Theoretical Study of the Oxidation Mechanisms of Naphthalene

Article pubs.acs.org/JPCA

Theoretical Study of the Oxidation Mechanisms of Naphthalene Initiated by Hydroxyl Radicals: The H Abstraction Pathway Abolfazl Shiroudi and Michael S. Deleuze* Center of Molecular and Materials Modelling, Hasselt University, Agoralaan, Gebouw D, B-3590 Diepenbeek, Belgium S Supporting Information *

ABSTRACT: Reaction mechanisms for the initial stages of naphthalene oxidation at high temperatures (T ≥ 600 K) have been studied theoretically using density functional theory along with various exchange-correlation functionals, as well as the benchmark CBS-QB3 quantum chemical approach. These stages correspond to the removal of hydrogen atoms by hydroxyl radical and the formation thereby of 1- and 2-naphthyl radicals. Bimolecular kinetic rate constants were estimated by means of transition state theory. The excellent agreement with the available experimental kinetic rate constants demonstrates that a twostep reaction scheme prevails. Comparison with results obtained with density functional theory in conjunction with various exchange-correlation functionals also shows that DFT remains unsuited for quantitative insights into kinetic rate constants. Analysis of the computed structures, bond orders, and free energy profiles demonstrates that the reaction steps involved in the removal of hydrogen atoms by OH radicals satisfy Hammond’s principle. Computations of branching ratios also show that these reactions do not exhibit a particularly pronounced site-selectivity.

1. INTRODUCTION

2.12 k(T ≥ 600K ) = (1.12−+0.73 )

Polycyclic aromatic hydrocarbons (PAHs) are ubiquitous environmental pollutants. Many PAHs are potentially genotoxic, mutagenic, or carcinogenic.1,2 They are emitted into the atmosphere during incomplete combustion and account for ∼20% of nonmethane hydrocarbons (NMHCs) in urban air.3 Chemical sinks for gas-phase PAHs include direct photolysis and reactions with reactive tropospheric gases such as ozone; nitrate radicals and hydroxyl radicals are the major reactants responsible for the homogeneous degradation of organics emitted into the atmosphere.4,5 Among the different oxidants, reaction with hydroxyl radical is usually the most important reaction.6,7 It plays a key role in determining the oxidation power of the atmosphere.8 Naphthalene is the most volatile and abundant PAH in the urban atmosphere and is reactive at ambient temperature and pressure.9,10 The reactions of OH radicals with naphthalene are of importance to both photochemical air pollution and hydrocarbon flame chemistry.11 Lorenz and Zellner12,13 have experimentally studied the reaction of OH radicals with naphthalene at temperatures lower than 410 K and at temperatures ranging from 636 to 873 K, by means of laser flash photolysis using laser-induced fluorescence.13−15 At T ≤ 410 K and T ≥ 600 K, a least-squares analysis of the temperature dependence of the measured rate constants yields the following Arrhenius expressions:13

× 10−17T 2 e−(969 ± 752)/ T cm 3 molecule−1 s−1

where the indicated errors correspond to two least-squares standard deviations. The first regression implies a negative activation energy, which can be interpreted as corresponding to the addition of OH radicals and its equilibration.13,16−18 In contrast, the second regression implies a positive activation energy, which has been ascribed to hydrogen abstraction.14 The only theoretical study so far of the thermochemistry for the latter reaction is the one by Qu et al.,8 at the BB1K/6311+G(3df,2p) level. At this level, it was found that the energy barriers for the removal of hydrogen atoms bonded to the C1 and C2 atoms (see Figure 1) by OH radicals amount to 4.79 and 4.89 kcal mol−1, respectively. Great care is required in using these data, because reaction barriers are known in general to be

Figure 1. Retained atom labeling for characterizing the structures of intermediate and transition states (see Tables 1 and 2 for numerical details).

1.11 k(T ≤ 410K ) = (1.05−+0.54 )

Received: January 6, 2014 Revised: April 15, 2014 Published: April 23, 2014

× 10−12 e(902 ± 240)/ T cm 3 molecule−1 s−1 © 2014 American Chemical Society

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dx.doi.org/10.1021/jp500124m | J. Phys. Chem. A 2014, 118, 3625−3636

The Journal of Physical Chemistry A

Article

Figure 2. Reaction pathways for H-abstraction at the C1 and C2 positions in naphthalene by hydroxyl radicals, yielding water and 1-naphthyl (P1) or 2-naphthyl (P2) radicals.

2. THEORY AND COMPUTATIONAL DETAILS

strongly dependent on the employed exchange-correlation functional.19 Also, to the best of our knowledge, the corresponding rate constants have never been theoretically analyzed. Therefore, besides providing energy barriers and reaction energies at a high many-body quantum mechanical level of theory (CBS-QB3), a main purpose of our work is to supply good kinetic equations, kinetic rate constants, and branching ratios for the purpose of fully unraveling the original experiments, by Lorenz and Zellner12,13 or Atkinson,14 on hydrogen abstraction from naphthalene by hydroxyl radicals at high temperatures (T ≥ 600 K). The aim of the present study is therefore to provide comprehensive and quantitative theoretical insights into the two reaction pathways 1 and 2 that are depicted in Figure 2. In this purpose, we shall first use density functional theory (DFT) along with various exchange-correlation functionals, and compare the obtained reaction energies and energy barriers with the results of benchmark theoretical calculations employing the high-level composite CBS-QB3 ab initio approach.20−28 With the CBS-QB3 approach, an extrapolation scheme is used to evaluate energies at the CCSD(T) level (coupled cluster theory along with single, double, and perturbative triple electronic excitations29−31) in the limit of a complete basis set (CBS). Kinetic parameters for the reaction pathways depicted in Figure 2 are correspondingly calculated by means of transition state theory (TST).32−39

All calculations that are discussed in the present work have been performed using the Gaussian 09 package of programs40 at the Flemish Supercomputer Center. Molecular structures were visualized with GaussView.41 The molecular structures and harmonic vibrational frequencies of all stationary points involved in the reaction pathways 1 and 2 depicted in Figure 1 were calculated using Density Functional Theory along with a variety of exchange-correlation functionals, namely, the Becke3-parameters-Lee−Yang−Parr (B3LYP) functional,42,43 the dispersion corrected ωB97XD exchange-correlation functional,44 the UM05−2x functional,45 and the UM06−2x functional,45,46 in conjunction with Dunning’s correlation-consistent basis set of triple-ζ quality augmented with diffuse functions (aug-cc-PVTZ basis set).47 The energies of reactants, intermediates, transition states, and products were re-evaluated using the so-called complete basis set CBS-QB3 model chemistry originally developed by Peterson and co-workers.20−28 This model chemistry involves low-level (SCF and ZPE) calculations using large basis sets, midsized sets for second-order correlation corrections, and small basis sets for high-level correlation corrections. They include an extrapolation of energies up to the CCSD(T) level29−31 in the limit of a complete basis set (CBS) in order to correct Møller−Plesset second-order (MP2) energies.31 3626



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monomers are performed using the whole supermolecular basis sets instead of the monomer basis sets. No symmetry constraints were imposed during the geometry optimizations. The keyword nosymm was used in order to guarantee this matter. In our study, the removal of hydrogen atoms from naphthalene by OH radicals is analyzed according to the scheme advocated by Singleton and Cvetanovic.63 With this scheme, it is assumed that this reaction occurs according to a two-step mechanism,64 involving first a fast pre-equilibrium between the reactants (C10H8 and OH radicals) and a prereactive complex (IM1), followed by the abstraction of a hydrogen atom leading to a postreactive complex (IM2) and, then to the products:

