Theoretical Study of the Addition of OH Radicals to trans-Geraniol-(3,7

Apr 13, 2010 - Instituto de Química, Departamento de Físico-Química, Universidade Federal do Rio de Janeiro, CT Bloco A sala 408, Ilha do Fundão-R...
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Theoretical Study of the Addition of OH Radicals to trans-Geraniol-(3,7-dimethylocta-2, 6-dien-1-ol), 6-Methyl-5-hepten-2-one, and 6-Hydroxy-4-methyl-4-hexenal Tadeu Leonardo,*,† Leonardo Baptista,‡ Edilson Clemente da Silva,† and Graciela Arbilla† Instituto de Quı´mica, Departamento de Fı´sico-Quı´mica, UniVersidade Federal do Rio de Janeiro, CT Bloco A sala 408, Ilha do Funda˜o-Rio de Janeiro-Brasil, and Faculdade de Tecnologia, Departamento de Quı´mica e Ambiental, UniVersidade Estadual do Rio de Janeiro, AVenida Presidente Dutra, km 298, Resende-RJ-Brasil ReceiVed: December 3, 2009; ReVised Manuscript ReceiVed: March 14, 2010

A combined density functional theory and transition state theory study of the gas-phase addition of OH to 3,7-dimethylocta-2,6-dien-1-ol (trans-geraniol), 6-methyl-5-hepten-2-one, and 6-hydroxy-4-methyl-4-hexenal is presented. In this study, all different possibilities for the addition of the OH radical to the C-C double bonds in trans-geraniol, 6-methyl-5-hepten-2-one, and 6-hydroxy-4-methyl-4-hexenal were considered. The geometries, energies, and harmonic vibrational frequencies at each stationary point were determined at the MPW1K/cc-pVDZ and BH&HLYP/cc-pVDZ levels. Global rate coefficients of 0.94 × 10-10 and 3.1 × 10-10 cm3 molecule-1 s-1, 2.11 × 10-11 and 7.53 × 10-11 cm3 molecule-1 s-1, and 2.70 × 10-13, and 4.37 × 10-12 cm3 molecule-1 s-1 were calculated using data obtained at the BH&HLYP/cc-pVDZ and MPW1K/cc-pVDZ levels of theory. These coefficients correspond to the sum of the rate coefficients of the individual paths for trans-geraniol, 6-hydroxy-4-methyl-4-hexenal, and 6-methyl-5-hepten-2-one, when reacting with OH radicals. The calculated rate coefficients are in good agreement with the available experimental data. I. Introduction Natural emissions of volatile organic compounds (VOCs) play a major role in the atmospheric chemistry of rural and remote areas, where they exceed those of anthropogenic origin by orders of magnitude. Vegetation is the most important natural source of these compounds.1 Biogenic VOCs are assumed to play a dominant role in the chemistry of the lower troposphere and atmospheric boundary layer.2-4 Terpenoids represent the most abundant VOCs emitted by plants,5 with a global emission rate estimated to be approximately 1150 Tg carbon year-1. Monoterpenoids in general may have acyclic, monocyclic, and bicyclic structures and occur in nature as hydrocarbons, alcohols, ketones, aldehydes, and ethers. The acyclic monoterpenoid 3,7-dimethylocta-2,6-dien-1-ol (trans-geraniol, 1) is found in the essential oils of plants in Brazil,2 such as oil-of-rose, palma rosa, and citronella oil (Java type).

It is also present in the air through emissions from these plants.3 The properties and reactions of this molecule are therefore important to the understanding of the chemical phenomena * Corresponding author. Fax: (55) 21 2562-7265. Tel: (55) 21 25627755. E-mail: [email protected]. † Universidade Federal do Rio de Janeiro. ‡ Universidade Estadual do Rio de Janeiro.

