Mechanism and Kinetics of the Atmospheric Oxidative Degradation of

Article pubs.acs.org/JPCA

Mechanism and Kinetics of the Atmospheric Oxidative Degradation of Dimethylphenol Isomers Initiated by OH Radical L. Sandhiya, P. Kolandaivel, and K. Senthilkumar* Department of Physics, Bharathiar University, Coimbatore 641 046, India S Supporting Information *

ABSTRACT: Dimethylphenols are highly reactive in the atmosphere, and their oxidation plays a vital role in the autoignition and combustion processes. The dominant oxidation process for dimethylphenols is by gas-phase reaction with OH radical. In the present study, the reaction of OH radical with dimethylphenol isomers is studied using density functional theory methods, B3LYP, M06-2X, and MPW1K, and also at the MP2 level of theory using 6-31G(d,p) and 6-31+G(d,p) basis sets. The activation energy values have also been calculated using the CCSD(T) method with 6-31G(d,p) and 6311+G(d,p) basis sets using the geometries optimized at the M06-2X/ 6-31G(d,p) level of theory. The reactions subsequent to the principal oxidation steps are studied, and the different reaction pathways are modeled. The positions of the OH and CH3 substituents in the aromatic ring have a great influence on the reactivity of dimethylphenol toward OH radical. Accordingly, the reaction is initiated in four different ways: H-atom abstraction from the phenol group, H-atom abstraction from a methyl group, H-atom abstraction from the aromatic ring by OH radical, or electrophilic addition of OH radical to the aromatic ring. Aromatic peroxy radicals arising from initial H-atom abstraction and subsequent O2 addition lead to the formation of hydroperoxide adducts and alkoxy radicals. The O2 additions to dimethylphenol−OH adduct results in the formation of epoxide and bicyclic radicals. The rate constants for the most favorable reaction pathways are calculated using canonical variational transition state theory with small curvature tunneling corrections. This study provides thermochemical and kinetic data for the oxidation of dimethylphenol in the atmosphere and demonstrates the mechanism for the conversion of peroxy radical into aldehydes, hydroperoxides, epoxides, and bicyclic radicals, and their lifetimes in the atmosphere.

1. INTRODUCTION Aromatic compounds such as benzene, toluene, and xylene are important pollutants in urban areas. Exceptional use of automobile fuel results in the substantial emission of aromatic compounds to the atmosphere.1−4 The atmospheric degradation of these aromatic compounds is initiated by reaction with OH radicals.5,6 Understanding the oxidation chemistry of aromatic compounds is important, because this reaction mechanism is considered to be a major uncertainty in stateof-the-art photochemical models.7 The photooxidation products of aromatic compounds are toxic and have mutagenic effects.7 The reaction between aromatic compounds and OH radicals produces cresols, phenols, and dimethylphenols.8 In order to understand the environmental implications of aromatic compounds present in the atmosphere, a detailed study on the degradation mechanism of these products is very essential. An accurate modeling of the reaction mechanism will provide information about the degradation products and their lifetimes. Among the aromatic compounds, dimethylphenol (DMP) is formed due to the oxidation of xylene by OH radicals in the atmosphere.8 In industry, DMP is obtained from coal tar or petroleum as byproducts in fractional distillation and in coal gasification.7 The reaction between DMP and OH radical will © XXXX American Chemical Society

form photooxidants, much more efficiently than other aromatics. This is because the alkyl-substituted aromatic compounds are chemically active in air masses where sufficient NOx is available to promote photooxidation. In addition, the isomers of DMP are ascribed high photochemical ozone creation potential (POCP) values comparable to those of other aromatic compounds.7 Hence the reaction between DMP and OH radical is potentially important in atmospheric science. Few experimental studies have focused on identifying the products formed during the atmospheric degradation of phenolic compounds,7,9 and very few aromatic intermediate radicals have been identified in gas phase reactions.10,11 However, the different reaction pathways leading to a variety of products are not interpreted properly due to the existence of multiple reaction steps and difficulties in experimental studies. For instance, the isolation of intermediates and transition states is very difficult through experimental techniques due to their short lifetimes. To overcome this difficulty, theoretical studies with quantum chemical calculations are used and are the best Received: December 8, 2012 Revised: April 16, 2013

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dx.doi.org/10.1021/jp3120868 | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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tools to identify and characterize the reaction pathways. In view of the above-mentioned exposures and the practical importance of the degradation of DMP by OH radical, the principal aim of this work is to characterize the full potential energy surface of the DMP + OH reaction by carefully mapping out the various degradation processes using computational methods. In the atmosphere, the reaction between DMP isomers and OH radicals proceeds through four different ways: by H-atom abstraction from the phenol group, by H-atom abstraction from a methyl group, by H-atom abstraction from the aromatic ring by OH radical, or by electrophilic addition of OH radical to the aromatic ring. The H-atom abstraction from the phenol group of DMP results in the formation of dimethylbenzoquinones and epoxides on subsequent O2 addition (see Scheme 1). The H-

Scheme 3. Reaction Scheme for the H-Atom Abstraction Reaction from Aromatic Ring of 3,5-DMP by OH Radical and Its Subsequent Reactions

Scheme 1. Reaction Scheme for the H-Atom Abstraction Reaction from Phenol Group of 2,3-DMP by OH Radical and Its Subsequent Reactions

This bicyclic radical is the source for the reaction pathways corresponding to the formation of ring-cleavage products.12 Scheme 4. Reaction Scheme for the Electrophilic Addition of OH Radical to the Aromatic Ring of 3,5-DMP and Its Subsequent Reactions

atom abstraction reactions from a methyl group and from the aromatic ring of DMP are subsequently followed by O2 addition reaction and lead to the formation of a peroxy radical intermediate. This intermediate has excess energy to react with HO2 and NO present in the atmosphere to produce hydroperoxide adducts and alkoxy radicals (see Schemes 2 and 3). The electrophilic addition reaction results in the formation of cyclohexadienyl radical which may further react with O2, leading to the formation of phenolic compounds and peroxy radical. The peroxy radical further isomerizes and cyclizes to yield epoxy and bicyclic radicals (see Scheme 4). Scheme 2. Reaction Scheme for the H-Atom Abstraction Reaction from Methyl Group of 2,3-DMP by OH Radical and Its Subsequent Reactions

The number and position of the OH and CH3 substituents have a great influence on the reactivity of aromatic compounds.9 This is because both OH and CH3 groups donate electron density to the ortho and para positions of aromatic compounds and leads to electrophilic addition reactions at these sites. Accordingly, DMP is more reactive than cresols but less reactive than trimethylphenols.8,9,13 Previous studies on reaction of phenolic compounds with OH radicals show that the reactions proceed mainly via electrophilic addition of OH to the aromatic ring.14,15 However, depending upon the position of the substituent, the reaction mechanism and the degradation products differ. It is expected that the reactive site activated by the OH group is more reactive than those activated by the CH3 group. Also, the presence of methyl groups at ortho and para positions provides steric hindrance to electrophilic addition and therefore this leads to reduction in reactivity. The presence of two methyl groups in the DMP isomers favors the reaction with OH radical and leads to the abstraction of H-atom from a methyl group by OH B



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electronic structure calculations were performed using the Gaussian 09 program package.33 The computed potential energy surface and associated transition state parameters were directly used to predict the rate constant as a function of temperature. The theoretical rate constants for the reactions are calculated using the canonical variational transition state theory (CVT)34,35 from which the rate constant is given by the formula

radical. The high resonance potential of the phenol group will direct the incoming OH radical to bind at the carbon atom site between two methyl groups of DMP isomers. The ortho−para directing property of OH and CH3 substituents has a profound influence on the initial reactivity of the aromatic compound. Thus the mechanism of the principal oxidation step of DMP and the mechanism and kinetics of the subsequent reactions from the principal oxidation step are important and interesting. In the present study, to rationalize the different initial processes, a theoretical investigation is performed on the reaction between OH radicals and six DMP isomers, 2,3-, 2,4-, 2,5-, 2,6-, 3,4-, and 3,5-DMP. Possible reaction pathways subsequent to the initial step outlined in Schemes 1−4 are characterized. The activation barrier for the formation of various degradation products is analyzed to predict the favorable reaction pathways for the oxidation of DMP in the atmosphere. Also, in order to predict the lifetime of DMP and degradation products in the atmosphere, the rate constants over the temperature range of the troposphere for the reactions involving major product channels are determined using variational transition state theory.16

kCVT(T ) = min kcGT(T , s) R

(1)

where the generalized transition state theory rate constant kGT(T,s) is defined as kcGT(T , s) =

