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Reaction Mechanism of Naphthyl Radicals with Molecular Oxygen. 1. Theoretical Study of the Potential Energy Surface Chong-Wen Zhou,†,‡,§ Vadim V. Kislov,† and Alexander M. Mebel†,* †

Department of Chemistry and Biochemistry, Florida International University, 11200 SW 8th Street, Miami, Florida 33199, United States ‡ College of Chemical Engineering, Sichuan University, Chengdu 610065, People’s Republic of China S Supporting Information *

ABSTRACT: Potential energy surfaces (PESs) of the reactions of 1- and 2-naphthyl radicals with molecular oxygen have been investigated at the G3(MP2,CC)//B3LYP/6-311G** level of theory. Both reactions are shown to be initiated by barrierless addition of O2 to the respective radical sites of C10H7. The end-on O2 addition leading to 1- and 2-naphthylperoxy radicals exothermic by 45−46 kcal/mol is found to be more preferable thermodynamically than the side-on addition. At the subsequent reaction step, the chemically activated 1- and 2-C10H7OO adducts can eliminate an oxygen atom leading to the formation of 1- and 2-naphthoxy radical products, respectively, which in turn can undergo unimolecular decomposition producing indenyl radical + CO via the barriers of 57.8 and 48.3 kcal/mol and with total reaction endothermicities of 14.5 and 10.2 kcal/mol, respectively. Alternatively, the initial reaction adducts can feature an oxygen atom insertion into the attacked C6 ring leading to bicyclic intermediates a10 and a10′ (from 1-naphthyl + O2) or b10 and b10′ (from 2-naphthyl + O2) composed from two fused six-member C6 and seven-member C6O rings. Next, a10 and a10′ are predicted to decompose to C9H7 (indenyl) + CO2, 1,2-C10H6O2 (1,2-naphthoquinone) + H, and 1-C9H7O (1-benzopyranyl) + CO, whereas b10 and b10′ would dissociate to C9H7 (indenyl) + CO2, 2-C9H7O (2-benzopyranyl) + CO, and 1,2-C10H6O2 (1,2-naphthoquinone) + H. On the basis of this, the 1-naphthyl + O2 reaction is concluded to form the following products (with the overall reaction energies given in parentheses): 1-naphthoxy + O (−15.5 kcal/mol), indenyl + CO2 (−123.9 kcal/mol), 1-benzopyranyl + CO (−97.2 kcal/mol), and 1,2-naphthoquinone + H (−63.5 kcal/mol). The 2-naphthyl + O2 reaction is predicted to produce 2-naphthoxy + O (−10.9 kcal/mol), indenyl + CO2 (−123.7 kcal/mol), 2-benzopyranyl + CO (−90.7 kcal/mol), and 1,2-naphthoquinone + H (−63.2 kcal/mol). Simplified kinetic calculations using transition-state theory computed rate constants at the high-pressure limit indicate that the C10H7O + O product channels are favored at high temperatures, while the irreversible oxygen atom insertion first leading to the a10 and a10′ or b10 and b10′ intermediates and then to their various decomposition products is preferable at lower temperatures. Among the decomposition products, indenyl + CO2 are always most favorable at lower temperatures, but the others, 1,2-C10H6O2 (1,2-naphthoquinone) + H (from a10 and b10′), 1-C9H7O (1-benzopyranyl) + CO (from a10′), and 2C10H7O (2-benzopyranyl) + O (from b10 and minor from b10′), may notably contribute or even become major products at higher temperatures.

1. INTRODUCTION Polycyclic aromatic hydrocarbons (PAHs) play an important role in the formation of combustion generated particles such as soot, which leads to poor local and regional air quality and has adverse effects on human health.1,2 Therefore, it is very important to investigate and understand the reaction mechanisms for the formation and removal of PAHs. The formation and growth of PAH have been extensively studied by kinetic models,3−17 but their oxidation reactions have not received the same attention so far. Meanwhile, these two processes are expected to process simultaneously and to compete with each other, and the results of the competition will effectively determine the amount of soot produced in combustion. A quantitative understanding of the processes involved during the combustion and oxidation of PAHs is © 2012 American Chemical Society

necessary to control their emission and the influence on the air quality. Therefore, it is critical to know the mechanism, rate constants, and product yields under different combustion conditions, such as temperature and pressure, for the oxidation reaction of PAHs. In the present work, we focus on the naphthyl radicals (shown in Scheme 1), which have been shown to play a significant role in the formation of larger PAHs during the incipient soot formation stages.13 The oxidation mechanism of phenyl radical (C6H5), a simpler homologue of PAH radicals, has received much attention in recent decades.18−29 The most detailed PES for Received: December 11, 2011 Revised: January 11, 2012 Published: January 12, 2012 1571

dx.doi.org/10.1021/jp2119313 | J. Phys. Chem. A 2012, 116, 1571−1585

The Journal of Physical Chemistry A

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and master-equation (ME) analyses. The rate constants measured experimentally were fitted to the following rate expression, k/(cm3 mol−1 s−1) = (1.53 ± 0.10) × 1012 exp[(900 ± 45)/RT] , whereas the rate expression derived from the theoretical VTST/ME calculations was k(760TorrAr)/(cm3 mol−1 s−1) = 7.99 × 1021T−3.18 exp(−756/T) at T = 200− 800 K. A good agreement between the experimental and theoretical rate constants found by Lin and co-workers33 supported the hypothesis that the C10H7 + O2 reaction at low temperature proceeds by the association−stabilization process giving rise to the naphthylperoxy radical, C10H7 + O2 → C10H7OO, which might further lose the terminal oxygen atom producing a naphthoxy radical, C10H7O. However, neither experimental nor theoretical data are available beyond the initial association step and a better understanding of the reaction mechanism and kinetics is still required for reliable modeling of the naphthyl oxidation process. The goal of the present work is to provide chemically accurate ab initio PES for the most important C10H7 + O2 reaction channels and to reveal the detailed reaction mechanism.

Scheme 1

the reaction of C6H5 with O2 has been reported by Tokmakov et al.,24 who identified the most energetically favorable reaction channels as shown in Scheme 2. Scheme 2

2. COMPUTATIONAL METHODS The geometries of various reactants, transition states, intermediates, and products in the reactions of 1- and 2naphthyl radicals with molecular oxygen, 1-C10H7 + O2 and 2C10H7 + O2, were initially optimized at the hybrid density functional B3LYP/6-311G** level of theory.34 The same method was used to obtain vibrational frequencies, molecular structural parameters, and zero-point energy (ZPE) corrections. All the stationary points were identified for local minima (number of imaginary frequencies NIMAG = 0) and transition states (NIMAG = 1). The intrinsic reaction coordinate (IRC)35 calculations were carried out to validate all connections between transition states and local minima. Since the scaling of B3LYP frequencies does not significantly affect relative energies of isomers and transition states, unscaled vibrational frequencies were used to calculate ZPE corrections. Optimized Cartesian coordinates of all the species in the considered pathways are collected in Tables S1 and S2 of the Supporting Information for the 1-C10H7 + O2 and 2-C10H7 + O2 systems, respectively, along with vibrational frequencies, rotational constants, ZPE corrections, and B3LYP, CCSD(T), MP2, and G3 total energies at 0 K, and CCSD T1 diagnostics. We applied the G3(MP2,CC)//B3LYP version36 of the original Gaussian 3 (G3) scheme37 for high-level single-point energy calculations to obtain more accurate energies for all of the species. The final total energies at 0 K obtained by using the B3LYP optimized geometries were computed as follows:

The initial adduct phenylperoxy radical C6H5O2 (1) can either rearrange to bicyclic dioxiranyl 8 and eventually to a seven-member ring 2-oxepinyloxy radical 10 or lose the terminal oxygen atom to yield the phenoxy radical + O products. The phenoxy radical can undergo thermal decomposition to cyclopentadienyl radical C5H5 + CO, whereas the 2oxepinyloxy radical can dissociate to various products including C5H5 + CO2, pyranyl + CO, o-benzoquinone + H, and 2-oxo2,3-dihydrofuran-4-yl + C2H2. The different primary product channels are likely to compete with each other. The oxidation of the naphthyl radical, the first species in the homologous series of PAH radicals, has not been studied in detail so far. In a theoretical work, Kunioshi et al.23 investigated the direct O abstraction mechanism in the reactions of phenyl C6H5 and 1-naphthyl 1-C10H7 with O2 at the B3LYP/6-31G(d) level. The rate constants of these two channels evaluated utilizing transition-state theory agreed with each other; however, the calculated rate constant of the C6H5 + O2 reaction was 29 000 times lower than that measured experimentally by Tan and Frank30 at 2000 K, and 3500 times lower than that reported by Emdee et al.31 Clearly, the direct O abstraction mechanism cannot account for the observed reaction rate constants. In other works on the C10H7 + O2 reaction available in the literature, Marinov et al.32 estimated the rate constant of 1-C10H7 + O2 producing C10H7O + O in their kinetic modeling of a laminar premixed n-butane flame to be 1 × 1013 cm3 mol−1 s−1 and, most recently, Lin and co-workers reported an experimental kinetic study of thermal rate constants for 2-C10H7 + O2 in the temperature range of 299−444 K employing cavity ringdown spectroscopy.33 They also used the G2MS//B3LYP/6-31+G(d,p) theoretical method to map out the barrierless association potential in the entrance channel and utilized these data to predict the association rate constant by the canonical VTST theory with the steady-state

E0[G3(MP2,CC)] = E[CCSD(T)/6‐311G(d,p)] + ΔEMP2 + E(HLC) + E(ZPE)

where ΔEMP2 = E[MP2/G3large] − E[MP2/6-311G(d,p)] is the basis set correction and ZPE is the zero-point energy. The higher level correction E(HLC) was not actually included here because it is not expected to make significant contributions to relative energies. Thereafter, we denote this G3-type approach used in our computations as G3 for brevity. In the coupled cluster and MP2 calculations, the energies were computed from restricted RHF-RCCSD(T) and unrestricted UMP2 energies, respectively. RHF-RCCSD(T) here denotes partially spin1572



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Figure 1. Potential energy diagram for the initial channels of the 1-naphthyl radical + O2 reaction: formation of C10H7O2 adducts, their decomposition to 1-C10H7O + O, and oxygen atom insertion into the C6 ring. The numbers show relative energies in kilocalories per mole calculated at the G3 and B3LYP/6-311G** + ZPE (in brackets) levels of theory.

