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Chemical mechanism and kinetics study on the ocimene ozonolysis reaction in atmosphere
Atmospheric Environment 45 (2011) 6197e6203
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Atmospheric Environment journal homepage: www.elsevier.com/locate/atmosenv
Chemical mechanism and kinetics study on the ocimene ozonolysis reaction in atmosphere Xiaomin Sun a, b, Jing Bai a, Yuyang Zhao a, Chenxi Zhang a, Yudong Wang a, Jingtian Hu a, * a b
Environment Research Institute, Shandong University, Jinan 250100, PR China State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Science, Lanzhou 730000, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 April 2011 Received in revised form 19 July 2011 Accepted 3 August 2011
The ocimene ozonolysis reaction is one of the most important processes for the formation of secondary organic aerosol (SOA). In this paper, molecular orbital theory has been performed for the reaction of ocimene with O3, and the detailed reaction mechanisms of active intermediates with H2O or NO are also presented. The geometry parameters and vibrational frequencies of the stationary points are calculated at the MPWB1K level with the 6-31G(d,p) basis set. Single-point energy calculations are carried out at the MPWB1K/6-311þG(3df,2p) level. On the basis of the quantum chemical information, the RiceeRamspergereKasseleMarcus (RRKM) theory and the canonical variational transition state theory (CVT) with small-curvature tunneling effect (SCT) are used to calculate the rate constants over the temperature range of 200e800 K. The arrhenius formulas of rate constants with the temperature are fitted, which can provide helpful information for the model simulation study. The atmospheric lifetimes of the reaction species are estimated according to the rate constants. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Ozonolysis reaction of ocimene SOA formation mechanism Chemical mechanism and kinetics study Rate constant Atmospheric lifetime
1. Introduction Ocimene, an important member in the monoterpene family, belongs to chain terpenes which are released to the atmosphere by the physiological process of vegetation (Alvarado et al., 1998; Noe et al., 2006). The 3,7-dimethyl-1,3,7-octatriene is called a-Ocimene, and the 3,7-dimethyl-1,3,6-octatriene is called b-Ocimene which has two isomers, cis-b-Ocimene and trans-b-Ocimene. In this paper the cis-b-Ocimene is mainly considered whose chemical structure is shown as follows. C4 C3 C5
C2
C6
C1 C7
C8 C9
C10
C10H16 There are three intramolecular C]C double bonds in ocimene, which is easy for ocimene to react with O3, OH, NO3 or other radicals in * Corresponding author. Tel.: þ86 531 8836 4416. E-mail addresses: [email protected], [email protected] (J. Hu). 1352-2310/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2011.08.010
the atmosphere and generate a series of oxidation products contributing to ambient secondary organic aerosol (SOA) and tropospheric ozone production (Griffin et al., 1999). Hoffmann used photochemical smog chamber to study the SOA particle formation and found that SOA yield from ocimene and other open chain terpenes is about 5% (Hoffmann and Odum, 1997). Compared with the original organic matter, secondary organic compounds show stronger polarity, hygroscopicity and solubility, and exert an enormous impact on aerosol optical property, nucleation capability, and human health. The formation of SOA is one of the hottest topics in atmospheric chemistry research today, which is of great significance in regional and global atmospheric chemistry, climate change and environmental effects. In the last three decades, numerous studies on ocimene were reported. In 1985, Atkinson reported the mechanism and the dynamics of several terpenes including ocimene which reacted with the NO3 at the temperature of 294 K (Atkinson et al., 1985). In 2001, Aschmann used experimental methods to study the first order reaction products of ocimene when reacting with OH, O3 and NO3, respectively, and also reported the products in the follow-up reactions with active free radical in the atmosphere (Aschmann et al., 2001). In 2002, Aschmann measured the yield of OH generated from gas phase reaction of O3 with a series of monoterpenes occurring at 296 K and 1 atm, and also pointed out that the ocimene and O3 reaction, addition reaction on the >C]C(CH3)2 double bond accounted for a higher proportion (Aschmann et al., 2002). In 2002, Reissell used Gas Chromatography (GC) to analyze oxidation
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products of ocimene ozonolysis at the condition of 296 2 K and 1 atm (Reissell et al., 2002). In 2003 Atkinson studied the chemical reaction rates, mechanisms and products which were generated by terpenoids in the troposphere, and calculated the atmospheric residence time. He pointed out that the lifetime of cis-/transocimene was 44 min (Atkinson and Arey, 2003). In 2004, Baker detected the reaction products and the reaction rates of ocimene with OH, O3 and NO3 at room temperature (Baker et al., 2004). In 2005, Simon, who studied the vegetation emission of terpenoids in the Mediterranean area, found that light and temperature on vegetation had a great influence on terpene emission of vegetation. The ocimene emission rate reached 8.65 mg g1 h1 at 30 C and the total monoterpene emission rate was 14.76 mg g1 h1 (Simon et al., 2005). Obviously, the ocimene took up the majority of 58.6%. In 2006, Lee studied oxidation products of several different types of terpenes reacting with OH and O3, and listed the pathways of O3 addition in different double bonds of myrcene (Lee et al., 2006). In 2011, Sun studied the chemical mechanism of the limonene ozonolysis reactions in the SOA formation using quantum chemistry method and carried out direct dynamic calculation (Sun et al., 2011). Quantum chemical calculation is particularly suitable for establishing a reaction mechanism and has been applied successfully to study on the chemistry reaction in the SOA formation (Volkamer et al., 2002; Klotz et al., 2002; Zhao et al., 2004, 2010; Zhang and Zhang, 2005; Qu et al., 2006). Up to now, there is no report about quantum chemical calculations on ocimene and ozone reaction mechanism on the formation of SOA. Based on the previous experimental data, the density functional theory (DFT) is used to study the reaction mechanisms of ocimene with ozone. The potential energy profiles are constructed. The possible reaction mechanisms about reaction intermediates with H2O and NO are described in detail. This study intends to lay a theoretical foundation for solving the difference among the mechanisms speculated by a number of experimental phenomena, and provide some information about the reaction mechanisms that can not be obtained with experimental methods. The dynamic data will be helpful for the atmospheric model simulation study. 2. Computational methods 2.1. Geometry optimization All the work is performed using the Gaussian 03 programs (Frisch et al., 2003) and SGI workstation. Usually, the multi reference methods (CASSCF or CASPT2) are better than the DFT method to treat systems with biradical character. But for such moderate system, it is time-wasting with multi reference methods. In this paper, we used unrestricted MPWB1K method to treat systems with an even number of electrons but partial open-shell character, such as ozone, the Criegee biradicals. The MPWB1K method is a hybrid density functional theory (DFT) model with excellent performance for thermochemistry, thermochemical kinetics, hydrogen bonding, and weak interactions. It is well-known that MPWB1K is an excellent method for predicting transition state geometries and thermochemical kinetics, based on the modified Perdew and Wang exchange functional (MPW) and Becke’s 1995 correlation functional (B95) (Zhao and Truhlar, 2004). MPW1K method has ever been applied to the study of ozonolysis reactions (Yang et al., 2007, 2008). In all reaction channels, the geometry structures of various reactants, transition states, intermediates and products are optimized at the MPWB1K/6-31G(d,p) level. The vibrational frequencies are also calculated at the same level to determine the nature of stationary points. The selection of basis set is important for getting precise results (Zhang et al., 2000). The single-point energy calculations are performed at a higher level of theory MPWB1K/6-311þG(3df,2p).