GT σkBT Q c (T , s) exp[−βVMEP(s)] βh ϕc R (T )

(2)

Here σ is the symmetry factor accounting for the possibility of more than one symmetry related reaction path, QcGT(T,s) is the classical partition function for the generalized transition state dividing surface, ϕcR(T) is the reactant partition function per unit volume, VMEP(s) is the classical potential energy at point s on the minimum energy path, kB is the Boltzmann constant, and h is the Planck constant. The quantity (βh)−1 is called the universal transition state frequency factor. Since the CVT rate constant neglects the tunneling, it underestimates the rate constant for the reactions in which quantum tunneling is predominant, especially at low temperatures. Hence, in order to account for the dynamical quantum effects of reaction coordinate tunneling, a multiplicative transmission coefficient κ(T)is used in eq 1 as

2. COMPUTATIONAL METHODS The geometries of the reactants, intermediates, transition states, and products on the ground state potential energy surface of the DMP + OH reaction system were optimized by the density functional theory (DFT) methods B3LYP,17,18 MPW1K,19 and M06-2X20 with the 6-31G(d,p) basis set. The hybrid density functional B3LYP is the most widely used method for studying chemical reactions.21,22 The MPW1K method is a competitive method in predicting the energies and geometries of the stationary points along the minimum energy path and provides promising accuracy for the calculation of reaction energies and kinetics.23 Recent studies show that DFT calculations with the M06-2X functional perform well for thermochemical and reaction mechanism studies.24,25 Hence, in the present work we employed the above three DFT functionals to study the reaction mechanism and kinetics. In M06-2X computations, an ultrafine integration grid was used. All the stationary points were characterized by harmonic vibrational frequency calculations. All local minima were confirmed with all positive frequencies, while the transition state structure on the potential energy surface has been characterized as a first-order saddle point with a single imaginary frequency. For all the studied reactions, the connectivity between the transition state and its corresponding reactant and product was verified by performing intrinsic reaction coordinate (IRC) calculations26 at all the above-mentioned levels of theories. The paths have been verified by following the Gonzalez−Schlegel steepest descent path in mass-weighted internal coordinates.27 The effect of adding diffuse functions on heavy atoms to the 6-31G(d,p) basis set on the structure and energetics of the stationary points on the potential energy surface (PES) is investigated. Also, all the stationary points were fully optimized and characterized using frequency calculations at the MP228−30 level of theory with the 6-31G(d,p) basis set. The single point energy calculations were performed at CCSD(T) with 6-31G(d,p) and 6-311+G(d,p) basis sets using the geometries optimized at the M06-2X method to assess the accuracy of DFT and MP2 results.31,32 The enthalpy of reaction and Gibbs free energy values were calculated by including thermodynamic corrections to the energy at 298.15 K and at 1 atm pressure. All the

kcCVT(T ) = κ(T ) kCVT(T )

(3)

The transmission coefficient κ(T) corresponding to tunneling is evaluated by small-curvature approximation to the vibrational adiabatic potential energy surface.36 In this approximation, the tunneling is assumed to occur along a multidimensional minimum energy path. The potential energy curve is approximated by a contracted adiabatic energy barrier which goes through the corrected zero point vibrational energy of the reactants, transition states, and products. The equilibrium constant (Kc in concentration units) for the reactions in equilibrium is evaluated using the standard formulas37

Kc = K pR′T

(4)

RT ln K p = −ΔGT °

(5)

where R′ is the ideal gas constant in liter atmosphere units, Kp is the equilibrium constant in pressure units, and ΔGT° is the standard Gibbs energy at 1 atm pressure. The rate constant calculations were performed by use of the GAUSSRATE 2009A38 program, which is an interface between the Gaussian 09 and POLYRATE 2010A39 programs.

3. RESULTS AND DISCUSSION As described above, the reaction between OH radicals and the isomers of DMP, 2,3-, 2,4-, 2,5-, 2,6-, 3,4- and 3,5-DMP, is found to proceed in four different ways. The initial step is different for different isomers, and the subsequent reaction for the most favorable initial reaction is studied in detail. The structural parameters of the reactive species obtained from DFT and MP2 calculations differ slightly. For instance, in the C



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Supporting Information, the calculated rate constants show positive temperature dependence except for the hydroperoxide adduct formed in the reaction of H-atom abstraction from a methyl group of 2,3-dimethylphenol. The TST and CVT rate constants are comparable in most of the cases. The effect of variational corrections for the studied reactions is negligible in most of the cases, and in some cases the effect is appreciable and is discussed. In all cases, the calculated Gibbs free energy values vary by about 1−2 kcal/mol over the studied temperature range (see Tables S15−S18 in the Supporting Information). Note that an error of 2 kcal/mol in the energy barrier will lead to an error in the calculated rate constant of 1 order of magnitude.43 3.1. H-Atom Abstraction from Phenol Group of DMP by OH Radical. In DMP isomers, the phenol group donates the electron density and favors the faster electrophilic attack of the reacting OH radical and the abstraction of H-atom from the phenol group. The relative energy (ΔE), relative enthalpy (ΔH), and Gibbs free energy (ΔG) for the stationary points involved in the H-atom abstraction from the phenol group of DMP isomers by OH radical are summarized in Table 1 and in

initial H-atom abstraction from the phenol group of DMP by OH radical, the average root-mean-square deviation (rmsd) between the internal coordinates obtained from M06-2X and B3LYP methods is 0.02 Å for the reactant, 0.05 Å for the transition state, and 0.04 Å for the product. The rmsd between the internal coordinates obtained using M06-2X and MPW1K methods is 0.03, 0.08, and 0.04 Å, respectively for the reactant, transition state, and product. The rmsd between the internal coordinates obtained from M06-2X and MP2 methods is 0.03, 0.07, and 0.06 Å, for the reactant, transition state, and product, respectively. The geometries of the stationary points involved in the reaction pathways obtained with 6-31G(d,p) and 631+G(d,p) basis sets do not differ significantly. The rmsd between the internal coordinates obtained using the B3LYP method with 6-31G(d,p) and 6-31+G(d,p) basis sets for the phenolic H-atom abstraction reaction is 0.02 Å for the reactants, 0.02 Å for the transition state, and 0.03 Å for the product. Note that the above-mentioned rmsd values include interactions of both bonded and nonbonded atoms. In most of the cases the energetics obtained with the DFT functionals are comparable. As expected, for a few cases, the energetics calculated using DFT functionals and the MP2 method differ significantly. On comparing the results obtained for various reaction paths, it is observed that the relative importance of the various reaction channels does not change with respect to the methods of calculation. The favorable reaction path in the studied reaction pathways is the same in DFT and MP2 methods. In recent studies, the M06-2X functional has been shown to give reliable barrier heights and the rate constant calculated using the energetics obtained with the M06-2X functional is in good agreement with experimental results.40,41 It has been reported in a recent study42 that the activation energy calculated at the CCSD(T) level of theory is accurate and the results obtained from the M06-2X functional are comparable with CCSD(T) results. In agreement with the above study, in the present investigation, except for a few cases, the activation energies calculated at M06-2X/6-31G(d,p) level of theory are comparable with the values obtained at the CCSD(T)//M06-2X/6-31G(d,p) level of theory. Also to test the reliability of the M06-2X results, the relative energies for the most favorable reaction pathways are calculated at the CCSD(T)/6-311+G(d,p)//M06-2X/6-31G(d,p) level of theory. The results are summarized in Tables S3, S7, S10, and S13 in the Supporting Information. The calculated relative energy values show that, except for a few cases, the results obtained at the CCSD(T)/6-311+G(d,p)//M06-2X/6-31G(d,p) level of theory are comparable with M06-2X results. Also, the CCSD(T) results obtained with the two basis sets 631G(d,p) and 6-311+G(d,p) are comparable. In a few cases, the deviation in the energy barrier calculated from different methods is about 2−4 kcal/mol. Hence, the structure and energetics obtained using the M06-2X functional with the 631G(d,p) basis set are discussed in detail and are used in further kinetic calculations. The reactant, intermediate, transition state, and product are labeled “R”, “I”, “TS”, and “P”, respectively, followed by a number. The rate constant for the most favorable reaction pathways is calculated over the temperature range 278−350 K. The rate constant calculated using conventional transition state theory (TST) and canonical variational transition state theory (CVT) along with the Gibbs free energy values over the studied temperature range are summarized in Tables S15−S19 in the Supporting Information. As given in Tables S15−S19 in the

