Theoretical Study of the Reaction Mechanism and Kinetics of the

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Theoretical Study of the Reaction Mechanism and Kinetics of the Phenyl + Allyl and Related Benzyl + Vinyl Associations Alexander N. Morozov, and Alexander Moiseevich Mebel J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b00345 • Publication Date (Web): 13 Feb 2019 Downloaded from http://pubs.acs.org on February 15, 2019

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The Journal of Physical Chemistry

Theoretical Study of the Reaction Mechanism and Kinetics of the Phenyl + Allyl and Related Benzyl + Vinyl Associations Alexander N. Morozov and Alexander M. Mebel* Department of Chemistry and Biochemistry, Florida International University, Miami, Florida 33199 Abstract. 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, RiceRamsperger-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 wellskipping 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.

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1. INTRODUCTION In hydrocarbon flames, growth of polycyclic aromatic hydrocarbons (PAHs) is linked to the formation of soot.1,2 Preventing soot formation is a long-standing research goal because soot particles are harmful to human health and have a negative effect on the global environment. Resonance-stabilized radicals (RSRs) are thought to play a key role in PAH growth. For example, expansion of radical conjugation was proposed as the driving force to facilitate the growth of large PAH species responsible for soot condensation.3 While the molecular mechanism of the transition from small gaseous PAHs to condensed soot remains a hot topic, the key role of RSRs in the “first ring” formation (benzene or phenyl radical) is well established.4,5 Quantitatively accurate description of the next step - the formation of the two-ring PAHs (naphthalene and indene) from the “first ring” species - is necessary to progress further our understanding of the overall growth process since this elementary step provides a model of a repetitive expansion by one extra six- or five-membered ring to form larger PAHs.6 The related experimental data like flame speciation profiles are generally produced under low-pressure conditions (e.g., 30–600 Torr), while combustion devices typically operate under high pressure (1–100 atm). This gap calls for accurate and predictive theoretical calculations of temperature (T) and pressure (P-) dependent rate constants and product branching ratios. High level ab initio calculations of potential energy surfaces (PESs) combined with the gas-phase reaction rate theory and master equation approach make available a priori kinetics where the calculated T,Pdependent rate constants have “kinetic accuracy”.7 Within the broader project to unravel the mechanism of PAH growth from one to two rings6 here we present a theoretical study of the association reaction of the phenyl radical (C6H5) with the allyl radical (C3H5). As an RSR species, allyl can be present in flames in significant amounts. For instance, allyl is readily produced in the pyrolysis of alkenes since the allylic C-H and C-C bonds are weaker than other types of chemical bonds in hydrocarbons. A recent combined experimental and theoretical study of exo-tetrahydrodicyclopentadiene (JP-10 fuel) showed that on time frames shorter than 100 µs, at temperature of 1500 K and 600 Torr pressure allyl is the major radical product of the thermal decomposition constituting ~13% of the product inventory.8,9 In hydrocarbon flames, hydrogen abstraction from benzene by small radicals like OH, CH3 or by a hydrogen atom is a common source of the phenyl radical.10,11 The barrierless 2 ACS Paragon Plus Environment

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association of the phenyl and allyl radicals produces the closed-shell species 3-phenylpropene (C9H10): C6H5 +C3H5  C6H5CH2CHCH2

(1)

Further 3-phenylpropene can dissociate into the 1-phenylallyl + H bimolecular product: C6H5CH2CHCH2 → C6H5CHCHCH2 + H.