CO2 three-member ring (see Figure 1). The energy of a1 is 3.7 kcal/mol lower that that of a1′, and the two conformations can easily rearrange to each other by rotation around the C−O bond, with the corresponding transition state TSa1−a1′ located 1.2 kcal/mol above a1′ at the B3LYP level of theory. G3 calculations give the energy of TSa1−a1′ 2.1 kcal/mol lower than that of a1′, indicating that this intermediate is not likely to exist and would spontaneously rearrange to a1. The well depth at a1 is calculated to be 45.1 kcal/mol at the G3 level relative to the initial reactants, which is similar to the well depth of 46.3 kcal/ mol in the C6H5 + O2 → phenylperoxy radical process.24 The B3LYP/6-311G** calculation underestimates this value by 2.3 kcal/mol. No barrier was found in the C6H5 + O2 → phenylperoxy addition reaction.24 To investigate whether a barrier exists on the 1-C10H7 + O2 → a1 pathway, we computed the PES profile between the reactants and a1 using partial geometry optimization with the C−O distance frozen at different values from 5.0 to 1.4 Å, while all other geometric parameters were optimized. These calculations were carried out at the B3LYP/6-311G** level within Cs symmetry constrains where the symmetry plane contains all atoms in the molecule. Within the Cs symmetry point group, both the separated reactants and the intermediate a1 have the same 2A″ electronic state, so that the O2 addition to the 1-naphthyl radical is symmetry-allowed. As seen in Figure 2a, the energy smoothly decreases as the O2 molecule approaches 1-C10H7 until a1 is formed. This result confirms that no distinct transition state exists on the 1-C10H7 + O2 → a1 reaction pathway, at least at the B3LYP level of theory. We have recently tested the accuracy of the B3LYP entrance channel potential for the smaller C6H5

adapted open-shell coupled cluster singles and doubles theory augmented with a perturbation correction for triple excitations starting from molecular orbitals obtained from restricted open shell Hartree−Fock (ROHF) calculations. It should be noted that CCSD T1 diagnostics values for all calculated structures do not exceed 0.03 and in most cases are in the range of 0.01− 0.02, indicating a rather mild multireference character of the wave functions, which means that CCSD(T) energies should be generally reliable. All B3LYP and MP2 calculations were carried out using the GAUSSIAN 9838 program package, whereas for RHF-RCCSD(T) calculations we used the MOLPRO 200239 program package. Thermal rate constants at the high-pressure limit utilized in a simplified kinetic analysis were computed using transition-state theory within rigid rotor/harmonic oscillator approximations.

3. RESULTS AND DISCUSSION On the basis of the previous results on the C6H5 + O2 reaction channels,24 here we consider similar channels for both 1-C10H7 + O2 and 2-C10H7 + O2 reaction systems. The C10H7O2 intermediates investigated in the present work are numbered in the same way as their C6H5O2 analogues in our previous study;24 the letters “a” and “b” are used to designate isomers relevant to the reactions of 1- and 2-naphthyl, respectively. 3.1. PES of the 1-C10H7 + O2 Reaction System. Entrance Reaction Channel. The reaction starts with addition of the oxygen molecule to the radical site of 1-C10H7. Three different isomers of the 1-C10H7OO species can be produced, two planar conformations of the 1-naphthylperoxy radical with the 2A″ electronic state, a1 and a1′, as well as a8 containing a 1573



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of the reactants, and the difference between the DFT and the most accurate G3 values exceeds 10 kcal/mol. Compound a8 has the 2A″ electronic state within the Cs symmetry group, with the planes containing the napthyl unit and the three-member CO2 ring perpendicular to each other. Similar to the C6H5 + O2 reaction, the oxygen molecule may attach to 1-C10H7 forming the a8 intermediate without any barrier. If O2 approaches the naphthyl radical asymmetrically and out-of-plane, some trajectories may bypass the transition state separating intermediates a1 and a8, placed 24.4 kcal/mol below the separated 1-C10H7 + O2 reactants, and proceed directly to a8. This hypothesis is supported by the fact that our attempts to find an asymmetric transition state connecting the reactants with a8 did not result in any saddle-point structure but led to the 1-C10H7 + O2 dissociation. However, the possibility of the direct barrierless formation of a8 from the reactants remains hypothetical for now; ab initio molecular dynamics simulations are required to confirm that such trajectories from 1-C10H7 + O2 to a8 actually exist and to evaluate their contribution to the total reaction flux. Formation of 1-Naphthoxy Radical. After a1 is produced, it can undergo a cleavage of the O−O bond and decompose to the 1-naphthoxy radical (1-C10H7O, a3) and the ground-state oxygen atom, O(3P). The ground electronic state of 1-C10H7O is 2A″ within Cs symmetry. The transition state TSa1−a2 has a nonplanar geometry where the departing oxygen atom is located out of the 1-C10H7O plane, with the CCOO dihedral angle being 83.8°. The pathway for the departure of oxygen atom from the 1-naphthylperoxy radical to form 1-naphthoxy is peculiar. IRC calculations show that starting from a1 the terminal oxygen atom leaves the molecular plane at first to climb the energy barrier at TSa1−a2. After the barrier is cleared and the O−O distance continues to increase, the PES bifurcates into two descending paths leading to two distinct C6H5O···O van der Waals complexes a2 and a2′ (see Figure 1). On the path to a2, the leaving oxygen atom tends toward the second C6 ring (to the left, as shown in Figure 1), whereas on the path to a2′ the O atom tends away from the second C6 ring (to the right). Also, on the path to a2′ the O atom eventually returns to the molecular plane and, as a result, a2′ has Cs symmetry and 2 A′ electronic state. Overall, the a1 → a2′ rearrangement is forbidden within Cs symmetry, and therefore it occurs via the nonsymmetric TSa1−a2. Alternatively, on the path to a2, the oxygen atom does not return to the 1-C10H7O plane and stays out of this plane, with the CCOO dihedral angle becoming 70.7° in a2, only ∼13° smaller than that in TSa1−a2. The reason for a2 to have the leaving oxygen away from the molecular plane apparently is due to steric hindrance of the second C6 ring. Next, the O atom completely leaves the C10H7O fragment without an exit barrier leading to the decomposition of a2 or a2′ to the 1-naphthoxy radical (a3) + O. Overall, the 1-C10H7 + O2 → 1-C10H7O + O reaction is calculated to be 15.5 (11.8) kcal/mol exothermic; the 1-C10H7O···O complexes a2/a2′ reside 1.1 (2.7/3.6) kcal/mol lower in energy than the 1C10H7O + O products and are separated from the 1naphthylperoxy radical a1 by a small barrier of 0.4 (0.8/1.7) kcal/mol, as calculated at the G3 (B3LYP) levels of theory. Clearly, the addition−elimination pathway to form the 1naphthoxy radical, 1-C10H7 + O2 → a1 → a2/a2′ → 1-C10H7O + O, is much more favorable than the oxygen abstraction mechanism suggested by Kunioshi et al.,23 who found a high barrier of 38.2 kcal/mol for the direct 1-C10H7 + O2 → 1C10H7O + O reaction. It is worth noting again the similarity

Figure 2. Potential energy profiles (without ZPE) calculated at the B3LYP/6-311G** level of theory for the 1-C10H7 + O2 → a1 (a) and 2-C10H7 + O2 → b1 (b) entrance channels. Dissociation energies (De) of the a1 and b1 adducts back to the reactants are given in kilocalories per mole (without ZPE).