Table 1. Relative Energies (ΔE in kcal/mol), Relative Enthalpies (ΔH in kcal/mol), and Gibbs Free Energies (ΔG in kcal/mol) of the Stationary Points on the Ground-State Potential Energy Surface for H-Atom Abstraction from Phenol Group of 2,3-DMP Calculated at M06-2X/631G(d,p) Level of Theory and Relative Energies (ΔE in kcal/mol) at CCSD(T)//M06-2X/6-31G(d,p) Level of Theory M06-2X

a

CCSD(T)

stationary point

ΔE

ΔH

ΔG

ΔE

2,3-DMP + OH RC TS1 PC I1 I1 + O2 TS2 P1 TS3a P2a

0.0 −0.56 6.44 −30.63 −32.34 0.0 25.66 −29.80 48.46 −27.49

0.0 −0.50 3.74 −30.39 −30.4 0.0 23.18 −26.86 50.07 −27.30

0.0 1.44 1.31 −30.65 −33.57 0.0 30.48 −15.02 57.02 −24.09

0.0 −1.21 4.92 −27.76 −28.18 0.0 18.31 −21.9 50.56 −36.28

Values calculated at B3LYP/6-31G(d,p) level of theory.

Table S1 in the Supporting Information. From Table 1 and in Table S1 in the Supporting Information, it is observed that the energy barrier for the abstraction of H-atom from the phenol group of 2,3-DMP is 6.44 kcal/mol, which is very less compared to that of other isomers. Hence, the subsequent reaction from this initial oxidation step alone is studied and the energetics obtained at M06-2X/6-31G(d,p) level of theory is tabulated in Table 1, and the energetics for the initial H-atom abstraction from other isomers is given in Table S1 in the Supporting Information. The energetics obtained at the B3LYP, MPW1K, and MP2 methods with the 6-31G(d,p) basis set and at the B3LYP/6-31+G(d,p) level of theory and the CCSD(T)/ 6-311+G(d,p) level of theory are summarized in Tables S2 and S3 of the Supporting Information. Scheme 1 illustrates the reaction scheme for phenolic H-atom abstraction from 2,3DMP and its subsequent reactions. Figure 1 shows the relative energy profile for this reaction pathway. The optimized structures of the reactive species corresponding to the favorable D



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methods are summarized in Table S4 in the Supporting Information. The kinetic scheme for the favorable reaction at 298 K is illustrated in Figure 3.

Figure 3. Kinetic scheme of the most favorable reaction of H-atom abstraction from phenol group of 2,3-DMP by OH radical.

Figure 1. Relative energy profile for H-atom abstraction reaction from phenol group of 2,3-DMP by OH radical and its subsequent reactions.

The H-atom abstraction from the phenol group of 2,3-DMP by OH radical begins with the formation of a hydrogen-bonded reaction complex, RC, in barrierless reaction. The optimized geometry of this complex has Cs symmetry and was identified as a true local minimum on the PES. In the reactant complex, the hydrogen bond is formed between the hydroxyl radical and the phenol group of 2,3-DMP. The OH radical acts as a donor toward the OH moiety of 2,3-DMP and a hydrogen bond length of 2.12 Å is observed. Then the RC proceeds toward a product complex, PC, through a transition state, TS1. In the product complex, the water molecule is hydrogen bonded to the phenoxy radical with a bond length of 2.61 Å (see Figure 2). This complex was identified as a true minimum on the PES. The product complex further breaks to form phenoxy radical, I1, and a water molecule as products. The barrier calculated for this initial reaction using the B3LYP method is only 0.85 kcal/ mol. On the other hand, the barrier heights calculated using M06-2X, MPW1K, and MP2 methods are 6.44, 1.31, and 26.21 kcal/mol, respectively. That is, the B3LYP and MPW1K functionals underestimate the energy barrier as observed earlier for loose transition states and H-atom abstraction reactions.44−46 On the other hand, the MP2 method highly overestimates the energy barrier as noted in the reaction of OH radical with toluene.47 From Table 1, it is noted that the reactant complex and the product complex optimized using the M06-2X functional lie below by 0.56 and 30.63 kcal/mol, with respect to the reactant. As observed for other H-atom abstraction reactions,48−50 this reaction is exothermic by −32.34 kcal/mol and exoergic by −33.57 kcal/mol. As shown in Figure 3, the forward rate constant calculated at 298 K for this initial reaction is 1.41 × 1017 s−1. The reverse reaction rate constant is 5.4 × 10−6 s−1. According to these values, the reversibility of the reaction is negligible, as reflected in the Keq reported in Figure 3. The tunneling factor Γ is negligible in the initial oxidation reaction due to the broad energy barrier of the initial step as suggested by a small imaginary vibrational frequency (−92.2 cm−1) of the transition state, TS1. The phenoxy radical, I1, can subsequently react with O2 leading to the formation of epoxide, P1, and 2,3-dimethylbenzoquinone, P2. These products were also observed experimentally in the atmospheric pressure ionization mass spectrum of the xylene reactions with OH radicals.15 The reaction between I1 and O2 results in the formation of an eight-

reaction of 2,3-DMP with OH radical are shown in Figure 2, and the structures of the other reactive species are shown in Figure S1 in the Supporting Information. The selected geometric parameters of the stationary points of the most favorable reaction pathways calculated using the different

Figure 2. Optimized structures of the reactive species corresponding to the most favorable reaction pathway of H-atom abstraction from phenol group of 2,3-DMP by OH radical. E



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conjugative effect, while the nonbonding electron pair of the phenol group is distributed into the aromatic ring. Hence, the incoming OH radical will naturally attack at the phenol site and favors the H-atom abstraction from this site. Thus, in 2,6-DMP the H-atom abstraction from a methyl group is not possible. The relative energies (ΔE), relative enthalpies (ΔH) and Gibbs free energies (ΔG) for the stationary points involved in the Hatom abstraction from methyl groups of DMP isomers by OH radicals are summarized in Table 2 and in Table S5 of the Supporting Information.

membered epoxide ring through a transition state, TS2, with an energy barrier of 25.5 kcal/mol. In this case, both B3LYP and M06-2X functionals with the 6-31G(d,p) basis set produce comparable energy barriers. At MPW1K/6-31G(d,p) and B3LYP/6-31+G(d,p) levels of theory, the energy barrier is less by 6−8 kcal/mol and the MP2 method shows an increase in the energy barrier by 6 kcal/mol with respect to the result obtained from the M06-2X/6-31G(d,p) level of theory. In the transition state structure, the reacting oxygen molecule dissociates and one of the oxygen atoms binds with C4- and C6-atoms of I1 and the other oxygen atom binds with C5- and C6-atoms of I1. The bond between the C1- and O-atoms of I1 possesses double bond character. From this transition state structure, a neutral epoxide product is formed. This reaction occurs in an exothermic and exoergic reaction with ΔH = −26.86 kcal/mol and ΔG = −15.02 kcal/mol. This reaction is the most favorable secondary reaction, and the rate constant calculated at 298 K for this reaction channel is 5.35 × 10−14 cm3 molecule−1 s−1. The variation transition state corresponding to this reaction is located at s = −0.001 Å. The tunneling factor is negligible for this reaction channel. The reaction between I1 and O2 also leads to the formation of 2,3-dimethylbenzoquinone, P2. This product was identified as a minimum in the PES at all the methods used in this study, except the M06-2X/6-31G(d,p) level of theory. At the M062X/6-31G(d,p) level of theory, several attempts were made to locate this stationary point as a minimum in the PES, but all the attempts led to a first order saddle point. Hence, for this reaction path the reaction energy profile and the energetics are discussed with the results obtained at the B3LYP/6-31G(d,p) level of theory. This product is formed via a transition state, TS2, and the energy barrier calculated at the B3LYP/631G(d,p) level of theory is 48.46 kcal/mol. The barrier heights calculated for this reaction using the MPW1K and MP2 methods are comparable with that of the B3LYP method with values of 46.26 and 48.67 kcal/mol, respectively. As shown in Figure 1, in the transition state structure TS2, the oxygen molecule binds with methyl carbon substituted in the third position, and the bond between the C-atom of the aromatic ring and the C-atom of the methyl group in the third position is broken. After the formation of this transition state, the oxygen molecule is cleaved from the methyl group and one of the Oatoms abstracts the H-atom from the aromatic ring and the other O-atom is substituted at the C-radical site with double bond character. Thus, 2,3-dimethylbenzoquinone and OH radical (P2) are formed as products. This product channel is exothermic by −27.3 kcal/mol and exoergic by −24.09 kcal/ mol. The calculated barrier height for the formation of 2,3dimethylbenzoquinone shows that this product formation does not contribute significantly to the overall environmental evolution of DMP. 3.2. H-Atom Abstraction from Methyl Group of DMP by OH Radical. The OH group of DMP is a strong ortho− para director. This is because one of the two lone pairs on the oxygen atom strongly interacts with the π electrons of the aromatic system and influences the ortho and para positions to possess greater electron density than the meta position. Hence, the OH group of DMP directs the reacting OH radical to attack at these electron-rich centers. This results in the abstraction of H-atom from a methyl group of DMP by OH radical. The methyl H-atom abstraction is observed in all the isomers except 2,6-DMP. The methyl groups in 2,6-DMP do not have nonbonding electron pairs and hence exhibit a hyper-