(2)

Theoretical studies of the C9H9 PES showed that 1-phenylallyl is a ready precursor of indene.6,1214

Crossed molecular beams15 and high temperature reactor (1200–1500 K)16 experimental

studies provided the experimental evidence of the formation of indene along with its acyclic isomers phenylallene, 1-phenylpropyne, and 3-phenylpropyne in the association reaction of the phenyl radical with C3H4 isomers allene and methylacetylene. However, both earlier RRKMME/B3LYP13,14 and more recent RRKM-ME/G3(MP2,CC)6 calculations agreed that for this reaction indene + H is a major channel only at low pressures and temperatures, whereas at combustion-like conditions indene is only a minor product. In our earlier work, we proposed that at typical combustion conditions, the formation of 1-phenylallyl followed by its decomposition via an H loss, reactions (1) - (2), represents a possible pathway to indene.6 The reaction mechanism and kinetics of this reaction sequence to indene is the subject of the present study. In addition to the channel (2) leading to 1-phenylallyl and the reverse decomposition of 3phenylpropene into the allyl + phenyl reactants, other decomposition channels, C6H5CH2CHCH2 → C6H5CH2 + C2H3,

(3)

C6H5CH2CHCH2  C6H5CHCHCH3 → C6H5CHCH + CH3,

(4)

C6H5CH2CHCH2 → C6H5CHCCH2 +H2,

(5)

C6H5CH2CHCH2 → C6H5CH3 +C2H2,

(6)

are also considered as plausible reaction pathways. In addition, the present study includes kinetics of the C6H5CH2 + C2H3 association where the CH2 group of benzyl interacts with the vinyl radical. This reaction is related to the phenyl + allyl association as its entrance channel is reversed reaction (3) and the exit channels comprise reversed reaction (1) and reactions (2), (4)– (6). Because 1-phenylallyl + H is one of the products of the possible channels for the benzyl + 3 ACS Paragon Plus Environment


vinyl reaction, this reaction presents another avenue for the PAH growth from one to two rings in hydrocarbon flames. The present theoretical study of the PES, reaction mechanism, T,Pdependent rate constants, and product branching ratios for the phenyl + allyl and related benzyl + vinyl associations should prove useful in kinetic modeling of PAH formation and growth in hydrocarbon flames. 2. THEORETICAL METHODS The equilibrium geometries of the reactants, transition states, intermediates, and products on the C9H10 PES of interest were obtained using density functional theory (DFT) calculations at the B3LYP/6-311G(d,p)17-19 level. The DFT/B3LYP/6-311G(d,p) method was used to compute vibrational frequencies and zero-point energy (ZPE) corrections. The energies of the stationary points were refined using the explicitly correlated coupled clusters CCSD(T)-F12/cc-pVTZf1220-22 method. It has been shown that for various test reactions the mean error of the energetics calculated using the employed methods is within 1 kcal/mol.23 The DFT calculations were carried out using the Gaussian 0924 program package. The coupled cluster calculations were performed using the MOLPRO 201025 program. Bimolecular rate constants for the reactions with barriers were calculated using transition state theory (TST). Energy and angular momentum-resolved (E,J-resolved) rate constants of the unimolecular reactions were calculated using Rice-Ramsperger-Kassel-Marcus (RRKM) theory.26 For the reactions with barriers, the number of states for a transition state and the density of states for the related local minima were generally calculated using the rigid-rotor, harmonicoscillator (RRHO) model. Low-frequency normal modes corresponding to internal rotation were considered as hindered rotors, which replaced the corresponding harmonic oscillators in RRHO. Hindered rotor potentials were scanned using the B3LYP/6-311G(d,p) level of theory. The barrierless unimolecular associations and reverse bimolecular decompositions in the exit channels of reactions (1) – (4) were treated using Variable Reaction Coordinate-Transition State Theory (VRC-TST).5,27,28 Within this theory, an E,J-resolved rate constant is evaluated by optimizing both the reactive flux through a dividing surface and the dividing surface itself.28 The multifaceted implementation of a spherical dividing surface was used in the calculations.5 A spherical dividing surface is constructed as the equidistant surface between the pivot points assigned to each of the departing fragments. For distances less than 5 Å (short-range), the 4 ACS Paragon Plus Environment

