Phenalenyl growth reactions and implications for prenucleation chemistry of aromatics in flames.

The energetics and kinetics of phenalene and phenalenyl growth reactions were studied theoretically. Rate constants of phenalene and phenalenyl H-abstraction and C2H2 addition to the formed radicals were evaluated through quantum-chemical and rate-theory calculations. The obtained values, assigned to all π radicals, were tested in deterministic and kinetic Monte Carlo simulations of aromatics growth under conditions of laminar premixed flames. Kekulé and non-Kekulé structures of the polycyclic aromatic hydrocarbons (PAHs) evolving in the stochastic simulations were identified by on-the-fly constrained optimization. The numerical results demonstrated an increased PAH growth and qualitatively reproduced experimental observations of Homann and co-workers of non-decaying PAH concentrations with nearly equal abundances of even and odd carbon-atom PAHs. The analysis revealed that the PAH growth proceeds via alternating and sterically diverse acetylene and methyl HACA additions. The rapid and diverse spreading in the PAH population supports a nucleation model as PAH dimerization, assisted by the non-equilibrium phenomena, forming planar aromatics first and then transitioning to the PAH-PAH stacking with size.

Acceleration of a Chemical Reaction due to Nonequilibrium Collisional Dynamics: Dimerization of Polyaromatics.

Nonequilibrium precursor mediated kinetics has been discovered for reactions of gaseous molecules at high temperatures. A theoretical analysis was carried out on dimerization of midsize polycyclic aromatic hydrocarbons (PAH), the presumed critical step in formation of carbonaceous particles in terrestrial and extraterrestrial environments. The nonequilibrium precursor state originates from inelastic collisional dynamics of two PAH monomers, with low-frequency modes acting as a sink for translational energy in the reaction coordinate. Owing to the prolonged lifetime of the nonequilibrium physical dimer, the probability of chemical dimerization increases by an order of magnitude. This phenomenon brings us closer to a solution for the carbon-particle inception puzzle and should prove useful for the fundamental understanding of gas-phase chemical reactions involving large molecules.

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.

Cleavage of an aromatic ring and radical migration.

The present study undertakes a theoretical evaluation of thermal decomposition of aromatic-ring radicals. Potential energy surfaces and associated reaction rate coefficients were calculated for 1- and 2-naphthalenyl, acetanaphthylenyl, and pyrenyl radicals. Kinetic Monte-Carlo simulations were performed to examine the rates of ring cleavage in two sooting laminar premixed flames of ethylene. The simulations showed that the thermal aromatic-ring cleavage is comparable in rate to oxyradical decomposition in a heavier-sooting flame. The simulation also revealed, unexpectedly, fast internal ring radical migration, comparable in frequency to reaction events of aromatic growth.

On the Mechanism of Soot Nucleation. III. The Fate and Facility of the E-Bridge.

Rotationally excited dimerization of aromatic moieties is a mechanism proposed recently to explain the initial steps of soot particle inception in combustion and pyrolysis of hydrocarbons. The product of such dimerization, termed E-bridge, is an angled molecular structure composed of two aromatic rings sharing a common bond. The present study explores the immediate fate of the E-bridge. The performed theoretical analysis indicates that abstraction of a bridge H atom by a gaseous H leads to a rapid transformation of the angled to planar structure. The implications of this result is that the collisionally activated E-bridge formation followed by its flattening effectively increases the size of "planar" aromatic precursors by combining two aromatic moieties with essentially collisional rates, instead of a slower "atom-by-atom" buildup. The faster growth speeds up PAH reaching a size when physical dimerization takes over. The dimerization can be further assisted by the biradicaloid valence structure of the flattened E-bridge.

Transformation of an Embedded Five-Membered Ring in Polycyclic Aromatic Hydrocarbons via the Hydrogen-Abstraction-Acetylene-Addition Mechanism: A Theoretical Study.