Table 2. Relative Energies (ΔE in kcal/mol), Relative Enthalpies (ΔH in kcal/mol), and Gibbs Free Energies (ΔG in kcal/mol) of the Stationary Points on the Ground-State Potential Energy Surface for H-Atom Abstraction from Methyl Group of 2,3-DMP Calculated at M06-2X/631G(d,p) Level of Theory and Relative Energies (ΔE in kcal/mol) at CCSD(T)//M06-2X/6-31G(d,p) Level of Theory M06-2X

CCSD(T)

stationary point

ΔE

ΔH

ΔG

ΔE

2,3-DMP + OH TS1 I1 I1 + O2 I2 I2 + HO2 TS2 P1 TS3 P2 TS4 P3 TS5 P4 I2 + NO TS6 I3 I3 + O2 TS7 P5

0.0 7.0 −20.95 0.0 −4.34 0.0 0.75 −20.23 21.21 −62.11 62.97 −40.87 16.44 −20.51 0.0 10.48 −34.62 0.0 61.52 51.29

0.0 4.71 −21.16 0.0 −3.66 0.0 −0.88 −21.38 18.64 −64.10 58.63 −42.05 19.92 −22.59 0.0 9.96 −32.54 0.0 60.63 49.58

0.0 6.54 −21.81 0.0 −1.33 0.0 −0.23 −27.12 19.21 −67.03 58.98 −44.42 20.52 −24.74 0.0 10.68 −31.19 0.0 64.09 48.50

0.0 6.58 −20.85 0.0 −4.58 0.0 0.38 −20.01 18.15 −60.12 61.69 −38.88 16.12 −20.97 0.0 9.05 −30.35 0.0 68.93 55.47

From Table 2 and Table S5 in the Supporting Information, it is observed that the H-atom abstraction from a methyl group is found to occur predominantly in 2,3-DMP with a small barrier of 7 kcal/mol at the M06-2X/6-31G(d,p) level of theory. Hence, the subsequent reactions from this principal oxidation step are studied in detail. The energy barrier for this initial step calculated using B3LYP, MPW1K, and MP2 methods is 5.09, 8.48, and 9.54 kcal/mol, respectively, and is comparable with the value calculated at the M06-2X/6-31G(d,p) level of theory. Scheme 2 illustrates the reaction pathways corresponding to methyl H-atom abstraction from 2,3-DMP by OH radical. The energetics obtained at the M06-2X/6-31G(d,p) level of theory are summarized in Table 2, and the results obtained using other methods are summarized in Tables S6 and S7 in the Supporting Information. The relative energy profile for the reaction pathways is shown in Figure 4. The optimized structures of the reactive species corresponding to the favorable reactions are shown in Figure 5. The optimized structures of the other reactive species are shown in Figure S2 in the Supporting Information. The selected geometric parameters of the F



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Figure 6. Kinetic scheme of the most favorable reaction of H-atom abstraction from methyl group of 2,3-DMP by OH radical.

The initial step results in the formation of a radical, I1, and a water molecule. This abstraction occurs through a transition state, TS1, in which the angle between the H-atom of the CH3 group which is being abstracted and the reacting OH radical is found to be 130°, which was 92° in the reactants (see Figure 5). From Tables 1 and 2, it is observed that the ΔG calculated for H-atom abstraction from a methyl group is higher by 11.76 kcal/mol than the ΔG calculated for the phenolic H-atom abstraction by OH radical. Also, the ΔH values show that the phenolic H-atom abstraction reaction is more exothermic by 9.23 kcal/mol than the methyl H-atom abstraction reaction. The forward rate constant for this initial methyl H-atom abstraction reaction at 298 K is 7.09 × 10−13 cm3 molecule−1 s−1. Experimental studies on H-atom abstraction from 2,3-DMP show that the rate constant for this abstraction reaction is of the order of 10−11−10−12 cm3 molecule−1 s−1.9,51 The calculated reverse rate constant for this reaction is 2.16 × 10−31 cm3 molecule−1 s−1. The transmission coefficient for this reaction is 7.11 at 298 K, which shows that the tunneling effect is significant in this H-atom abstraction step. The variational correction for this reaction is about 1.5 over the whole temperature range. The variational transition state is located at s = −0.118 Å. The initially formed radical, I1, is found to react more rapidly with O2, resulting in the formation of a peroxy radical intermediate, I2, in a barrierless reaction. The heat of formation of this peroxy radical is −3.66 kcal/mol. The bonding between the radical I1 and OO fragment is relatively weak; hence this reaction is a reversible reaction with an equilibrium constant of 37.4 between I1 + O2 and I2. The forward rate constant for this reaction is 8.10 × 10−13 cm3 molecule−1 s−1. The reverse rate constant for the decomposition of the peroxy radical is 1.24 × 10−14 cm3 molecule−1 s−1. For this reaction path, the adiabatic energy barrier is zero and the tunneling effect is negligible. The calculated rate constants reveal that the peroxy radical formation is not relevant to atmospheric chemistry because this peroxy adduct decomposes back to reactants. Alternatively, the reaction of this peroxy radical with HO2 is important while determining the atmospheric fate of peroxy radicals.49,52 The reaction between I2 and HO2 proceeds by the abstraction of Hatom from HO2 by peroxy radical, resulting in the formation of the 2-hydroperoxymethyl-3-methylphenol adduct, P1, with the elimination of an oxygen molecule. This reaction has a loose transition state structure, TS2, with an energy barrier of only 0.75 kcal/mol above the reactants, I2 + HO2, at the M06-2X/631G(d,p) level of theory. The above energy barrier is comparable with the values obtained from other DFT methods, 1.52 and 0.13 kcal/mol at the B3LYP and MPW1K levels of theories, respectively, with the 6-31G(d,p) basis set. The

Figure 4. Relative energy profile for H-atom abstraction reaction from methyl group of 2,3-DMP by OH radical and its subsequent reactions.

Figure 5. Optimized structures of the reactive species corresponding to the most favorable reaction pathway of H-atom abstraction from methyl group of 2,3-DMP by OH radical.

stationary points of the most favorable reaction pathways calculated using the different methods is summarized in Table S8 in the Supporting Information. The kinetic scheme for the most favorable reaction pathway is given in Figure 6. G



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kcal/mol. The intermediate I3 can react with O2 resulting in the formation of ozone. The energy barrier associated with the transition state TS7 for this ozone formation along with 3methyl-2-nitrosooxymethylphenol is 61.52 kcal/mol. This reaction step is endothermic by 49.58 kcal/mol and endoergic by 48.50 kcal/mol. The energy barrier for the reaction of peroxy radical with HO2 is very less compared to that of the reaction with NO. Hence, the reaction of peroxy radical with HO2 is the dominant exit pathway for the peroxy radical. 3.3. H-Atom Abstraction from Aromatic Ring of DMP by OH Radical. The reaction between DMP and OH radical is also initiated by H-atom abstraction from the aromatic ring. This reaction is observed only in 3,5- and 2,5-DMP isomers. This is due to the fact that the methyl group present in the third position acts as a para director and drives the OH radical to react predominantly with the H-atom attached to the C4atom of the aromatic ring. Similarly, in the case of 2,5-DMP, methyl groups act as ortho and para directors and the OH radical abstracts the H-atom from either C3- or C4-atoms of the aromatic ring. The subsequent reactions from this initial step lead to different products from those discussed earlier. The energy barrier for the reaction of 3,5-DMP with OH radical is 3.35 kcal/mol, and that for the reaction of 2,5-DMP with OH radical is 7.52 kcal/mol at the M06-2X/6-31G(d,p) level of theory, which shows that the former reaction is more favorable than the latter. Hence, the reaction mechanism for 3,5-DMP with OH radical is discussed. Scheme 3 illustrates the reaction scheme for the H-atom abstraction from the aromatic ring of 3,5-DMP and its subsequent reactions. Figure 7 shows the