+ O2 system using the multireference complete active space self-consistent field (CASSCF) method to optimize geometries of various structures along the minimal energy reaction path (MEP) for the end-on O2 addition to the phenyl radical and the multireference perturbation theory CASPT2 method to refine their single-point energies. While the details of these CASPT2(19,14)//CASSCF(9,9)/aug-cc-pVDZ calculations will be described in a future publication, they have confirmed that the C6H5 + O2 → C6H5OO process is barrierless and showed that the MEP computed at the B3LYP level is similar to that obtained at CASPT2//CASSCF and thus qualitatively reliable. On the basis of the resemblance between the C10H7 + O2 and C6H5 + O2 reactions, we can expect that the B3LYP-calculated MEP for the former is also trustworthy. Another indication that the naphthyl + O2 reaction occurs without an entrance barrier comes from the combined experimental and theoretical study of thermal rate constants for 2-C10H7 + O2 by Lin and coworkers.33 First, the experimental measurements showed a slight negative temperature dependence of the rate constants at T = 299−444 K that is typical for barrierless reactions. Second, theoretical rate constants calculated utilizing the G2MS// B3LYP/6-31+G(d,p) MEP, which was also consistent with the B3LYP/6-31+G(d,p) potential, agreed reasonably well with the experiment. Thus, we can conclude that, similarly to the phenyl + O2 and 2-C10H7 + O2 reactions, the 1-C10H7 + O2 → a1 process is barrierless. Alternatively, the O2 addition can also lead to the formation of a8, in which two oxygen atoms and the attacked carbon form a three-member ring. This structure lies 38.3 kcal/mol lower in energy than the reactants at the G3 level. At the B3LYP/6311G** level, the energy of a8 is 27.8 kcal/mol lower than that 1574



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between the C6H5OO (phenylperoxy)24 and 1-C10H7OO (1naphthylperoxy) systems. On the dissociation pathway of C10H7OO to C10H7O + O, the transition state lies 28.9 kcal/ mol above the initial intermediate a1 (cf. 36.3 kcal/mol in C6H5OO) and, after the barrier is cleared, the 1-C10H7O···O complex a2 is stabilized by 0.4 and 1.1 kcal/mol relative to the transition state and 1-C10H7O + O, respectively (cf. 0.4 and 1.3 kcal/mol in C6H5OO). Oxygen Insertion into the Naphthalene Ring. Alternatively to losing the terminal O atom, the 1-naphthylperoxy radical a1 can undergo various rearrangements, which can eventually lead to different reaction products. At the initial stage, the transformation of a1 involves insertion of an oxygen atom into the aromatic ring. First, a1 can isomerize to a8 through a closure of the three-member COO ring, overcoming a barrier of 20.7 kcal/mol at TSa1−a8 (see Figure 1). The barrier height calculated for this process is 3.6 kcal/mol lower than the COO ring-closure barrier in the C6H5OO system, 24.3 kcal/mol at the G2M level of theory.24 Then, one of the oxygens inserts into the ring to produce intermediates a10 or a10′, in which the six-member ring linked with O2 expands to form a sevenmember ring containing six carbons and one oxygen atom, and the second O atom remains attached to the attacked carbon through a CO bond. The process is highly exothermic as the intermediates a10 and a10′ lie 98.7 and 100.5 kcal/mol below the initial reactants, respectively. After clearing the barrier at TSa8−a10, the system encounters bifurcation of the descending path (a valley-ridge inflection point on the PES) and then relaxes either to a10 where the inserted O oxygen atom is in the meta position with respect to the second C6 ring or to a10′ where the O atom is in the ortho position. If the O atoms were distinguishable (different isotopes), four distinct a10-/a10′-type isomers could be formed. The topography of the PES in the area between the C6H5O2 intermediates 8 and 10 has been described in detail in our previous work on the phenyl + O2 reaction,24 and a similar behavior is expected here for the naphthyl + O2 system in the region between a8 and a10/a10′. Noteworthy, the geometry of TSa8−a10 is very similar to that of the corresponding TS8−9 in the C6H5O2 system, with the CO and OO distances in the symmetric CO2 ring being 1.374 and 1.828 Å in the former vs 1.377 and 1.828 Å in the latter, respectively. Decomposition of 1-Naphthoxy Radical. Now, we consider the decomposition mechanism of the 1-naphthoxy radical a3 shown in Figure 3a. The first step involves the formation of a fused tricyclic intermediate a4 which lies 57.7 kcal/mol above a3 via the transition state TSa3−a4 with a barrier of 57.8 kcal/ mol. Thus, a4 is separated from a3 by a tiny reverse barrier of 0.1 kcal/mol. From a4, the reaction proceeds by breaking a C− C bond in the three-member ring with a barrier (at TSa4−a5) of 0.5 and 58.2 kcal/mol relative to a4 and a3, respectively, which leads to intermediate a5 lying 26.6 kcal/mol above a3. Subsequently, a5 loses carbon monoxide to produce the indenyl radical 7 + CO. The transition state on this pathway lies 31.9 kcal/mol above the naphthoxy radical a3, and the C9H7 + CO products reside 14.5 kcal/mol above a3. In summary, the reaction mechanism of the indenyl radical formation through decomposition of the 1-naphthoxy radical can be described as 1-C10H7O (a3) → TSa3−a4 → a4 → TSa4−a5 → a5 → TSa5−a7 → 7 + CO, and the highest in energy transition state is TSa4−a5, 58.2 kcal/mol above the initial reactant a3. The indenyl radical is predicted to be the major product of thermal decomposition of 1-naphthoxy radical, like

Figure 3. Potential energy diagram for dissociation channels of 1naphthoxy (a) and 2-naphthoxy (b) radicals to indenyl C9H7 + CO. The numbers show relative energies in kilocalories per mole calculated at the G3 and B3LYP/6-311G** + ZPE (in brackets) levels of theory.

cyclopentadienyl was earlier identified as the dominant product in the decomposition of phenoxy radical.40−45 The energetics of the two decomposition processes is also quite similar; the C6H5O → C5H5 + CO reaction was calculated to be endothermic by 18.1 kcal/mol and to have the highest barrier of 53.8 kcal/mol.24 Next, we consider the evolution of the a10 and a10′ intermediates following the oxygen insertion into the naphthalene ring. It should be noted that the barriers for reverse isomerization of a10 and a10′ back to a8 are very high, 73.6 and 75.2 kcal/mol, respectively, that is, significantly higher than the barriers on isomerization and dissociation pathways of these intermediates. Therefore, the formation of a10 and a10′ is most likely to be irreversible; once they are formed they proceed to isomerize or dissociate. Formation of 1,2-Naphthoquinone from a10. As shown in Figure 4a, intermediate a10 can isomerize to a20 via a two-step pathway involving an open-chain isomer a21. The isomerization from a10 to a21 can be described as the rotation of the C(H)Oring group containing the ring oxygen. Once this rotation occurs via TSa10−a21, the ring C−O bond is broken and openchain intermediate a21 is formed via a barrier of 33.3 kcal/mol. The open-chain isomer a21 resides 27.3 kcal/mol higher in energy than a10 and can further undergo a ring closure producing a new C6 aromatic ring and leaving both oxygen atoms in out-of-ring positions. This process occurs via TSa21−a20 and leads to formation of intermediate a20, in which the two out-of-ring oxygens are located in the ortho position with 1575



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Figure 4. Potential energy diagram for dissociation channels of the a10 (a) and a10′ (b) intermediates in the 1-C10H7 + O2 reaction. The numbers show relative energies with respect to a10 (a) and a10′ (b) in kilocalories per mole calculated at the G3 and B3LYP/6-311G** + ZPE (in brackets) levels of theory. The numbers in italics for a10, a10′, and the final products show relative energies with respect to the initial 1-C10H7 + O2 reactants calculated at the same G3 and B3LYP/6-311G** + ZPE (in brackets) levels.

respect to each other and a C(H)(O) group is positioned in a vertex of the newly formed six-member ring. The barrier for this process is as low as 1.5 kcal/mol, indicating that a21 could be only a metastable minimum on the path from a10 to a20. Isomer a20 lies 24.2 kcal/mol above a10. Once a20 is formed, the oxygen atom can continue its migration around the ring. However, the oxygen migration pathways were not competitive in the phenyl radical + O2 system, and hence we do not consider them here. Alternatively, a20 can split the hydrogen atom from the C(H)(O) fragment. The H loss can occur through three different channels; one of them is direct, and two are stepwise. The direct H loss occurs via a barrier of 16.3 kcal/ mol relative to a20, with the corresponding transition state TSa20−a14 residing 40.5 kcal/mol above a10. The energy of the final product, 1,2-C10H6O2 (1,2-naphthoquinone, a14) + H, is 35.2 kcal/mol higher than that of a10, but 63.5 kcal/mol lower than that of the initial reactants 1-C10H7 + O2. In another channel, the H atom first migrates over the neighboring C−C bond of the ring to create a CH2 group in intermediate a37 via the transition state TSa20−a37, which lies 40.4 kcal/mol above a10. Next, the H atom is eliminated from the CH2 group to form the 1,2-naphthoquinone product through transition state TSa37−a14, 35.9 kcal/mol higher in energy than a10. The intermediate a37 is rather stable and lies 1.3 and 100.0 kcal/ mol below a10 and the initial reactants, respectively. In the third channel, the H atom of C(H)(O) in a20 undergoes a 1,2(C,O)−H shift via a barrier of 19.0 kcal/mol relative to a20 (43.2 kcal/mol above a10) to form an even more stable structure a39, 15.7 kcal/mol lower in energy than a10. Then

the hydrogen atom can be eliminated from the OH group to form 1,2-naphthoquinone via TSa39−a14. The barrier for this H loss reaction is 57.0 and 41.3 kcal/mol relative to a39 and a10, respectively. Thus, the most energetically favorable pathways to 1,2-naphthoquinone are a10 → a21 → a20 → a14 + H and a10 → a21 → a20 → a37 → a14 + H. C9H7 (Indenyl) + CO2 Product Channel Starting from a10. As seen in Figure 4a, starting from the pivotal intermediate a10, the reaction can also proceed to the C9H7 (indenyl, 7) + CO2 products. First, the seven-member C6O ring in a10 can fuse into two rings, giving rise to a tricyclic isomer a11 consisting of a six-member C6, a five-member C5, and a four-member C3O ring. The barrier of this step is 34.2 kcal/mol with respect to a10, whereas the tricyclic intermediate a11 resides 17.4 kcal/ mol above a10. Two different reaction pathways can then lead from a11 to indenyl C9H7 + CO2. In the first mechanism, initially, the C−C bond in the four-member cycle breaks to form intermediate a13, which lies 15.2 kcal/mol above a10. The reaction proceeds via transition state TSa11−a13 located 29.2 kcal/mol higher in energy than a10. This is followed by the cleavage of the C−O bond connecting the CO2 group with the C9H7 moiety resulting in the final products, C9H7 + CO2. The barrier for this process is 17.9 and 33.1 kcal/mol relative to a13 and a10, respectively. Alternatively, the C9H7 + CO2 products can be formed from a11 through one concerted step via transition state TSa11−a7 residing 32.0 kcal/mol above a10, in which both the C−C and C−O bonds in the four-member ring attached to the C9H7 fragment are broken simultaneously. The 1576