Each transition state calculation is verified by the intrinsic reaction coordinate (IRC) to determine certain reactants and products. 2.2. Kinetic calculation The initial information obtained from ab initio calculations allows us to calculate the rate constants including the tunneling effects. The kinetic calculations have been carried out using RiceeRamspergereKasseleMarcus (RRKM) theory modified by Hou (Hou and Wang, 2007) and the POLYRATE 9.7 program (Corchado et al., 2007). (1) RiceeRamspergereKasseleMarcus (RRKM) theory This method has been successfully used in the previous study (Wang et al., 1999, 2010). The microcanonical rate constants are calculated using the following equation:
vffiffiffiffiffiffiffi u s u Ii N E Eis ki ðEÞ ¼ ai ki t IM hrj ðEÞ Ij
i ¼ 1; 2; 3; j ¼ 1:
Here ai is the statistical factor for the path degeneracy; ki is the tunneling factor; Iis ; IjIM are the moments of inertia (IaIbIc) of transition sate i and intermediate j; NðE Eis Þ is number of states with the energy above the barrier height Eis for i. Beyer-Swinehart algorithm is employed to calculate the density and number of states. Equation for calculating collision deactivation rate is given as follows:
u ¼ bc ZLJ ½He2 Here, bc is the collision efficiency calculated by Troe’s weak collision approximation with energy transfer parameter DE. ZLJ is the Lennard-Jones collision frequency. [He2] is the concentration of helium gas selected as bath gas. (2) Canonical Variational Transition state (CVT) theory The canonical variational transition state theory (CVT) with small-curvature tunneling effect (SCT) is used to calculate the rate constants over the temperature range of 200e800 K. The rotational partition functions are calculated classically, and the vibrational modes are treated as quantum-mechanical separable harmonic oscillators. The centrifugal-dominant SCT correction method is used in the rate constants calculation. In order to calculate the rate constants, a series of points are selected, which lie not only on the reactant side but also on the product side along the minimum energy path. For each point, the frequency is calculated to obtain the information of Cartesian coordinates, gradient and Hessian matrix. 3. Results and discussion The main possible reaction paths of ocimene with O3 are drawn in Scheme 1. Fig. 1, Figs. S1 and S2 show the potential energy profile of ocimene reaction with ozone and secondary reactions, labeled as channel A, B, C, respectively. The optimized geometries of the reactants, intermediates, transition states and products are shown in supplementary Fig. S3. Table 1 lists the rate constants of the elementary reaction (1)e(9) in channel A at 200e800 K. Table 2 lists the lifetimes of reactant species in atmosphere according to the rate constants. The arrhenius formulas (Units are s1 and cm3 Molecule1 s1 for unimolecular and bimolecular reactions, respectively) for elementary reactions involved in the reaction channel A over the temperature range are listed in Table 3.
X. Sun et al. / Atmospheric Environment 45 (2011) 6197e6203
TSa3 IMa3 TSa2 ERa(2) A
IMa1
TSa1
IMa4 ERa(3)
IMa5
TSa4 ERa(4)
Pa1+H2O
+ Pa2 +H2 O
IMa2
ERa(1)
+H2O
6199
TSa6 IMa7
ERa(6)
TSa7 IMa8
ERa(7)
Pa3+H2O
IMa6 TSa5 ERa(5)
TSa8
+
ERa(8)
IMa9
+H2 O
TSa9 IMa10
ERa(9)
Pa4+H2O
Pa5 ERb(6) C10 H16 +O3
B
TSb1 IMb1
IMb2
Pb1+C3H6O2
+N O TSb3 - NO 2 (3) ERb
TSb6
TSb4
ERb(1)
IMb3 TSb2 ERb(2)
IMb4
+H2O
TSb5 IMb5
Pb2+H2O
ERb(5)
ERb(4)
+ C3H6O
TSc2 ERc(2) C
TSc1
IMc1 ERc(1)
CH2O + +H2O IMc3
IMc4
TSc3
IMc5
ERc(3)
IMc2 Pc2 TSc5 ERc(5)
+O3
+
IMc6
TSc4 ERc(4)
Pc1+H2O
TSc6
Pc3+C3H6O2 IMc7 TSc7 ERc(7) ERc(6)
CH2O2 Scheme 1. The main possible reaction paths for the reaction of ocimene with O3.
3.1. The reaction of ocimene with O3 In the ocimene, there exists three C]C double bonds, i.e., three active reaction sites. Thus, the reaction with ozone has three different reaction channels, labeled as Channel A, B, and C, which are listed in Scheme 1. The potential energy surface profiles of Channel A, B, and C are drawn in Fig. 1, Figs. S1 and S2, and the
optimized geometries of the stationary points are shown in Fig. S3. And the spin multiplicity and the Cartesian coordinates of all products are offered in Supplementary information. 3.1.1. Reaction channel A In Channel A, O3 adds to the C3]C5 bond of ocimene to produce IMa1, which is a barrierless process. In the IMa1, the C3eO2 and
Fig. 1. The profile of the potential energy surface for ocimene react with O3 and secondary reactions, channel A.