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optimized pivot points usually represent the orbitals of an incipient bond while for long-range distances the pivot points coincide with the centers of mass of the departing fragments. The optimization of a pivot point is a computationally demanding task.5 For this reason, the optimal position of the short-range pivot points for the allyl radical were taken from the previous study of the propargyl + allyl association reaction,5 i.e. the pivot points were placed 0.5 Å apart from the terminal carbons perpendicular to the allyl molecular plane. The optimal position of the shortrange pivot points for the 1-phenylallyl radical in the 1-phenylallyl + H reaction was found to be at 0.5 Å distance apart from the bonding carbon and perpendicular to the 1-phenylallyl molecular plane. For all other species the positions of the corresponding bonding atoms were used as the positions of the short-range pivot points. Figure 1 illustrates the positions of the short-range pivot points for reactions (1)–(4). Because of the multireference character of the wave function for radical-radical interactions on a dividing surface, single-point potential energies of randomly generated dividing surface structures were calculated using the second-order perturbation theory CASPT2 method29,30 with the cc-pvdz basis set.20 To avoid discontinuities in the potential describing the interaction between radicals, one of which is RSR, it is required to include the delocalized radical orbitals in the active space. The present CASPT2 calculations were carried out using the (10e,10o) active space which, for computational reasons, includes not only the delocalized radicals but the complete π system of the reactant/bimolecular products plus the orbital of an incipient bond. This size of the active space precluded the usage of the CASPT2 method in calculations of a geometry relaxation correction.5 For this reason, the minimum energy path (MEP) geometry relaxation corrections were obtained using complete active space CASSCF31(10e,10o) to optimize geometries of MEP structures. The complete basis set (CBS) correction32 was applied based on the CASPT2(10e,10o)/cc-pVnZ (n = D, T, Q) energies of the unrelaxed MEP structures. In summary, energies of various structures during the VRC-TST calculations were probed at the CASPT2(10e,10o)/cc-pVDZ level of theory and then, ad hoc one-dimensional corrections depending only on the RCC/RCH distance corresponding to the forming C-C/C-H bond were included: E = Erigid[CASPT2(10e,10o)/cc-pVDZ] + E[geom] + E[CBS], where Erigid are single point energies of interacting fragments when brought into a particular dividing surface configuration without geometry relaxation relative to the energy of these 5 ACS Paragon Plus Environment


fragments been separate. Below we use “rigid” referring such a configuration. E[geom] is the geometry relaxation correction computed as a difference of CASPT2(10e,10o)/cc-pVDZ energies of an optimized structure along the MEP corresponding to a particular value of the RCC/RCH distance and the rigid structure at the same R. E[CBS] was computed as follows: E[pVTZ] = Erigid[CASPT2(10e,10o)/cc-VTZ] – Erigid[CASPT2(10e,10o)/cc-VDZ], E[pVQZ] = Erigid[CASPT2(10e,10o)/cc-VQZ] – Erigid[CASPT2(10e,10o)/cc-VTZ], E[CBS] = E[pVQZ] + 0.69377(E[pVQZ] - E[pVTZ]). The T,P-dependent phenomenological rate constants were calculated by solving the onedimensional master equation33 (ME) using the MESS program package.34 The collisional energy transfer and Lennard-Jones parameters for ME were taken from the previous study of the C9Hx/Ar systems.6 Namely, the Lennard-Jones parameters were (ε/cm−1, σ/Å) = (390, 4.46) and n = 0.62, α300 = 424 cm-1 were used in the “exponential down” model35 of the collisional energy transfer for the temperature dependence of the range parameter α for the deactivating wing of the energy transfer function α(T) = α300(T/300 K)n. Supporting Information (SI) provides the table of fitting parameters for modified Arrhenius expressions for the reactions considered (Table S1), Cartesian coordinates of all stationary structures, their vibrational frequencies, relative energies, and hindered rotor potentials in the form of an input file for RRKM-ME calculations using the MESS code.