occurring in the atmosphere over rural regions of Brazil where such vegetation has been planted. This compound is also a significant component of indoor cleaner emissions. 6-Methyl5-hepten-2-one and 6-hydroxy-4-methyl-4-hexenal (2 and 3, respectively) are atmospheric reaction products of biogenically emitted linalool,6 a terpene emitted from orange blossoms2,6 and from certain pine trees in southern Europe,4,6 as well as trans-geraniol.2,7 Ciccioli et al.8 reported the occurrence of this compound in urban, suburban, and forest areas in a concentration range of 0.1-5 ppbv, with the highest levels close to vegetation. Additionally, diurnal variations of concentration showed midway maxima, and Helmig et al.9 detected it in fall, winter, spring, and summer campaigns in the remote troposphere over Hawaii and in remote areas. The primary atmospheric degradation pathways of transgeraniol, 6-methyl-5-hepten-2-one, and 6-hydroxy-4-methyl-4hexenal10 involve reactions with OH radicals, NO3 radicals, and ozone. The atmospheric residence time of these compounds is mainly determined by these reactions. Laboratory studies have been performed to investigate the reaction of the OH radical with trans-geraniol10 and 6-methyl5-hepten-2-one.6 These reactions are primarily initiated by OH radical addition to the carbon-carbon double bond in these compounds to give OH adduct radicals. The experimental rate coefficients in the range (1.7-2.8) × 10-10 cm3 molecule-1 s-1 for trans-geraniol10 and (1.2-1.9) × 10-10 cm3 molecule-1 s-1 for 6-methyl-5-hepten-2-one6 at 298 K have been reported. No kinetic data are available for 6-hydroxy-4-methyl-4-hexenal. Although several theoretical studies have investigated the addition of OH radicals to other alkenes and terpenes, such as R- and β-pinenes,4,11 only reactions involving ozone with transgeraniol, 6-hydroxy-4-methyl-4-hexenal, and 6-methyl-5-hepten2-hexenal have been reported.12 Two additional sites, which are indicated by the numbers 1 and 2 in 1, are available in transgeraniol. For each site, four different transition state structures are possible, leading to eight adduct products. For 6-hydroxy-

10.1021/jp911499y  2010 American Chemical Society Published on Web 04/13/2010

J. Phys. Chem. A, Vol. 114, No. 17, 2010 5469 4-methyl-4-hexenal and 6-methyl-5-hepten-2-one, four possible adducts may be formed in each case. The proposed reaction paths are illustrated in the Results and Discussion, and the calculated structures are also shown. Hydrogen atom abstraction may occur to a small extent10 and was not considered herein. Suh et al.13 and Lei et al.14 successfully described the addition of OH and NO3 radicals to isoprene using DFT methods in conjunction with high level electronic structure methods and canonical transition state theory. According to these works, DFT methods provide accurate geometries for the species that participate in the mechanism, but the energy may be corrected by the CCSD(T) method. Both studies evaluated the high pressure rate coefficient by variational canonical transition state theory for each adduct formation, and good agreement with the experimental results was obtained. In this work, the barrier heights of each pathway were calculated to determine which C-C double bond and which position and side is energetically favored. DFT methods were employed to obtain the geometries, energies, and harmonic vibrational frequencies of each stationary point. On the basis of the quantum-chemical results, the bimolecular rate coefficients at the high-pressure limit were calculated using the thermodynamic interpretation of transition state theory (TST). Rate coefficients were calculated assuming that the OH radical addition is the dominant step. Calculated rate coefficients were compared to the available experimental data. The identification of the more stable adducts may be useful to explain the formation of the products identified experimentally.10 It was not possible to correct the energy values with high level electronic structure methods due to computational constraints. Regardless, DFT results lead to a correct description of the main pathways. II. Theoretical Method A. Quantum-Chemical Calculations. Theoretical computations were performed by using the Gaussian 03 software package15 to evaluate the structures and energetics of the reactants, transition states, and products involved in the reaction. Each reported minimum has all real frequencies, and each reported transition structure has only one imaginary frequency. The minima associated with each transition structure were connected through intrinsic reaction coordinate (IRC) calculations. The geometries, energies, and harmonic vibrational frequencies of each stationary point considered in this study were initially determined by using the MPW1K16,17 functional and the cc-pVDZ basis set. The transition states were searched by using constrained geometry optimization at fixed C-O bond lengths at the MPW1K/3-21G(d) level. The authors first considered the equilibrium structures of the adducts as the initial starting point for the transition states. The C-O bond length was then successfully increased by a fixed increment relative to the equilibrium C-O bond length of the adduct. MPW1K is a DFT method suggested by Truhlar and coworkers18 and has been developed on the basis of the MPW1PW91 functional (Barone and Adamo’s Becke-style oneparameter functional using the modified Perdew-Wang exchange function and Perdew-Wang 91 correlation functional19). MPW1K is competitive in predicting energies and geometries of compounds, especially in predicting the classical barrier height and standard reaction enthalpies.20,21 The geometry of each stationary point was then recomputed at the BH&HLYP22/cc-pVDZ level of theory. The calculated absolute energies, harmonic frequencies, and zero-point energies of all the molecules considered in this work are given in the Supporting Information.