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Table 1 The rate constants of the elementary reaction (1)e(9) at 200e800 K. T(K)
ERa(1) cm3 molecule1 s1
ERa(2) s1
ERa(3) s1
ERa(4) cm3 molecule1 s1
ERa(5) s1
ERa(6) cm3 molecule1 s1
ERa(7) s1
ERa(8) s1
ERa(9) cm3 molecule1 s1
200 220 240 260 280 298.15 300 320 340 360 380 400 450 500 550 600 650 700 750 800
3.73E16 4.43E16 5.13E16 5.83E16 6.54E16 7.19E16 7.26E16 7.97E16 8.68E16 9.40E16 1.01E15 1.08E15 1.26E15 1.44E15 1.62E15 1.80E15 1.98E15 2.16E15 2.34E15 2.52E15
3.10E15 2.00E13 6.54E12 1.27E10 1.63E09 1.24EL08 1.50E08 1.06E07 5.96E07 2.79E06 1.12E05 3.91E05 5.60E04 4.81E03 2.84E02 1.26E01 4.52E01 1.36Eþ00 3.56Eþ00 8.35Eþ00
1.56E05 4.97E04 8.88E03 1.02E01 8.18E01 4.26ED00 4.98Eþ00 2.42Eþ01 9.72Eþ01 3.34Eþ02 1.01Eþ03 2.73Eþ03 2.21Eþ04 1.18Eþ05 4.61Eþ05 1.44Eþ06 3.75Eþ06 8.53Eþ06 1.74Eþ07 3.24Eþ07
7.11E37 1.20E34 8.68E33 3.30E31 7.54E30 9.05E29 1.15E28 1.26E27 1.05E26 6.97E26 3.83E25 1.79E24 4.79E23 6.88E22 6.30E21 4.10E20 2.05E19 8.30E19 2.84E18 8.50E18
2.19E14 1.32E11 2.73E09 2.49E07 1.19E05 2.56EL04 3.42E04 6.44E03 8.58E02 8.57E01 6.72Eþ00 4.28Eþ01 2.13Eþ03 6.95Eþ09 3.51Eþ10 5.22Eþ10 7.30Eþ10 9.75Eþ10 1.25Eþ11 1.56Eþ11
7.54E09 1.23E08 2.15E08 3.49E08 5.87E08 1.10E07 2.34E07 5.96E07 1.95E06 3.43E06 6.46E06 1.31E05 2.92E05 7.29E05 7.98E05 2.08E04 7.00E04 2.91E03 1.57E02 1.20E01
2.09E22 3.83E22 7.09E22 1.32E21 2.47E21 4.35E21 4.61E21 8.60E21 1.60E20 2.94E20 5.37E20 9.69E20 4.03E19 1.55E18 5.44E18 1.75E17 5.12E17 1.42E16 3.10E16 6.45E16
4.40E25 8.49E22 4.64E19 9.62E17 9.32E15 3.48EL13 4.91E13 1.58E11 3.38E10 5.15E09 5.90E08 5.31E07 5.51E05 2.27E03 4.80E02 6.13E01 5.31Eþ00 3.40Eþ01 1.70Eþ02 6.99Eþ02
3.11E29 9.42E28 1.64E26 1.87E25 1.53E24 8.17E24 9.59E24 4.83E23 2.04E22 7.40E22 2.37E21 6.80E21 6.54E20 4.16E19 1.96E18 7.33E18 2.30E17 6.25E17 1.52E16 3.35E16
Bold values are examples that have been discussed at the temperature of 298.15 K.
C5eO3 bond lengths are 2.930 and 2.910 Å, respectively. The energy of IMa1 is 7.67 kcal mol1 lower than that of the total energy of the original reactants. With a small barrier of 2.81 kcal mol1, IMa2 with a five-member ring is formed via Tsa1. In the TSa1, the C3eO2 and the C5eO3 bond lengths are 2.430 and 2.272 Å. This process is strongly exothermic by up to 67.88 kcal mol1. In the ERa(2), the C3eC5 and O1eO3 bonds in the five-member ring of the IMa2 would break, obtaining Pa2 and IMa3 via TSa2 with a barrier of 21.59 kcal mol1. Compared to IMa2, the C3eC5 and O1eO3 bond lengths in TSa2 are elongated by 19.0% and 39.3%, respectively. This step occurs after the energy absorption of 11.87 kcal mol1. There is a competitive reaction with ERa(2), i.e., ERa(5). In the ERa(5), the C3eC5 and O1eO2 bonds in the fivemember ring of IMa2 would break to form Pa5 and IMa6 via the energy absorption of 5.15 kcal mol1. The reaction barrier of this process is 25.47 kcal mol1. Compared to IMa2, the C3eC5 and
Table 2 The lifetimes (s) of reactant species in atmosphere according to the rate constants at 200e800 K. T(K)
ERa(1)a
ERa(2)
ERa(4)b
ERa(5)
ERa(7)
ERa(9)b
200 220 240 260 280 298.15 300 320 340 360 380 400 450 500 550 600 650 700 750 800
9.94Eþ03 8.37Eþ03 7.23Eþ03 6.36Eþ03 5.67Eþ03 5.16ED03 5.11Eþ03 4.65Eþ03 4.27Eþ03 3.94Eþ03 2.67Eþ07 3.43Eþ03 2.94Eþ03 2.57Eþ03 2.29Eþ03 2.06Eþ03 1.87Eþ03 1.72Eþ03 1.58Eþ03 1.47Eþ03
3.23Eþ14 5.00Eþ12 1.53Eþ11 7.87Eþ09 6.13Eþ08 8.06ED07 6.67Eþ07 9.43Eþ06 1.68Eþ06 3.58Eþ05 8.93Eþ04 2.56Eþ04 1.79Eþ03 2.08Eþ02 3.52Eþ01 7.94Eþ00 2.21Eþ00 7.35E01 2.81E01 1.20E01
2.62Eþ18 1.55Eþ16 2.14Eþ14 5.64Eþ12 2.47Eþ11 2.06ED10 1.62Eþ10 1.48Eþ09 1.77Eþ08 2.67Eþ07 4.86Eþ06 1.04Eþ06 3.88Eþ04 2.70Eþ03 2.95Eþ02 4.54Eþ01 9.08Eþ00 2.24Eþ00 6.55E01 2.19E01
4.57Eþ13 7.58Eþ10 3.66Eþ08 4.02Eþ06 8.40Eþ04 3.91ED03 2.92Eþ03 1.55Eþ02 1.17Eþ01 1.17Eþ00 1.49E01 2.34E02 4.69E04 1.44E10 2.85E11 1.92E11 1.37E11 1.03E11 8.00E12 6.41E12
4.78Eþ21 2.61Eþ21 1.41Eþ21 7.58Eþ20 4.05Eþ20 2.30ED20 2.17Eþ20 1.16Eþ20 6.25Eþ19 3.40Eþ19 1.86Eþ19 1.03Eþ19 2.48Eþ18 6.45Eþ17 1.84Eþ17 5.71Eþ16 1.95Eþ16 7.04Eþ15 3.23Eþ15 1.55Eþ15
5.98Eþ10 1.98Eþ09 1.13Eþ08 9.95þ06 1.22þ06 2.28D05 1.94þ05 3.85þ04 9.12þ03 2.51þ03 7.85þ02 2.73þ02 2.84þ01 4.47þ00 9.4901 2.5401 8.0902 2.9802 1.2202 5.5503
Bold values are examples that have been discussed at the temperature of 298.15 K. a O3 concentration is about 2.688 1011 molecule cm3. b H2O concentration is about 5.375 1017 molecule cm3.