Five-membered rings are constituents of many polycyclic aromatic hydrocarbons (PAHs), and their presence on the edges of large PAHs has been repeatedly observed experimentally. However, modern kinetic combustion models often do not consider the growth of PAHs through the transformation of the five-membered rings. In connection with the above, we carried out a theoretical study of the mechanism of hydrogen-abstraction-acetylene-addition (HACA) transformation of an embedded five-membered ring on the armchair PAH edge to a six-membered ring, considering cyclopenta[d,e,f]phenanthrene (4,5-methylenephenanthrene) as a prototype system for this process. The potential energy surface for the reactions of cyclopenta[d,e,f]phenanthrenyl radicals produced by direct H abstractions from cyclopenta[d,e,f]phenanthrene with acetylene has been compiled at the G3(MP2,CC)//B3LYP/6-311G(d,p) level of theory including zero-point vibrational energy corrections. The computed energies and molecular parameters were then used to solve the Rice-Ramsperger-Kassel-Marcus master equation in order to calculate the reaction rate at various pressures and temperatures, which were fitted to the modified Arrhenius equation for further kinetic modeling. The results show that the HACA transformation of the embedded five-membered ring to a six-membered ring is possible, albeit slow. The most viable reaction mechanism involves the R2 + C2H2 reaction, where the acetylene molecules add to a σ-radical in the six-membered ring adjacent to the five-membered ring via a low entrance barrier. The predominant product of R2 + C2H2 is predicted to be 3-ethynyl-4H-cyclopenta[def]phenanthrene Pr5 via immediate H elimination from the initial addition complex. Next, Pr5 undergoes H-assisted isomerization to 4aH-pentaleno[4,3,2,1-cdef]phenanthrene Pr4, and the latter adds a H-atom eventually forming the 1-pyrenylmethyl radical Pr3: R2 + C2H2 ⇆ 3-ethynyl-4H-cyclopenta[def]phenanthrene (Pr5) + H or 4aH-pentaleno[4,3,2,1-cdef]phenanthrene (Pr4) + H; Pr5 + H ⇆ Pr4 + H; Pr4 + H → 1-pyrenylmethyl (Pr3). This HACA sequence may be competitive with the methyl radical addition to the R1 radical formed by H abstraction from the CH2 group in the five-membered ring of cyclopenta[d,e,f]phenanthrene, which provides a pathway to pyrene following two H-atom losses. Relative contributions of the two mechanisms of the five- to six-membered ring transformation would strongly depend on the branching ratios of the R1 and R2 radicals produced by the H abstractions and the available concentration of C2H2 versus CH3 and hence differ in different flames.

On the mechanism of soot nucleation. II. E-bridge formation at the PAH bay.

A recently proposed mechanism of soot nucleation (M. Frenklach and A. M. Mebel, Phys. Chem. Chem. Phys., 2020, 22, 5314-5331) based upon the formation of a rotationally-activated dimer in the collision of an aromatic molecule and a radical leading to a stable, doubly-bonded E-bridge between them, rooted in the existence of a five-membered ring on the molecule edge, has been further investigated with a focus on the 5-6 E-bridge forming in the reaction of a PAH cyclopenta group with a bay site of another PAH. As a prototype reaction of this kind, we examined the reaction between 4-phenanthrenyl and acenaphthylene and, to project these results to larger aromatic structures, we also explored the size effect of the E-bridge forming reactions by computing the 1-naphthyl + acenaphthylene system and comparing these results with the prior results for pyrenyl + acepyrene. The two systems have been studied through high-level G3(MP2,CC)//B3LYP/6-311G(d,p) ab initio calculations of their potential energy surfaces combined with the RRKM/Master Equation calculations of reaction rate constants. With PAH monomers of similar sizes involved, the formation of E-bridge structures at the bay radical sites appeared to be faster and lead to increased nucleation rates as compared to the zigzag-forming ones. A model combining both the bay and zigzag rotationally-induced formation of E-bridges successfully reaches the level of nucleation fluxes comparable to those of the irreversible pyrene dimerization, thus affirming the rotationally-activated dimerization as a feasible mechanism for soot particle nucleation.