In addition, this approach includes an empirical correction for spin contamination in open-shell species. The CBS-QB3 method involves five steps, starting with a geometry optimization at the B3LYP level of theory,23,43 followed by a calculation of vibrational frequencies and thermodynamic state functions48 obtained from canonical partition functions that were computed for an ideal gas, using Boltzmann statistical thermodynamics along with the Rigid Rotor-Harmonic Oscillator approximation (RRHO).49,50 Specifically, the CBS-QB3 method involves the following steps:28 B3LYP/6-311G(2d,d,p) geometry optimization; B3LYP/6311G(2d,d,p) frequency calculation with a 0.99 scale factor for the ZPE; CCSD(T)/6-31+G* energy calculation; MP4(SDQ)/6-31+G(d(f),p) energy calculation; UMP2/6-311+G(3d2f,2df,2p) energy calculation and CBS extrapolation. When applied to aromatic systems, the B3LYP approach is known to deliver geometrical parameters (bond lengths and bond angles) of quality comparable to CCSD(T) results.51 B3LYP geometries are therefore widely employed in other benchmark quantum mechanical approaches, such as the W1 approach.52 A weakness of the B3LYP approach is that it neglects dispersion forces, which may have some influence on torsional characteristics. However, since H abstraction from naphthalene merely yields changes in bond lengths and bond angles without any noticeable change in torsion angles, this deficiency should not have particularly strong effect on the computed internal reaction energies (or enthalpies) and internal energy barriers (or enthalpies). The CBS-QB3 method amounts to an extrapolation of energies to the level of Coupled Cluster Theory including single, double, and perturbative triple excitations [CCSD(T)], in conjunction with a complete basis set. The CBS-QB3 method was developed with the idea that a major source of error in quantum mechanical calculations arises from truncation of the basis set. The N−1 asymptotic convergence of MP2 pair energies calculated from pair natural orbital expansions is used to extrapolate energies to the CBS limit.21,23,25,27 This approach is known to yield a mean absolute deviation of 1.1 kcal mol−1 on the G2/97 test set27 for reaction energies. A more recent work indicates a maximum error of 2.8 kcal mol−1 for the G2 test set of reaction energies, as well as average and mean absolute errors of 0.2 and 0.98 kcal mol−1.53 It seems justified therefore to employ the CBS-QB3 method as a benchmark quantum chemical approach, in order to calibrate the accuracy of DFT methods employing necessarily approximate exchange-correlation functionals. This is only in case of an extreme spin contamination of the underlying UHF wave functions in which more accurate but also much more costly methods, such as the G2 or G4 approaches, should be used.54 However, spin-contamination for doublet radicals is known to be very small in symmetry-broken UHF-based CCSD calculations, even when the UHF spin contamination is very large.55 For example, for the NO2 radical, for UHF and UHFbased CCSD wave functions, the value of ⟨S2⟩ is 1.18 and 0.76, respectively.55 Intrinsic reaction coordinate (IRC) calculations56 were carried out at the B3LYP/6-31G (d,p) level using the second-order Gonzalez-Schlegel integration method,57,58 in order to verify whether the located transition state structures connect the expected energy minima. Energy barriers obtained on DFT grounds were systematically corrected for basis set superposition errors (BSSEs),59 according to the counterpoise method proposed by Boys and Bernardi.60−62 In this a posteriori correction method, the energy calculations for the individual

k1

step 1: C10H8 + OH• HooI C10H8···OH• k −1

k2

step 2: C10H8···OH• → C10H 7• + H 2O

In the above scheme, k1 and k−1 denote the rate constants of the forward and backward reactions associated with the first step, whereas k2 is the rate constant corresponding to the second step. A steady-state analysis of the overall reaction pathway leads to the following expression for the associated rate constant:63,65 koverall =

k1k 2 k −1 + k 2

(1)

Even though the energy barrier for k−1 has about the same height as that for k2, the entropy change for the reverse reaction (IM1 → R) is much larger than that for the formation of the products (IM1 → P). Thus, k−1 is expected to be considerably larger than k2.63 Therefore, the overall rate constant can be rewritten as koverall = Kck 2

(2)

with Kc = k1/k−1 the equilibrium constant for fast pre-equilibrium between the reactants and the pre-reactive complex (step 1): Kc =

[C10H8···OH•] [C10H8][OH•]

(3)

By appling basic statistical thermodynamic principles (see in particular eq 26.3−20 in ref 66) this equilibrium constant can be obtained (see Table S1 of the Supporting Information) according to Kc =

Q IM1 Q naph. Q OH•

×

Vm(T ) NAv

⎡ (E IM1 − Enaph − EOH•) ⎤ ⎥ × exp⎢ − ⎢⎣ ⎥⎦ RT

(4)

with NAv the Avogadro number, R the ideal gas constant, and Vm(T) = RT/P the molar volume of an ideal gas. The kinetic rate constant characterizing the unimolecular dissociation reaction of the pre-reactive complex is obtained in the high pressure limit by means of transition state theory:32−39,67 k 2 = κ (T ) ×

⎡ (E − E IM1) ⎤ Q σkBT × TS1 × exp⎢ − TS1 ⎥ ⎣ ⎦ h Q IM1 RT (5)

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Table 1. Structural Parameters for the Reactant, Intermediate, Transition State, and Product on the Chemical Reaction Pathway 1 for the Oxidation of Naphthalene by OH• into 1-Naphthyl Radicala ωB97XD/aug-cc-pVTZ

B3LYP/aug-cc-pVTZ Parameter

R

IM1

TS1a

P1

R

IM1

TS1a

P1

UM05−2x/aug-cc-pVTZ


R

R

IM1

TS1a

P1

IM1

r (C1−C2)

1.370 1.384

1.361 1.351 1.365 1.371

1.356 1.346 1.365 1.368

1.357 1.346 1.366 1.367

r (C1−C9)

1.417 1.422

1.407 1.396 1.415 1.419

1.407 1.397 1.413 1.415

1.406 1.396 1.415 1.417

r (C2−C3)

1.412 1.408

1.417 1.422 1.410 1.411

1.414 1.420 1.410 1.412

1.414 1.420 1.412 1.414

r (C9−C10)

1.428 1.426

1.433 1.437 1.418 1.416

1.420 1.425 1.416 1.415

1.418 1.396 1.419 1.418

r (C1−H11)

1.083 1.079

1.243 -

1.226 -

1.198 -

r (H11−O13)

-

1.261 0.962 -

∠ (C1−H11−O13) -

2.417

74.68 169.77

-

1.083 1.081

-

2.656

1.080 1.079

1.271 0.957 -

71.75 167.27

-

-

2.892

1.083 1.082

1.309 0.958 -

67.88 162.32

-

-

3.293

TS1a

B3LYP/6-311G(2d,d,p)

P1

R

1.358 1.349 1.374 (1.365) [1.381] 1.408 1.398 1.420 (1.412) [1.422] 1.417 1.421 1.415 (1.408) [1.412] 1.421 1.424 1.431 (1.417) [1.420] 1.208 1.085 (1.081) [1.092] 1.295 0.959 -

59.95 164.91

-

-

IM1

TS1a

1.384

1.364 1.354 (1.357) (1.348)

P1

1.424

1.410 1.400 (1.403) (1.394

1.414

1.420 1.425 (1.412) (1.417)

1.430

1.435 1.440 (1.420) (1.424)

1.081

1.253 (1.243)

-

2.479

1.244 0.962 (1.233) 75.22 165.02 -

a

Bond lengths are in angstroms (Å) and bond angles are in degrees (°). The values in parentheses are obtained at the BB1K/6-31+G(d,p) level.8 The values in bracket are the experimental data.59,60

heights.74 In this limit, since partition functions are proportional to the molar volume (see, e.g., ref 66), koverall (eq 7) only depends on the temperature. Our kinetic analysis is essentially the same as that by Uc et al.,65 for hydrogen abstraction from benzene and toluene by hydroxyl radicals and shows that the pre-reactive complex (IM1) has no direct influence on the overall kinetics. However, since there is a possibility of quantum mechanical tunneling through the IM1 → TS1x → IM2x (x = a, b) energy barriers, the existence of the reactant complex implies that the actual barrier is higher and that there are additional energy levels from where tunneling may occur; thus, the tunneling factor increases. Therefore, the pre-reactive complex IM1 does have some indirect influence on the kinetics of these pathways, through the interplay of the tunneling factor κ(T). Accordingly, one can ignore reactant complexes in addition channels, but they are essential for quantitative calculations of hydrogen abstraction rate constants.