O1eO2 bonds in the TSa5 are elongated by 22.7% and 38.5%, respectively. Since ERa(2) has a lower potential barrier than ERa(5), it occurs more easily. IMa3 is an oxygenated free radical with high activity which would further react easily in the atmosphere. For example, intramolecular hydrogen migration takes place in IMa3 in the ERa(3), i.e., the H1 atom of the C4eH1 bond transfers to O1 atom to form five-member ring via transition state TSa3, and generates IMa4. In the TSa3, the breaking of the C4eH1 bond and the formation of the O1eH1 bond occur simultaneously. The O2eO1, C4eH1, O1eH1 bond lengths are 1.375, 1.324 and 1.329 Å, respectively. The reaction barrier is 18.69 kcal mol 1 and the reaction heat is 14.00 kcal mol1. Similar to IMa3, IMa6 also undergoes intramolecular hydrogen migration, labeled as ERa(8). The H8 atom of the C6eH8 migrates to the O1 atom to form a five-member ring and generate IMa9 via transition state TSa8 with a barrier of 35.86 kcal mol1. The lengths of the O3eO1, C6eH8 and O1eH8 bond are 1.474, 1.347 and 1.468 Å in the TSa8, respectively. This process is strongly exothermic by up to 30.23 kcal mol1. 3.1.2. Reaction channel B The reaction channel B is similar to the reaction Channel A. IMb1 is produced from O3 addition to the C7]C8 double bond of ocimene. Then the subsequent elementary reactions are listed as follows. The DEb is the potential barrier and the DEr is the reaction heat in the elementary reaction.
Table 3 Arrhenius formulas (units are s1 and cm3 molecule1 s1 for unimolecular and bimolecular reactions, respectively) for elementary reactions involved in the reaction channel A over the temperature range of 200e800 K. ERa(1) ERa(2) ERa(3) ERa(4) ERa(5) ERa(6) ERa(7) ERa(8) ERa(9)
k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T)
¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼
4.18 9.05 4.29 1.20 1.80 5.98 1.26 7.48 4.44
1015 exp(511.26/T) 105 exp(9486.72/T) 1011 exp(7559.32/T) 1011 exp(11,710.67/T) 1021 exp(16,692.89/T) 101 exp(4176.44/T) 1014 exp(4147.90/T) 1011 exp(16,698.18/T) 1012 exp(8005.20/T)
X. Sun et al. / Atmospheric Environment 45 (2011) 6197e6203
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IMb1/TSb1/IMb2
DEb ¼ 1:66 kcal mol1
DEr ¼ 73:08 kcal mol1
ERb(1)
IMb2/TSb2/IMb3 þ C3 H6 O
DEb ¼ 27:89 kcal mol1
DEr ¼ 2:21 kcal mol1
ERb(2)
IMb3/TSb4/IMb4
DEb ¼ 18:62 kcal mol1
DEr ¼ 23:33 kcal mol1
ERb(4)
IMb2/TSb6/Pb1 þ C3 H6 O2
DEb ¼ 23:89 kcal mol1
DEr ¼ 6:95 kcal mol1
ERb(6)
3.1.3. Reaction channel C The third addition fashion is O3 addition to the C1]C2 double bond in Ocimene, which is labeled as Channel C. After IMc1 is formed, it isomerizes to IMc2 which contains a five-member ring via TSc1. Similar to the above two reaction pathways, there are also two competitive reactions with IMc2, ERc(2) and ERc(5). The reaction pathways are described as follows.
IMa5, the O4eH2 and O2eO1 bonds break up while the C4eO4 and O1eH2 bonds are formed simultaneously. The length of C4eO4, O2eO1, O1eH2 and O4eH2 bond in the TSa4 is 2.040, 1.808, 1.485 and 1.020 Å. This process is strongly exothermic by up to 67.06 kcal mol1. The reaction of IMa6 is similar to that of IMa4, and another Van der Waals complex IMa7 is formed. The main difference is that a five-member ring is formed in IMa7 which includes
IMc1/TSc1/IMc2
DEb ¼ 2:22 kcal mol1
DEr ¼ 64:61 kcal mol1
ERc(1)
IMc2/TSc2/IMc3 þ CH2 O
DEb ¼ 22:08 kcal mol1
DEr ¼ 1:37 kcal mol1
ERc(2)
IMc2/TSc5/Pc2 þ CH2 O2
DEb ¼ 24:75 kcal mol1
DEr ¼ 2:69 kcal mol1
ERc(5)
The above three channels share some common properties. For example, the O3 addition to form five-member ring, the H migration. As for the adducts of ocimene with O3, the Criegee biradicals would be generated when the five-member ring ruptured, for example, IMa3 and Pa2, IMa6 and Pa5, Pb1 and C3H6O2, IMb3 and C3H6O, IMc3 and CH2O, Pc2 and CH2O2. The polarities for most of them are higher than that of ocimene, which results in the decrease in volatility. These intermediates can be oxidized continuously into the semi-volatility compounds, which are highly potential to form the SOA through the hydration or absorption on the aerosol surface the same as the D-limonene with O3.
the O5, H6 atoms in H2O molecule and C5, O3 and O1 atoms in IMa6. With a potential barrier of 7.69 kcal mol1, the O5eH6 bond of the H2O breaks and the O5eC5 and H6eO1 bonds of IMa7 is produced via TSa6, and IMa8 is obtained in ERa(6). In TSa6, the length of C5eO5, O5eH6 and O1eH6 bond is 1.980 Å, 1.048 Å and 1.475 Å. The reaction heat is 37.87 kcal mol1. Finally, IMa8 is isomerized to Pa3 and H2O via a four-member ring transition state TSa7. As for other reaction involved with H2O molecule, for example, the ERa(9) in channel A, ERb(5) in channel B, and ERc(4) in the channel C, the mechanisms are the same as ERa(4). The H2O molecule can be regenerated and act as an activator which plays an important role in the formation of SOA in atmosphere.