On the mechanism of soot nucleation.

The mechanism of carbon particulate (soot) inception has been a subject of numerous studies and debates. The article begins with a critical review of prior proposals, proceeds to the analysis of factors enabling the development of a meaningful nucleation flux, and then introduces new ideas that lead to the fulfillment of these requirements. In the new proposal, a rotationally-activated dimer is formed in the collision of an aromatic molecule and an aromatic radical; the two react during the lifetime of the dimer to form a stable, doubly-bonded bridge between them, with the reaction rooted in a five-member ring present on the molecule edge. Several such reactions were examined theoretically and the most promising one generated a measurable nucleation flux. The consistency of the proposed model with known aspects of soot particle nanostructure is discussed. The foundation of the new model is fundamentally the H-Abstraction-Carbon-Addition (HACA) mechanism with the reaction affinity enhanced by rotational excitation.

Diagnostics of Data-Driven Models: Uncertainty Quantification of PM7 Semi-Empirical Quantum Chemical Method.

We report an evaluation of a semi-empirical quantum chemical method PM7 from the perspective of uncertainty quantification. Specifically, we apply Bound-to-Bound Data Collaboration, an uncertainty quantification framework, to characterize (a) variability of PM7 model parameter values consistent with the uncertainty in the training data and (b) uncertainty propagation from the training data to the model predictions. Experimental heats of formation of a homologous series of linear alkanes are used as the property of interest. The training data are chemically accurate, i.e., they have very low uncertainty by the standards of computational chemistry. The analysis does not find evidence of PM7 consistency with the entire data set considered as no single set of parameter values is found that captures the experimental uncertainties of all training data. A set of parameter values for PM7 was able to capture the training data within ±1 kcal/mol, but not to the smaller level of uncertainty in the reported data. Nevertheless, PM7 was found to be consistent for subsets of the training data. In such cases, uncertainty propagation from the chemically accurate training data to the predicted values preserves error within bounds of chemical accuracy if predictions are made for the molecules of comparable size. Otherwise, the error grows linearly with the relative size of the molecules.

Quantum Monte Carlo Study of the Reactions of CH with Acrolein: Major and Minor Channels.

Acrolein is an important unsaturated hydrocarbon, containing both C═O and C═C bonds, and responsible for atmospheric pollution. A recent study of major reactions of CH with acrolein has been supplemented with computations of other reactions of the system. Similar to the previous approach, the quantum Monte Carlo (QMC) method in the accurate diffusion Monte Carlo (DMC) method was implemented. Single determinant wave functions were used as trial functions for the random walks. Rate coefficients and product branching ratios were computed by solving master equations using the MultiWell software suite. At room temperature, the dominant product channels are 2-methylvinyl + CO (P6), 1,3-butadienal + H (P2), and furan + H (P1). At elevated temperatures, 2,3-butadienal + H (P10) is also a major product. The chain decomposition pathway to form C3H4 + HCO was not competitive with the cyclization pathway at any of the temperatures studied. The DMC branching fractions of the products formed in the subject reaction are in reasonable accord with previous experimental and theoretical values. The computed rate coefficients were found to be independent of pressure at temperatures relevant to combustion (1500-2500 K).

When Rate Constants Are Not Enough.