3. RESULTS AND DISCUSSION Potential Energy Surface Important channels on the C9H10 PES related to the phenyl + allyl reaction are shown in Figure 2. The entrance channel, the barrierless addition of allyl to the radical site of phenyl by a terminal CH2 group, produces 3-phenylpropene (C9H10). The CCSD(T)-F12/cc-pVTZ-f12 computed energy of 3-phenylpropene relative to the reactants, -88.3 kcal/mol, is close to the G3(MP2,CC) result, -88.4 kcal/mol, calculated previously.6 The viable channels for a direct dissociation of 3-phenylpropene include the reverse decomposition into the phenyl (C6H5) + allyl 6 ACS Paragon Plus Environment

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(C3H5) reactants (1), the H–loss pathway leading to the 1-phenylallyl (C9H9) + H product (2), and the decomposition into the benzyl (C7H7) + vinyl (C2H3) radicals (3). Let us start with reaction (2) which motivated the present study. The energetics of all possible 3-phenylpropene → C9H9 + H reactions were estimated using the G3(MP2,CC) computed energies for the 3phenylpropene + H → C9H9 + H2 reactions published by Kislov et al.36 They found that the H– abstraction from the sp3 CH2 group of 3-phenylpropene is favored significantly over other H– abstraction channels. Namely, the barrier for H-abstraction from the sp3 CH2 group is from 9.1 to 12.1 kcal/mol lower and the reaction energy is from 25.1 to 29.8 kcal/mol lower than those for the other H-abstraction channels, depending on the particular channel.36 Therefore, relative to the other sites, the H–loss from the sp3 CH2 group is favored by at least 25 kcal/mol. For example, the H–loss from the terminal carbon of the side chain in 3-phenylpropene requires 27.8 kcal/mol more energy than the 1-phenylallyl + H decomposition channel. Hence, in the present study only reaction (2), 3-phenylpropene → 1-phenylallyl + H, was deemed as a significant channel of H– loss. The computed energy of the 1-phenylallyl + H bimolecular product is -10.3 kcal/mol (here and below energy values are given relative to the energy of the phenyl + allyl reactants). This CCSD(T)-F12/cc-pVTZ-f12 result differs by 2.3 kcal/mol from -8 kcal/mol computed previously at the G3(MP2,CC) level of theory.6 Reaction (2), a pathway to indene, competes with reaction (3), the barrierless decomposition of 3-phenylpropene into the benzyl + vinyl bimolecular product. The computed relative energy of the bimolecular product of reaction (3) is 0.5 kcal/mol. Another important competitor of reaction (2) is reverse reaction (1), the barrierless decomposition of 3-phenylpropene into the phenyl + allyl product (Figure 2). Let us proceed with channels which, as compared to reactions (1) - (3), are not favored by entropy or/and enthalpy of the transition states. Alternatively to the H-loss, a hydrogen of the sp3 CH2 group of 3-phenylpropene can migrate to the terminal CH2 group via a transition state (TS) located at 14.8 kcal/mol. This isomerization forms the C9H10 intermediate i2 (Figure 2) of reaction (4). The computed energy of i2 is -93.0 kcal/mol. The isomerization is followed by the barrieless decomposition of i2 into the styrenyl (C8H7) + methyl (CH3) bimolecular product. The computed energy of this product is 8.2 kcal/mol. Another alternative for a hydrogen of the sp3 CH2 group of 3-phenylpropene is to participate in an H2-loss via a TS at 3.5 kcal/mol to form the phenylallene (C9H8) + H2 bimolecular product, reaction (5). The computed energy of the product of reaction (5) is -53.5 kcal/mol. Reaction (6) describes the exit channel where a hydrogen atom 7 ACS Paragon Plus Environment


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of the terminal CH2 group migrates to the sp3 CH2 group in concert with the loss of acetylene via a TS at 23.0 kcal/mol. The computed energy of the toluene (C7H8) + acetylene (C2H2) bimolecular product is -54.5 kcal/mol. The MEP potentials for the barrierless associations/dissociations of interest computed for the