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Figure 5. Potential energy diagram for the initial channels of the 2-naphthyl radical + O2 reaction: formation of C10H7O2 adducts, their decomposition to 2-C10H7O + O, and oxygen atom insertion into the C6 ring. The numbers show relative energies in kilocalories per mole calculated at the G3 and B3LYP/6-311G** + ZPE (in brackets) levels of theory.

C9H7O (a18) via a barrier of only 2.2 kcal/mol, and the 1benzopyranyl + CO products are 97.2 kcal/mol exothermic with respect to the 1-naphthyl + O2 reactants. Interestingly, while both a10 and a10′ can dissociate to indenyl + CO2, only a10 can decompose to 1,2-naphthoquinone + H and only a10′ can form 1-benzopyranyl + CO. This difference is attributed to the presence of the second C6 ring, the position of the oxygen atom with respect to this ring, and the character of the transition states for the seven-member ring opening initiating the 1,2-C10H6O2 (a14) + H and 1-C9H7O (a18) + CO product channels. For instance, the a10 → a21 rearrangement takes place by rotation of the HCOring group but, in a10′, the COring group is linked directly to the second carbon ring in place of the H atom, making the rotation impossible. Similarly, the a10′ → a23′ isomerization occurs by rotation of the (H)CCOout group but a10 has the second carbon ring in place of the corresponding hydrogen atom preventing the rotation process from happening. 3.2. PES of the 2-C10H7 + O2 Reaction System. Entrance Reaction Channel. The 2-naphthyl + O2 reaction starts with addition of the oxygen molecule to the radical site of 2-C10H7. This can lead to three different isomers of the 2C10H7OO species, two conformations of 2-naphthylperoxy radical, b1 and b1′, and a tricyclic b8 adduct with a CO2 ring (see Figure 5). Energies of the two different 2-naphthylperoxy conformers b1 and b1′ are close, and they can isomerize to one another by rotation around the CO bond via a low barrier of 2.5−2.6 kcal/mol. Both b1 and b1′ have the 2A″ electronic state within Cs symmetry, with b1 being slightly more stable than b1′. The well depth at b1 is calculated to be 45.8 kcal/mol at the G3

C9H7 + CO2 products lie 25.2 and 123.9 kcal/mol below a10 and the initial reactants 1-C10H7 + O2, respectively. C9H7 (Indenyl) + CO2 Product Channel Starting from a10′. The indenyl + CO2 products can be also formed from a10′ (see Figure 4b). At the first step, a10′ rearranges to a11′ via a barrier of 34.7 kcal/mol, which is similar to that for the a10 → a11 isomerization described above. The tricyclic intermediate a11′ lying 17.3 kcal/mol above a10′ is 1.9 kcal/mol more stable than its a11 analogue. Next, a11′ decomposes to C9H7 + CO2 via a two-step mechanism, in which the C−O bond in the fourmember ring of a11′ is cleaved first via a barrier of only 3.7 kcal/mol to form a metastable intermediate a12′, which is separated from the final products by a barrier of only 0.2 kcal/ mol. The channel in which the C−C bond in the four-member ring of a11′ breaks first could not be identified because an intermediate analogous to a13 could not be found as a local minimum. Formation of 1-Benzopyranyl Radical, 1-C9H7O, from a10′. The seven-member ring in a10′ can be subjected to a ring opening to a23′. This process involves rotation of the (H)CCOout group containing the out-of-ring oxygen around the adjacent C−C bond and occurs via TSa10′−a23′ with a barrier of 33.0 kcal/mol. Next, a23′ can undergo a ring closure resulting in a six-member ring in the a17′ intermediate with an oxygen atom incorporated in the ring and an out-of-ring CO group. The ring-closure barrier is 18.7 kcal/mol relative to a23′, and this step is rate controlling for this channel because the corresponding TSa23′−a17′ residing 43.9 kcal/mol above a10′ has the highest energy along this pathway. Compound a17′ can easily lose the out-of-ring CO group and decompose to 11577



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the 2-naphthoxy radical (b3) + oxygen atom. While comparing the C6H5OO (phenylperoxy)24 and 2-C10H7OO (2-naphthylperoxy) systems, note that on the dissociation pathway of C6H5OO to C6H5O + O(3P), the transition state lies 36.3 kcal/ mol above the initial intermediate and, after the barrier is cleared, the produced C6H5O···O van der Waals complex is stabilized by 0.4 and 1.3 kcal/mol with respect to the transition state and C6H5O + O(3P), respectively. A quantitative difference between the two systems is found in the relative energies of the O−O bond scission transition states with respect to products; the transition state for the phenylperoxy case is 0.9 kcal/mol lower in energy than C6H5O + O(3P), and for 2-naphthylperoxy the corresponding transition state is 2.5 kcal/mol lower than 2-C10H7O + O(3P). Moreover, the C6H5O···O complex is less strongly bound (by 1.3 kcal/mol) than 2-C10H7O···O (by 5.0 kcal/mol), which is close to the binding energy of the C2H3O···O complex (4.0 kcal/mol) in the C2H3 + O2 reaction system.46 In terms of the energetics of the O elimination pathway, the 1-naphthylperoxy radical considered in section 3.1 is more similar to C6H5OO than 2naphthylperoxy. Oxygen Insertion into the Aromatic Ring. Instead of losing the terminal O atom, the 2-naphthylperoxy radical b1 (b1′) can undergo various rearrangements, which can eventually lead to different reaction products. The reaction mechanism starts from insertion of an oxygen atom into the aromatic ring. First, b1 can isomerize to b8 through a closure of the three-member COO ring, overcoming a barrier of 23.4 kcal/mol at TSb1−b8 (see Figure 5). The barrier height calculated for this process is similar to the COO ring-closure barrier in the C6H5OO system, 24.3 kcal/mol at the G2M level of theory.24 Next, one of the oxygen atoms can insert into the ring in two distinct positions to form two different intermediates b10 and b10′ via the same transition state TSb8−b10 because the reaction path bifurcates after the barrier is cleared. This process is similar to the 8 → 10 isomerization in the C6H5OO system described in detail in the previous work24 and to the a8 → a10/a10′ rearrangement in the 1-C10H7 + O2 reaction (section 3.1) and involves valleyridge inflection points on the downhill path after the transition state. Compounds b10 and b10′ contain a seven-member C6O ring with the oxygen atom located in the para and meta positions relative to the second C6 ring, respectively (Figure 5), whereas the second oxygen atom remains outside the ring and is bound to the attacked carbon atom. Compound b10 is calculated to be 2.9 kcal/mol more stable than b10′. Decomposition of 2-Naphthoxy Radical. The decomposition mechanism of the 2-naphthoxy radical b3 shown in Figure 3b is somewhat similar to that for 1-naphthoxy, but the energetics differs notably. The first step involves a formation of a fused tricyclic intermediate b4 which lies 40.6 kcal/mol above b3 through the transition state TSb3−b4 with energy barrier of 44.7 kcal/mol. This is followed by breaking two different C−C bonds in the three-member ring of b4 to form two distinct intermediates b5 and b5′ residing 22.3 and 43.1 kcal/mol higher in energy than b3, via two different transition states TSb4−b5 and TSb4−b5′, which lie 48.3 and 60.4 kcal/mol above b3, respectively. The difference in energies between b5 and b5′ is attributed to the fact that b5 is resonantly stabilized but b5′ is not. Subsequently, b5 and b5′ can lose carbon monoxide to produce the indenyl radical 7 via transition states TSb5−7 and TSb5′−7 lying 27.6 and 47.6 kcal/mol higher in energy than b3, respectively, and the formed C9H7 + CO products are 10.2 kcal/mol endothermic with respect to the 2-naphthoxy radical.