B. Kinetic Calculations. The bimolecular rate coefficients at the high-pressure limit were calculated using the thermodynamic interpretation of the transition state theory (TST) equation: 23

k)

kbT -∆G#/RT e h

where ∆G# is the free energy of activation, kb is Boltzmann’s constant, and h is Planck’s constant with T ) 298.15 K and a standard state of 1 mol L-1. III. Results and Discussion A. Geometries, Energetic, and Rate Coefficient Calculations for the OH Radical-Addition to trans-Geraniol. Four transition states, TS 1a, TS 1b, TS 1c, and TS 1d were identified as associated with the formation of the adducts from transgeraniol on site 1 (adducts 1a, 1b, 1c, and 1d, respectively). The optimized geometries of trans-geraniol, transition states structures, and adducts, were calculated at the BH&HLYP/ccpVDZ level of theory and are shown in Figure 1. A similar analysis was made for site 2, and four transitions states, TS 2a, TS 2b, TS 2c, and TS 2d, were observed and associated with the formation of the adducts 2a, 2b, 2c, and 2d, respectively. The optimized geometries of transition state structures and adducts, calculated at the BH&HLYP/cc-pVDZ level of theory, are depicted in Figure 2. The C-O distances in transition states TS 1a, TS 1b, TS 1c, and TS 1d were between 2.12 and 2.14 Å, which was 0.69-0.73 Å longer than those of the corresponding adducts at the BH&HLYP/cc-pVDZ level of theory. For Site 2, the C-O distances in transition states TS 2a, TS 2b, TS 2c, and TS 2d were between 2.10 and 3.48 Å, which was 0.67-2.04 Å longer than those of the corresponding adducts at the BH&HLYP/ccpVDZ level of theory. All TS geometric parameters were similar to the corresponding values for reactants. Similar results for geometric parameters were previously obtained for the theoretical study of OH radical addition to d-limonene,24 which reported C-O distances in the transition states to be between 2.0 and 2.50 Å. According to that work,24 four possible prereactive complexes in the reaction pathways were obtained. Similar complexes, however, were obtained in this work for the OH radical reaction with trans-geraniol at the DFT level. Complex formation is endoergic and possibly does not take part in the reaction mechanism. As observed in Figure 2, there was no steric hindrance to OH radical approach to each double bond or for side groups to interact with the OH group following adduct formation. It is possible that adduct formation would be governed by the electronic structure of geraniol and the OH radical (molecular orbital energy and coefficients). The free energies of activation for the reaction pathways calculated at the MPW1K/cc-pVDZ and BH&HLYP/cc-pVDZ levels of theory are summarized in Table 1. Values predicted at the MPW1Kcc-pVDZ and BH&HLYP/cc-pVDZ levels differed by 23% or less. Both levels of theory indicated that pathways 2d and 2b were the major channels for adduct formation. The Gibbs free-energy profiles for the OH radical addition to trans-geraniol, calculated at the BH&HLYP/ccpVDZ level, are shown in Figure 3a,b. As expected for a reaction between a neutral molecule and a small radical to give a more stable species, the formation of the adducts was strongly exothermic, and the internal energy was retained, leading to the formation of chemically excited intermediates. The high-pressure rate coefficients for OH radical addition to trans-geraniol, shown in Table 2, were calculated using the

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Figure 1. Stationary points determined at the BH&HLYP/cc-pVDZ level of theory for the OH radical addition to trans-geraniol 1 double bond (bond distances in angstroms).