3.2. Secondary reactions In the reaction channel A, B and C, those Criegee biradicals are important intermediates produced in the oxidation process of ocimene with O3. As their removal from the troposphere, these radical intermediates could further react with H2O or NO, because NO or H2O are abundant in atmosphere. Bonn focused on the investigation of the influence of water vapor on the size distribution of the newly formed aerosol particles during the reaction of monoterpenes and ozone measured by a scanning mobility particle sizer (Bonn et al., 2002). The secondary reactions about these intermediates are discussed in the following. 3.2.1. The reaction in the presence of H2O In the channel A, the profile of the potential energy surface shows that the reaction of IMa4 with H2O is a barrierless association to produce a Van der Waals complex IMa5. Then IMa5 will form Pa1 and H2O via TSa4 with a barrier of 32.08 kcal mol1. The detailed process is as follows: the O4 and H2 atoms in the H2O and the O1, O2, C3, C4 atoms in IMa4 constitute a six-member ring in
3.2.2. The reaction in the presence of NO and O3 It is widely accepted that the O abstraction by NO radical takes place easily once the peroxy-hydrocarbon exists in atmosphere. Take ERb(3) in the reaction channel B for example, the O1 atom of IMb3 can be extracted by NO to obtain products Pb1 and NO2 via the transition state TSb3. In the TSb3, the length of O3eO1 and NeO1 bond is 1.434 and 1.363 Å. The potential barrier, reaction enthalpy and Gibbs free energy are 1.94 kcal mol1, 69.59 kcal mol1 and 69.82 kcal mol1, respectively. The reaction barrier of NO extraction O is very low and the Gibbs free energy is a large negative value which indicates that this reaction is controlled both thermodynamically and kinetically. Since the intermediates or products still have C]C double bonds, they can react with O3 sequentially. For example, Pc2 can react with O3 to form a Van der Waals complex IMc6, and then to form IMc7 via TSc6 with a small barrier of 1.85 kcal mol1. The process is O3 addition to the C7]C8 double bond of the Pc2. The C7eO3 bond and the C8eO2 bond length is 2.323 and 2.309 Å in the TSc6, and a carboneoxygen five-member ring is formed in IMc7. The reaction heat
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of this step is 70.81 kcal mol1. Subsequently, the C7eC8 and O1eO3 bonds in the five-member ring of IMc7 break simultaneously via TSc7 to produce new Criegee biradicals Pc3 and C3H6O2. The C7eC8 and O1eO3 bond length in the TSc7 elongates by 21.0% and 39.2% compared with the IMc7. The potential barrier is 23.10 kcal mol1 and the reaction heat is 7.04 kcal mol1 in ERc(7).
3.3. Rate constants Since the mechanisms of these three reaction channels are very similar, the elementary reactions in Channel A are chosen as examples to discuss. The RiceeRamspergereKasseleMarcus (RRKM) theory modified by Hou (Hou and Wang, 2007) and the canonical variational transition state theory (CVT) with small-curvature tunneling (SCT) effect (Qu et al., 2009; Zhang et al., 2008, 2009) are used to calculate the rate constants. The results are listed in Table 2. For the dimolecular reaction or the unimolecular dissociation reaction, the RRKM theory is used to calculate the rate constants of elementary reactions as follows:
C10 H16 þ O3 /IMa1/TSa1/IMa2
ERa(1)
IMa2/TSa2/IMa3 þ Pa2
ERa(2)
IMa4 þ H2 O/IMa5/TSa4/Pa1 þ H2 O
ERa(4)
IMa2/TSa5/IMa6 þ Pa5
ERa(5)
IMa6 þ H2 O/IMa7/TSa6/IMa8
ERa(6)
IMa8/TSa7/Pa3 þ H2 O
ERa(7)
IMa9 þ H2 O/IMa10/TSa9/Pa4 þ H2 O
ERa(9)
The elementary reaction IMa8 / TSa7 / Pa3 þ H2O ERa(7) is taken as an example to consider the pressure effect. From 0.5 atm to 1 atm, the rate constants changed from 8.71E21 to 4.35E21. The rate constants of other elementary reactions do not vary with pressure. So it can be found that the pressure has little effect on the rate constants in the present case which is inconsistent with Drozd’s result, since the excess energy is disregarded and all species is assumed to be thermalized (Drozd and Donahue, 2011). Then the 1 atm pressure is chosen to discuss the rate constants under the temperature from 200 K to 800 K. As for the unimolecular isomerization reaction, such as ERa(3) and ERa(8), the CVT/SCT method is used to calculate the rate constants. The pressure effect can be ignored since the molecular number of the reactants and products is the same.
IMa3/Tsa3/IMa4
ERa(3)
IMa6/Tsa8/IMa9
ERa(8)
From the rate constants of elementary reactions, the ERa(3) and ERa(6) have large rate constants, and ERa(3) is the largest one. The ERa(1), ERa(2) and ERa(5) have the medium values. The ERa(4), ERa(7), ERa(8) and ERa(9) have smaller values, and the ERa(4), is the smallest one. It is obvious that the calculated rate constants exhibit typical nonArrhenius behavior, i.e., k(T) ¼ a 10bTc exp(d/T). The arrhenius formulas for elementary reactions involved in the reaction channel A over the temperature range are listed in Table 3. The formula of the rate constants with temperature are helpful for the atmospheric aerosol model study.