where kB and h are the Boltzmann’s and Planck’s constants, respectively. In the above equations, Qnaph, QOH, QIM1, and QTS1 represent the total molecular partition functions for the isolated reactants (naphthalene and OH radical), of the pre-reactive molecular complex (IM1), and of the transition state (TS1) associated with the unimolecular dissociation reaction (step 2), respectively. Enaph, EOH, EIM1, and ETS1 are the corresponding energies, including B3LYP/6-311G(2d,d,p) estimates for zero-point vibrational contributions. In eq 4, κ(T) and σ denote the tunneling factor68 and reaction symmetry number characterizing step 2:69 2 1 ⎛ hνi ⎞ κ (T ) = 1 + ⎜ ⎟ 24 ⎝ kBT ⎠

(6)

where νi is the imaginary vibrational frequency characterizing the transition state. Therefore, upon combining eqs 3−5, we find koverall =

QTS1 ⎛ ΔE ⎞ σkBT V (T ) × × m × exp⎜ − 0 ⎟ ⎝ RT ⎠ h Q naph. Q OH• NAv

3. RESULTS AND DISCUSSION 3.1. Structural Characteristics of Stationary Points. The optimized molecular structures of the intermediate complexes (IM1 and IM2), transition states (TS1 and TS2), and products (P1 and P2) in the reactions between naphthalene and OH radicals along pathways 1−2 are presented in Tables 1 and 2, according to the atom labels given in Figure 1. In analogy to the oxidation mechanism of benzene initiated by OH radicals,19 a pre-reactive molecular complex (IM1) has been identified (Figure 2) in the reactions of naphthalene with OH radicals. According to Alvarez-Idaboy et al.,75 such a pre-reactive complex is a common feature to reactions in between radical species and unsaturated molecules, which finds its origin in long-range Coulomb interactions between the reactant molecules.76 According to our best CBS-QB3 data, this intermediate complex is located at about 2.5 kcal mol−1 below the total energy of the reactants, and is characterized by H11−O13 and H12−O13 bond lengths equal to 2.479 and 2.779 Å, respectively (Figure 1). Proceeding further

(7)

with ΔE0 the net vibrationally adiabatic barrier for the overall reactions scheme:69 ΔE0 = E TS1 − E Naph − EOH•

(8)

Thus, the vibrationally adiabatic barrier at high pressures can be calculated as the difference between the energies of the transition states and reactants, without having to consider the pre-reactive complex. In the present work, rate constants and branching ratios for each reaction pathway were evaluated in the high pressure limit, according to eqs 2−8, and using B3LYP/6-311G(2d,d,p) molecular partition functions that were computed using the vibrational ground state as energy reference, along with the CBS-QB3 estimates for activation energies. We note that TST gives an estimate of the upper limit of kinetic rate constants as a function of the temperature, and is known to give reliable estimations of rate constants71,72 in the high pressure limit,73 especially for cases with significant barrier 3628



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Table 2. Structural Parameters for the Reactant, Intermediate, Transition State, And Product on the Chemical Reaction Pathway 2 for the Oxidation of Naphthalene by OH• into 2-Naphthyl Radicala ωB97XD/aug-cc-pVTZ

B3LYP/aug-cc-pVTZ Parameter

R

IM1

TS1b

P2

R

IM1

TS1b

P2



R

R

IM1

TS1b

P2

IM1

r (C1−C2)

1.370 1.384

1.360 1.350 1.365 1.371

1.355 1.346 1.365 1.368

1.357 1.346 1.366 1.367

r (C1−C9)

1.417 1.422

1.421 1.427 1.415 1.419

1.421 1.424 1.413 1.415

1.417 1.423 1.415 1.417

r (C2−C3)

1.412 1.408

1.402 1.391 1.410 1.411

1.401 1.391 1.410 1.412

1.403 1.392 1.412 1.414

r (C3−C4) r (C2−H12)

1.370 1.372 1.082 1.080

1.373 1.377 1.365 1.364 1.241 1.081 1.080

1.367 1.370 1.365 1.364 1.225 1.078 1.078

1.366 1.370 1.366 1.367 1.197 1.081 1.081

r (H12−O13)

-

1.261 0.962 -

1.269 0.957 -

1.307 0.958 -

∠ (C2−H12−O13) -

2.861

69.04 170.18

-

-

2.876

68.62 167.49

-

-

2.974

66.63 163.00

-

-

3.326

TS1b


P2

R

1.358 1.348 1.374 (1.365) [1.381] 1.419 1.424 1.420 (1.412) [1.422] 1.404 1.394 1.415 (1.408) [1.412] 1.368 1.371 1.374 1.206 1.085 (1.080) [1.092] 1.292 0.959 -

59.41 165.57

-

-

IM1

TS1b

1.384

1.364 1.354 (1.356) (1.348)

P2

1.424

1.424 1.429 (1.415) m

1.414

1.405 1.395 (1.399) m

1.374 1.082

1.376 1.380 1.254 (1.242)

2.779

1.235 0.962 (1.230) 71.22 165.26 -

a

Bond lengths are in angstroms (Å) and bond angles are in degrees (°). The values in parentheses are obtained at the BB1K/6-31+G(d,p) level.8 The values in bracket are the experimental data.59,60

remains almost planar, which justifies using the B3LYP approach at the start of the CBS-QB3 computations and for evaluating vibrational frequencies. At the level of the transition states TS1a and TS1b, the breaking C−H bond is elongated by ∼15.5% (∼0.17 Å in absolute value), compared to the equilibrium structure computed for naphthalene. In contrast, the forming O−H bond has, quite naturally, a larger length than in the isolated H2O molecule. Compared with the latter, the elongation of the O−H bond in the transition states TS1a and TS1b is on the order of ∼29% (∼0.28 Å in absolute value). At the starting B3LYP/6-311G(2d,d,p) level of theory used to optimize the geometries of reactants, transition states, and adducts, the spin contamination [⟨S2⟩obs−0.75] never exceeds 0.036 and can thus, for all practical purposes, be regarded as negligible. Upon exploring further the B3LYP/6-311G(2d,d,p) potential energy surface describing the interaction between the incoming hydroxyl radical and hydrogen atoms at the C1 and C2 positions in naphthalene, we found another pre-reactive complex with the OH radical on top of the ring (Table 3, Figure 4). By analogy with the study by Uc et al.,65 the identified pre-reactive complexes can be referred to as ipso- and ortho-adducts (Figure 4). At the ωB97XD/aug-cc-pVTZ and CBS-QB3 levels of theory, the ipso and ortho intermediates have almost equal energies, with the ipso intermediate being more stable by 0.2 kcal mol−1 only. These two pre-reactive complexes are connected by a very flat potential, so there is little chemical significance to this tiny energy difference except at very low temperatures. Besides, the ipso-complex does not readily connect to the transition states TS1a and TS1b leading to the postreactive complexes (IM2a and IM2b), and subsequently to the products (1- or 2-naphthyl radicals and water). The ipsointermediate can only reversibly convert to the ortho one, or back to the reactants. Even at low temperatures, its influence on the kinetics of hydrogen removal from naphthalene by a hydroxyl radical must be therefore extremely limited. Therefore, in the sequel of the discussion, unless specified, the ipso intermediate will be ignored, and the ortho intermediate will simply be referred to as the IM1 intermediate.

along reaction pathways 1 or 2, the abstraction process of H11 or H12 via the transition states TS1a and TS1b require activation energies of ∼2.2 and ∼2.4 kcal mol−1 relative to the reactant energies (Figure 3). Two postreactive molecular

Figure 3. Potential energy diagram for the reaction pathways 1−2 obtained using the CBS-QB3 method.