TST equation and the free energies of activation obtained at the BH&HLYP/cc-pVDZ and MPW1K/cc-pVDZ levels. As expected, rate coefficients for pathways 2b and 2d, calculated using energy data obtained at both levels of theory, were at least 2 orders of magnitude higher than the values calculated for the other pathways. These were the preferred pathways for the reaction. Because the rate of reaction is dominated by the first step, the apparent rate coefficient was estimated by adding the rate coefficients of pathways 1 and 2 (Table 2). The values 3.1 × 10-10 and 0.94 × 10-10 cm3 molecule-1 s-1, calculated using the MPW1K/cc-pVDZ and BH&HLYP/cc-pVDZ energy data, respectively, are in good agreement with the experimental studies. For the reaction with trans-geraniol, the most recent experimental measurements suggest a rate coefficient within the range of (1.7-2.8) × 10-10 cm3 molecule-1 s-1 at 298 K.10 This value is also similar to that calculated by Forester et al.10 (1.8 × 10-10 cm3 molecule-1 s-1) using the Environmental Protection Agency’s rate constant calculation software AOPWIN.25

Results obtained using both functionals indicated that more than 97% of OH radical addition to trans-geraniol led to adducts 2b and 2d. The BH&HLYP functional predicted that 72.3% and 25.5% of adducts 2d and 2b were formed. A slight difference was observed at the MPW1K/cc-pVDZ level, which predicted that 61.9% and 38.7% of adducts 2d and 2b were formed. However, both levels of theory predict that the trans-geraniol is attacked mainly at Site 2d. The branching ratio at the lowpressure limit, the further reaction of the intermediates, and the final branching ratio of products should be calculated using the Rice-Ramsperger-Kassel-Marcus in conjunction with the master equation (RRKM/ME). The obtained thermochemical and kinetic parameters are in good agreement with the experimental behavior observed for reactions between OH radicals and unsaturated alcohols, for which the presence of an OH group adjacent to the double bond leads to an increase in the reaction rate by a factor of 2, in comparison to the rate for the corresponding alkenes.26,27 According to the literature,28 electron withdrawing groups adjacent to double bonds increase the coefficient of the HOMO

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Figure 2. Stationary points determined at the BH&HLYP/cc-pVDZ level of theory for the OH radical addition to trans-geraniol 2 double bond (bond distances in angstroms).

TABLE 1: Gibbs Free Energy of Activation for OH Radical Addition to trans-Geraniol at 298 Ka pathway

MPW1K/cc-pVDZ

BH&HLYP/cc-pVDZ

1a 1b 1c 1d 2a 2b 2c 2d

5.71 6.00 5.96 6.07 6.30 2.65 7.08 2.36

7.18 6.87 7.27 7.09 8.26 3.57 5.05 2.99

a Each pathway leads to a different adduct, as discussed in the text. Values are in kcal mol-1.

orbital relating to the β-carbon of the double bond because the OH radical presents a low energy SOMO of -13.02 eV (the experimental ionization energy was considered as the SOMO energy), which is indicative of an electrophilic character. Therefore, it is expected that the OH radical would attack the double bond at the β-carbon.

The magnitude of the theoretical overall rate coefficient, which approached 10-11 cm3 molecule-1 s-1, is in agreement with previous experimental values determined for the OH radical addition to unsaturated alcohols.29,30 In all the previous experimental studies, the carbon-carbon double bonds were considered as playing important roles in the formation of reaction products, which supports the assumption that the OH radical addition step is the rate limiting step of the mechanism. The final products in atmospheric conditions would depend on several factors, such as nitrogen oxide concentrations and the abundance of other oxidants. As pointed out by Atkinson31 and Forester et al.10 the reaction of the OH-geraniol adducts with O2 forms hydroxyalkyl peroxy radicals, which then react with atmospheric gases and lead to the products detected experimentally:4,10,16,31 hydroxyacetaldehyde (glycolaldehyde), acetone, and 4-oxopentanal. Addition to site 2, the main pathway, produces the radical (CH3)2Cd CHCH2CH2C(CH3)(OH)CH( · )CH2OH. Subsequent addition of O2 to the radical leads to formation of the peroxy radical

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Figure 3. Gibbs free-energy profile for (a) OH addition to trans-geraniol 1 double bond and (b) OH addition to trans-geraniol 2 double bond.