According to the rate constants of elementary reaction, the atmospheric lifetime of the reactants can be calculated. For the first order reaction, such as monomolecular pyrolysis or photolysis reaction, the lifetime s is the reciprocal of the rate constant k, i.e., s ¼ 1=k. In Drozd’s discussions, the reactions of Criegee Intermediates with much excess energy are influenced by pressure (Drozd and Donahue, 2011). So the lifetime of Criegee Intermediates as IMa3 and IMa6 is not reported in order to avoid misleading. Then the lifetime of the reactants in ERa(1), ERa(2), ERa(4), ERa(5), ERa(7) and ERa(9) can be obtained at the range of 200e800 K and listed in Table 2. Those lifetime at the room temperature is taken as example to discuss. The lifetimes of C10H16 was 86 min. It belongs to short lifetime species. In comparison, IMa2 (2.56 d) and IMa9 (2.60 d) are belonging to middle lifetime species. Because of high barriers, IMa4 and IMa8 belong to long lifetime species. 4. Conclusion In this paper, a theoretical study on ocimene ozonolysis reaction is performed at the MPWB1K/6-311þG(3df,2p)//MPWB1K/6-31G(d,p) level. A detailed description of the possible oxidation mechanism in the presence of H2O or NO is provided. The rate constants are calculated using the RRKM theory and the CVT/SCT method. Some valuable results are found. (1) The information of the stationary points including the reactants, intermediates, transition states and products are calculated, which are useful to further understand the chemical formation process of SOA. There exist three reaction channels, all of which can take place. The potential barriers of three intramolecular reaction sites in ocimene with the O3 have little in common. The C]C(CH3)2 site accounts for a large proportion of the reaction, which is consistent with the experimental results. (2) In the subsequent reaction, H2O molecule acts as an activator of OH transfer in ERa(4), ERa(6) and ERa(9) which promotes the chemistry process. The O abstraction reactions from peroxy hydrocarbons with NO molecule are favorable in both thermodynamics and dynamics. (3) The oxidation process occurs spontaneously once it is initiated by O3. Most of the obtained products have high polarity and water-solubility, which contributes to the formation of SOA through the hydration or absorption reaction on aerosol surface. (4) According to values of the lifetime, the C10H16 belongs to the short lifetime species, and IMa2 and IMa9 belong to middle lifetime species while the IMa4 and IMa8 belong to long lifetime ones. Acknowledgments This work is supported by National Natural Science Foundation of China (No. 20903062, No. 20873074 and No. 20737001), Natural Science Foundation of Shandong Province (No. Q2008B07), Independent Innovation Foundation of Shandong University (No. 2010TS064) and Open Project from State Key Laboratory of Environmental Chemistry and Ecotoxicology, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences (No. KF2009-10). The authors thank Professor Donald G. Truhlar for providing the POLYRATE 9.7 program and Professor Baoshan Wang for providing the RRKM program. Appendix. Supplementary information Supplementary information associated with this article can be found, in the online version, at doi:10.1016/j.atmosenv.2011.08.010.
X. Sun et al. / Atmospheric Environment 45 (2011) 6197e6203
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Contents lists available at ScienceDirect
Atmospheric Environment journal homepage: www.elsevier.com/locate/atmosenv
Chemical mechanism and kinetics study on the ocimene ozonolysis reaction in atmosphere Xiaomin Sun a, b, Jing Bai a, Yuyang Zhao a, Chenxi Zhang a, Yudong Wang a, Jingtian Hu a, * a b
Environment Research Institute, Shandong University, Jinan 250100, PR China State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Science, Lanzhou 730000, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 April 2011 Received in revised form 19 July 2011 Accepted 3 August 2011
The ocimene ozonolysis reaction is one of the most important processes for the formation of secondary organic aerosol (SOA). In this paper, molecular orbital theory has been performed for the reaction of ocimene with O3, and the detailed reaction mechanisms of active intermediates with H2O or NO are also presented. The geometry parameters and vibrational frequencies of the stationary points are calculated at the MPWB1K level with the 6-31G(d,p) basis set. Single-point energy calculations are carried out at the MPWB1K/6-311þG(3df,2p) level. On the basis of the quantum chemical information, the RiceeRamspergereKasseleMarcus (RRKM) theory and the canonical variational transition state theory (CVT) with small-curvature tunneling effect (SCT) are used to calculate the rate constants over the temperature range of 200e800 K. The arrhenius formulas of rate constants with the temperature are fitted, which can provide helpful information for the model simulation study. The atmospheric lifetimes of the reaction species are estimated according to the rate constants. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Ozonolysis reaction of ocimene SOA formation mechanism Chemical mechanism and kinetics study Rate constant Atmospheric lifetime
1. Introduction Ocimene, an important member in the monoterpene family, belongs to chain terpenes which are released to the atmosphere by the physiological process of vegetation (Alvarado et al., 1998; Noe et al., 2006). The 3,7-dimethyl-1,3,7-octatriene is called a-Ocimene, and the 3,7-dimethyl-1,3,6-octatriene is called b-Ocimene which has two isomers, cis-b-Ocimene and trans-b-Ocimene. In this paper the cis-b-Ocimene is mainly considered whose chemical structure is shown as follows. C4 C3 C5
C2
C6
C1 C7
C8 C9
C10
C10H16 There are three intramolecular C]C double bonds in ocimene, which is easy for ocimene to react with O3, OH, NO3 or other radicals in * Corresponding author. Tel.: þ86 531 8836 4416. E-mail addresses: [email protected], [email protected] (J. Hu). 1352-2310/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2011.08.010
the atmosphere and generate a series of oxidation products contributing to ambient secondary organic aerosol (SOA) and tropospheric ozone production (Griffin et al., 1999). Hoffmann used photochemical smog chamber to study the SOA particle formation and found that SOA yield from ocimene and other open chain terpenes is about 5% (Hoffmann and Odum, 1997). Compared with the original organic matter, secondary organic compounds show stronger polarity, hygroscopicity and solubility, and exert an enormous impact on aerosol optical property, nucleation capability, and human health. The formation of SOA is one of the hottest topics in atmospheric chemistry research today, which is of great significance in regional and global atmospheric chemistry, climate change and environmental effects. In the last three decades, numerous studies on ocimene were reported. In 1985, Atkinson reported the mechanism and the dynamics of several terpenes including ocimene which reacted with the NO3 at the temperature of 294 K (Atkinson et al., 1985). In 2001, Aschmann used experimental methods to study the first order reaction products of ocimene when reacting with OH, O3 and NO3, respectively, and also reported the products in the follow-up reactions with active free radical in the atmosphere (Aschmann et al., 2001). In 2002, Aschmann measured the yield of OH generated from gas phase reaction of O3 with a series of monoterpenes occurring at 296 K and 1 atm, and also pointed out that the ocimene and O3 reaction, addition reaction on the >C]C(CH3)2 double bond accounted for a higher proportion (Aschmann et al., 2002). In 2002, Reissell used Gas Chromatography (GC) to analyze oxidation
