the presence of palladium catalyst, Pd(0) formed an adduct by coordinating to C = C bonds and decreased the DG^# of the process to 29.58 kcal/mol, and consequently provided a facilitated media for the reaction to follow the [2+2+2] to produce more stable fused tetracyclic benzenoid aromatic by passing through the lower energy barrier.     

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.     

Aromaticity and activation strain analysis of [3 + 2] cycloaddition reactions between group 14 heteroallenes and triple bonds

We have computationally explored the trend in reactivity of [3 + 2] cycloaddition reactions between H(2)E=C=PH and HC≡CH as the terminal position in the phosphaallene is varied along E = C, Si, Ge, Sn, Pb. The reaction barrier drops significantly from E = C (nearly 50 kcal/mol) to E = Si-Pb (ca. 20 kcal/mol). Activation strain analyses tie this trend to a reduction in activation strain in the heavier phosphaallene analogues which, in contrast to the parent compound H(2)C=C=PH, do already possess the bent geometry required in the TS.     

Transition structures and exo/endo stereoselectivities of concerted [6 + 4] cycloadditions with density functional theory

Density functional theory transition structures were located for three concerted [6 + 4] cycloaddition reactions involving cis-hexatriene and butadiene, cyclopentadiene and cycloheptatriene, and cyclopentadiene and tropone. Geometries, energies, and entropies were computed at the Becke3LYP/6-31G* level. The activation energy of the concerted [6 + 4] cycloaddition of hexatriene and butadiene is 33.3 kcal/mol, about 8 kcal/mol above the activation energy of the butadiene plus ethylene [4 + 2] cycloaddition. The endo concerted [6 + 4] transition state is 1.1 kcal/mol higher than the exo. The [6 + 4] reaction of cyclopentadiene and cycloheptatriene has a barrier of 25.9 kcal/mol, while the cyclopentadiene–tropone barrier drops to 20.7 kcal/mol. Received: 3 December 1998 / Accepted: 18 February 1999 / Published online: 7 June 1999     

Exploring two-state reaction pathways in the photodimerization of cyclohexadiene.

The ground- (S0) and lowest triplet-state (T1) pathways associated with dimerization of cyclohexadiene to give [2+2] and [4+2] cycloadducts have been theoretically studied at the UBLYP and UB3LYP levels of theory with the 6-31G* basis set. The DFT energies were validated by CCSD(T) single-point energy calculations. These cycloaddition reactions follow stepwise mechanisms with formation of bis-allylic biradical (BB) intermediates. In the S0 ground state, the interaction between two cyclohexadiene molecules with formation of BB intermediate IN(S0) has a large activation enthalpy of 32.0 kcal mol(-1). On the other hand, C-C bond-formation in the lowest triplet state (T1) leading to BB intermediate IN(T1) has a low activation enthalpy of 5.0 kcal mol(-1), but the subsequent ring closure involves a very large activation enthalpy of 43.4 kcal mol(-1). Triplet-to-singlet intersystem crossing from IN(T1) to IN(S0) favors cyclization to give the corresponding [2+2] and [4+2] cycloadducts.     

Reaction paths of the [2+2] cycloaddition of X=C=Y molecules (X, Y=S or O or CH2). Ab initio study

The reaction paths of [2+2] cycloaddition of the X=C=Y cumulenes were modeled at the MP2/aug-cc-pVDZ level. Cycloadditions of allene and CO2, CS2, or OCS lead in part to the same four-membered products as dimerizations of either ketene or thioketene or addition of ketene and thioketene, respectively. All the reactions studied are concerted and mostly asynchronous. The majority of the allene cycloadditions studied are endoergic and proceed with much higher activation barriers than do the alternative (thio)ketene additions. In comparison with the energy of the substrates, the four-membered cycles incorporating S-atoms are stabilized more than the analogous structures with O-atoms built into the rings. There are also some products that are thermodynamically disfavored, yet seem to be obtainable thanks to a relatively low barrier of the reaction. The AIM analysis of the electron density distribution in the transition state structures allowed distinguishing pericyclic from pseudopericyclic and nonplanar-pseudopericyclic types of reaction.