(CH2(OH)CHOO · ) and the radical (CH3)2CdCHCH2CH2C(CH3)(OH)( · ). The reaction of the peroxy radical with NO forms NO2 and glycolaldehyde. When the OH adduct is formed on site 1, the peroxy radicals react with NO by the abstraction of an oxygen atom followed by the homolytic scission of the r(C6C7) bond. The formation of acetone and 4-oxopentanal may be explained by the OH radical addition to site 1. Because the rate coefficients for this path are at least 2 orders of magnitude lower than the rate coefficients for the addition to site 2, the mechanism for the formation of these products may be more complex. The addition of the OH radical to the double bond of the (CH3)2CdCHCH2CH2C(CH3)(OH)( · ) radical (site 1) and the further scission of the r(C6C7) bond in the presence of O2 leads to the formation of 4-oxopentanal and a CH3C(O2)CH3 radical, which further leads to acetone through reaction with NO.

TABLE 2: Calculated TST Rate Coefficients for the Adduct Formation in the OH Radical Addition to trans-Geraniola pathway 1a 1b 1c 1d 2a 2b 2c 2d overall experimental* a

BH&HLYP/ cc-pVDZ (×10-10)

MPW1K/cc-pVDZ (×10-10)

0.00056 0.00094 0.00048 0.00064 0.00009 0.24 0.02 0.68 0.94

0.0067 0.0041 0.0044 0.0036 0.0025 1.2 0.00066 1.9 3.1

2.31 ( 0.58

Values calculated at 298 K using the BH&HLYP/cc-pVDZ and MPW1K/cc-pVDZ energy data. Units of cm3 molecule-1 s-1.

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Figure 4. Stationary points determined at the BH&HLYP/cc-pVDZ level of theory for the OH radical addition to 6-hydroxy-4-methyl-4-hexenal (bond distances in angstroms).

Forester10 reported that the major product was 4-oxopentanal and proposed the formation of radicals through the addition of a OH radical to both sites 1 and 2 and the subsequent scission of the C-C bonds. These scission products would react with atmospheric gases (O2 and NO) to form the observed products. It seemed important to further study the subsequent reactions of OH-geraniol adducts and also the OH radical reactions with the main products under atmospheric conditions32 to elucidate the entire mechanism and explain the experimental branching ratios. B. Geometries, Energetics, and Rate Coefficient Calculations of the OH Radical Addition to 6-Methyl-5-hepten-2one and 6-Hydroxy-4-methyl-4-hexenal. Using the same methodology as in section IIIA, four transition states, TS 3a, TS 3b, TS 3c, and TS 3d, were localized for the OH radical addition to 6-hydroxy-4-methyl-4-hexenal, which led to adducts 3a, 3b, 3c, and 3d. IRC calculations confirmed that each TS effectively connects reactants and products. The optimized geometries of 6-hydroxy-4-methyl-4-hexenal, transition states structures, and adducts, calculated at the BH&HLYP/cc-pVDZ level of theory are shown in Figure 4. Similarly, four transition states, TS 4a, TS 4b, TS 4c, and TS 4d, were determined for 6-methyl-5-hepten-2-one, and they were associated with the

