Low-Temperature Mechanisms for the Formation of Substituted Azanaphthalenes through Consecutive CN and C₂H Additions to Styrene and <i>N</i>‑Methylenebenzenamine: A Theoretical Study

Ab initio G3­(MP2,CC)/B3LYP/6-311G** calculations of potential energy surfaces (PESs) for the reactions of cyano and ethynyl radicals with styrene and N-methylenebenzenamine have been performed to investigate a possible formation mechanism of the prototype nitrogen-containing polycyclic aromatic compounds: (substituted) 1- and 2-azanaphthalenes. The computed PESs and molecular parameters have been used for RRKM and RRKM-Master Equation calculations of reaction rate constants and product branching ratios under single-collision conditions and at pressures from 3 to 10–6 mbar and temperatures of 90–200 K relevant to the organic aerosol formation regions in the stratosphere of a Saturn’s moon Titan. The results show that ethynyl-substituted 1- and 2-azanaphthalenes can be produced by consecutive CN and C2H additions to styrene or by two C2H additions to N-methylenebenzenamine. All CN and C2H radical addition complexes are formed in the entrance channels without barriers, and the reactions are computed to be exothermic, with all intermediates and transition states along the favorable pathways residing lower in energy than the respective initial reactants. The reactions are completed by dissociation of chemically activated radical intermediates via H losses, so that collisional stabilization of the intermediates is not required to form the final products. These features make the proposed mechanism viable even at very low temperatures and under single-collision conditions and especially significant for astrochemical environments. In Titan’s stratosphere, collisional stabilization of the initial CN + styrene reaction adducts may be significant, but substantial amounts of 2-vinylbenzonitrile and 2-ethynyl-N-methylenebenzenamine can still be produced and then react with C2H to form substituted azanaphthalenes

On the Mechanism of Soot Nucleation. IV. Molecular Growth of the Flattened E‑Bridge

Rotationally excited dimerization of aromatic moieties, a mechanism proposed recently to explain the initial steps of soot particle inception in combustion and pyrolysis of hydrocarbons, produces a molecular structure, termed E-bridge, combining the two aromatics via five-membered aromatic rings sharing a common bond. The present study investigates a hydrogen-mediated addition of acetylene to the fused five-membered ring part of the E-bridge forming a seven-membered ring. The carried out quantum-mechanical and rate theoretical calculations indicate the plausibility of such capping reactions, and kinetic Monte Carlo simulations demonstrate their frequent occurrence. The capping frequency, however, is limited by “splitting” the fused five-membered bridge due to five-membered ring migration. A similar migration of edge seven-membered rings is shown to be also rapid but short, as their encounter with five-membered rings converts them both into six-membered rings

Reactions of C₂H with 1- and 2-Butynes: An Ab Initio/RRKM Study of the Reaction Mechanism and Product Branching Ratios

Ab initio CCSD(T)/cc-pVTZ(CBS)//B3LYP/6-311G** calculations of the C6H7 potential energy surface are combined with RRKM calculations of reaction rate constants and product branching ratios to investigate the mechanism and product distribution in the C2H + 1-butyne/2-butyne reactions. 2-Ethynyl-1,3-butadiene (C6H6) + H and ethynylallene (C5H4) + CH3 are predicted to be the major products of the C2H + 1-butyne reaction. The reaction is initiated by barrierless ethynyl additions to the acetylenic C atoms in 1-butyne and the product branching ratios depend on collision energy and the direction of the initial C2H attack. The 2-ethynyl-1,3-butadiene + H products are favored by the central C2H addition to 1-butyne, whereas ethynylallene + CH3 are preferred for the terminal C2H addition. A relatively minor product favored at higher collision energies is diacetylene + C2H5. Three other acyclic C6H6 isomers, including 1,3-hexadiene-5-yne, 3,4-hexadiene-1-yne, and 1,3-hexadiyne, can be formed as less important products, but the production of the cyclic C6H6 species, fulvene, and dimethylenecyclobut-1-ene (DMCB), is predicted to be negligible. The qualitative disagreement with the recently measured experimental product distribution of C6H6 isomers is attributed to a possible role of the secondary 2-ethynyl-1,3-butadiene + H reaction, which may generate fulvene as a significant product. Also, the photoionization energy curve assigned to DMCB in experiment may originate from vibrationally excited 2-ethynyl-1,3-butadiene molecules. For the C2H + 2-butyne reaction, the calculations predict the C5H4 isomer methyldiacetylene + CH3 to be the dominant product, whereas very minor products include the C6H6 isomers 1,1-ethynylmethylallene and 2-ethynyl-1,3-butadiene