Real-world chemical systems consisting of multiple isomers and multiple reaction channels often react significantly prior to attaining a steady state energy distribution (SED). Detailed elementary reaction models, which implicitly require SED conditions, may be invalid when non-steady-state energy distributions (NSED) exist. NSED conditions may result in reaction rates and product yields that are different from those expected for SED conditions, although this problem is to some extent reduced by using phenomenological models and rate constants. The present study defines pragmatic diagnostics useful for identifying NSED conditions in stochastic master equation simulations. A representative example is presented for each of four classes of common combustion species: RO2 radicals, aliphatic hydrocarbons, alkyl radicals, and polyaromatic radicals. An example selected from the seminal work of Tsang et al. demonstrates that stochastic simulations and eigenvalue methods for solving the master equation predict the same NSED effects. NSED effects are common under relatively moderate combustion conditions, and accurate simulations may require a master equation analysis.

A quantum Monte Carlo study of the reactions of CH with acrolein.

To assist understanding of combustion processes, we have investigated reactions of methylidyne (CH) with acrolein (CH2CHCHO) using the quantum Monte Carlo (QMC) and other computational methods. We present a theoretical study of the major reactions reported in a recent experiment on the subject system. Both DFT and MP2 computations are carried out, and the former approach is used to form the independent-particle part of the QMC trial wave function used in the diffusion Monte Carlo (DMC) variant of the QMC method. In agreement with experiment, we find that the dominant product channel leads to formation of C4H4O systems + H with leading products of furan + H and 1,3-butadienal + H. Equilibrium geometries, atomization energies, reaction barriers, transition states, and heats of reaction are computed using the DFT, MP2, and DMC approaches and compared to experiment. We find that DMC results are in close agreement with experiment. The kinetics of the subject reactions are determined by solving master equations with the MultiWell software suite.

Oxidation of Graphene-Edge Six- and Five-Member Rings by Molecular Oxygen.

To gain qualitative and quantitative understanding of oxidation processes of large polycyclic aromatics, soot particles, and graphene edges, a theoretical study is reported for the pyrenyl-O2 reaction system. First, possible reaction pathways and their energetics were investigated using high-level ab initio calculations. The results were utilized in RRKM-master equation calculations of rate coefficients and relative product yields at temperatures and pressures relevant to combustion. Finally, the deduced oxidation mechanisms of six- and five-member rings and the computed rate coefficients were employed in kinetic Monte Carlo simulations of oxidation of a graphene "molecule" evolving in flame-like environments. Among the major findings from the latter simulations are the following: The oxidation system exhibits two basic pathways, thermal decomposition and regeneration of oxyradicals. Their competition is temperature-dependent, with the former dominating at higher and the latter at lower temperatures. The overall oxidation of the graphene substrate is computed to be time-dependent, with the initial rates consistent with the known experimental data.

Interval prediction of molecular properties in parametrized quantum chemistry.

The accurate evaluation of molecular properties lies at the core of predictive physical models. Most reliable quantum-chemical calculations are limited to smaller molecular systems while purely empirical approaches are limited in accuracy and reliability. A promising approach is to employ a quantum-mechanical formalism with simplifications and to compensate for the latter with parametrization. We propose a strategy of directly predicting the uncertainty interval for a property of interest, based on training-data uncertainties, which sidesteps the need for an optimum set of parameters.

Pathways to soot oxidation: reaction of OH with phenanthrene radicals.

Energetics and kinetics of the oxidation of possible soot surface sites by hydroxyl radicals were investigated theoretically. Energetics were calculated by employing density functional theory. Three candidate reactions were selected as suitable prototypes of soot oxidation by OH. The first two, OH + benzene and OH + benzene-phenol complex, did not produce pathways that lead to substantial CO expulsion. The third reaction, OH attack on the phenanthrene radical, had multiple pathways leading to CO elimination. The kinetics of the latter reaction system were determined by solving the master equations with the MultiWell suite of codes. The barrierless reaction rates of this system were computed using the VariFlex program. The computations were carried out over the ranges 1500-2500 K and 0.01-10 atm. At higher temperatures, above 2000 K, the oxidation of phenanthrene radicals by OH followed a chemically activated path. At temperatures lower than 2000 K, chemical activation was not sufficient to drive the reaction to products; reaction progress was impeded by intermediate adducts rapidly de-energizing before reaching products. In such cases, the reaction system was modeled by treating the accumulating adducts as distinct chemical species and computing their kinetics via thermal decomposition. The overall rate coefficient of phenanthrene radical oxidation by OH forming CO was found to be insensitive to pressure and temperature and is approximately 1 × 10(14) cm(3) mol(-1) s(-1). The oxidation of phenanthrene radicals by OH is shown to be controlled by two main processes: H atom migration/elimination and oxyradical decomposition. H atom migration and elimination made possible relatively rapid rearrangement of the aromatic edge to form oxyradicals with favorable decomposition rates. The reaction then continues down the fastest oxyradical pathways, eliminating CO.