addition of a diffuse function in the basis set also does not significantly alter the barrier; i.e., the barrier calculated at the B3LYP/6-31+G(d,p) level of theory is 2.44 kcal/mol. However, the energy barrier calculated at the MP2/6-31G(d,p) level of theory is 20.87 kcal/mol, which is higher than the value calculated using DFT methods. This difference in energy barrier may be due to the large structural change in TS2; the rmsd value of 1.2 Å between the internal coordinates obtained at MP2 and DFT methods is noted. As shown in Figure 5, in the transition state structure TS2, two strong hydrogen bonds are formed. One between the terminal oxygen atom (O3) of the peroxy radical and the H10-atom of HO2 with a bond length of 1.46 Å and another H-bond has been observed between O3- and H4-atoms of the peroxy radical with a bond length of 1.82 Å. At the MP2/6-31G(d,p) level of theory, in TS2 the H-bond length between H10- and O3-atoms is 1.12 Å and that between O3- and H4-atoms is 1.23 Å. The computed enthalpy and Gibbs free energy values reported in Table 2 show that this reaction is exothermic by −21.38 kcal/mol and is exoergic by −27.12 kcal/mol. For this reaction, the tunneling effect is negligible due to the broad energy barrier of this reaction pathway as evident from the small imaginary vibrational frequency (−371.9 cm−1) of TS2. The rate constant calculated at 298 K for this hydroperoxide adduct formation is 9.31 × 10−12 cm3 molecule−1 s−1. The variational effect for this reaction varies from 4.8 to 5 for a reaction temperature of 278− 350 K. The variation transition state is located at the reaction coordinate, s = 0.002 Å. This reaction is found to be the most favorable due to the small barrier of 0.75 kcal/mol. The energy profile corresponding to the reaction between peroxy radical and HO2 is illustrated in Figure 4. The hydroperoxide adduct (P1) has sufficient energy to undergo unimolecular decomposition and yields a large number of products. The lowest energy pathway is the formation of 2hydroxy-6-methylbenzaldehyde, P2, through a transition state, TS3, with a barrier of 21.21 kcal/mol in a highly exothermic reaction with ΔH = −64.10 kcal/mol. The next highest energy pathway is the elimination of H2O and 2-hydroxymethyl-3methylphenoxy radical, P3, in an exothermic reaction with ΔH = −42.05 kcal/mol, through a transition state, TS4, with a barrier height of 62.97 kcal/mol. The next possible reaction is the structural rearrangement of the hydroperoxide adduct leading to the formation of 8-methyl-1-oxa-spiro[2.5]octan-4one (P4) through a transition state, TS5. The barrier height for this reaction is 16.44 kcal/mol. This reaction is the least exothermic among the three pathways studied with a ΔH value of −22.59 kcal/mol. The calculated energy barriers corresponding to the formation of products P2−P4 show that these reaction pathways do not contribute significantly to the elimination of DMP in the atmosphere. In polluted areas, there is a significant concentration of aromatics and nitrogen oxides. At ambient conditions, the reaction of peroxy radicals with NO is generally fast. Hence, the study of a possible reaction mechanism between the peroxy radical intermediate, I2, and NO is important. During this reaction, the O−O bond of the peroxy radical is cleaved and one of the oxygen atoms binds with NO. Then, the NO2 group is bonded with another O-atom of the peroxy radical and peroxynitrate adduct, I3, is formed. A transition state, TS6, is found between the intermediate states I2 and I3 with a barrier height of 10.48 kcal/mol. As reported in Table 2, this reaction occurs with a large energy drop of −32.54 kcal/mol with respect to the reactants and the reaction is exoergic by −31.17

Figure 7. Relative energy profile for H-atom abstraction reaction from aromatic ring of 3,5-DMP by OH radical and its subsequent reactions.

relative energy profile for the reaction pathways. The optimized structures of the reactive species corresponding to the favorable reaction pathway from this initial step are depicted in Figure 8. The optimized structures of the reactive species of the other reaction pathways are shown in Figure S3 of the Supporting Information. The ΔE, ΔH, and ΔG values calculated at the M06-2X/6-31G(d,p) level of theory for the stationary points in the reaction path are summarized in Table 3, and the energetics obtained using the other methods are given in Tables S9 and S10 in the Supporting Information. The selected geometric parameters of the stationary points of the most favorable reaction pathways calculated using the different methods are H



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summarized in Table S11 in the Supporting Information. The kinetic scheme for the favorable reaction pathway is shown in Figure 9.

Figure 9. Kinetic scheme of the most favorable reaction of H-atom abstraction from aromatic ring of 3,5-DMP by OH radical.

The initial step results in the formation of a phenyl radical, I1, and a water molecule through transition state, TS1, with a barrier of 3.35 kcal/mol. This reaction is slightly endothermic by 0.12 kcal/mol at the M06-2X/6-31G(d,p) level of theory. The ΔH values calculated with MPW1K and MP2 methods show that the reaction is endothermic by 1.14 and 6.11 kcal/ mol, respectively, while the B3LYP method shows that the reaction is slightly exothermic by −1.5 kcal/mol. As shown in Figure 7, the calculated rate constant for this reaction at 298 K is 9.86 × 10−12 cm3 molecule−1 s−1 with a tunneling factor of 1.16. That is, the tunneling effect is negligible for this reaction due to the small magnitude of the imaginary frequency of TS1 (369.5i cm−1). The rate constant calculated using experimental methods for the H-atom abstraction from 3,5-dimethylphenol is of the order of 10−10−10−11 cm3 molecule−1 s−1.51 The reverse rate constant for this initial reaction is 9.82 × 10−33 cm3 molecule−1 s−1, which reveals that the forward reaction is more favorable than the reverse reaction. The variational transition state corresponding to this reaction is located at s = −0.128 Å. The tabulated values show that the energy barrier calculated for this reaction is the lowest one among all the other initial Hatom abstraction steps, indicating that the H-atom abstraction reaction from the aromatic ring is kinetically favorable. However, by comparing the ΔH values, the lowest energy pathway is observed for the methyl H-atom abstraction reaction with an exothermicity of −21.16 kcal/mol and hence the methyl H-atom abstraction reaction is thermodynamically favorable. The phenyl radical, I1, can further react with O2 molecule present in the atmosphere. In this reaction, O2 binds with the C4-atom of the aromatic ring from which the H-atom was abstracted in the initial reaction (see Figure 8). From this reaction a peroxy radical, I2, is formed spontaneously, whose ΔH is only 0.05 kcal/mol at the M06-2X/6-31G(d,p) level of theory. The ΔH value obtained for this reaction using the other DFT methods and the MP2 method is comparable with that of the M06-2X/6-31G(d,p) level of theory. However, the energy barrier for formation of peroxy radical, I2, in the methyl Hatom abstraction reaction is about 3.61 kcal/mol, lower than that of the peroxy radical, I2, in this reaction. This reaction proceeds via barrierless transition leading to a rate constant of 1.14 × 10−3 cm3 molecule−1 s−1 at 298 K. The peroxy radical, I2, further transforms into new products other than discussed in previous reactions. As observed in the

Figure 8. Optimized structures of the reactive species corresponding to the most favorable reaction pathway of H-atom abstraction from aromatic ring of 3,5-DMP by OH radical.