level relative to the initial reactants, whereas the B3LYP/6311G** calculation underestimates this value by 2.3 kcal/mol. Similar to the reaction of 1-C10H7 with O2, no barrier was found for the O2 addition to 2-C10H7 to produce the 2naphthylperoxy radical. This conclusion was supported by the calculated minimal energy path between the reactants and b1 obtained using partial geometry optimizations, where the length of the forming C−O bonds was kept fixed at various values from 5.0 to 1.4 Å, while all other geometric parameters were optimized. As seen from the potential energy curve plotted against the length of the forming C−O bond in Figure 2b, the energy monotonically and smoothly decreases as the O2 molecule approaches 2-C10H7 until b1 is produced. This result confirms that no distinct transition state exists on the 2-C10H7 + O2 → b1 reaction pathway, and we can conclude that this reaction is barrierless, which is also in agreement with the results of G2MS//B3LYP/6-31+G(d,p) calculations by Lin and co-workers and with the observed negative temperature dependence of the reaction rate constants measured in the 299−444 K range.33 The O2 addition can also lead to the formation of intermediate b8, in which the attacked carbon and two oxygen atoms form a three-member ring. Compound b8 lies 33.0 kcal/mol lower in energy than the 2-C10H7 + O2 reactants at the G3 level, whereas at B3LYP/6-311G** the relative energy of b8 is calculated to be −23.5 kcal/mol relative to 2-C10H7 + O2, and thus the B3LYP and the most accurate G3 values are almost 10 kcal/mol apart. Compound b8 has a Cs-symmetric structure with the 2A″ electronic state, in which the plane containing two six-member rings and the threemember ring plane are perpendicular to each other. No barrier is predicted to exist on the 2-C10H7 + O2 → b8 pathway. As for 1-C10H7 + O2 → a8, this result is still hypothetical and can be confirmed in the future by ab initio MD simulations of reaction trajectories in the entrance channel. Formation of 2-Naphthoxy Radical. After the 2-naphthylperoxy radical b1 is produced, it can undergo a cleavage of the O−O bond and decompose to the 2-naphthoxy radical plus oxygen atom, 2-C10H7O + O(3P). The ground electronic state of Cs-symmetric 2-C10H7O is 2A″. The transition state for the oxygen atom elimination, TSb1−b2, has a nonplanar geometry where the departing oxygen atom is located out of the 2C10H7O plane, with the dihedral CCOO angle of 78.8°. The pathway for the departure of the oxygen atom from the 2naphthylperoxy radical to form 2-naphthoxy is similar to that for the 1-naphthylperoxy → 1-naphthoxy + O reaction. IRC calculations show that the terminal oxygen atom leaves the molecular plane to climb a 32.4 kcal/mol barrier from b1 to TSb1−b2, which lies 13.4 (8.1) kcal/mol below the initial reactants at the G3 (B3LYP) levels of theory. After the barrier is cleared, the O−O distance continues to increase, and the O atom eventually returns to the 2-C10H7O plane to form van der Waals complexes b2 or b2′ (see Figure 5), both of which have Cs symmetry and the 2A′ electronic state. Similar to the path from a1 to a2/a2′ via TSa1−a2, after clearing the barrier at TSb1−b2 the PES bifurcates into two descending paths leading to b2 and b2′, in which the departing oxygen forms hydrogen bonds with α- and β-H atoms, respectively (see Figure 5). The complex b2 resides 15.9 kcal/mol lower in energy than the initial 2-C10H7 + O2 reactants and is stabilized by 2.5 and 5.0 kcal/mol relative to the TSb1−b2 transition state separating it from b1 and the 2-C10H7O + O(3P) products, respectively. The complex b2′ is practically isoergic to b2. A further increase of the O−O distance leads to the decomposition of b2 or b2′ to 1578



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Figure 6. Potential energy diagram for dissociation channels of the b10 intermediate in the 2-C10H7 + O2 reaction. The numbers show relative energies with respect to b10 in kilocalories per mole calculated at the G3 and B3LYP/6-311G** + ZPE (in brackets) levels of theory. The numbers in italics for b10 and the final products show relative energies with respect to the initial 2-C10H7 + O2 reactants calculated at the same G3 and B3LYP/6-311G** + ZPE (in brackets) levels.

the (H)CCO fragment rotates, breaking the symmetry, and its C1 atom is drawn closer to the Oring atom with the C−O distance of 1.90 Å. The C−O bond is completely formed after clearing the TSb23−b17 transition state, which leads to the intermediate b17 with a six-member ring incorporating an oxygen atom and the COout group connected to the ring. The barrier of this process is 22.0 kcal/mol relative to b23, and the transition state lies 39.3 kcal/mol higher in energy than the intermediate b10. Once formed, b17 can then easily decompose to 2-benzopyranyl radical (2-C9H7O, b18) + CO by cleaving the out-of-ring C−C bond via TSb17−b18, which lies 19.3 kcal/mol above b10. The breaking C−C bond in the transition state is 0.31 Å longer than that in b17, and the barrier is only 3.1 kcal/mol relative to b17. The final products, 2C9H7O + CO, lie 90.7 kcal/mol below the 2-C10H7 + O2 reactants. Formation of 2,3-Naphthoquinone Product from b10. The seven-member ring in b10 can also undergo a ring opening to b21 via the isomerization process involving the rotation of the HCOring fragment around the adjacent C−C bonds. Once this rotation takes place via a barrier of 26.0 kcal/mol at TSb10−b21, one of the C−O bonds in the ring breaks and an open-chain intermediate b21 forms, which resides 18.3 kcal/ mol above b10. The b21 intermediate can undergo two sequential rotations around C−C bonds in its side chains leading to b23 via intermediate b22. Both b22 and b23 represent different conformers of b21, and the rotational barriers for b21 → b22 and b22 → b23 are 2.1 and 7.4 kcal/ mol, respectively. Compound b23 can then decompose to 2benzopyranyl + CO as described in the previous paragraph. In an alternative but rather unfavorable channel, the b21 intermediate can feature a six-member ring closure via TSb21−b20 to form the intermediate b20 in which both oxygen atoms are located in out-of-ring positions. On the path to the transition state, the HCOring fragment rotates again and its C atom linked to the O atom is drawn closer to the C atom attached to the other O atom in the second side chain, with the

Comparing different channels shown in Figure 3b, we can see that the pathway from b4 to the indenyl radical + CO products via b5 is much more favorable energetically than that via b5′. The highest in energy transition state on the path to indenyl radical from 2-naphthoxy lies 48.3 kcal/mol above 2-C10H7O, which is ∼10 kcal/mol lower than the critical transition state for the decomposition of 1-naphthoxy to C9H7 + CO. We can conclude that the loss of the carbonyl group is more favorable from 2-naphthoxy radical than from 1-naphthoxy and phenoxy radicals; for phenoxy the highest in energy transition state on the path of the C6H5O → C5H5 + CO reaction resides 53.8 kcal/mol above the reactant.24 Next, we separately consider isomerization and dissociation processes of b10 and b10′. Similarly to the a10 and a10′ intermediates in the 1-C10H7 + O2 reaction, the formation of b10 and b10′ from b8 is most likely to be irreversible due to the high barriers of 76.4/73.5 kcal/mol for the reverse b10/b10′ → b8 isomerization. Formation of the 2-C9H7O (2-Benzopyranyl) + CO Products from b10. As seen in Figure 6, the seven-member ring in b10 can undergo a ring opening to b23 followed by a ring closure, eventually forming a six-member ring in the b17 intermediate with an oxygen atom incorporated in the ring and an out-of-ring CO group. Compound b17 is a precursor of the 2-C9H7O (2-benzopyranyl, b18) + CO products. The process from b10 to b23 can be described in terms of rotation of the (H)CCOout group containing the out-of-ring oxygen around the adjacent C−C bond. This rotation takes place via TSb10−b23, and once it is completed, the C−O bond in the ring is broken and an open-chain intermediate b23 is produced. The barrier for this process is calculated to be 21.2 kcal/mol relative to b10. Isomer b23 lies 16.7 kcal/mol above b10, has a planar structure with the 2A″ electronic state, and is stabilized by an intramolecular hydrogen bond, H···O, between two side chains formed after the ring opening, with the H−O distance of 1.81 Å. Next, b23 can undergo a six-member ring closure via TSb23−b17 to form the intermediate b17. At the transition state, 1579



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Figure 7. Potential energy diagram for dissociation channels of the b10′ intermediate in the 2-C10H7 + O2 reaction. The numbers show relative energies with respect to b10′ in kilocalories per mole calculated at the G3 and B3LYP/6-311G** + ZPE (in brackets) levels of theory. The numbers in italics for b10′ and the final products show relative energies with respect to the initial 2-C10H7 + O2 reactants calculated at the same G3 and B3LYP/6-311G** + ZPE (in brackets) levels.