From aromaticity to self-organized criticality in graphene.

The unique properties of graphene are rooted in its peculiar electronic structure where effects of electron delocalization are pivotal. We show that the traditional view of delocalization as formation of a local or global aromatic bonding framework has to be expanded in this case. A modification of the π-electron system of a finite-size graphene substrate results in a scale-invariant response in the relaxation of interatomic distances and reveals self-organized criticality as a mode of delocalized bonding. Graphene is shown to belong to a diverse class of finite-size extended systems with simple local interactions where complexity emerges spontaneously under very general conditions that can be a critical factor controlling observable properties such as chemical activity, electron transport, and spin-polarization.

Thermal decomposition of pentacene oxyradicals.

The energetics and kinetics of the thermal decomposition of pentacene oxyradicals were studied using a combination of ab initio electronic structure theory and energy-transfer master equation modeling. The rate coefficients of pentacene oxyradical decomposition were computed for the range of 1500-2500 K and 0.01-10 atm and found to be both temperature and pressure dependent. The computational results reveal that oxyradicals with oxygen attached to the inner rings are kinetically more stable than those with oxygen attached to the outer rings. The latter decompose to produce CO at rates comparable to those of phenoxy radical, while CO is unlikely to be produced from oxyradicals with oxygen bonded to the inner rings.

A diffusion Monte Carlo study of the O-H bond dissociation of phenol.

The homolytic O-H bond dissociation energy (BDE) of phenol was determined from diffusion Monte Carlo (DMC) calculations using single determinant trial wave functions. DMC gives an O-H BDE of 87.0 +/- 0.3 kcal/mol when restricted Hartree-Fock orbitals are used and a BDE of 87.5 +/- 0.3 kcal/mol with restricted B3LYP Kohn-Sham orbitals. These results are in good agreement with the extrapolated B3P86 results of Costa Cabral and Canuto (88.3 kcal/mol), the recommended experimental value of Borges dos Santos and Martinho Simões (88.7 +/- 0.5 kcal/mol), and the G3 (88.2 kcal/mol), CBS-APNO (88.2 kcal/mol), CBS-QB3 (87.1 kcal/mol) results of Mulder.

Detailed kinetic Monte Carlo simulations of graphene-edge growth.

A new detailed chemical-kinetic Monte Carlo model of graphene-edge growth is presented. The model employs a fine-grained approach to chemically resolved species, allows for incorporation of five-member rings into growing structures, and links the stochastic kinetic steps to a geometry optimization, thereby properly accounting for curving of molecular structures. The evolving morphology is greatly affected by the rates of key reactions and hence by surface-site steric environment and gas-phase species concentrations. The evolving graphene morphology and growth rates seemingly reach "asymptotic" behavior, independent of the initial substrate. Most noteworthy, growing layers become significantly curved. The curvature occurs regardless of initial substrate at both 1500 and 2000 K with higher curvature occurring at the lower temperature. More intriguing is the observation that, at 2000 K, transition from planar to curved growth does not commence immediately but occurs at some later time, seemingly when the growing graphene reaches a size significantly larger than coronene. No curvature is produced in numerical simulations at 2500 K, indicating that high-energy environments cause the five-member-ring to be less stable, thus preventing them from forming.