rigid

fragments,

with

account

of

the

correction

for

geometry

relaxation,

Erigid[CASPT2(10e,10o)/cc-VDZ] + E[geom], and both with the geometry and CBS corrections, Erigid[CASPT2(10e,10o)/cc-VDZ] + E[geom] +E[CBS], are shown in Figure 3. For the phenyl + allyl and benzyl + vinyl fragments (Figure 3a, 3c), the computed E[geom] varies from about -20 kcal/mol at RCC = 2 Å to about -1 kcal/mol at RCC = 5 Å. For the styrenyl + methyl fragments (Figure 3d), E[geom] varies from about -4 kcal/mol at RCC = 2 Å to about 0 kcal/mol at RCC = 5 Å. For these three carbon-carbon interactions, the corresponding CBS corrections show a uniform dependence on RCC with E[CBS] decreasing from about -2 kcal/mol at RCC = 2 Å to 0 kcal/mol for RCC larger than 3.5 Å. For the 1-phenylallyl + H fragments (Figure 3b), the computed corrections vary from about -20 and -2 kcal/mol at RCH = 1.6 Å to nearly zero at RCH = 5 Å for E[geom] and E[CBS], respectively. Our results show that E[geom] is the major correction in the employed implementation of VRC-TST. Reaction kinetics Scheme 1 is the kinetic scheme used in the RRKM/ME calculations. The total highpressure-limit (HP) rate constant for the phenyl + allyl association is on the order of 10-10 cm3 molecule-1 s-1 and shows an inverse temperature dependence decreasing by a factor of 1.8 in the 500–2500 K range (Figure 4). The temperature dependent rate constants for this reaction calculated at finite pressures of 30 Torr, 1, 10, and 100 atm fall off the HP behavior at about 1000, 1250, 1500 and 1800 K, respectively (Figure 4). The inverse temperature dependence of the total HP rate constant indicates the increasing with temperature entropic penalty on the recombination of the reactants. The HP rate constants for the allyl + propagyl and allyl + allyl recombination reactions5 show a similar inverse T-dependence (Figure 4) but the phenyl + allyl recombination is clearly faster because phenyl is not an RSR and hence is more reactive. The computed rate constants for the main channels of the phenyl + allyl reaction: phenyl + allyl  3-phenylpropene

(1), 8

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phenyl + allyl  1-phenylallyl + H (p1), phenyl + allyl  benzyl + vinyl

(p2)

are presented in Figure 5. The results show that, at finite pressures, the fall-off behavior of the total phenyl + allyl rate constants correlates with the yield of the p1 and p2 bimolecular products. In the temperature range of 500–1250 K the rate constants of the reactions forming p1 and p2 show Arrhenius-like temperature dependence and inverse pressure dependence, i.e. in the pressure range of 30 Torr–100 atm the rate constant of the reaction to p1 decreases by a factor of ~500, the rate constant of the reaction to p2 decreases by a factor of 2.0103 (Figure 5). At temperatures above 1250 K the rate constants of reactions producing p1 and p2 fall off the Arrhenius-like behavior and converge to 4.010-12 and 5.110-11 cm3 molecule-1 s-1, respectively. The computed branching ratio of the bimolecular products, p2/p1, 1, 7, 10, and 12 at 500, 1000, 1500, and 2000 K, respectively, depends mainly on temperature. The increasing with temperature yield of p2 relative to that of p1 indicates a favorable entopic cost of the dissociation into benzyl + vinyl relative to the dissociation into 1-phenylallyl + H. Overall, in the 30 Torr– 100 atm range of pressure, the calculated yield of the bimolecular products becomes significant only at temperatures above 1250 K. At lower temperatures, collisional stabilization of 3phenylpropene results in close to 100% relative yield of this adduct (Figure 5). The unimolecular rate constants for the main channels of decomposition/isomerization of 3-phenylpropene (Figure 6) increase with increasing pressure whilst showing well defined Arrhenius dependence on temperature. The relative yield of the 3-phenylpropene decomposition/isomerization products depends mainly on temperature. Figure 7 shows the branching ratios computed at 1 atm. In the temperature range of 500–1000 K the relative yield of the C9H10 intermediate, i2, changes from about 100% to 2.4% and tends to 0% as temperature rises above 1000 K. The relative yield of the indene precursor, 1-phenylallyl + H, tops at 25% at 700 K and steadily decreases with increasing temperature to 4.4% at 2000 K. The decompositions into the phenyl + allyl and benzyl + vinyl radicals are the main channels of the unimolecular decomposition of 3-phenylpropene at temperatures above 1000 K. The relative yield of the phenyl + allyl bimolecular product varies from about 1.4% at 500 K to 57% at 1000 K and to 49.7% at 2000 K. The relative yield of the benzyl + vinyl bimolecular product varies from about 0% at 500 K to 29.9% at 1000 K and to 45.6% at 2000 K. 9 ACS Paragon Plus Environment