complexes IM2a and IM2b are identified further on the product side of the reaction barriers, which corresponds to the dissociation of IM1 into a water molecule and a 1- or 2-naphthyl radical species. These postreactive molecular complexes are stabilized by a hydrogen bonding between the oxygen atom in the OH radicals and a H atom bonded to an aromatic ring. They are located at ∼1.1 to ∼1.5 kcal mol−1 below the products. With reaction energies around −6.0 to −6.4 kcal mol−1, the removal of a hydrogen atom from naphthalene by a hydroxyl radical appears to be a rather strongly exothermic process. Inspection of the B3LYP/6-311G(2d,d,p) geometries obtained for the transition states TS1a (TS1b) along pathway 1 (2) shows that the breaking of the C1−H11 (C2−H12) bond and the formation of the O13−H11 (O13−H12) bond is a concerted process. During the reaction, the carbon backbone 3629



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Table 3. Structural Characteristics of the IM1-ipso-Intermediatea Method/aug-cc-pVTZ

a

parameter

B3LYP

ωB97XD

UM05−2x

UM06−2x


r (C1−C2) r (C1−C9) r (C2−C3) r (C3−C4) r (C9−C10) r (C1−H11) r (C2−H12) r (H11−O13) r (H12−O13) ∠ (C1−H11−O13) ∠ (C2−H12−O13)

1.372 1.417 1.413 1.372 1.428 1.083 1.082 4.350 3.855 54.04 63.40

1.366 1.415 1.412 1.366 1.417 1.083 1.081 4.124 3.970 53.39 56.34

1.367 1.414 1.412 1.367 1.415 1.080 10.78 4.032 3.902 52.53 54.99

1.368 1.416 1.413 1.366 1.418 1.082 1.079 4.029 3.907 53.17 55.06

1.375 1.420 1.417 1.375 1.432 1.085 1.084 4.362 3.540 55.47 71.25

Bond lengths are in angstroms (Å) and bond angles are in degrees (°).

Figure 4. Identified equilibrium structures for the pre-reactive intermediate IM1 (ipso- and ortho-), the loose complex between naphthalene and the OH radical.

The fact that the relative elongation of the C−H bond is smaller than that inferred for the forming O−H bond indicates that the transition states TS1a and TS1b are structurally closer to the reactants than to the products. This is in line with Hammond’s principle,77 and the observation that the removal of a hydrogen atom from naphthalene by a hydroxyl radical is an exothermic process. 3.2. Bond Order Analysis. A balanced measure of the extent of bond formation or bond breaking along a reaction pathway is provided by the concept of bond order (B), which has often been used to investigate the molecular mechanism of chemical reactions.78 To follow the nature of the process, Wiberg bond indices have been computed according to an NBO analysis,79,80 as implemented in Gaussian 09. There are several breaking/forming bond processes along the fragmentation process, and the global nature of the reaction can be monitored by means of the so-called synchronicity (Sy),81 defined according to the following expression:

Sy = 1 −

where the superscripts R, TS, and P refer to the reactants, transition states, and products, respectively. The relative change in bond order is ultimately given as a percentage %EV = δBi × 100

The average change in bond order is then obtained by means of δBav =

(9)

In the above equation, n is the number of bonds directly involved in the reaction, and the relative variation of the bond index (δBi) for a bond i at the level of the transition state is estimated as follows:

δBi =

BiTS − BiR BiP − BiR

1 n

n

∑ δBi i=1

(12)

The synchronicity parameter Sy varies between 0 and 1, which is the case when all of the bonds implicated in the reaction center have broken or formed at exactly the same extent in the TS. In principle, the Sy values obtained in this way are independent of the location of the TS.82 The synchronicity value of a fully asynchronic processes is Sy = 0, whereas Sy = 1 for a fully concerted synchronic process.83 Bond indices were calculated for those bonds that were substantially altered by OH addition, namely, the C1−C2, C2− C3, C3−C4, C4−C10, C1−C9, C9−C10, C1−H11, C2−H12, H11− O13, H12−O13, and O13−H14 bonds (Figure 1); all other bonds remain practically unaltered during the reaction. The calculated Wiberg indices Bi for the reactants, transition states, and products enable us (Table 4) to examine the progress of the reactions 1 and 2, and to discuss the position of the transition states between reactants and products. For both reactions, according to the relative changes in bond order, the most strongly affected chemical bond is the O13−H14 single bond. The chemical reaction pathways 1 and 2 are characterized by a

⎡ n |δBi − δBav | ⎤ ⎢⎣∑i = 1 δBav ⎥⎦ 2n − 2

(11)

(10) 3630



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Table 4. Bond Order Analysis of the Structures Involved in the Chemical Reaction Pathways 1 and 2 [B3LYP/6-311G(2d,d,p) results]a bond reaction

C1−C2

C2−C3

C3−C4

C4−C10

C9−C10

C1−C9

C1−H11

H11−O13

O13−H14

0.9263 0.5198 0.0000 43.884

0.0000 0.3491 0.8132 42.929

0.8575 0.8182 0.8132 88.713

C2−H12

H12−O13

δBav

Sy

0.5283

0.8103

0.4834

0.8162

(1) Bi(R) Bi(TS) Bi(P) %EV

1.5542 1.5641 1.5875 29.730

1.3081 1.2858 1.2732 63.897

1.5542 1.5589 1.5635 50.538

1.2709 1.2719 1.2723 71.429

1.2326 1.2160 1.2080 67.480

1.2709 1.2744 1.2916 16.908

Bi(R) Bi(TS) Bi(P) %EV

1.5542 1.5616 1.5837 25.085

1.3081 1.3133 1.3350 19.331

1.5542 1.5381 1.5278 60.985

1.2709 1.2722 1.2743 38.235

1.2326 1.2346 1.2362 55.556

1.2709 1.2518 1.2398 61.415

(2) 0.8575 0.8192 0.8132 86.456

0.9268 0.5161 0.0000 44.314

0.0000 0.3557 0.8132 43.741

a

Wiberg bond indexes (Bi), % evolution through the reaction coordinate (%EV), average bond index variation (δBav), and synchronicity parameter (Sy) are shown.

synchronicity value around ∼0.81, which reveals a chemical process that is concerted, but not fully synchronic. Hammond’s postulate77 states that the structure of a transition state resembles that of the species nearest to it in free energy. This can be quantified in terms of a parameter L, defined as the ratio between the elongation of the C−H bond and the elongation of the H−O bond:

L=

δr(C − H) δr(H − O)

Density Functional Theory, the spin contamination [⟨S2⟩obs− 0.75] never exceeds 0.045 and can thus also, for all practical purposes, be regarded as insignificant. Comparison of the CBS-QB3 results with data obtained using various exchange-correlation functionals (Tables 5 and 6) shows that the standard and widely used B3LYP functional performs rather poorly in calculating reaction and activation energies. A much better agreement with the benchmark CBS-QB3 results is obtained with the ωB97XD, UM05−2x, and UM06−2x functionals. Nevertheless, differences in reaction and activation energies of the order of 1 kcal mol−1 or more are still noticed when comparing the ωB97XD, UM05−2x, and UM06−2x results with the CBS-QB3 estimates. This along with the extreme variability of the DFT results with respect to the employed exchange-correlation functional shows that DFT still remains unsuited for highly quantitative studies of kinetic rate constants. 3.4. Calculations of Kinetic Parameters. Total and individual rate constants and the relative contribution from each pathway to the total rate constant at temperatures ranging from 636 to 873 K are listed and compared with available experimental values12−15 in Figure 5 and Table 7. As previously expected, k−1 is considerably (103 times) larger than k2, on both pathways 1 and 2. We have assumed that the total rate constant (k) for the hydrogen abstraction process can be calculated as the sum of the individual rate constants for the two reaction pathways that are depicted in Figure 2: ktotal = koverall(1) + koverall(2). In line with energy barriers that do not differ by more than 0.24 kcal mol−1 (see Figure 3), pathways 1 and 2 exhibit global kinetic rate constants of equal magnitude. Our calculated total rate constants appear to be in excellent agreement with the available experimental data,12−15 an observation which validates the two-step reaction scheme proposed by Singleton and Cvetanovic.63 These rate constants only differ by one order of magnitude for the experimental ones. At the reported temperatures, this means that the errors on the corresponding Gibb’s free activation energies are between ∼2.9 and 4.0 kcal mol−1. These errors are quite acceptable, considering that the main contribution to these Gibb’s free reaction energies and activation energies are essentially entropic in origin (see Tables S3 and S4 of the Supporting Information). More elaborate treatments of statistical thermodynamical partition functions, taking dispersion forces, anharmonic effects, and hindered rotations into account, are presumably needed for improving further the agreement between theory and experiment.