formation of adducts 4a, 4b, 4c, and 4d, respectively. Results calculated at the BH&HLYP/cc-pVDZ level of theory are given in Figure 5. The C-O distances in the transition states were between 2.10 and 2.21 Å, which was 0.66-0.78 Å longer than those of the corresponding adducts at the BH&HLYP/cc-pVDZ level of theory. For 6-methyl-5-hepten-2-one, the C-O distances in the transition states were between 2.11 and 2.16 Å, which was 0.67-0.73 Å longer than those of the corresponding adducts calculated at the BH&HLYP/cc-pVDZ level of theory. These values were similar to those obtained for trans-geraniol in the previous section. Additionally, all the TS structures have geometric parameters similar to those of the reactants. As observed previously for the trans-geraniol reaction, there was no steric hindrance to OH radical addition to 6-hydroxy-4methyl-4-hexenal and 6-methyl-5-hepten-2-one, and it was expected that the reactions would be governed by the electronic structure of the reactants. The free energies of activation for the reaction pathways calculated at the MPW1K/cc-pVDZ and BH&HLYP/cc-pVDZ levels of theory are summarized in Table 3 for the 6-hydroxy4-methyl-4-hexenal and 6-methyl-5-hepten-2-one reactions.

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Figure 5. Stationary points determined at the BH&HLYP/cc-pVDZ level of theory for the OH radical addition to 6-methyl-5-hepten-2-one (bond distances in angstroms).

TABLE 3: Gibbs Free Energy of Activation for OH Radical Addition to 6-Hydroxy-4-methyl-4-hexenal and 6-Methyl-5-hepten-2-one, at 298 Ka pathway

MPW1K/cc-pVDZ

BH&HLYP/cc-pVDZ

3a 3b 3c 3d 4a 4b 4c 4d

2.92 6.80 5.80 6.66 6.38 7.36 4.64 7.36

3.66 8.70 7.05 7.94 7.76 8.70 6.31 8.69

a

Values are in kcal mol-1.

For the OH radical addition to 6-hydroxy-4-methyl-4-hexenal, the lowest free energies of activation were 2.92 and 3.66 kcal mol-1, which were calculated at the BH&HLYP/cc-pVDZ and MPW1K/cc-pVDZ levels, respectively, for pathway 3a. The highest values were for pathway 3b, which were found to be 6.80 and 8.70 kcal mol-1, as calculated at the BH&HLYP/ccpVDZ and MPW1K/cc-pVDZ levels.

For the OH radical addition to 6-methyl-5-hepten-2-one, the lowest free energies of activation were 6.31 and 4.64 kcal mol-1 for pathway 4c, as calculated at the BH&HLYP/cc-pVDZ and MPW1K/cc-pVDZ levels of theory. The highest values were for pathway 4b, which were found to be 8.70 and 7.36 kcal mol-1, as calculated at the BH&HLYP/cc-pVDZ and MPW1K/ cc-pVDZ levels. The values predicted at both levels differed by about 20%. The Gibbs free energy profiles for the OH radical addition to 6-hydroxy-4-methyl-4-hexenal and 6-methyl-5hepten-2-one, calculated at the BH&HLYP/cc-pVDZ level, are shown in Figure 6a,b. For the OH radical addition to 6-hydroxy-4-methyl-4-hexenal, pathway 3a is most favorably from the point of view of kinetic and thermodynamic parameters. For the 6-methyl-5-hepten-2one reaction, pathway 4c has the lowest free energy of activation and leads to the most stable adduct. As observed for transgeraniol adducts formation, all channels are strongly exoergic. Calculated high-pressure rate coefficients are shown in Table 4. For the OH radical addition to 6-hydroxy-4-methyl-4-hexenal, the calculated rate coefficient for pathway 3a, using the

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Figure 6. Gibbs free-energy profile for (a) OH radical addition to 6-hydroxy-4-methyl-4-hexenal and (b) OH radical addition to 6-methyl-5hepten-2-one.

BH&HLYP/cc-pVDZ energy data, is 2.1 × 10-11 cm3 molecule-1 s-1, and this accounts for 99.5% of the addition process. Using the MPW1K/cc-pVDZ data, the rate coefficient for the formation of adduct 3a is 7.4 × 10-11 cm3 molecule-1 s-1, which corresponds to 98.9% of adduct formation. At both levels of theory, the rate coefficients are at least 2 orders of magnitude higher than those for the other pathways with 3a being the dominant path. For the OH radical addition to 6-methyl-5-hepten-2-one, the calculated rate coefficients are 4.3 × 10-15 and 2.4 × 10-13 cm3 molecule-1 s-1, for pathways 4b and 4c. These values were calculated using the BH&HLYP/cc-pVDZ energy data. By using the MPW1K/cc-pVDZ data, the values 4.1 × 10-14 and 4.0 × 10-12 cm3 molecule-1 s-1, were calculated for pathways 4b and 4c. At both levels of theory, pathway 4c accounts for 89% of adduct formation at the BH&HLYP/cc-pVDZ level and is the dominant pathway.