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products of ocimene ozonolysis at the condition of 296 2 K and 1 atm (Reissell et al., 2002). In 2003 Atkinson studied the chemical reaction rates, mechanisms and products which were generated by terpenoids in the troposphere, and calculated the atmospheric residence time. He pointed out that the lifetime of cis-/transocimene was 44 min (Atkinson and Arey, 2003). In 2004, Baker detected the reaction products and the reaction rates of ocimene with OH, O3 and NO3 at room temperature (Baker et al., 2004). In 2005, Simon, who studied the vegetation emission of terpenoids in the Mediterranean area, found that light and temperature on vegetation had a great influence on terpene emission of vegetation. The ocimene emission rate reached 8.65 mg g1 h1 at 30 C and the total monoterpene emission rate was 14.76 mg g1 h1 (Simon et al., 2005). Obviously, the ocimene took up the majority of 58.6%. In 2006, Lee studied oxidation products of several different types of terpenes reacting with OH and O3, and listed the pathways of O3 addition in different double bonds of myrcene (Lee et al., 2006). In 2011, Sun studied the chemical mechanism of the limonene ozonolysis reactions in the SOA formation using quantum chemistry method and carried out direct dynamic calculation (Sun et al., 2011). Quantum chemical calculation is particularly suitable for establishing a reaction mechanism and has been applied successfully to study on the chemistry reaction in the SOA formation (Volkamer et al., 2002; Klotz et al., 2002; Zhao et al., 2004, 2010; Zhang and Zhang, 2005; Qu et al., 2006). Up to now, there is no report about quantum chemical calculations on ocimene and ozone reaction mechanism on the formation of SOA. Based on the previous experimental data, the density functional theory (DFT) is used to study the reaction mechanisms of ocimene with ozone. The potential energy profiles are constructed. The possible reaction mechanisms about reaction intermediates with H2O and NO are described in detail. This study intends to lay a theoretical foundation for solving the difference among the mechanisms speculated by a number of experimental phenomena, and provide some information about the reaction mechanisms that can not be obtained with experimental methods. The dynamic data will be helpful for the atmospheric model simulation study. 2. Computational methods 2.1. Geometry optimization All the work is performed using the Gaussian 03 programs (Frisch et al., 2003) and SGI workstation. Usually, the multi reference methods (CASSCF or CASPT2) are better than the DFT method to treat systems with biradical character. But for such moderate system, it is time-wasting with multi reference methods. In this paper, we used unrestricted MPWB1K method to treat systems with an even number of electrons but partial open-shell character, such as ozone, the Criegee biradicals. The MPWB1K method is a hybrid density functional theory (DFT) model with excellent performance for thermochemistry, thermochemical kinetics, hydrogen bonding, and weak interactions. It is well-known that MPWB1K is an excellent method for predicting transition state geometries and thermochemical kinetics, based on the modified Perdew and Wang exchange functional (MPW) and Becke’s 1995 correlation functional (B95) (Zhao and Truhlar, 2004). MPW1K method has ever been applied to the study of ozonolysis reactions (Yang et al., 2007, 2008). In all reaction channels, the geometry structures of various reactants, transition states, intermediates and products are optimized at the MPWB1K/6-31G(d,p) level. The vibrational frequencies are also calculated at the same level to determine the nature of stationary points. The selection of basis set is important for getting precise results (Zhang et al., 2000). The single-point energy calculations are performed at a higher level of theory MPWB1K/6-311þG(3df,2p).
Each transition state calculation is verified by the intrinsic reaction coordinate (IRC) to determine certain reactants and products. 2.2. Kinetic calculation The initial information obtained from ab initio calculations allows us to calculate the rate constants including the tunneling effects. The kinetic calculations have been carried out using RiceeRamspergereKasseleMarcus (RRKM) theory modified by Hou (Hou and Wang, 2007) and the POLYRATE 9.7 program (Corchado et al., 2007). (1) RiceeRamspergereKasseleMarcus (RRKM) theory This method has been successfully used in the previous study (Wang et al., 1999, 2010). The microcanonical rate constants are calculated using the following equation:
vffiffiffiffiffiffiffi u s u Ii N E Eis ki ðEÞ ¼ ai ki t IM hrj ðEÞ Ij
i ¼ 1; 2; 3; j ¼ 1:
Here ai is the statistical factor for the path degeneracy; ki is the tunneling factor; Iis ; IjIM are the moments of inertia (IaIbIc) of transition sate i and intermediate j; NðE Eis Þ is number of states with the energy above the barrier height Eis for i. Beyer-Swinehart algorithm is employed to calculate the density and number of states. Equation for calculating collision deactivation rate is given as follows:
u ¼ bc ZLJ ½He2 Here, bc is the collision efficiency calculated by Troe’s weak collision approximation with energy transfer parameter DE. ZLJ is the Lennard-Jones collision frequency. [He2] is the concentration of helium gas selected as bath gas. (2) Canonical Variational Transition state (CVT) theory The canonical variational transition state theory (CVT) with small-curvature tunneling effect (SCT) is used to calculate the rate constants over the temperature range of 200e800 K. The rotational partition functions are calculated classically, and the vibrational modes are treated as quantum-mechanical separable harmonic oscillators. The centrifugal-dominant SCT correction method is used in the rate constants calculation. In order to calculate the rate constants, a series of points are selected, which lie not only on the reactant side but also on the product side along the minimum energy path. For each point, the frequency is calculated to obtain the information of Cartesian coordinates, gradient and Hessian matrix. 3. Results and discussion The main possible reaction paths of ocimene with O3 are drawn in Scheme 1. Fig. 1, Figs. S1 and S2 show the potential energy profile of ocimene reaction with ozone and secondary reactions, labeled as channel A, B, C, respectively. The optimized geometries of the reactants, intermediates, transition states and products are shown in supplementary Fig. S3. Table 1 lists the rate constants of the elementary reaction (1)e(9) in channel A at 200e800 K. Table 2 lists the lifetimes of reactant species in atmosphere according to the rate constants. The arrhenius formulas (Units are s1 and cm3 Molecule1 s1 for unimolecular and bimolecular reactions, respectively) for elementary reactions involved in the reaction channel A over the temperature range are listed in Table 3.
X. Sun et al. / Atmospheric Environment 45 (2011) 6197e6203
TSa3 IMa3 TSa2 ERa(2) A
IMa1
TSa1
IMa4 ERa(3)
IMa5
TSa4 ERa(4)
Pa1+H2O
+ Pa2 +H2 O
IMa2
ERa(1)
+H2O
6199
TSa6 IMa7
ERa(6)
TSa7 IMa8
ERa(7)
Pa3+H2O
IMa6 TSa5 ERa(5)
TSa8
+
ERa(8)
IMa9
+H2 O
TSa9 IMa10
ERa(9)
Pa4+H2O
Pa5 ERb(6) C10 H16 +O3
B
TSb1 IMb1
IMb2
Pb1+C3H6O2
+N O TSb3 - NO 2 (3) ERb
TSb6
TSb4
ERb(1)
IMb3 TSb2 ERb(2)
IMb4
+H2O
TSb5 IMb5
Pb2+H2O
ERb(5)
ERb(4)
+ C3H6O
TSc2 ERc(2) C
TSc1
IMc1 ERc(1)
CH2O + +H2O IMc3
IMc4
TSc3
IMc5
ERc(3)
IMc2 Pc2 TSc5 ERc(5)
+O3
+
IMc6
TSc4 ERc(4)
Pc1+H2O
TSc6
Pc3+C3H6O2 IMc7 TSc7 ERc(7) ERc(6)
CH2O2 Scheme 1. The main possible reaction paths for the reaction of ocimene with O3.