Table 3. Relative Energies (ΔE in kcal/mol), Relative Enthalpies (ΔH in kcal/mol), and Gibbs Free Energies (ΔG in kcal/mol) of the Stationary Points on the Ground-State Potential Energy Surface for H-Atom Abstraction from the Aromatic Ring of 3,5-DMP Calculated at M06-2X/631G(d,p) Level of Theory and Relative Energies (ΔE in kcal/mol) at CCSD(T)//M06-2X/6-31G(d,p) Level of Theory M06-2X

CCSD(T)

stationary point

ΔE

ΔH

ΔG

ΔE

3,5-DMP + OH TS1 I1 I1 + O2 I2 I2 + HO2 TS2 P1 I2 + NO TS3 P2

0.0 3.35 −1.75 0.0 0.1 0.0 51.6 11.84 0.0 11.88 1.77

0.0 3.72 0.12 0.0 0.05 0.0 53.34 10.59 0.0 10.44 1.53

0.0 6.68 −5.04 0.0 0.05 0.0 54.46 7.22 0.0 10.78 −2.04

0.0 3.33 −2.11 0.0 0.37 0.0 43.6 5.6 0.0 11.66 2.39

I



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methyl H-atom abstraction reaction, there are two promising pathways identified for the exit pathway for the peroxy radical, I2. The peroxy radical undergoes the H-atom abstraction reaction while reacting with HO2. The hydroperoxide adduct (P1) and O2 are formed through a transition state, TS2, with a barrier height of 51.6 kcal/mol. The reaction is endothermic by 10.59 kcal/mol and endoergic by 7.22 kcal/mol. From Tables 2 and 3, it is observed that the formation of hydroperoxide adduct in the methyl H-atom abstraction reaction has lower energy and is the more favorable reaction pathway than the hydroperoxide adduct formation due to H-atom abstraction from the aromatic ring. Thus the reaction of peroxy radical with HO2 in this reaction is not competitive to determine the fate of the peroxy radical, I2. The other competing exit pathway for the peroxy radical, I2, is its reaction with NO to form an alkoxy radical (P2) and NO2. This reaction pathway is identified through a transition state, TS3, with a barrier of 11.88 kcal/mol. This reaction occurs in an endothermic and exoergic reaction with ΔH = 1.53 kcal/mol and ΔG = −2.05 kcal/mol at the M06-2X/6-31G(d,p) level of theory. The ΔH and ΔG values calculated using MP2 and MPW1K methods are comparable with those using the M062X method, but the B3LYP method with the 6-31G(d,p) and 631G+(d,p) basis sets overestimated the ΔH and ΔG values by about 10 kcal/mol. This is the most accessible reaction pathway with a rate constant of 2.35 × 10−19 cm3 molecule−1 s−1. Interestingly, the reverse reaction, that is the decomposition of P2 and NO2 to I2 and NO, is faster with a reaction rate constant of 0.86 × 10−8 cm3 molecule−1 s−1. This reverse reaction is important near the tropopause or in highly polluted areas, where bimolecular reactions facilitate the peroxy radical decomposition.53,54 As shown in Figure 9, the equilibrium constant for the formation and decomposition of this product channel is 2.72 × 10−3. The variational transition state corresponding to this reaction is located at s = 0.002 Å. It is noted that the reaction pathway leading to the formation of P1 and O2 is not competitive to determine the fate of peroxy radical, I2. Comparison of the energy barrier corresponding to the reaction of NO with peroxy radical formed in the methyl-H atom abstraction reaction and that of the reaction in the Hatom abstraction from the aromatic ring show that the former reaction leads to the formation of more stable products than the latter (see Tables 2 and 3); that is, the formation of the peroxynitrate adduct as an intermediate in the former reaction is more important and favorable than the formation of alkoxy radical intermediate in the latter reaction. 3.4. Electrophilic Addition of OH Radical to DMP. The important reaction between aromatic compounds and OH radicals is addition of the OH radical to the aromatic ring. In DMP, the phenol group and methyl groups donate the electrons into the ring by resonance and favor the OH radical attack at ortho and para positions of DMP. Thus, this reaction occurs predominantly in 3,5-DMP, because the methyl group present at the third position of DMP directs the OH radical toward the para position. This leads to the formation of the cyclohexadienyl adduct, I1, through a transition state, TS1. Scheme 4 displays the reaction mechanism for electrophilic addition of OH radical to 3,5-DMP and the subsequent reactions. The ΔE, ΔH, and ΔG values for these reactions calculated at the M06-2X/6-31G(d,p) level of theory are summarized in Table 4, and the values obtained using other methods are summarized in Tables S12 and S13 in the Supporting Information. Figure 10 shows the energy profile for

Table 4. Relative Energies (ΔE in kcal/mol), Relative Enthalpies (ΔH in kcal/mol), and Gibbs Free Energies (ΔG in kcal/mol) of the Reactive Species Corresponding to Electrophilic Addition of OH Radical to the Aromatic Ring of 3,5-DMP Calculated at M06-2X/6-31G(d,p) Level of Theory and Relative Energies (ΔE in kcal/mol) at CCSD(T)//M06-2X/6-31G(d,p) Level of Theory M06-2X

CCSD(T)

stationary point

ΔE

ΔH

ΔG

ΔE

3,5-DMP + OH TS1 I1 I1 + O2 TS2 P1 TS3 I2 TS4 P2 TS5 P3 TS6 P4 TS7 P5

0.0 3.36 −17.67 0.0 9.93 −32.34 1.95 −12.88 2.96 −24.69 8.78 −19.83 9.01 −28.22 2.96 −10.82

0.0 3.72 −15.44 0.0 7.18 −31.01 1.56 −10.17 2.79 −24.62 7.44 −20.12 7.88 −27.77 2.8 −10.71

0.0 6.76 −12.75 0.0 12.89 −30.03 1.40 −2.88 3.58 −23.14 8.26 −19.12 12.58 −26.77 3.6 −10.19

0.0 3.33 −14.02 0.0 8.46 −29.34 2.29 −13.06 3.13 −31.86 9.6 −11.85 7.99 −20.28 3.13 −10.4

Figure 10. Relative energy profile for electrophilic addition of OH radical to the aromatic ring of 3,5-DMP and its subsequent reactions.

the electrophilic addition reaction. Figure 11 shows the optimized structures of the reactive species involved in the most favorable reactions. The optimized structures of other reactive species are shown in Figure S4 in the Supporting Information. The selected geometric parameters of the stationary points of the most favorable reaction pathway calculated using the different methods are summarized in Table S14 in the Supporting Information. The rate constant and equilibrium constant of the most favorable reaction pathway are shown in Figure 12. The cyclohexadienyl adduct, I1, is formed through a transition state, TS1, with a barrier of 3.36 kcal/mol at the M06-2X/6-31G(d,p) level of theory. The energy barrier calculated using other DFT functionals is smaller than the above value by 3.3 and 1.93 kcal/mol, respectively, at the B3LYP and MPW1K methods. The barrier calculated at the J



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the reaction is found to be slightly exothermic and exoergic with values of −2.51 and −2.18 kcal/mol, respectively. As given in Figure 12, the calculated rate constant at 298 K for this adduct formation is 0.95 × 10−21 cm3 molecule−1 s−1 and it encompasses the results of previous experimental studies on aromatic compounds.5,55 This reaction is reversible with a reverse rate constant of 9.84 × 10−24 cm3 molecule−1 s−1. The variational transition state for this reaction is located at s = −0.127 Å. The equilibrium constant Kc for this reaction is 65.2 with a tunneling factor of 1.16. The loss of H-atom from the adduct, I1, resulted in the formation of dimethyldihydroxybenzene (I3) (see Scheme 4) with an energy barrier of 31.02 kcal/mol at the B3LYP/6-31G(d,p) level of theory. The large energy barrier shows that this reaction is unfeasible, and hence the subsequent reaction pathways from I3 are not studied in detail. This reaction pathway is characterized only at the B3LYP/6-31G(d,p) level of theory, while the other methods do not show H-atom loss from I1. Also, it is expected that the elimination of a methyl group from I1 requires a large energy barrier. The adduct I1 reacts with O2 either by O2 addition to form peroxy radical or by H-atom abstraction to yield phenolic compounds. Previous studies show that unimolecular reaction is possible for peroxy radical which leads to the formation of epoxide radicals and bicyclic radicals.15,56 Many theoretical55−60 and experimental12,21 studies have focused on characterizing the reaction between aromatic compound−OH adducts and O2. The mechanism of H-atom abstraction by O2 from OH initiated reactions of aromatic compounds was studied earlier by Klotz et al.61 They proposed the mechanism for the reaction of a toluene−OH adduct with O2, resulting in the formation of HO2. Reaction of O2 with the adduct I1 results in H-atom abstraction from the OH group attached at the C4-atom through a transition state, TS2 (see Figure 11). This leads to the formation of 3,5-dimethyl-1,4-diphenol and HO2 (P1).The energy barrier for this reaction is 9.93 kcal/mol at the M06-2X/ 6-31G(d,p) level of theory. This value is comparable with the barrier of 9.88 kcal/mol obtained using the MPW1K method. However, the B3LYP method underestimates the energy barrier as 2.11 and 1.38 kcal/mol at the 6-31G(d,p) and 6-31+G(d,p) basis sets, respectively. On the other hand, the MP2 method highly overestimates the energy barrier by about 33 kcal/mol. The ΔH value obtained for this reaction is −31.01 kcal/mol at the M06-2X/6-31G(d,p) level of theory, which agrees with a previous theoretical value of −29.9 kcal/mol.60 The reaction is exoergic by −30.03 kcal/mol. The ΔH and ΔG values calculated using the M06-2X method are comparable with those using the other DFT methods. At the MP2/6-31G(d,p) level of theory, the reaction is found to be highly exothermic and exoergic with values of −70.1 and −69.35 kcal/mol, respectively. The reaction between I1 and O2 can also lead to the formation of a peroxy radical, I2. The peroxy radical is formed by the binding of O2 molecule with the C3-atom of the aromatic ring of I1, to which the methyl group is attached. The formation of this peroxy radical, I2, is associated with a transition state, TS3, with a barrier of 1.95 kcal/mol, which is less than that of the previous H-atom abstraction reaction leading to the formation of phenol. As illustrated in Figure 11, in the transition state structure TS3, an intramolecular hydrogen bond is formed between the oxygen atom of the peroxy group and H-atom in the methyl group. The calculated rate constant for peroxy radical formation is 2.89 × 10−9 cm3