TABLE 4: Calculated TST Rate Coefficients for Adduct Formation in the OH Radical Addition to 6-Hydroxy4-methyl-4-hexenal and 6-Methyl-5-hepten-2-onea pathway 3a 3b 3c 3d overall 4a 4b 4c 4d overall experimental a

BH&HLYP/ cc-pVDZ (×10-11)

MPW1K/cc-pVDZ (×10-11)

2.1 0.00043 0.0069 0.0015 2.11 0.0021 0.00043 0.024 0.00043 0.0269

7.4 0.01 0.057 0.013 7.48 0.021 0.0041 0.4 0.0041 0.429 15.7

Values calculated at 298 K using the BH&HLYP/cc-pVDZ and MPW1K/cc-pVDZ energy data. The units are cm3 molecule-1 s-1.

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Assuming that the adduct formation is the rate determining step, apparent rate coefficients were estimated by adding the rate coefficients of pathways 3 for 6-hydroxy-4-methyl-4hexenal and 4 for 6-methyl-5-hepten-2-one (Table 4). An apparent rate coefficient of 7.53 × 10-11 cm3 molecule-1 s-1 was estimated for the OH radical addition to 6-hydroxy-4methyl-4-hexenal at 298 K using the MPW1K/cc-pVDZ energy data. To the authors’ knowledge, no experimental data are available for comparison. Under the same conditions, the value 4.37 × 10-12 cm3 molecule-1 s-1 was estimated for the 6methyl-5-hepten-2-one reaction, which shows a reasonable agreement with the experimental result. The theoretical rate coefficient may be improved by a variational treatment as stated by Suh et al.13 and Lei et al.14 However, this is the scope of a future work that will include a RRKM/master equation analysis and the further steps of oxidation. Free energies of activation for the adduct formation were lower for the 6-hydroxy-4-methyl4-hexenal in comparison to 6-methyl-5-hepten-2-one as a consequence of the activation effect of the hydroxyl on the reactivity of the double bond.27,29,30 IV. Conclusions This paper presents a theoretical study of OH radical addition to trans-geraniol, 6-hydroxy-4-methyl-4-hexenal, and 6-methyl5-hepten-2-one. To the authors’ knowledge, theoretical reaction barrier heights for adduct formation have not been previously reported. A combined quantum-chemical and TST approach has been employed to determine the structures and energies of relevant species in the reaction systems and to predict the kinetic parameters of OH radical addition to these compounds. According to these calculations, the OH radical addition to the trans-geraniol on site 2 is the dominant process, which is expected for reactions of OH radicals with double bonds in the vicinity of electronegative groups. The addition reactions are highly exothermic and may lead to chemically activated adducts that may be subsequently subjected to prompt unimolecular reactions or collisional stabilization. It should be noted that the experimental rate coefficient determined by Forester et al.,10 is a global value corresponding to the sum of all possible pathways. Considering that the adduct formation is the determinant step for the OH-trans-geraniol mechanism, the apparent rate coefficient may be estimated by adding the rate coefficients for pathways 1 and 2. The theoretical results obtained in this work indicate that the only relevant pathways are the formation of adducts 2b and 2d. The estimated value of 3.1 × 10-10 cm3 molecule-1 s-1, calculated using MPW1K/cc-pVDZ data, is in good agreement with the experimental results. For the trans-geraniol reaction, the most recent experimental measurements suggest a rate coefficient in the range of (1.7-2.8) × 10-10 cm3 molecule-1 s-1 at 298 K. For the OH radical addition to 6-hydroxy-4-methyl-4-hexenal and 6-methyl-5-hepten-2-one, pathways 3a and 4c, respectively, are the dominant processes. The addition reactions are also highly exothermic and may lead to chemically activated adducts that may be subsequently subjected to prompt unimolecular reactions or collisional stabilization. Experimental rate coefficients determined for 6-hydroxy-4-methyl-4-hexenal are global values corresponding to the sum of all possible pathways. The estimated value of 4.37 × 10-12 cm3 molecule-1 s-1, calculated using MPW1K/cc-pVDZ energy values, is in reasonable agreement with the experimental results. For 6-hydroxy-4-methyl4-hexenal a value of 7.53 × 10-11 cm3 molecule-1 s-1 was obtained. The theoretical results support the experimental findings that the OH group “activates” the adjacent double bond,