Our PES and reactive flux calculations also allow us to evaluate the kinetics of the benzyl + vinyl reaction where vinyl adds to the CH2 group of benzyl, another possible channel of the PAH growth from one to two rings stemming from the studied C9H10 PES. The computations showed that the main channels of the benzyl + vinyl recombination are i) benzyl + vinyl  3phenylpropene, ii) benzyl + vinyl  1-phenylallyl + H, and iii) benzyl + vinyl  phenyl + allyl. The corresponding rate constants and branching ratios computed at pressures and temperatures of interest are shown in Figure 8. In the temperature range of 500–1250 K the rate constants of the reactions yielding the bimolecular products, ii)-iii), show Arrhenius-like temperature dependence and inverse pressure dependence (Figure 8). At higher temperatures, the rate constants of channels ii) and iii) fall off the Arrhenius-like behavior and converge to 2.410-12 and 2.810-11 cm3 molecule-1 s-1, respectively. The computed branching ratio of the phenyl + allyl to 1phenylallyl + H bimolecular products does not show pressure dependence and varies with temperature as follows: 3, 10, 12, and 12 at 500, 1000, 1500, and 2000 K, respectively. In the 30 Torr–100 atm pressure range, the calculated yield of the bimolecular products of channels ii) and iii) becomes larger than 1% only at temperatures above 1250 K while at lower temperatures the computed yield of 3-phenylpropene is close to 100% (Figure 8). At high pressure conditions, the computed yield of 3-phenylpropene remains significant up to 2500 K. For example, at 100 atm the computed yield of 3-phenylpropene is 100 and 41.6 % for 500 and 2500 K, respectively (Figure 8). Thus, the overall kinetics of the vinyl addition to the CH2 group of benzyl is similar to that of the phenyl + allyl association as collisional stabilization of 3-phenylpropene is predicted to be the main phenomenon under combustion conditions.

4. CONCLUSIONS The PES for the allyl and phenyl association was studied at the CCSD(T)-F12/cc-pVTZf12//B3LYP/6-311G** level of theory. The first step of the reaction produces 3-phenylpropene which can further dissociate into variety of bimolecular products including the barrierless dissociation into the indene precursor 1-phenylallyl + H. The state-of-the-art implementation of VRC-TST5 was used in kinetic studies of the barrierless channels of the computed PES. RRKMME calculations of the T,P-dependent rate constants and relative yields of the products showed 10 ACS Paragon Plus Environment

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that at a typical combustion condition of 1500 K and 1 atm the phenyl + allyl reaction is a minor source of 1-phenylallyl + H, with its yield reaching only 1.2 %. Under these conditions, the calculated rate constant of the phenyl + allyl  1-phenylallyl + H reaction is 1.110-12 cm3 molecule-1 s-1 while the rate constant of the phenyl + allyl  benzyl + vinyl reaction is 1.210-11 cm3 molecule-1 s-1. The kinetic calculations also showed that collisional stabilization of 3phenylpropene dominates at temperatures below 1000 K and, at high pressure, remains important up to 2500 K. The present results show that the phenyl + allyl  3-phenylpropene, benzyl + vinyl  3-phenylpropene, 3-phenylpropene  1-phenylallyl + H, 3-phenylpropene  benzyl + vinyl, and 3-phenylpropene  phenyl + allyl reactions are of importance in kinetic modeling of combustion flames; at 1500 K and 1 atm the calculated rate constants for these reactions are 8.410-11 and 4.710-11 cm3 molecule-1 s-1 for the bimolecular reactions and 1.1103, 8.9103, and 1.0104 s-1 for the unimolecular decomposition channels of 3-phenylpropene, respectively. It is worth noting that in the 30 Torr–100 atm range of pressures the dissociation of 3phenylpropene was calculated to have the maximum relative yield, 25%, of the 1-phenylallyl + H bimolecular product at the temperature of 700 K but the dissociation process is very slow at this temperature. In summary, while the well-skipping mechanism to form 1-phenylallyl directly in the allyl + phenyl and benzyl + vinyl reactions appeared to be not significant, the reactions can somewhat contribute to the formation of the indene precursor via the 3-phenylpropene stabilization/dissociation sequence and most of all, similar to the phenyl + propene reaction,36 via the formation of 3-phenylpropene, which then can undergo H-abstraction by available radicals to produce 1-phenylallyl. The alternative contribution of the allyl + phenyl reaction to the formation of two-ring PAH is the production of benzyl radical either by well-skipping or stabilization/dissociation mechanisms; in turn, benzyl can readily react with acetylene or propargyl radical to form indene or naphthalene precursors, respectively.6,37,38 ASSOCIATED CONTENT Supporting Information Rate constant parameterization using modified Arrhenius expressions (Table S1), Cartesian coordinates, vibrational frequencies, relative energies and hindered rotor potentials in the form of a MESS input file. The Supporting Information is available free of charge at the ACS Publication website. 11 ACS Paragon Plus Environment