Figure 11. Optimized structures of the reactive species corresponding to the most favorable reaction pathway of electrophilic addition of OH radical to the aromatic ring of 3,5-DMP.

B3LYP/6-31+G(d,p) level of theory agrees well with that obtained at the M06-2X/6-31G(d,p) level of theory, with a value of 3.75 kcal/mol. It is apparent from Table S6 in the Supporting Information that the MP2 method substantially overestimated the barrier, compared to the values predicted by DFT methods. Since the aromatic ring is electron rich, this adduct is more stable with a Gibbs free energy of −12.75 kcal/ mol and the reaction is exothermic with ΔH = −15.44 kcal/ mol. The ΔH and ΔG values obtained at the B3LYP and MPW1K methods are comparable with the values obtained at the M06-2X method. At the MP2/6-31G(d,p) level of theory, K



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Figure 12. Kinetic scheme of the most favorable reaction of electrophilic addition of OH radical to the aromatic ring of 3,5-DMP.

molecule−1 s−1 at 298 K. The peroxy radical reaction is reversible under tropospheric conditions, and the calculated reverse rate constant is 1.16 × 10−13 cm3 molecule−1 s−1. The variational transition state corresponding to this reaction is located at s = 0.002 Å. As shown in Figure 12, the equilibrium constant for the formation and decomposition of peroxy radical is 2.84 × 104. This value is consistent with the theoretical value obtained for the reaction of O2 with hydroxycyclohexadienyl radical.60 The reversibility of the peroxy radical reaction suggests that many isomers of the peroxy radicals are likely to form. A previous theoretical study62 on the reaction between benzene−OH adduct and O2 revealed that the O2 addition reaction occurs preferentially at the ortho position of the aromatic ring. Hence, in the present work the peroxy radical for which the OO fragment attached at the ortho position is studied. The competing exit pathway for this peroxy radical is its isomerization reaction. As shown in Scheme 4, the peroxy radical isomerizes to epoxy radicals P2, P3, and P4. These epoxy radicals were previously predicted experimentally for the reaction of OH−xylene adducts with O2.15 As shown in Figure 11, the epoxide radical P2 is formed by the dissociation of the peroxy group in I2, in which one of the O-atom binds with the C2- and C4-atoms and the other O-atom binds with the C5atom of the aromatic ring. In the epoxide radical P3, one of the oxygen atoms binds with C3- and C5-atoms and the other Oatom binds with C2- and C4-atoms of the aromatic ring. The epoxide radical P4 is formed due to the attachment of dissociated O-atoms with the C2- and C3-atoms and with C5and C6-atoms. The activation barriers for the formation of these epoxy radicals P2, P3, and P4 through transition states TS4, TS5, and TS6 are 2.96, 8.78, and 9.01 kcal/mol, respectively. From Table 4, it is noted that the epoxy formation reactions are exothermic. The ΔG values in Table 4 show that the formation of P4 is the lowest energy pathway with a value of −26.77 kcal/mol. The epoxide radical P4 is more stable by 25.37 kcal/mol than its peroxy radical precursor, I2 (see Table 4). The formation of epoxide radical P2 is most favorable due

to its small barrier of 2.96 kcal/mol. These epoxide radicals subsequently undergo ring cleavage to form epoxy carbonyls and more dominantly cyclohexaneones.15,56 The peroxy radical can cyclize to favor the formation of bicyclic radicals. The formation of the bicyclic radical P5 involves a five-membered ring in which O2 is attached with the C1- and C3-atoms. The transition state structure, TS7, calculated for this cyclization of the peroxy radical is shown in Figure 11. In line with the previous result for the cyclization of hydroxyl-2,4-cyclohexadienyl-6-peroxyl radical,60 the barrier height for this cyclization reaction is 2.96 kcal/mol. From Table 4, it is observed that the ΔH value obtained for this reaction is −10.71 kcal/mol and the reaction is exoergic by −10.19 kcal/ mol. The above results show that the epoxide radical P2 is energetically more stable than the bicyclic radical P5. This is due to the fact that the epoxide radical possesses a delocalized allyl-π system. The ΔE values summarized in Table 4 show that the probabilities for the formation of P2 and P5 are almost the same. As shown in Figure 9, the rate constants calculated for the formation of P2 and P5 at 298 K are 5.34 × 1010 and 5.34 × 10 11 s−1, respectively. The variational transition states corresponding to the formation of P2 and P5 product channels are calculated at s = −0.0001 and 0.0001 Å, respectively. Thus, the peroxy radical isomerizes to epoxide and bicyclic radicals and represents the accessible isomeric pathways to propagate the oxidation of 3,5-dimethylphenol by OH radical and the formation of various aromatic ring cleavage products. 3.5. Comparison of OH Initiated Reactions with DMP and with Other Aromatic Compounds. To understand the reactivities of aromatic compounds, the reaction of DMP with OH radical is compared with the reactions of other aromatic compounds with OH radicals. The comparison is made between OH initiated reactions of DMP and those of benzene, toluene, and xylene. The oxidation of benzene in the atmosphere was studied in detail by Olivella et al.60 In this study, the addition of O2 on different positions of the benzene− OH adduct leads to different products. The H-atom abstraction from the benzene−OH adduct by O2 resulting in the formation L



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xylene−OH adduct is only −0.51 kcal/mol,62,68 while the reaction enthalpy for 3,5-DMP−OH−O2−peroxy radical formation is −3.45 kcal/mol. The above results reveal that the reaction of O2 with 3,5-DMP−OH adduct results in more stable products than the p-xylene−OH−O2−peroxy radical. Also, the calculations of Fan and Zhang62 show that the reaction energy for cyclization of the peroxy radical is 9.07 kcal/ mol, while the reaction energy for the cyclization of the peroxy radical resulting from O2 addition to 3,5-DMP−OH is −10.71 kcal/mol. The comparison of the results obtained for the oxidation of DMP by OH radical with other aromatic compounds reveals that the reactivity of aromatic compounds toward OH radical depends on the number and position of the substituent. On comparing the energy barriers, it is observed that the H-atom abstraction from the aromatic ring of 3,5-DMP and electrophilic addition of OH radical to 3,5-DMP is more favorable than the H-atom abstraction from a methyl group and the phenol group of 2,3-DMP. Thus, the electrophilic addition reaction and H-atom abstraction from the aromatic ring is kinetically favored. The calculated rate constant values for the initial reaction show that the initial H-atom abstraction from the phenol group of 2,3-DMP is thermodynamically favorable with a rate constant of 1.46 × 1017s−1. 3.6. Tropospheric Implications. The theoretical investigation presented in this study elucidates many of the unknown phenomena underlying the tropospheric chemistry of dimethylphenols. The four types of initial oxidation reactions strongly influence the air quality. The products formed in the subsequent reactions affect the oxidative capacity of the atmosphere and have a direct impact on the climate through the formation of secondary organic aerosols. The phenoxy, phenyl, and cyclohexadienyl radicals formed in the initial channel behave like alkyl radicals and react rapidly with O2 yielding peroxy radicals. The peroxy radicals react with HO2 and NO resulting in the formation of hydroperoxide adducts and alkoxy radicals. The reaction between a peroxy radical and HO2 slows down the free radical driven photochemical oxidation reactions and reduces the formation of ozone. The reaction between peroxy radical and NO results in the oxidation of NO, which leads to autoignition and combustion processes. Further, the epoxy and bicyclic radicals formed from favorable reaction pathways will trap the photooxidation initiated by dimethylphenol. Since the high propensity of dimethylphenol for the formation of secondary organic aerosols has direct health effects, the understanding of the tropospheric chemistry of dimethylphenol is very important.