Leonardo et al. which may be observed by comparing the rate coefficient for OH radical attack on sites 1 and 2 of trans-geraniol and the rate coefficients for the 6-hydroxy-4-methyl-4-hexenal reaction with the rate coefficients of the 6-methyl-5-hepten-2-one reaction. Forrester et al.10 observed 4-oxopentanal as the major oxidation product; however, the observed products were formed in reactions of the OH-geraniol adduct with atmospheric gases. A further theoretical study should investigate these reactions to elucidate the major pathway for the reaction of OH adducts under atmospheric conditions. The accuracies of the calculated rate coefficients strongly depend on the accuracies of the predicted barrier heights and vibration frequencies of the transition states and the reactants. A higher level of calculation would provide a better agreement with experimental results. The calculated energy profiles for the adduct formation show that large excessive energy is released, which results in the formation of highly excited intermediate species. The fates of these species should be evaluated by RRKM/master equation formulism. In spite of all these considerations, taking into account their relatively low computational cost, the density functional methods used in this work have proven to be quite useful and efficient. Acknowledgment. We acknowledge financial support from CNPq and CAPES. Supporting Information Available: Tables of absolute energies, zero-point energies, and free energies for all the species investigated in this study. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Zimmerman, P. R.; Chatfield, R. B.; Fishman, J.; Crutzen, P. J.; Hanst, P. Geophys. Res. Lett. 1978, 5, 679–682. (2) Nunes, F. M. N.; Veloso, M. C. C.; Pereira, P. A. de P.; de Andrade, J. B. Atmos. EnViron. 2005, 39, 7715–7730. (3) Nazaroff, W. W.; Weschler, C. J. Atmos. EnViron. 2004, 38, 2841– 2865. (4) Ramı´rez-Ramı´rez, V. M.; Peiro´-Garcı´a, J.; Nebot-Gil, I. Chem. Phys. Lett. 2004, 391, 152–156. (5) Gill, K. J.; Hites, R. A. J. Phys. Chem. A. 2002, 106, 2538. (6) Smith, A. M.; Rigler, E.; Kwok, E. S. C.; Atkinson, R. EnViron. Sci. Technol. 1996, 30, 1781–1785. (7) Fruekilde, P.; Hjorth, H.; Jensen, N. R.; Kotzias, D.; Larsen, B. Atmos. EnViron. 1998, 32, 1893–1902. (8) Ciccioli, P.; Brancaleoni, E.; Frattoni, M.; Cecinato, A.; Brachetti, A. Atmos. EnViron. 1993, 27A, 1891–1901. (9) Helmig, D.; Pllock, W.; Greenberg, J.; Zimmerman, P. J. Geophy. Res. 1996, 101 (14), 697. (10) Forester, C. D.; Ham, J. E.; Wells, J. R. Atmos. EnViron. 2007, 41, 1188–1199. (11) Hoffmann, T.; Bandur, R.; Marggraf, U.; Lincheid, M. J. Geophys. Res. 1998, 103, 25569–25578. (12) Zhang, R.; Suh, I.; Zhao, J.; Zhang, D.; Fortner, E. C.; Tie, X.; Molina, L. T.; Molina, M. J. Science 2004, 304, 1487–1490. (13) Suh, I.; Lei, W.; Zhang, R. J. Phys. Chem. A 2001, 105, 6471– 6478. (14) Lei, W.; Zhang, R.; McGivern, W. S.; Derecskei-Kovacs, A.; North, S. W. Chem. Phys. Lett. 2000, 326, 109–114. (15) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J. Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.;

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