AUTHOR INFORMATION Corresponding Author Email: [email protected] The authors declare no competing financial interest. ACKNOWLEDGEMENTS This work was supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Sciences of U.S. Department of Energy (Grant No. DE-FG02-04ER15570). We acknowledge the Instructional & Research Computing Center (IRCC, web: http://ircc.fiu.edu) at Florida International University for providing HPC computing resources that have contributed to the research results reported within this paper.


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FIGURE CAPTIONS Figure 1. Pivot points for a) phenyl + allyl, b) 1-phenylallyl + H, c) benzyl + vinyl, and d) styrenyl + methyl systems are shown in red color. Reactive flux minimizations were carried out with respect to the distances shown by the dashed line (for allyl the optimal pivot point distance was taken from Ref. 5). Figure 2. Potential energy diagram for the phenyl + allyl reaction calculated at the CCSD(T)F12/cc-pVTZ-f12//B3LYP/6-311G(d,p) + ZPE[B3LYP/6-311G(d,p)] level of theory. All relative energies are given in kcal/mol. Figure 3. Minimum energy path potentials for the barrierless association/dissociation of a) phenyl + allyl, b) 1-phenylallyl + H, c) benzyl + vinyl, and d) styrenyl + methyl computed for the rigid fragments, black circles, Erigid; with account of the correction for geometry relaxation, blue circles, Erigid + E[geom]; and both with the geometry and CBS corrections, red circles, Erigid + E[geom] + E[CBS]. Figure 4. Temperature dependence of the total rate constant for the phenyl + allyl reaction calculated at 30 Torr–100atm pressures; the total HP rate constants for the allyl + allyl and allyl + propagyl reactions from Ref. 5 are shown for comparison. Figure 5. T,P-dependent rate constants and the relative yields for the main channels of the phenyl + allyl reaction yielding: a) 3-phenylpropene, b) 1-phenylallyl + H, c) benzyl + vinyl. Color code: black – 30 Torr, blue – 1atm, red – 10 atm, green – 100atm pressure. Figure 6. T,P-dependent rate constants for the main channels of 3-phenylpropene decomposition/isomerization reactions yielding a) i2 , b) 1-phenylallyl + H, c) phenyl + allyl, d) benzyl + vinyl. Color code: black – 30 Torr, blue – 1atm, red – 10 atm, green – 100atm pressure. Figure 7. Temperature dependence of the relative yield of the 3-phenylpropene decomposition/isomerization products computed at 1 atm. Figure 8. T,P-dependent rate constants an the relative yields for the main channels of the vinyl addition to the CH2 group of benzyl yielding: a) 3-phenylpropene, b) 1-phenylallyl + H, c) phenyl + allyl. Color code: black – 30 Torr, blue – 1atm, red – 10 atm, green – 100atm pressure. 13 ACS Paragon Plus Environment