C9H7 (Indenyl) + CO2 Product Channel Starting from b10. The pivotal intermediate b10 can also decompose to the C9H7 (indenyl) + CO2 products. At the first step of this product channel, the seven-member C6O ring in b10 can fuse into two rings producing a tricyclic intermediate b11 containing a sixmember C6, a five-member C5, and a four-member C3O ring, via a barrier of 29.3 kcal/mol relative to b10. The b10 → b11 isomerization is followed by two distinct two-step processes leading to the C9H7 (indenyl) + CO2 products. In the first channel, the intermediate b11 is subjected to the C−O bond cleavage in the four-member ring leading to b12 in which the CO2 group is linked to the five-member cycle via a C−C bond. The barrier for this process is 15.2 kcal/mol, with the corresponding transition state TSb11−b12 lying 13.1 kcal/mol higher in energy than b10. Next, the out-of-ring C−C bond can be broken leading to the indenyl + CO2 products via TSb12−7, residing 13.0 kcal/mol above b10. The intermediate b12 is thus metastable as it is separated from b11 and the products by tiny barriers of 0.3 and 0.2 kcal/mol, respectively. In the second channel, the C−C bond in the four-member ring of b11 breaks first to form intermediate b13 through the transition state of TSb11−b13, which lies 38.4 kcal/mol above b10. Then, the outof-ring CO2 group can be eliminated by the cleavage of the C− O bond connecting the CO2 group with the C9H7 moiety, thus leading to C9H7 + CO2. The barrier for the last reaction step is 14.0 kcal/mol with the transition state TSb13−7 lying 49.6 kcal/ mol higher in energy then the intermediate b10. The resulting C9H7 + CO2 products are 123.7 kcal/mol exothermic with respect to initial reactants 2-C10H7 + O2. Clearly, the pathway from b11 to the C9H7 + CO2 products via b12 is preferable over that via b13. Pathways to the C4H3O2 (2-Oxo-2,3-dihydrofuran-4-yl) + C 6H 4 (o-Benzyne) Products Starting from b12. The intermediate b12 can also isomerize to another tricyclic structure b32 through the formation of a new O−C bond

C−C distance for the forming bond being 1.78 Å in TSb21−b20. After the barrier of 29.0 kcal/mol is cleared, the aromatic radical intermediate b20 is produced. The transition state for this process and the b20 intermediate lie 47.3 and 44.7 kcal/ mol above b10, respectively. Next, the 2,3-naphthoquinone (b14) product can be formed through two different stepwise mechanisms. First, the H atom of the C(H)(O) group can migrate to form a CH2 group in intermediate b37 via transition state TSb20−b37. The corresponding energy barrier is 10.9 kcal/ mol, and the transition state lies 55.6 kcal/mol higher in energy than b10. Then the 2,3-naphthoquinone product b14 can be formed from b37 by an H loss from the CH2 group via a barrier of 62.1 kcal/mol. The transition state for this process, TSb37−b14, resides 55.2 kcal/mol above b10, whereas the product b14 lies 54.7 kcal/mol higher in energy than b10, but 41.7 kcal/mol lower in energy than the initial reactants 2-C10H7 + O2. An alternative mechanism to produce b14 proceeds from b20 via intermediate b39. The H atom in the C(H)(O) group can migrate to the adjacent O atom through the transition state TSb20−b39, which lies 61.2 kcal/mol above b10. After overcoming the corresponding energy barrier of 16.5 kcal/mol, intermediate b39 is produced which lies 19.3 kcal/mol below b10. Then the H atom of the OH group can be eliminated through TSb39−b14, which lies 56.9 kcal/mol above b10, producing 2,3-naphthoquinone + H via a barrier of 76.2 kcal/ mol. No direct H loss pathway was found from b20 to b14. Apparently, the path involving the H shift to b37 followed by H elimination is more preferable here, similar to the C6H5O2 system (20 → 37 → 14 in our previous work24). While comparing two different product channels starting from b21, one can see that the b21 → b20 → b37 → b14 + H path is less likely than b21 → b22 → b23 → b17 → b18 + CO because the critical transition state for the former is 16.3 kcal/mol higher than that for the latter. 1580



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with the transition state TSb11′−7 lying 24.4 kcal/mol higher in energy than b10′. The concerted mechanism of the production of indenyl + CO2 from b11′ is likely to be more favorable, because its transition state is 3.8 kcal/mol lower in energy than the critical transition state TSb13′−7 on the two-step b11′ → b13′ → C9H7 + CO2 pathway. Formation of the 2-C9H7O (2-Benzopyranyl) + CO Products from b10′. The seven-member ring in the structure b10′ can first ring-open to b23′ and then ring-close to b17′, which contains a six-member ring with one oxygen atom within the ring and an out-of-ring CO group. Compound b17′ is yet another precursor of the 2-C9H7O (2-benzopyranyl) + CO products. The isomerization process from b10′ to b23′ can be described as a rotation of the (H)CCOout group containing the out-of-ring oxygen atom. Once the rotation takes place via TSb10′−b23′, the C−O bond in the ring breaks with the formation of an open-chain intermediate b23′ via a barrier of 20.8 kcal/ mol. b23′, which lies 11.3 kcal/mol above b10′ and next undergoes a six-member ring closure to form the intermediate b17′. On the path to the transition state TSb23′−b17′, the (H)CCOout fragment rotates and its C atom linked to the CO group is drawn closer to the second O atom, the C−O distance being 1.80 Å in TSb23′−b17′. The barrier for the ring closure is 37.6 kcal/mol relative to b23′, and the transition state resides 48.9 kcal/mol higher in energy than b10′. Noteworthy, the intermediate b17′ is ∼20 kcal/mol less stable than its analogues a17′ and b17. This is attributed to the fact that in a17′ and b17 the second C6 ring is aromatic (as confirmed by all nearly equal C−C bond lengths of 1.39−1.41 Å), but in b17′ it is not (the C−C bond lengths alternate). Compound b17′ easily decomposes to 2-C9H7O (b18) + CO through TSb17′−b18 by cleaving the out-of-ring C−C bond. The transition state exhibits an early character as the breaking C−C bond is elongated by only 0.19 Å as compared to that in b17′, and the barrier is as low as 2.9 kcal/mol relative to b17′, with the 2C9H7O + CO products lying 90.7 kcal/mol below the 2-C10H7 + O2 reactants. The rate-determining step for the production of 2-C9H7O + CO from b10′ appears to be the ring closure b23′ → b17′. The high energy of b17′ causes this barrier to be significantly higher than the respective barriers leading to a17′ and b17 from a23′ and b23, respectively, making the pathway from b10′ to 2-C9H7O + CO much less favorable. Formation of 1,2-Naphthoquinone Product from b10′. The seven-member ring in b10′ can also undergo another ringopening rearrangement followed by a ring closure eventually leading to an intermediate b20′ in which both oxygen atoms are located in out-of-ring positions. The isomerization process from b10′ to b21′ can be described in terms of the rotation of the C(H)Oring fragment around the adjacent C−C bond. Once this rotation takes place via TSb10′−b21′, the C−O bond in the ring is broken and an open-chain intermediate b21′ is formed via a barrier of 20.0 kcal/mol. The intermediate b21′ formed in this process lies 14.3 kcal/mol above b10′. Next, b21′ can undergo a six-member ring closure via TSb21′−b20′ to form b20′. While approaching the transition state, the HCO fragment rotates and two C atoms attached to oxygens are drawn closer to one another, with the C−C distance being 2.05 Å in TSb21′−b20′. After the barrier of 8.3 kcal/mol is cleared, the aromatic radical intermediate b20′ is produced. The transition state TSb21′−b20′ and b20′ lie 22.6 and 19.8 kcal/mol below the intermediate b10′. Then, 1,2-naphthoquinone b14′ (the same as a14) can be formed through three different direct or two-step channels. The direct H loss from b20′ occurs via a barrier of 14.3 kcal/mol

between one of the oxygens in the CO2 group and the carbon atom in the five-member ring located in the meta position with respect to CO2. The O−C bond is formed via the transition state of TSb12−b32 which lies 22.2 kcal/mol above b10, with the barrier for this process being 9.4 kcal/mol relative to b12. On the contrary to b11, the two newly formed five-member rings in b32 (which are evolved from the seven-member ring in b10) are C5 and C4O having two common C−C bonds. At the subsequent reaction steps, two C−C bonds connecting the C6 and C4O rings in b32 can break sequentially via two different intermediates b30 and b30′, with b30 having a structure of a C4O five-member cycle with one out-of-ring oxygen atom and a C6H4 ring both in ortho positions with respect to the ring oxygen. The transition state TSb32−b30 corresponding to the b32 → b30 rearrangement resides 41.3 kcal/mol above b10, and the barrier for this C5-ring-opening process in b32 is 29.2 kcal/mol. The next reaction step is a cleavage of the exocyclic C−C bond with a barrier of 52.1 kcal/mol at TSb30−b31, which leads to the cyclic C4OH3O (2-oxo-2,3-dihydrofuran-4-yl, b31) + C6H4 (o-benzyne) products. These products lie 20.9 kcal/ mol below the initial 2-C10H7 + O2 reactants. The b30′ intermediate has a structure of a C4O five-member cycle with one oxygen atom in the ring and the C6H4 ring both in ortho positions with respect to the out-of-ring O atom. The transition state corresponding to the b32 → b30′ rearrangement, TSb32−b30′, resides 45.5 kcal/mol higher in energy than b10, and the barrier for this C5-ring-opening step is 33.4 kcal/mol. The intermediate b30′ can then undergo the exocyclic C−C bond cleavage via a barrier of 48.9 kcal/mol at TSb30′−b31, leading to the same C4OH3O + C6H4 products. The highest in energy transition states on the b10 → b11 → b12 → b32 → b30 (b30′) → C4OH3O + C6H4 pathway are TSb30−b31 and TSb30′−b31 at the final reaction step, which respectively lie 75.6 and 76.0 kcal/mol higher in energy than b10. However, the b12 intermediate is only metastable with respect to its dissociation to the C9H7 + CO2 products; hence, the 2-oxo2,3-dihydrofuran-4-yl + o-benzyne channel is much less preferable both thermodynamically and kinetically, and these products are unlikely to be formed. Therefore, we do not consider similar reaction channels leading to C4OH3O + C6H4 from the analogues of the b10 intermediate, such as a10, a10′, and b10′. C9H7 (Indenyl) + CO2 Product Channel Starting from b10′. Evolution of the b10′ intermediate can lead to the formation of the C9H7 (indenyl) + CO2 products (see Figure 7). Along this channel, the seven-member C6O ring in b10′ can first fuse into a five-member C5 and a four-member C3O rings with a common C−C bond in a tricyclic structure b11′. The barrier for this process located at TSb10′−b11′ is 25.6 kcal/mol with respect to b10′. Then, two different reaction pathways can produce the C9H7 + CO2 products from b11′. In the first mechanism, initially the C−C bond in the four-member ring breaks to form intermediate b13′, which is equivalent to a13. The transition state for this process, TSb11′−b13′, lies 18.1 kcal/ mol above intermediate b10′. This is followed by the cleavage of the C−O bond connecting the CO2 group with the C5 ring of the C9H7 fragment, resulting in the final C9H7 + CO2 products via a barrier of 17.9 kcal/mol with the transition state TSb13′−7 (same as TSa13−7) lying 28.2 kcal/mol above b10′. The second channel leads to the C9H7 + CO2 products directly from b11′, in one concerted step, in which both C−C and C−O bonds linking the CO2 group to the C9H7 moiety are broken simultaneously. The barrier for this process is 28.9 kcal/mol 1581