Theoretical Study of the Reaction Mechanism and Kinetics of the Phenyl + Allyl and Related Benzyl + Vinyl Associations

Potential energy surfaces for the allyl + phenyl and benzyl + vinyl barrierless radical association reactions have been studied at the CCSD­(T)-F12/cc-pVTZ-f12//B3LYP/6-311G** level of theory. Variable reaction coordinate transition state theory (VRC-TST) has been employed to evaluate high-pressure limit rate constants for the barrierless channels. Then, Rice–Ramsperger–Kassel–Marcus master equation (RRKM-ME) calculations have been performed to assess phenomenological rate constants and product branching ratios of various reaction channels at different temperatures and pressures. The initial step of both radical association reactions produces 3-phenylpropene which can further dissociate into a variety of bimolecular products including the indene precursor 1-phenylallyl + H. The results showed that at typical combustion conditions the collisional stabilization of 3-phenylpropene dominates both the phenyl + allyl and benzyl + vinyl reactions at temperatures below 1000 K and remains important at high pressures up to 2500 K. The main bimolecular products of the two reactions at high temperatures are predicted to be benzyl + vinyl and phenyl + allyl, respectively. The well-skipping mechanism to form 1-phenylallyl directly in the allyl + phenyl and benzyl + vinyl reactions appeared to be not significant, however, the reactions can provide some contributions into the formation of the indene precursor via the 3-phenylpropene stabilization/dissociation sequence and most of all, via the formation of 3-phenylpropene itself, which then can undergo H-abstraction by available radicals to produce 1-phenylallyl. The allyl + phenyl reaction can also contribute to the formation of two-ring PAH by producing benzyl radical at high temperatures, either by the well-skipping or stabilization/dissociation mechanisms; in turn, benzyl can readily react with acetylene or propargyl radical to form indene or naphthalene precursors, respectively. Rate expressions for all important reaction channels in a broad range of temperatures and pressures have been generated for kinetic modeling

Theoretical Study on the Reaction Mechanism of CO₂ with Mg

Ab initio QCISD(T)/6-311+G(3df)//MP2/6-31+G(d) calculations of potential energy surface for the reaction of Mg atoms with CO2 show that re-forming of carbon dioxide to carbon monoxide can be significantly enhanced in the presence of Mg atoms. The overall endothermicity of the Mg + CO2 → MgO + CO reaction is calculated to be about 66 kcal/mol, almost twice lower than the energy needed for spin-forbidden unimolecular decomposition of CO2 to CO + O(3P). The Mg + CO2 reaction is spin-allowed and the barrier, 68.8 kcal/mol, is greatly reduced as compared to the barrier for the unimolecular decomposition, 131 kcal/mol. The reaction proceeds via the MgOCO cyclic intermediate which lies 14.3 kcal/mol higher in energy than the reactants and stabilized with respect to Mg + CO2 by a barrier of 5.9 kcal/mol. The catalytic role of Mg atoms for re-forming of CO2 to CO is discussed. The reverse MgO + CO → Mg + CO2 reaction is highly exothermic and has a barrier of 2.8 kcal/mol indicating that magnesium oxide can be rapidly reduced by carbon monoxide producing Mg atoms and carbon dioxide. Highly accurate full valence active space MRCI calculations with extrapolation to the complete basis set allowed us to propose a new value for the standard heat of formation of MgO in the gas phase, 31.4−31.9 and 33.5−34.0 kcal/mol for ΔHf°(0 K) and ΔHf°(298 K), respectively. The result is 20 kcal/mol higher than the present recommended value and new experimental measurements of thermochemical data for gaseous MgO are suggested