Figure 1


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Page 15 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2



Figure 3.

a)

0 -10

-20

-20

E, kcal/mol

-10

-30 -40

-40 -50

-60

-60

1.5 0

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5 1.5

RCC, angstrom

c)

0

-10

-10

-20

-20

-30 -40

-60

-60

2.5

3.0

3.5

4.0

4.5

5.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

4.5

5.0

5.5

RCH, angstrom

d)

-40 -50

2.0

2.0

-30

-50

1.5

b)

-30

-50

E, kcal/mol

E, kcal/mol

0

E, kcal/mol

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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5.5 1.5

2.0

2.5

RCC, angstrom

3.0

3.5

4.0

RCC, angstrom


Page 17 of 26

-1

Figure 4

1E-10 30 Torr, phenyl + allyl 1 atm, phenyl + allyl 10 atm, phenyl + allyl 100 atm, phenyl + allyl HP, phenyl + allyl HP, allyl + allyl HP, allyl + propagyl

3

-1

Rate Constants, cm molecule s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1E-11 0.5

1.0

1.5

1000/T, K

-1


2.0


Figure 5

100 90 80

-11

10

50 40 30 10 0

-12

10

0.5

1.0

1.5

2.0

b)

0.5

1.0

1.5

2.0

0.5

1.0

1.5

2.0

0.5

1.0

1.5

2.0

8

-12

10

-13

10

6

-14

Relative yield, %

10

-15

10

-16

10

-17

10

-18

10

-19

4

2

10

-20

10

0

-21

10

-1 -1

-10

10 10

0.5

1.0

1.5

2.0

c)

100

-11

90

-12

10

80

-13

10

Relative yield, %

-1 3

-1


60

20

-11

3

70

Relative yield, %

3

-1


-1

a) -10

10

10


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-14

10

-15

10

-16

10

-17

10

-18

10

70 60 50 40 30

-19

20

-20

10

10 10

0

-21

10

0.5

1.0

1.5

2.0

-1

1000/K, K

-1

1000/K, K


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Figure 6

7

10

a)

9

10

b)

7

10

Rate constants, s

-1

5

10

5

10

3

10

3

10

1

10

1

10

-1

10

-1

10

-3

10

-3

10

-5

-5

10

10

-7

-7

10

9

10

c)

0.5

10

1.0

9

10

7

10

5

10

3

10

1

10

-1

0.5

1.0

5

10

3

10

1

10

-1

10

-3

10

-5

10

-1

10

-3

10

-5

10

-7

10

d)

7

10

Rate constants, s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-7

0.5

10

1.0 -1

0.5

1.0 -1

1000/K, K

1000/K, K



Figure 7

100 i2, C9H10

90

phenyl + allyl 1-phenylallyl + H benzyl + vinyl

80

Relative yield, %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 26

70 60 50 40 30 20 10 0 0.5

1.0

1000/T, K


1.5 -1

2.0

Page 21 of 26

Figure 8

10

a)

100 90 80

-11

10

40 30 20 10 0

10

1.0

1.5

2.0

0.5

1.0

1.5

2.0

0.5

1.0

1.5

2.0

1.5

2.0

b)

-12

10

8

-13

10

-14

Relative yield, %

10

-15

10

-16

10

-17

10

-18

10

-19

10

6

4

2

-20

10

0

-21

10

-1 -1

-10

10 10

0.5

1.0

1.5

2.0

c)

100

-11

90

-12

10

80

-13

10

Relative yield, %

-1 -1 3

50

-12

-11


60

10

0.5

3

70

Relative yield, %

3

-1


-1

-10


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-14

10

-15

10

-16

10

-17

10

-18

10

70 60 50 40 30

-19

20

-20

10

10 10

0

-21

10

0.5

1.0

1.5

2.0

0.5

1.0

-1

1000/K, K

-1

1000/K, K



Scheme 1. The kinetic scheme of the phenyl + allyl reaction used in the RRKM/ME calculations.


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Theoretical Study of the Reaction Mechanism and Kinetics of the

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