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Table 1. Thermal Rate Constants (s−1) and Product Branching Ratios Calculated at the Higher Pressure Limit (a) 1-C10H7 + O2 Reaction rate constants T, K

a1 → a2/a2′

500 700 1000 1200 1500 1700 2000 2500

7.51 4.32 2.97 3.83 4.96 1.65 6.48 3.04

× × × × × × ×

branching ratios, % a1 → a10/a10′

1-C10H7O + O

a10/a10′

× × × × × × × ×

0.2 2.0 11.5 21.3 36.1 44.3 54.1 64.7

99.8 98.1 88.5 78.7 63.9 55.7 45.9 35.3

4.57 2.17 2.28 1.41 8.78 2.08 5.49 1.66

104 107 108 109 1010 1010 1011

103 106 108 109 109 1010 1010 1011

rate constants a10 → C9H7 + CO2

T, K 500 700 1000 1200 1500 1700 2000 2500

1.24 2.64 4.88 9.14 1.73 6.98 3.32 1.96

branching ratios, %

a10 → 1,2-C10H6O2 + H

−3

× × × × × × × ×

4.07 5.66 4.36 1.44 4.91 2.61 1.71 1.45

10 101 104 105 107 107 108 109

× × × × × × × ×

C9H7 + CO2

1,2-C10H6O2 + H

98.6 88.0 55.3 37.3 22.0 16.4 11.4 7.4

1.4 12.0 44.7 62.7 78.0 83.6 88.6 92.6

−6

10 10−1 103 105 106 107 108 109

rate constants a10′ → C9H7 + CO2

T, K 500 700 1000 1200 1500 1700 2000 2500

1.87 4.51 9.04 1.76 3.45 1.40 6.77 4.09

× 10−4 × × × × × ×

103 105 106 107 107 108

branching ratios, % a10′ → 1-C9H7O + CO

C9H7 + CO2

1-C9H7O + CO

2.22 × 10−7 9.58 × 10−2 1.68 × 103 7.56 × 104 3.44 × 106 2.07 × 107 1.56 × 108 1.56 × 109 (b) 2-C10H7 + O2 Reaction.

99.9 97.9 84.3 69.9 50.0 40.3 30.3 20.8

0.1 2.1 15.7 30.1 50.0 59.7 69.8 79.2

rate constants

T, K 500 700 1000 1200 1500 1700 2000 2500 T, K 500 700 1000 1200 1500

T, K

b1 → b2/b2′

500 700 1000 1200 1500 1700 2000 2500

6.54 1.07 1.60 2.76 4.85 1.88 8.59 4.86

b10 → C9H7 + CO2 4.53 2.35 1.49 1.86 2.32 7.66 2.92 1.34

× × × × × × × ×

−1

10 103 106 107 108 108 109 1010

b10′ → C9H7 + CO2 1.88 3.25 8.88 7.92 7.14

× × × × ×

101 104 106 107 108

× × × × × × × ×

10−1 104 107 108 109 1010 1010 1011 rate constants

b10 → 2-C9H7O + CO −4

1.69 × 10 2.03 × 101 1.37 × 105 4.26 × 106 1.33 × 108 6.78 × 108 4.19 × 109 3.36 × 1010 rate constants b10′ → 2-C9H7O + CO 9.28 1.70 8.80 6.04 4.18

× × × × ×

10−9 10−2 102 104 106

branching ratios, % b1 → b10/b10′

2-C10H7O + O

b10/b10′

× × × × × × × ×

2.2 14.8 45.0 59.8 73.2 78.5 83.4 87.9

97.8 85.2 55.0 40.2 26.8 21.5 16.6 12.1

2.95 6.13 1.96 1.86 1.77 5.13 1.71 6.69

101 104 107 108 109 109 1010 1010

branching ratios, % b10 → 2,3-C10H6O2 + H −12

2.84 × 10 3.37 × 10−5 7.38E+00 9.02 × 102 1.12 × 105 1.10 × 106 1.44 × 107 2.69 × 108

C9H7 + CO2 100.0 99.1 91.6 81.3 63.4 53.0 41.0 28.4

2-C9H7O + CO 0.0 0.9 8.4 18.7 36.6 46.9 58.8 71.0 branching ratios, %

2,3-C10H6O2 + H 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.6

b10′ → 2,3-C10H6O2 + H

C9H7 + CO2

2-C9H7O + CO

1,2-C10H6O2 + H

3.05 × 10−5 2.93E+00 1.69 × 104 4.99 × 105 1.50 × 107

99.9 98.9 90.4 79.0 59.7

0.0 0.0 0.0 0.1 0.3

0.1 1.1 9.6 20.9 40.0

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Table 1. continued rate constants

branching ratios, %

T, K

b10′ → C9H7 + CO2

b10′ → 2-C9H7O + CO

b10′ → 2,3-C10H6O2 + H

C9H7 + CO2

2-C9H7O + CO

1,2-C10H6O2 + H

1700 2000 2500

2.01 × 109 6.47 × 109 2.42 × 1010

3.08 × 107 2.90 × 108 3.70 × 109

7.48 × 107 4.61 × 108 3.61 × 109

48.4 35.8 23.1

0.7 1.6 3.5

50.9 62.6 73.4

energy transition states on the insertion pathways lie 20.7 (a1 → a8 → a10/a10′) and 25.8 kcal/mol (b1 → b8 → b10/b10′) above a1 and b1, respectively, i.e., ∼9 kcal/mol lower than the energy required for the O atom loss from these adducts. The oxygen insertion process is highly exothermic and most likely irreversible because barriers on further decomposition/isomerization pathways involving a10, a10′, b10, and b10′ are calculated to be much lower than those for reverse isomerization of these intermediates back to a8/b8. If the a10, a10′, b10, and b10′ intermediates (analogues of the oxepyniloxy radical in the C6H5O2 system24) are formed, their most favorable dissociation pathways include the following (with the highest barriers with respect to the decomposing a10, a10′, b10, or b10′ intermediates given in parentheses in kilocalories per mole):