(13)

Values of L larger than 1 indicate that the transition state lies closer to the products, whereas values of L smaller than 1 indicate on the contrary that the transition state lies closer to the reactants.84 The values obtained for the parameter L for pathways 1 and 2 amount to 0.60 and 0.62, respectively, which confirms that the transition states are structurally closer to the reactants than to the products. The two reaction pathways being characterized by early transition states are expected to be exoergic. 3.3. Energetic and Thermodynamic Parameters. A schematic potential energy diagram of the reaction pathways 1 and 2 is given in Figure 3. CBS-QB3 estimates at room temperature for Gibbs free reaction energies (ΔGr) and energy barriers (ΔG‡) are listed in Tables 5 and 6. In line with the structural characteristics of the transition states discussed previously, both reaction pathways 1 and 2 are exothermic (ΔHr < 0) and exoergic (ΔGr < 0) processes. Upon comparing the Gibb’s free reaction energies for pathways 1 and 2, it can be noted that pathway 1 involving H-abstraction at the C1-position in naphthalene is significantly less exergonic than pathway 2 (H-abstraction at the C2-position). Under thermodynamic control, i.e., at chemical equilibrium, the formation of 2-naphthyl should therefore predominate. Results obtained from this study confirm for all employed exchange-correlation functionals the importance of BSSE-CP corrections, even when using a basis set as large as the aug-ccpVTZ one. BSSE values for TS1a and TS1b are in the 0.193− 0.311 and 0.177−0.283 kcal mol−1 ranges, respectively. At the CBS-QB3 level, since the basis set is complete, BSSEs are assumed to identically cancel. As is readily apparent from Table S2 of the Supporting Information, spin contamination of the UHF electronic wave functions used at the start of all CBS-QB3 computations never exceeds 0.11 in the present study and can thus, for all practical purposes, be regarded as marginal. The obtained CBS-QB3 results may therefore safely be regarded as benchmark results. Besides, it is worth noticing that, at all employed levels of 3631


3.489 −1.545 −2.007 −6.950 −7.003

−2.968

−5.760 −5.732 −4.989 −5.063

−2.867 0.153 −6.274 −6.303 −5.283 −5.356

−2.745 0.226 −7.130 −6.709 −4.636 −5.036

−2.942

0.000 −3.141

ΔE0K

−6.679 −6.216 −4.353 −4.758

−3.047

−2.998

0.000 −2.937

ΔH298 K

−2.213 −2.283 −6.293 −6.669

3.449

3.211

0.000 2.188

ΔG298 K

Values obtained at the BB1K/6-31+G(d,p) level.8 bBSSE-corrected relative energies.

3.377

−3.112

−3.003

0.000 3.195

ΔG298 K

0.000 −1.148

ΔH298 K

0.000 −1.423

ΔE0K

ωB97XD/aug-cc-pVTZ

−3.026 0.237 −7.201 −7.129 −4.937 −5.333

−3.285

0.000 −3.511

ΔE0K

−6.868 −6.665 −4.639 −5.033

−3.603

−3.348

0.000 −3.824

ΔH298 K

−1.591 −2.262 −6.603 −6.982

3.148

2.701

0.000 2.854

ΔG298 K


−3.495 0.229 −8.421 −8.262 −6.184 −6.431

−3.716

0.000 −3.945

ΔE0K

−7.951 −7.861 −5.900 −6.159

−3.992

−4.214

0.000 −4.612

ΔH298 K

−3.104 −2.966 −7.842 −8.063

3.451

3.224

0.000 3.017

ΔG298 K


−2.474 0.000 −7.639 −7.487 −6.094 −6.408

−2.474

0.000 −2.668

ΔE0K

−7.204 −6.930 −5.804 −6.114

−2.566

−2.566

0.000 −2.359

ΔH298 K

CBS-QB3

−2.201 −2.622 −7.765 −8.062

3.668

3.668

0.000 1.438

ΔG298 K

−4.02 [8] −4.30 [8]

literature ΔH (kcal mol−1)

3632

a

0.000 7.487 7.716 7.489 8.058

0.000 −0.148 0.0339

−0.030 −0.472

ΔG298 K‡ 0.000 1.419 1.526 0.292 1.826 2.031 0.263 1.322 1.564

0.000 0.876 1.111

ΔH298 K‡

8.867 8.973

0.000 8.599 8.283

ΔG298 K‡

ωB97XD/aug-cc-pVTZ ΔE0K‡ 0.000 3.419 3.532 0.311 3.638 3.672 0.283 3.132 2.798

0.000 2.830 3.065

ΔH298 K‡

10.683 10.964

0.000 10.705 10.561

ΔG298 K‡

UM05−2x/aug-cc-pVTZ ΔE0K‡

Values obtained at the BB1K/6-311+G(3df,2p) level.8 bBSSE-corrected relative energies.

0.000 0.338 0.534 0.193 0.430 0.439 0.177

Naphthalene + OH• TS1a TS1ab BSSE energy-TS1a TS1b TS1bb BSSE energy-TS1b

ΔH298 K‡

B3LYP/aug-cc-pVTZ

ΔE0K‡

species

method

0.000 3.075 3.226 0.298 3.441 3.752 0.261

ΔE0K‡

2.974 3.251

0.000 2.527 2.762

ΔH298 K‡

10.379 10.767

0.000 10.264 10.203

ΔG298 K‡

UM06−2x/aug-cc-pVTZ 0.000 2.169 2.169 0.000 2.411 2.411 0.000

ΔE0K‡

1.939 1.939

0.000 1.601 1.601

ΔH298 K‡

CBS-QB3

9.431 9.431

0.000 9.506 9.506

ΔG298 K‡

4.89 [8]

4.79 [8]

literature ΔE‡ (kcal mol−1)

Table 6. Internal Energies, Enthalpies and Gibb’s Free Energies (in kcal mol−1) of Transition States Relative to the Reactants along the Chemical Pathways 1−2 for the Oxidation of Naphthalene into 1- and 2-Naphthyl Radicalsa

a

naphthalene + OH• IM1-ipso [C10H8··· OH]• IM1-ortho [C10H8··· OH]• IM1-orthob BSSE energy- IM1-ortho IM2a [C10H8···H2O]• IM2b [C10H8···H2O]• P1 (1-naphthyl+H2O) P2 (2-naphthyl+H2O)

species

B3LYP/aug-cc-pVTZ

method

Table 5. Internal Energies, Enthalpies, and Gibb’s Free Energies (in kcal mol−1) of Intermediate States Relative to the Reactants along the Chemical Pathways 1−2 for the Oxidation of Naphthalene into 1- and 2-Naphthyl Radicalsa

The Journal of Physical Chemistry A Article



Article

Figure 6. Plot of our computed bimolecular rate constants versus experimental data. Legend: (●) theoretical rate constant for pathway 1; (■) theoretical rate constant for pathway 2; (⧫) experimental data.12−15

Figure 5. Arrhenius plot of our computed bimolecular rate constants versus experimental data. Legend: (●) theoretical rate constant for pathway 1; (Δ) theoretical rate constant for pathway 2; (⧫) theoretical total rate constant for pathways 1 and 2; (■) experimental data.12−15

Table 8. Wigner Tunneling Factor for the Reaction of Naphthalene with OH Radicals at Temperatures Ranging from 636 to 873 K

The associated Wigner factors approach unity (Table 8), which shows that tunneling effects have only a limited influence on the computed rate constants. Our calculated rate constants for pathways 1 and 2 vary from 3.51 × 10−12 to 6.47 × 10−12 and from 6.78 × 10−12 to 1.29 × 10−11 cm3 molecule−1 s−1, respectively. The fact that the rate constants for these two pathways are almost equal indicates that there is no significant selectivity for the removal of a hydrogen atom from the C1 or C2 positions in naphthalene by a hydroxyl radical. It can be seen from Table 7 that the rate constants increase gradually with increasing temperatures (Figure 6). Fitting these data through a least-squares procedure within the selected temperature range to a three-parameter Arrhenius-like equation [k(T) = A.Tn.exp(−Ea/RT)] gives the following regressions:

temperature pathway

636

665

727

873

(1) (2)

1.3380 1.3474

1.3091 1.3178

1.2587 1.2659

1.1794 1.1844

Pathway 1: k1(T ) = 5.33 × 10−13 T 0.503 exp( −867.1/T ) [in cm3 molecule−1 s−1]

(14)

Pathway 2: k 2(T ) = 2.49 × 10−15 T1.319 exp( −389.7/T ) [in cm 3 molecule−1 s−1]

(15)

Branching ratios for the reaction pathways 1 and 2 are reported in Table 7. These ratios were computed as the selected temperatures, as follows: R(1) =

kR → P1 kR → P1 + kR → P2

Figure 7. Evaluation of branching ratios as a function of the temperature for pathways 1−2.