Reaction Mechanism of N₂/H₂ Conversion to NH₃: A Theoretical Study

Ab initio G2M(MP2)//MP2/6-31G** calculations have been performed to study the molecular and radical chain reaction mechanisms of nitrogen hydrogenation through sequential additions of three H2 molecules to N2 producing NH3 + NH3. All reaction steps of the molecular mechanism are shown to be slow owing to high barriers for the molecular hydrogen additions. The three-center 1,1-H2 additions are significantly more preferable as compared to the four-center 1,2-additions. The most favorable reaction pathway involves the steps N2 + H2 → TS1a → NNH2, NNH2 + H2 → TS3a → H2NNH2, H2NNH2 → TS4 → HNNH3, and HNNH3 + H2 → TS5 → NH3 + NH3, with the barriers calculated as 125.2, 30.7, 60.5, and 24.6 kcal/mol, respectively. The addition of the first molecular hydrogen is thus the rate-determining stage of nitrogen hydrogenation. The formation of hydrazine can be facilitated by a spontaneous reaction of two cis-HNNH molecules by the dihydrogen transfer mechanism. The radical chain mechanism includes the N2 + H → N2H, N2H + H2 → HNNH + H, HNNH + H → N2H3, N2H3 + H2 → H2NNH2 + H, H2NNH2 + H → NH2 + NH3, and NH2 + H2 → NH3 + H sequential reactions with the barriers of 17.1, 41.6, 6.4, 29.1, 10.7, and 10.6 kcal/mol, respectively. Nitrogen hydrogenation can be catalyzed by H atoms with the barrier for the slowest reaction step decreasing from 125 to 42 kcal/mol. The reaction of two NH(3Σ-) radicals is predicted to be fast and to form N2 + H2 with high exothermicity. The reaction of two NH2 radicals can produce NNH2 + H2 with exothermicity of 19.8 kcal/mol and a barrier of 10.9 kcal/mol relative to the reactants, or NH3 + NH(3Σ-), through a barrierless, 14.3 kcal/mol exothermic, but spin-forbidden channel. We also report rate constants and equilibrium constants for all considered reactions calculated using the transition state theory and ab initio energies and molecular parameters, which can be employed for kinetic modeling of chemical processes involving nitrogen- and hydrogen-containing substances

Theoretical Study on the Reaction Mechanism of Nickel Atoms with Carbon Dioxide

Ab initio and density functional calculations of the potential energy surfaces for the Ni + CO2 → NiO + CO reaction in the lowest triplet and singlet electronic states have been carried out at the B3LYP/6-31G*, B3LYP/6-311G*, B3LYP/6-311+G(3df), CCSD(T)/6-311G*, and CCSD(T)/6-311+G(3df) theoretical levels. The reaction is calculated to preferentially occur in the triplet state and to proceed by the formation of a cyclic four-member ring C2v-symmetric NiOCO intermediate (t-cyc) that lies ∼19 kcal/mol above the reactants. The barrier for the initial reaction step is about 23 kcal/mol. From t-cyc the reaction continues via transition state t-TS2 toward the linear t-CONiO complex. The latter is stabilized by ∼10 kcal/mol with respect to the products, NiO (3Σ-) + CO, and can dissociate producing them without exit barrier. The highest barrier at the reaction pathway, about 53 kcal/mol, occurs at t-TS2. The reverse NiO (3Σ-) + CO reaction yielding Ni atoms and CO2 with exothermicity of 36 kcal/mol is shown to have a barrier of 15 kcal/mol relative to the reactants occurring at the second reaction step. On this basis, nickel oxide is expected to be less efficient for oxidizing CO to CO2 than the oxides of alkaline earth metals. Reduction of CO2 to CO can be significantly enhanced in the presence of Ni atoms due to much lower endothermicity (36−37 kcal/mol) and activation barrier (∼53 kca/mol) for the t-Ni + CO2 → NiO (3Σ-) + CO reaction as compared to those for the unimolecular decomposition of carbon dioxide. The accuracies of different theoretical methods for calculations of the reaction energies have been compared

Activation of Methane by Neutral Transition Metal Oxides (ScO, NiO, and PdO): A Theoretical Study

Density functional B3LYP calculations have been employed to investigate potential energy surfaces for the reactions of scandium, nickel, and palladium oxides with methane. The results show that NiO and PdO are reactive toward methane and can form molecular complexes with CH4 bound by 9−10 kcal/mol without a barrier. At elevated temperatures, the dominant reaction channel is direct abstraction of a hydrogen atom by the oxides from CH4 with a barrier of ∼16 kcal/mol leading to MOH (M = Ni, Pd) and free methyl radical. A minor reaction channel is an insertion into a C−H bond to produce CH3MOH molecules via transition states lying 19−20 kcal/mol above the initial reactants. For instance, for PdO, the rate constant of the hydrogen abstraction channel evaluated using the transition state theory for the 300−1000 K temperature range, kmethyl = 7.12 × 10-11 exp(−17 329/RT) cm3 s-1 molecule-1, is 2−3 orders of magnitude higher than the insertion rate constant and the branching ratio for the PdOH + CH3 products is 98−99%. The preferable channel of dissociation of CH3NiOH is a cleavage of the Ni−C bond leading to the radical NiOH + CH3 products without an exit barrier, while CH3PdOH is more likely to undergo 1,2-CH3 migration to produce a PdCH3OH complex and eventually Pd plus methanol. PdOH and CH3 can recombine producing CH3PdOH and isomerization, and dissociation of this molecule results in further transformation of methyl radical into methanol. However, the NiOH + CH3 reaction is expected only to produce CH3NiOH or to restore the initial reactants, NiO + CH4. ScO is not reactive with respect to methane at low and ambient temperatures. At elevated temperatures, the ScO + CH4 reaction can proceed via a barrier of 22.4 kcal/mol to form a CH3ScOH molecule with exothermicity of 9.8 kcal/mol. CH3ScOH is not likely to decompose to the methyl radical and ScOH because this process is 58.9 kcal/mol endothermic