with the transition state TSb20′−b14′ residing 34.1 kcal/mol higher in energy than b10′. In the second pathway, the H atom of the HCO group at C1, can migrate to the adjacent C10 atom via transition state TSb20′−b37′ producing b37′ via a barrier of 19.3 kcal/mol, and the transition state lies 39.1 kcal/mol higher in energy than b10′. 1,2-Naphthoquinone can then be formed by the H loss from C10 in b37′ through a barrier of 26.7 kcal/ mol. The corresponding transition state TSb37′−b14′ resides 35.5 kcal/mol above b10′. The third mechanism to produce b14′ proceeds from b20′ via intermediate b39′. The H atom attached to C1 can migrate to the O atom of the same HCO group through the transition state TSb20′−b39′ which lies 39.1 kcal/mol above b10′, nearly the same in energy as TSb20′−b37′. Then, the intermediate b39′, located 27.4 kcal/mol below b10′, is produced after overcoming the barrier of 19.3 kcal/mol. Next, the H atom in the OH group can be eliminated via TSb39′−b14′, which lies 35.9 kcal/mol above b10′, leading to the 1,2-naphthoquinone + H products via a barrier of 62.9 kcal/ mol. Noteworthy, 1,2-naphthoquinone is 21.5 kcal/mol more stable than 2,3-naphthoquinone due to the fact that the second C6 ring is aromatic in 1,2-C10H7O2 but not aromatic in 2,3C10H7O2. In addition to the channels producing 1,2naphthoquionone, intermediate b21′ formed after the initial ring opening in b10′ can be also involved in the production of 2-benzopyranyl by isomerizing to b23′. At the first step of this isomerization, the HCCO group in b21′ rotates around the adjacent C−C bond resulting in b22′ via a barrier of 6.2 kcal/ mol. Next, the HCO group of the other side chain rotates, leading to b23′ after overcoming a barrier of 4.2 kcal/mol. The subsequent b23′ → 2-C9H7O + CO dissociation mechanism was described in the previous subsection. Meanwhile, the b21′ → b20′ → 1,2-C10H6O2 + H channel is clearly preferable over b21′ → b22′ → b23′ → b17′ → 2-C9H7O + O because the highest in energy transition state for the former, TSb20′−b14′, lies 14.8 kcal/mol lower than that for the latter, TSb23′−b17′. 3.3. Summary of Most Favorable Reaction Pathways. Both 1-napthyl + O2 and 2-naphthyl + O2 reactions proceed by barrierless addition of the oxygen molecule to the radical site of naphthyl radicals. The end-on addition is preferable thermodynamically and leads to naphthoperoxy adducts a1, b1, or b1′ stabilized by 45−46 kcal/mol relative to the reactants. The addition can be followed by elimination of the oxygen atom producing 1- and 2-naphthoxy radicals, which lie 29.6 and 34.9 kcal/mol above the initial adducts, C10H7OO, but with the overall reactions being exothermic by 15.5 and 10.9 kcal/mol, respectively. The naphthoxy radicals may then undergo thermal unimolecular decomposition to C9H7 (indenyl radical) + CO via rate-controlling barriers positioned 58.2 (a4 → a5) and 48.3 kcal/mol (b4 → a5) above 1- and 2-C10H7O, respectively. A reaction channel that may compete with the O atom loss involves insertion of one of the oxygen atoms into the aromatic ring leading (via tricyclic adducts a8 and b8) to the intermediates a10 and a10′ (the 1-naphthyl + O2 reaction) or b10 and b10′ (the 2-naphthyl + O2 reaction), containing fused six-member C6 and seven-member C6O rings. The highest in

3.4. Qualitative Kinetic Analysis. A careful quantitative kinetic analysis of this complex system would require variational calculations of thermal reaction rate constants for the barrierless entrance reaction channels C10H7 + O2 → C10H7OO and oxygen atom elimination pathways, C10H7OO → C10H7O + O. These calculations will need to be combined with RRKM-master equation calculations of temperature- and pressure-dependent rate constants for all other reaction steps of importance, which would allow one to determine the overall k(T,P) and branching ratios of possible products and also stabilized C10H7O2 intermediates at a variety of combustion conditions. While we plan such a quantitative study in the near future, at this stage we carry out a simplified qualitative analysis of product branching ratios via transition state theory computations of thermal rate constants at the high-pressure limit. In particular, we first compute and compare rate constants for the O atom loss from the naphthylperoxy adducts a1 and b1 and for their isomerization to a10/a10′ and b10/ b10′ and then calculate dissociation rate constants of the a10, a10′, b10, and b10′ intermediates to different products. For simplicity, for each process we select only the highest in energy transition state as rate-determining and hence treat each dissociation channel as direct, i.e., intermediate → critical TS → products. For the C10H7OO (a1/b1) → 1-/2-C10H7O + O reactions occurring via barriers submerged under the final products and then via the C10H7O···O complexes, we consider the tighter distinct transition between C10H7OO and the 1583



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at high temperatures. The 1- and 2-naphthoxy radicals can in turn undergo unimolecular decomposition producing indenyl radical + CO via the barriers of 58.2 and 48.3 kcal/mol, respectively. At lower temperatures, the initial reaction adducts are likely to undergo an oxygen atom insertion into the attacked aromatic ring producing bicyclic intermediates a10 and a10′ (1-naphthyl) or b10 and b10′ (2-naphthyl) made of two fused six-member C6 and seven-member C6O rings. Compounds a10 and a10′ are predicted to decompose to C9H7 (indenyl) + CO2, 1,2-C10H6O2 (1,2-naphthoquinone) + H, and 1-C9H7O (1-benzopyranyl) + CO, whereas b10 and b10′ would dissociate to C9H7 (indenyl) + CO2, 2-C9H7O (2-benzopyranyl) + CO, and 1,2-C10H6O2 + H. Thus, the 1-naphthyl + O2 reaction is expected to give the 1-naphthoxy + O, indenyl + CO2, 1-benzopyranyl + CO, and 1,2-naphthoquinone + H products at various combustion temperatures, whereas the 2naphthyl + O2 reaction would form 2-naphthoxy + O, indenyl + CO2, 2-benzopyranyl + CO, and 1,2-naphthoquinone + H. Meanwhile, to predict the overall reaction rate constants and product branching ratios at various temperatures and pressures, variational calculations of thermal rate constants for the barrierless entrance channels C10H7 + O2 → C10H7OO and oxygen atom elimination pathways, C10H7OO → C10H7O + O, combined with multichannel-multiwell RRKM-ME calculations of product branching ratios for all other important reaction steps, are required. The availability of the C10H7O2 PES and molecular parameters of the species involved in the reactions reported in the present paper makes such future sophisticated quantitative kinetic analysis possible.

complexes as critical. This is warranted at combustion temperatures where Gibbs energies of these tighter TSs are expected to be higher than those for loose variational TSs between the complexes and the C10H7O + O products. For the a10 → a21 → a20 (→ a37) → 1,2-C10H6O2 + H channel, the direct H loss from a20 has a slightly higher in energy TSa20−b14 (40.5 kcal/mol relative to a10) than the critical TSa20−b37 for the two-step H elimination (40.4 kcal/mol), but rate constants calculated via TSa20−b14 are higher than those via TSa20−b37 because of a looser transition-state character for the former. The resulting rate constants and relative product yields are collected in Table 1. One can see that for 1-naphthylperoxy radical a1, the initial adduct in the reaction of 1-naphthyl radical with O2, insertion of an O atom into the attacked aromatic ring is preferable at temperatures up to ∼1700 K, but at higher temperatures dissociation of a1 to 1-naphthoxy radical + O becomes favorable, with the calculated relative yield of 1C10H7O + O reaching ∼65% at 2500 K. If intermediate a10 is produced, it is predicted to decompose to C9H7 (indenyl) + CO2 or 1,2-C10H6O2 (1,2-naphthoquinone) + H, with the branching ratios of 55−7 and 45−93%, respectively, in the temperature range of 1000−2500 K. Thus, the C9H7 + CO2 products are favorable only at temperatures up to around 1000 K, whereas at higher temperatures 1,2-C10H6O2 + H become major and eventually dominant decomposition products of a10. The predicted products of thermal unimolecular decomposition of a10′ are C9H7 + CO2 (84−21%) and 1-C9H7O (1benzopyranyl) + CO (16−79%) in the temperature range of 1000−2500 K. The indenyl + CO2 products are favored at lower temperatures, whereas 1-benzopyranyl + CO take over above 1500 K. The initial adduct of 2-C9H7 + O2, 2napthylperoxy radical b1, prefers to undergo an oxygen atom insertion into the ring producing b10 or b10′ when the temperature is lower than 1200 K, but when the temperature reaches 1200 K and above, decomposition of b1 to 2-C10H7O + O is more favorable, with the estimated relative yield being as high as ∼88% at 2500 K. Once b10 is formed, it is more likely to decompose to C9H7 + CO2 at T ≤ 1700 K and to 2-C9H7O (2-benzopyranyl) + CO at T > 1700 K, whereas the yield of 2,3-C10H6O2 (2,3-naphthoquinone) + H is predicted to be negligible. The branching ratio of the C9H7 + CO2 products decreases from 92% at 1000 K to 28% at 2500 K, whereas the branching ratio for 2-C9H7O + CO increases from 8% at 1000 K to 71% at 2500 K. Finally, unimolecular decomposition of b10′ leads mostly to the C9H7 + CO2 products at lower temperatures (90 and 60% at 1000 and 1500 K, respectively) and to 1,2-C10H6O2 + H at high temperatures (63 and 73% at 2000 and 2500 K, respectively). 2-C9H7O + CO are predicted to be only minor dissociation products of b10′ with their branching ratio reaching a maximum of 3.5% at 2500 K.

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ASSOCIATED CONTENT

S Supporting Information *

Calculated total energies, ZPE, CCSD T1 diagnostics, moments of inertia, rotational constants, optimized Cartesian coordinates, and vibrational frequencies of all intermediates and transition states involved in the 1- and 2-C10H7 + O2 reactions (Tables S1 and S2, respectively). This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address §

Combustion Chemistry Centre, National University of Ireland, Galway, Ireland. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS C.-W.Z. thanks the Chinese Science Council for her fellowship supporting her exchange visit to the Florida International University. This work was also funded by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Sciences of the U.S. Department of Energy (Grant No. DE-FG02-04ER15570).

4. CONCLUSIONS Potential energy surfaces of various channels in the reactions of 1- and 2-naphthyl radicals with molecular oxygen have been investigated at the G3(MP2,CC)//B3LYP level of theory. Both reactions are shown to start with barrierless addition of O2 to the radical sites of naphthyl radicals. The end-on addition of O2 producing 1- and 2-naphthylperoxy radicals is thermodynamically preferable and is predicted to be 45−46 kcal/mol exothermic. Next, the 1- and 2-C10H7OO adducts can eliminate an oxygen atom, leading to the formation of 1- and 2naphthoxy radical products, respectively. The O loss process from C10H7OO producing C10H7O is predicted to be favorable

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