(16)

Table 7. Overall Rate Constants (in cm3 molecule−1 s−1) and Branching Ratios (%) for the Reported Reaction Channels at Temperatures Ranging from 636 to 873 K by Means of TST Theory (P = 1.0 bar) rate constant T (K)

IM1→R k−1 (s−1)

636 665 727 873

2.42 2.23 1.92 1.51

× × × ×

1014 1014 1014 1014

IM1→P1 k2a (s−1) 4.48 4.67 5.09 6.05

× × × ×

1011 1011 1011 1011

IM1→P2 k2b (s−1) 8.67 9.09 9.97 1.21

× × × ×

1011 1011 1011 1012

branching ratio

R→P1 ktot (1) 3.51 3.78 4.46 6.47

× × × ×

10−12 10−12 10−12 10−12 3633

R→P2 ktot (2) 6.78 7.36 8.74 1.29

× × × ×

10−12 10−12 10−12 10−11

ktot [k(1)+k(2)]

R(1)

R(2)

10−11 10−11 10−11 10−11

34.05 33.93 33.79 33.40

65.95 66.07 66.21 66.60

1.03 1.11 1.32 1.94

× × × ×

kexp [12−15] (1.1 (1.1 (1.4 (3.0

± ± ± ±

0.1) 0.2) 0.2) 0.5)

× × × ×

10−12 10−12 10−12 10−12


The Journal of Physical Chemistry A R(2) =

kR → P2 kR → P1 + kR → P2

■

Article

ASSOCIATED CONTENT

S Supporting Information *

(17)

Table S1: Temperature dependence of the equilibrium constants for the first bimolecular reaction step (R⇆IM1) along the chemical pathways 1−2 at different temperatures. Table S2: Expectation value of the ⟨S2⟩ operator at the reported theoretical levels. Table S3: Internal energies, enthalpies, and Gibb’s free energies (in kcal mol−1) of intermediate states relative to the reactants along the chemical pathways 1−2 for the oxidation of naphthalene into 1- and 2-naphthyl radicals at a pressure of 1.0 bar and different temperatures [B3LYP/6311G(2d,d,p) results]. Table S4: Internal energies, enthalpies, and Gibb’s free energies (in kcal mol−1) of transition states relative to the reactants along the chemical pathways 1−2 for the oxidation of naphthalene into 1- and 2-naphthyl radicals at a pressure of 1.0 bar and different temperatures [B3LYP/6311G(2d,d,p) results]. This material is available free of charge via the Internet at http://pubs.acs.org.

When taking tunneling corrections into account (Table 8), abstraction of the H-bonded to the C1- and C2-atoms accounts for 34.05−33.4% and 65.95−66.6% of the overall adduct products, respectively. These branching ratios for pathways 1 and 2 only slightly vary with the temperature (Figure 7), which demonstrates that under the considered experimental conditions the removal of hydrogen atoms in naphthalene by a hydroxyl radical is essentially a nonselective process. Only a slight preference for the removal of a hydrogen atom from the C2 position can be reported. Some caution is required, however, because of the limitations inherent to our calculations. Calculations of branching ratios within accuracy of a few percent would indeed require more sophisticated treatments for calculating partition functions and energy differences, taking, in particular, anharmonic and dispersion forces hindered rotations into account.

■

4. CONCLUSIONS Reaction mechanisms for the initial stages of naphthalene oxidation at high temperatures (T ≥ 600 K) have been studied theoretically using Density Functional Theory in conjunction with various exchange-correlation functionals (B3LYP, ωB97XD, UM05−2x, and UM06−2x) and the aug-cc-pVTZ basis set. These stages correspond to the removal of hydrogen atoms by hydroxyl radicals and the formation thereby of 1- and 2-naphthyl radicals. The supplied reaction energies and activation barriers incorporate zero-point vibrational energy differences and counterpoise corrections for basis set superposition errors. Comparison has been made with the results of benchmark calculations employing the composite CBS-QB3 approach. This comparison indicates that the most reliable exchange-correlation functionals for kinetic calculations are the UM05-2x and UM06-2x ones. Bimolecular kinetic rate constants were correspondingly estimated by means of transition state theory, on the grounds of partition functions calculated using the rigid rotor-harmonic oscillator approximation. The all-in-all rather excellent agreement with the available experimental kinetic rate constants confirms that the two-step reaction scheme proposed by Singleton and Cvetanovic63 is valid. Since the main contributions to Gibb’s free reaction and activation energies were found to be entropic in origin, more elaborate treatments of statistical thermodynamical partition functions, taking dispersion forces, anharmonic effects, and hindered rotations85 into account, should certainly be considered for improving further the agreement between theory and experiment. Analysis of the computed structures, bond orders, and free energy profiles demonstrate that the reaction steps involved in the removal of hydrogen atoms by OH radicals satisfy Hammond’s principle: indeed, whatever the site of the reaction in naphthalene, the transition states for the first exergonic bimolecular reaction steps are structurally closer to the prereactive molecular complexes. The energy profiles for removal of hydrogen atoms at the C1 and C2 positions are very similar, with differences in activation energies and reaction energies that do not exceed ∼0.3 kcal mol−1. Therefore, these reaction processes do not appear to exhibit a particularly pronounced site-selectivity: only a slight preference for a reaction at site C1 and formation thereby of 1-naphthyl can be reported from the computed branching ratios.

AUTHOR INFORMATION

Corresponding Author

*Tel: +32-11-268303; E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS A. Shiroudi acknowledges a PhD fellowship from the “Bijzonder Onderzoeksfonds” (BOF) of Hasselt University. All calculations presented in this work have been performed at the Flemish Supercomputer Center (Vlaams Supercomputer Centrum). This cluster has been financed by budgets obtained from the Katholieke Universiteit Leuven, from individual contributions by users, and financing obtained from the Hercules foundation and the Flemish government. The authors acknowledge useful discussions on reaction kinetics with Prof. Dr. S. Canneaux, Université de Lille 1, France.