Theoretical Investigation of the Mechanism and Product Branching Ratios of the Reactions of Cyano Radical with 1- and 2‑Butyne and 1,2-Butadiene

Ab initio CCSD­(T)/cc-pVTZ­(CBS)//B3LYP/6-311g­(d,p) calculations of the C₅H₆N potential energy surface have been performed to investigate the reaction mechanism of cyano radical (CN) with C₄H₆ isomers 1- and 2-butyne and 1,2-butadiene. They were followed by RRKM calculations of the reaction rate constants and product branching ratios under single-collision conditions in the 0–5 kcal/mol collision energy range. With the assumption of equal probabilities of the barrierless terminal and central addition of the cyano radical to 1-butyne, 2-cyano-1,3-butadiene + H, and cyanoallene + CH₃ are predicted to be the major reaction products with a branching ratio of ∼2:1. The terminal CN addition to C¹ favors the formation of cyanoallene + CH₃, whereas the central CN addition to C² enhances the formation of 2-cyano-1,3-butadiene + H. For the CN + 2-butyne reaction, the dominant product is calculated to be 1-cyano-prop-1-yne + CH₃, and the CH₃ loss occurs directly from the initial adduct formed by the barrierless CN addition to either of the two acetylenic carbon atoms. A small amount of the H loss product, 3-cyano-1,2-butadiene (1-cyano-1-methylallene), can be also formed as was observed in earlier crossed molecular beam experiments. Three different products are predicted for the CN + 1,2-butadiene reaction, which also occurs without entrance barriers. If various initial complexes formed by the CN addition to C¹, C², C³, or to the CC double bonds in 1,2-butadiene are produced in the entrance channel with equal probabilities, the dominating product (70–60%) is 2-cyano-1,3-butadiene + H, and the other significant products include 1-cyano-prop-3-yne + CH₃ (19–25%) favored by the initial CN addition to C¹ and cyanoallene + CH₃ (11–15%) preferred for the CN addition to C³. The H abstraction HCN + C₄H₅ products may also be formed either from the initial CN addition adducts through a CN roaming mechanism or via certain trajectories directly from the initial reactants, but their yield is not expected to be significant, at least at low temperatures. The energetics, mechanisms, and product branching ratios of the cyano radical reactions with various C₄H₆ isomers and their analogous isoelectronic C₂H + C₄H₆ reactions have been summarized and compared

Theoretical Study of TiO-Catalyzed Hydrogenation of Carbon Dioxide to Formic Acid

Density functional B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d,p) calculations have been performed for the potential energy surface of the CO2/H2/TiO system. The results demonstrate that titanium oxide can serve as a catalyst for the gas-phase hydrogenation of carbon dioxide to formic acid. The most favorable reaction pathways are CO2 + H2 + TiO(3Δ) → H2 + η2-CO2−TiO → TS2 → η2-CO2−HTiOH → TS3 → OC(H)OTiOH → TS4 → cyc-HCO2TiOH → TS5 → cis-HOC(H)OTiO → cis-HCOOH + TiO(3Δ) and (starting from the OC(H)OTiOH intermediate) OC(H)OTiOH → TS6 → trans-HC(O)O(H)TiO → trans-HCOOH + TiO(3Δ). In these mechanisms, the highest relative energies with respect to the initial reactants are found for the final products, 7.4 and 11.0 kcal/mol for the trans and cis conformers of formic acid, respectively, and all transition states have lower energies. Therefore, in the gas phase, titanium oxide can be an efficient catalyst; the activation energy for the TiO-catalyzed hydrogenation of CO2 coincides with its endothermicity. However, the highest barriers for individual reaction steps are lowered to 60.1 and 54.5 kcal/mol, respectively, as compared to 73.8 kcal/mol for the uncatalyzed CO2 + H2 → HCOOH reaction, indicating that in the condensed phase TiO would not be a particularly efficient catalyst