of phenol takes place with a barrier of 3 kcal/mol at the B3LYP level of theory. In the present study, the formation of phenol in the reaction of the 3,5-DMP−OH adduct with O2 occurs through a barrier of 2.11 kcal/mol at the B3LYP level of theory and 9.93 kcal/mol at the M06-2X level of theory. The ΔH value for the formation of peroxy radicals from the benzene−OH adduct is −9.8 kcal/mol, and in the present study, 3,5-DMP− OH−O2 peroxy radical is formed with an enthalpy of −10.17 kcal/mol. The decomposition of benzyl hydroperoxide adduct was studied theoretically by Silva et al.63 This decomposition leads to benzaldehyde, benzyne, and benzoxyl with reaction enthalpies of −8.3, 111.1, and 31.1 kcal/mol, respectively. On the other hand, the products 2-hydroxy-6-methylbenzaldehyde, 2-hydroxymethyl-3-methylphenoxy radical and 8-methyl-1-oxaspiro[2.5]octan-4-one are formed from 2,3-dimethylphenol hydroperoxide decomposition with reaction enthalpies of −62.11, −40.87, and −20.51 kcal/mol, respectively. Several theoretical studies have been performed to investigate the oxidation of toluene in the atmosphere.56,64−67 Suh et al. reported the possibility for the formation of peroxy, bicyclic, and epoxide radicals from the OH−toluene reactions.56 The relative stability of peroxy radicals formed from the reactions of O2 with OH−toluene adduct was found to be within 2 kcal/mol. In the present study, the peroxy radicals formed from the reactions of the 3,5-DMP−OH adduct with O2 is stable by 4 kcal/mol. The activation barrier for the formation of the OH−toluene−O2−peroxy radical is about 5 kcal/mol.56 In the present study, the barrier for peroxy radical formation from the 3,5-DMP−OH adduct + O2 reaction is about 2 kcal/mol at the M06-2X/6-31G(d,p) level of theory. An experimental work by Bohn10 revealed that the equilibrium constant for the formation of the OH−toluene−O2−peroxy radical is 3.25 × 10−19. However, in the present study the equilibrium constant for the formation and decomposition of the 3,5-DMP−OH−O2−peroxy radical is 2.84 × 104. The OH−toluene−O2−peroxy radical is vibrationally excited due to its large exoergicity, and hence the excited peroxy radical further undergoes different reactions. However, as discussed earlier, the 3,5-DMP−OH−O2−peroxy radical is exoergic by only −5.89 kcal/mol and hence it only isomerizes to epoxide and bicyclic radicals. Suh et al.56 reported an activation barrier of 10 kcal/mol for the isomerization of peroxy radical to bicyclic radical. In the present study, the barrier for bicyclic radical formation from the 3,5-DMP−OH−O2−peroxy radical is about 3 kcal/mol with DFT methods. The bicyclic radicals formed from the OH−toluene−O2−peroxy radical involve high-lying transition states and unstable structures, which further decompose into epoxy radicals. In the present study, the 3,5-DMP−OH−O2−peroxy radical directly isomerizes to both bicyclic and stable epoxy radicals. Kwok et al. studied the reaction between xylene and OH radical and showed that the initially formed OH−xylene adduct reacts with O2 with a rate constant of 2 × 10−16 cm3 molecule−1 s−1 to form peroxy radical.15 From this peroxy radical, epoxide and bicyclic radicals are formed. In the present study, the rate constant for the reaction of 3,5-DMP−OH adduct with O2 is 2.89 × 10−9 cm3 molecule−1 s−1. Recent theoretical studies by Fan and Zhang predicted that the OH addition occurs exclusively at the ortho positions of p- and m-xylenes.62,68 The reaction enthalpy for the formation of p-xylene−OH adduct is −4.5 kcal/mol, and in the present study, the reaction enthalpy for the formation of 3,5-DMP−OH adduct is −15.44 kcal/mol. The reaction enthalpy for O2 addition to the p-

4. CONCLUSIONS The theoretical results presented in this study provide the complete reaction mechanism for oxidation of DMP in the atmosphere. The results reveal that, depending upon the position of the substituent, the reaction between DMP and OH radical is initiated in four different ways: H-atom abstraction from the phenol group, H-atom abstraction from a methyl group, H-atom abstraction from the aromatic ring by OH radical, or electrophilic addition of OH radical to aromatic ring. From the analysis of the results, the following main conclusions are arrived at. 1. The H-atom abstraction from the phenol group is found to occur predominantly in 2,3-DMP, and the reaction pathway involves barrierless formation of hydrogen-bonded reactant and product complexes through a transition state lying 6.44 kcal/ M



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of DMP with OH radicals are shown in Figures S1−S4. This material is available free of charge via the Internet at http:// pubs.acs.org.

mol above the reactants. This initial step subsequently reacts with O2 to form epoxide and 2,3-dimethylbenzoquinone. 2. The methyl H-atom abstraction by OH radical is found to occur predominantly in 2,3-DMP, leading to the formation of an alkyl radical which further reacts with O2 and subsequently favorably with HO2 to form hydroperoxide and O2. This hydroperoxide is involved in autoignition and facilitates the decomposition reactions leading to benzaldehydes and phenoxy radicals in highly exothermic reactions. The methyl H-atom abstraction reaction is observed in all the isomers of DMP except 2,6-DMP. 3. The H-atom abstraction from the aromatic ring by OH radical is found to occur likely in 3,5- and 2,5-DMP isomers due to the ortho−para directive influence of the methyl group. The O2 addition to the initially formed radical results in the formation of a peroxy radical which exits through reaction with NO to form an alkoxy radical and NO2. This reaction is the most hazardous one due to the regeneration of NO2, which is responsible for ozone depletion. 4. The electrophilic addition of OH radical to the aromatic ring is found to occur favorably in 3,5-DMP, resulting in the formation of a cyclohexadienyl radical which subsequently reacts with O2 to form phenolic compounds and peroxy radical. The peroxy radical further isomerizes to form epoxide radicals and cyclizes to form a bicyclic radical. The epoxide radical is found to be more stable than the bicyclic radical and its peroxy radical precursor. The epoxy radical and the bicyclic radical are found to form equivalently with a barrier of 2.96 kcal/mol. The bicyclic radical further breaks into glyoxal and butanedial products, which are more hazardous than the parent dimethylphenol. 5. The calculated energy barriers for the initial reactions show that the electrophilic addition of OH radical to 3,5-DMP is kinetically favorable, and the calculated rate constants for the initial reactions show that the H-atom abstraction from the phenol group of 2,3-DMP by OH radical is thermodynamically favorable. 6. Thus the positions of the OH and CH3 substituents on the aromatic ring influence the reactivity of the substituted aromatic compounds, and depending upon the initial oxidation step, the subsequent reaction mechanism and the reaction products are different.

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AUTHOR INFORMATION

Corresponding Author

*Fax: +91-422-2422387. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the reviewers for their useful comments to improve the manuscript. L.S. is thankful to the Department of Science and Technology (DST), India, for awarding an INSPIRE Fellowship. K.S. is thankful to the University Grants Commission (UGC), India, for granting the research project under Major Research Project.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The energy barriers (ΔE), enthalpies of reaction (ΔH), and Gibbs free energies (ΔG) for the initial reactions of DMP isomers with OH radicals calculated at M06-2X/6-31G(d,p) level of theory are summarized in Tables S1 and S5. The energy barriers (ΔE), enthalpies of reaction (ΔH), and Gibbs free energies (ΔG) for the proposed reactions of DMP with OH radicals calculated at B3LYP, MPW1K, and MP2 levels of theories with 6-31G(d,p) basis set and also at B3LYP/631+G(d,p) level of theory are summarized in Tables S2, S6, S9, and S12. The relative energies calculated at CCSD(T)/6311+G(d,p)//M06-2X/6-31G(d,p) level of theory are summarized in Tables S3, S7, S10, and S13. The selected geometric parameters of the stationary points of the most favorable reaction pathways are summarized in Tables S4, S8, S11, and S14. The Gibbs free energies and rate constants of the most favorable reaction channels over the temperature range 278− 350 K are summarized in Tables S15−S18. The optimized structures of the reactive species corresponding to the reactions N



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