■

REFERENCES

(1) Tokiwa, H.; Ohnishi, Y.; Rosenkranz, H. S. Mutagenicity and Carcinogenicity of Nitroarenes and Their Sources in the Environment. CRC Crit. Rev. Toxicol. 1986, 17, 23−60. (2) Josephy, P. D.; Mannervik, B.; De Montellano, P. O. Molecular Toxicology; Oxford University Press: Oxford, 1997. (3) Nishino, N.; Atkinson, R.; Arey, J. Formation of Nitro Products from the Gas-Phase OH Radical-Initiated Reactions of Toluene, Naphthalene, and Biphenyl: Effect of NO2 Concentration. Environ. Sci. Technol. 2008, 42, 9203−9209. (4) Hendry, D. G.; Kenley, R. A. Atmospheric Reaction Products of Organic Compounds; U.S. Environmental Protection Agency EPA560112-79-001, 1979. (5) Atkinson, R.; Darnall, K. R.; Lloyd, A. C.; Winer, A. M.; Pitts, J. N. Kinetics and Mechanisms of the Reaction of the Hydroxyl Radical with Organic Compounds in the Gas Phase. Adv. Photochem. 1979, 11, 375−488. (6) Bunce, N. J.; Liu, L.; Zhu, J. Reaction of Naphthalene and Its Derivatives with Hydroxyl Radicals in the Gas Phase. Environ. Sci. Technol. 1997, 31, 2252−2259. (7) Atkinson, R.; Arey, J. Atmospheric Chemistry of Gas-Phase Polycyclic Aromatic Hydrocarbons: Formation of Atmosphere Mutagens. Environ. Health Perspect. 1994, 102, 117−126. (8) Qu, X.; Zhang, Q.; Wang, W. Mechanism for OH-Initiated Photooxidation of Naphthalene in the Presence of O2 and NOx: A DFT Study. Chem. Phys. Lett. 2006, 429, 77−85.

3634



Article

(9) Arey, J.; Zielinska, B.; Atkinson, R.; Winer, A. M. Polycyclic Aromatic Hydrocarbon and Nitroarene Concentrations in Ambient Air During a Wintertime high-NOx Episode in the Los Angeles Basin. Atmos. Environ. 1967, 21, 1437−1444. (10) Arey, J.; Atkinson, R.; Zielinska, B.; McElroy, P. A. Diurnal Concentrations of Volatile Polycyclic Aromatic Hydrocarbons and Nitroarenes during a Photochemical Air Pollution Episode in Glendora. California. Environ. Sci. Technol. 1989, 23, 321−327. (11) Graedel, T. E. Chemical Compounds in the Atmosphere; Academic Press: New York, 1978. (12) Lorenz, K.; Zellner, R. Kinetics of the Reactions of OH-Radicals with Benzene, Benzene-d6 and Naphthalene. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 629−636. (13) Lorenz, K.; Zellner, R. Kinetics of the Reactions of OH Radicals with Benzene, Naphthalene and Phenanthrene between 400 and 1000 K; ; 8th International Symposium on Gas Kinetics; University of Nottingham, U.K.; July 15−20, 1984. (14) Atkinson, R. Kinetics and Mechanisms of the Gas-Phase Reactions of the Hydroxyl with Organic Compounds. J. Phys. Chem. Ref. Data, Monograph 1989, 1, 1−246. (15) Sander, L. C.; Wise, S. A. In NIST Chemistry WebBook; NIST Standard Reference Database 69; National Institute of Standards and Technology; http://kinetics.nist.gov/. (16) Perry, R. A.; Atkinson, R.; Pitts, J. N., Jr. Kinetics and Mechanism of the Gas Phase Reaction of Hydroxyl Radicals with Aromatic Hydrocarbons over the Temperature Range 296−473 K. J. Phys. Chem. 1977, 81, 296−304. (17) Atkinson, R.; Aschmann, S. M.; Pitts, J. N. Kinetics of the Reactions of Naphthalene and Biphenyl with Hydroxyl Radicals and with Ozone at 294 ± 1 K. Environ. Sci. Technol. 1984, 18, 110−113. (18) Atkinson, R.; Aschmann, S. M. Kinetics of the Reactions of Naphthalene, 2-Methylnaphthalene, and 2,3-Dimethylnaphthalene with OH Radicals and with O3 at 295 ± 1 K. Int. J. Chem. Kinet. 1986, 18, 569−573. (19) Hollman, D. S.; Simmonett, A. C.; Schaefer, H. F. The Benzene + OH Potential Energy Surface: Intermediates and Transition States. Phys. Chem. Chem. Phys. 2011, 13, 2214−2221. (20) Montgomery, J. A.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. IV. An Improved Atomic Pair Natural Orbital Method. J. Chem. Phys. 1994, 101, 5900−5909. (21) Montgomery, J. A.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VI. Use of Density Functional Geometries and Frequencies. J. Chem. Phys. 1999, 110, 2822−2827. (22) Ochterski, J. W.; Petersson, G. A.; Montgomery, J. A. A Complete Basis Set Model Chemistry. V. Extensions to Six or More Heavy Atoms. J. Chem. Phys. 1996, 104, 2598−2619. (23) Nyden, M. R.; Petersson, G. A. Complete Basis Set Correlation Energies. I. The Asymptotic Convergence of Pair Natural Orbital Expansions. J. Chem. Phys. 1981, 75, 1843−1862. (24) Petersson, G. A.; Bennett, A.; Tensfeld, T. G.; Al-Laham, M. A.; Shirley, W.; Matzaris, J. A Complete Basis Set Model Chemistry. I. The Total Energies of Closed-Shell Atoms and Hydrides of the FirstRow Elements. J. Chem. Phys. 1988, 89, 2193−2218. (25) Petersson, G. A.; Al-Laham, M. A. A Complete Basis Set Model Chemistry. II. Open-Shell Systems and the Total Energies of the FirstRow Atoms. J. Chem. Phys. 1991, 94, 6081−6090. (26) Petersson, G. A.; Yee, A. K.; Bennett, A. Complete Basis Set Correlation Energies. III. The Total Correlation Energy of the Neon Atom. J. Chem. Phys. 1983, 83, 5105−5128. (27) Montgomery, J. A.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VII. Use of the Minimum Population Localization Method. J. Chem. Phys. 2000, 112, 6532− 6542. (28) Casasnovas, R.; Frau, J.; Ortega-castro, J.; Salva, A.; Donoso, J.; Munoz, F. Simplification of the CBS-QB3Method for Predicting GasPhase Deprotonation Free Energies. Int. J. Quantum Chem. 2010, 110, 323−330.

(29) Bartlett, R. J.; Watts, J. D.; Kucharski, S. A.; Noga, J. NonIterative Fifth-Order Triple and Quadruple Excitation Energy Corrections in Correlated Methods. Chem. Phys. Lett. 1990, 165, 513−522. (30) Stanton, J. F. Why CCSD(T) Works: A Different Perspective. Chem. Phys. Lett. 1997, 281, 130−134. (31) Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory; McGraw-Hill: New York, 1989. (32) Eyring, H. The Activated Complex in Chemical Reactions. J. Chem. Phys. 1935, 3, 107−115. (33) Johnston, H. S. Gas Phase Reaction Rate Theory; The Roland Press Co: New York, 1966. (34) Laidler, K. J. Theories of Chemical Reaction Rates; McGraw-Hill: New York, 1969. (35) Weston, R. E.; Schwartz, H. A. Chemical Kinetics; Prentice-Hall: New York, 1972. (36) Rapp, D. Statistical Mechanics; Holt, Reinhard, and Winston: New York, 1972. (37) Nikitin, E. E. Theory of Elementary Atomic and Molecular Processes in Gases; Clarendon Press: Oxford, 1974. (38) Smith, I. W. M. Kinetics and Dynamics of Elementary Gas Reactions; Butterworths: London, 1980. (39) Steinfeld, J. I.; Francisco, J. S.; Hase, W. L. Chemical Kinetics and Dynamics; Prentice-Hall: Englewood Cliffs, NJ, 1989. (40) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision B.01; Gaussian: Wallingford, CT, 2009. (41) Dennington, I. I. R.; Keith, T.; Millam, J.; Eppinnett, K.; Hovell, W. L.; Gilliland, R. GaussView, version 3.09; Semichem, Inc.: Shawnee Mission, KS, 2003. (42) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (43) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (44) Chai, J. D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615−6620. (45) Zhao, Y.; Truhlar, D. G. Density Functionals with Broad Applicability in Chemistry. Acc. Chem. Res. 2008, 41, 157−167. (46) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-class Functionals and 12 other Functionals. Theor. Chem. Acc. 2008, 120, 215−241. (47) Dunning, T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007−1023. (48) Sousa, J. A.; Silva, P. P.; Machado, A. E. H.; Reis, M. H. M.; Romanielo, L. L.; Hori, C. E. Application of Computational Chemistry Methods to Obtain Thermodynamic Data for Hydrogen Production from Liquefied Petroleum Gas. Braz. J. Chem. Eng. 2013, 30, 83−93. (49) McQuarrie, D. A. Statistical Mechanics; Harper and Row: New York, 1976. (50) Herzberg, G. H. Molecular Spectra and Molecular Structure. II. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand Reinhold: New York, 1945. (51) Martin, J. M. L.; El-Yazal, J.; François, J. P. Basis Set Convergence and Performance of Density Functional Theory Including Exact Exchange Contributions for Geometries and Harmonic Frequencies. Mol. Phys. 1995, 86, 1437−1450. (52) Martin, J. M. L.; De Oliveira, G. Towards Standard Methods for Benchmark Quality Ab Initio Thermochemistry-W1 and W2 Theory. J. Chem. Phys. 1999, 111, 1843−1856. 3635



Article

(53) Ess, D. H. Quantum Mechanical Theory of Reactivity and Selectivity in Organic and Organometallic Reactions; Ph.D. Dissertation; University of California, Los Angeles, 2007. (54) Vandeputte, A. G.; Sabbe, M. K.; Reyniers, M. F.; Speybroeck, V. V.; Waroquier, M.; Marin, G. B. Theoretical Study of the Thermodynamics and Kinetics of Hydrogen Abstractions from Hydrocarbons. J. Phys. Chem. A 2007, 111, 11771−11786. (55) Stanton, J. F. On the Extent of Spin Contamination in OpenShell Coupled-Cluster Wave Functions. J. Chem. Phys. 1994, 101, 371−374. (56) Gonzalez, C.; Schlegel, H. B. An Improved Algorithm for Reaction Path Following. J. Chem. Phys. 1989, 90, 2154−2161. (57) McIver, J. W., Jr. Structure of Transition States. Are They Symmetric? Acc. Chem. Res. 1974, 7, 72−77. (58) Fukui, F. A Formulation of the Reaction Coordinate. J. Phys. Chem. 1970, 74, 4161−4163. (59) Wiberg, K. B. Properties of Some Condensed Aromatic Systems. J. Org. Chem. 1997, 62, 5720−5727. (60) Ketkar, S. N.; Fink, M. The Molecular Structure of Naphthalene by Electron Diffraction. J. Mol. Struct. (THEOCHEM) 1981, 77, 139− 147. (61) Zhang, Z.; Lin, L.; Wang, L. Atmospheric Oxidation Mechanism of Naphthalene Initiated by OH Radical. A Theoretical Study. Phys. Chem. Chem. Phys. 2012, 14, 2645−2650. (62) Boys, S. F.; Bernardi, F. Calculation of Small Molecular Interactions by Differences of Separate Total Energies-Some Procedures with Reduced Errors. Mol. Phys. 1970, 19, 553−566. (63) Singleton, D. L.; Cvetanovic, R. J. Temperature Dependence of the Reaction of Oxygen Atoms with Olefins. J. Am. Chem. Soc. 1976, 98, 6812−6819. (64) Alvarez-Idaboy, J. R.; Diez, N. M.; Vivier-Bunge, A. A Quantum Chemical and Classical Transition State Theory Explanation of Negative Activation Energies in OH Addition to Substituted Ethenes. J. Am. Chem. Soc. 2000, 122, 3715−3720. (65) Uc, V. H.; Alvarez-Idaboy, J. R.; Galano, A.; Vivier-Bunge, A. Theoretical Explanation of Nonexponential OH Decay in Reactions with Benzene and Toluene under Pseudo-First-Order Conditions. J. Phys. Chem. A 2008, 112, 7608−7615. (66) Mortimer, R. G. Physical Chemistry, 3rd ed.; Elsevier Academic Press: Burlington, 2008. (67) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombonitation Reactions; Blackwell Scientific: Oxford, 1990. (68) Wigner, E. P. Uber das Uberschreiten von Potentialschwellen bei Chemischen Reaktionen. Z. Phys. Chem. 1932, B19, 203−216. (69) Canneaux, S.; Bohr, F.; Henon, E. KiSThelP: A Program to Predict Thermodynamic Properties and Rate Constants from Quantum Chemistry Results. J. Comput. Chem. 2013, 35, 82−93. (70) Hammaecher, C.; Canneaux, S.; Louis, F.; Cantrel, L. A Theoretical Study of the H-Abstraction Reactions from HOI by Moist Air Radiolytic Products (H, OH, and O (3P)) and Iodine Atoms (2P3/2). J. Phys. Chem. A 2011, 115, 6664−6674. (71) Varma, D. H.; Raghunath, P.; Lin, M. C. Ab Initio Chemical Kinetics for the Reaction of an H Atom with Si3H8. J. Phys. Chem. A 2010, 114, 3642−3648. (72) Wu, S. Y.; Raghunath, P.; Wu, J. S.; Lin, M. C. Ab Initio Chemical Kinetic Study for Reactions of H Atoms with SiH4 and Si2H6: Comparison of Theory and Experiment. J. Phys. Chem. A 2010, 114, 633−639. (73) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. A Fifth-Order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157, 479−483. (74) Rao, H. B.; Zeng, X. Y.; He, H.; Li, Z. R. Theoretical Investigations on Removal Reactions of Ethenol by H Atom. J. Phys. Chem. A 2011, 115, 1602−1608. (75) Alvarez-Idaboy, J. R.; Mora-Diez, N.; Boyd, R. J.; Viver-Bunge, A. On the Importance of Prereactive Complexes in Molecule-Radical Reactions: Hydrogen Abstraction from Aldehydes by OH. J. Am. Chem. Soc. 2001, 123, 2018−2024.

(76) Zhou, C. W.; Mebel, A. M.; Li, X. Y. An Ab Initio/RiceRamsperger-Kassel-Marcus Study of the Reactions of Propenols with OH. Mechanism and Kinetics of H Abstraction Channels. J. Phys. Chem. A 2009, 113, 10667−10677. (77) Hammond, G. S. A Correlation of Reaction Rates. J. Am. Chem. Soc. 1953, 77, 334−338. (78) Lendvay, G. Bond Orders from Ab Initio Calculations and a Test of the Principle of Bond Order Conservation. J. Phys. Chem. 1989, 93, 4422−4429. (79) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Intermolecular Interactions from a Natural Bond Orbital, Donor-Acceptor Viewpoint. Chem. Rev. 1988, 88, 899−926. (80) Reed, A. E.; Weinstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735−746. (81) Moyano, A.; Periclas, M. A.; Valenti, E. A Theoretical Study on the Mechanism of the Thermal and the Acid-Catalyzed Decarboxylation of 2-Oxetanones (β-Lactones). J. Org. Chem. 1989, 54, 573− 582. (82) Lopez, V.; Quijano, J.; Luna, S.; Ruiz, P.; Rios, D.; Parra, W.; Zapata, E.; Gaviria, J.; Notario, R. Experimental and Computational Study of the Thermal Decomposition of 3-Buten-1-ol in m-Xylene Solution. Struct. Chem. 2013, 24, 1811−1816. (83) Rosas, F.; Dominguez, R. M.; Tosta, M.; Mora, J. R.; Marquez, E.; Cordova, T.; G. Chuchani, G. The Mechanism of the Homogeneous, Unimolecular Gas-Phase Elimination Kinetic of 1,1Dimethoxycyclohexane: Experimental and Theoretical Studies. J. Phys. Org. Chem. 2010, 23, 743−750. (84) Rayez, M. T.; Rayez, J. C.; Sawerysyn, J. P. Ab Initio Studies of the Reactions of Chlorine Atoms with Fluoro- and Chloro-Substituted Methanes. J. Phys. Chem. 1994, 98, 11342−11352. (85) Canneaux, S.; Vandeputte, R.; Hammaecher, C.; Louis, F.; Ribaucour, M. Thermochemical Data and Additivity Group Values for Ten Species of O-Xylene Low-Temperature Oxidation Mechanism. J. Phys. Chem. A 2012, 116, 592−610.

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Theoretical Study of the Oxidation Mechanisms of Naphthalene

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