3.1. The reaction of ocimene with O3 In the ocimene, there exists three C]C double bonds, i.e., three active reaction sites. Thus, the reaction with ozone has three different reaction channels, labeled as Channel A, B, and C, which are listed in Scheme 1. The potential energy surface profiles of Channel A, B, and C are drawn in Fig. 1, Figs. S1 and S2, and the
optimized geometries of the stationary points are shown in Fig. S3. And the spin multiplicity and the Cartesian coordinates of all products are offered in Supplementary information. 3.1.1. Reaction channel A In Channel A, O3 adds to the C3]C5 bond of ocimene to produce IMa1, which is a barrierless process. In the IMa1, the C3eO2 and
Fig. 1. The profile of the potential energy surface for ocimene react with O3 and secondary reactions, channel A.
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Table 1 The rate constants of the elementary reaction (1)e(9) at 200e800 K. T(K)
ERa(1) cm3 molecule1 s1
ERa(2) s1
ERa(3) s1
ERa(4) cm3 molecule1 s1
ERa(5) s1
ERa(6) cm3 molecule1 s1
ERa(7) s1
ERa(8) s1
ERa(9) cm3 molecule1 s1
200 220 240 260 280 298.15 300 320 340 360 380 400 450 500 550 600 650 700 750 800
3.73E16 4.43E16 5.13E16 5.83E16 6.54E16 7.19E16 7.26E16 7.97E16 8.68E16 9.40E16 1.01E15 1.08E15 1.26E15 1.44E15 1.62E15 1.80E15 1.98E15 2.16E15 2.34E15 2.52E15
3.10E15 2.00E13 6.54E12 1.27E10 1.63E09 1.24EL08 1.50E08 1.06E07 5.96E07 2.79E06 1.12E05 3.91E05 5.60E04 4.81E03 2.84E02 1.26E01 4.52E01 1.36Eþ00 3.56Eþ00 8.35Eþ00
1.56E05 4.97E04 8.88E03 1.02E01 8.18E01 4.26ED00 4.98Eþ00 2.42Eþ01 9.72Eþ01 3.34Eþ02 1.01Eþ03 2.73Eþ03 2.21Eþ04 1.18Eþ05 4.61Eþ05 1.44Eþ06 3.75Eþ06 8.53Eþ06 1.74Eþ07 3.24Eþ07
7.11E37 1.20E34 8.68E33 3.30E31 7.54E30 9.05E29 1.15E28 1.26E27 1.05E26 6.97E26 3.83E25 1.79E24 4.79E23 6.88E22 6.30E21 4.10E20 2.05E19 8.30E19 2.84E18 8.50E18
2.19E14 1.32E11 2.73E09 2.49E07 1.19E05 2.56EL04 3.42E04 6.44E03 8.58E02 8.57E01 6.72Eþ00 4.28Eþ01 2.13Eþ03 6.95Eþ09 3.51Eþ10 5.22Eþ10 7.30Eþ10 9.75Eþ10 1.25Eþ11 1.56Eþ11
7.54E09 1.23E08 2.15E08 3.49E08 5.87E08 1.10E07 2.34E07 5.96E07 1.95E06 3.43E06 6.46E06 1.31E05 2.92E05 7.29E05 7.98E05 2.08E04 7.00E04 2.91E03 1.57E02 1.20E01
2.09E22 3.83E22 7.09E22 1.32E21 2.47E21 4.35E21 4.61E21 8.60E21 1.60E20 2.94E20 5.37E20 9.69E20 4.03E19 1.55E18 5.44E18 1.75E17 5.12E17 1.42E16 3.10E16 6.45E16
4.40E25 8.49E22 4.64E19 9.62E17 9.32E15 3.48EL13 4.91E13 1.58E11 3.38E10 5.15E09 5.90E08 5.31E07 5.51E05 2.27E03 4.80E02 6.13E01 5.31Eþ00 3.40Eþ01 1.70Eþ02 6.99Eþ02
3.11E29 9.42E28 1.64E26 1.87E25 1.53E24 8.17E24 9.59E24 4.83E23 2.04E22 7.40E22 2.37E21 6.80E21 6.54E20 4.16E19 1.96E18 7.33E18 2.30E17 6.25E17 1.52E16 3.35E16
Bold values are examples that have been discussed at the temperature of 298.15 K.
C5eO3 bond lengths are 2.930 and 2.910 Å, respectively. The energy of IMa1 is 7.67 kcal mol1 lower than that of the total energy of the original reactants. With a small barrier of 2.81 kcal mol1, IMa2 with a five-member ring is formed via Tsa1. In the TSa1, the C3eO2 and the C5eO3 bond lengths are 2.430 and 2.272 Å. This process is strongly exothermic by up to 67.88 kcal mol1. In the ERa(2), the C3eC5 and O1eO3 bonds in the five-member ring of the IMa2 would break, obtaining Pa2 and IMa3 via TSa2 with a barrier of 21.59 kcal mol1. Compared to IMa2, the C3eC5 and O1eO3 bond lengths in TSa2 are elongated by 19.0% and 39.3%, respectively. This step occurs after the energy absorption of 11.87 kcal mol1. There is a competitive reaction with ERa(2), i.e., ERa(5). In the ERa(5), the C3eC5 and O1eO2 bonds in the fivemember ring of IMa2 would break to form Pa5 and IMa6 via the energy absorption of 5.15 kcal mol1. The reaction barrier of this process is 25.47 kcal mol1. Compared to IMa2, the C3eC5 and
Table 2 The lifetimes (s) of reactant species in atmosphere according to the rate constants at 200e800 K. T(K)
ERa(1)a
ERa(2)
ERa(4)b
ERa(5)
ERa(7)
ERa(9)b
200 220 240 260 280 298.15 300 320 340 360 380 400 450 500 550 600 650 700 750 800
9.94Eþ03 8.37Eþ03 7.23Eþ03 6.36Eþ03 5.67Eþ03 5.16ED03 5.11Eþ03 4.65Eþ03 4.27Eþ03 3.94Eþ03 2.67Eþ07 3.43Eþ03 2.94Eþ03 2.57Eþ03 2.29Eþ03 2.06Eþ03 1.87Eþ03 1.72Eþ03 1.58Eþ03 1.47Eþ03
3.23Eþ14 5.00Eþ12 1.53Eþ11 7.87Eþ09 6.13Eþ08 8.06ED07 6.67Eþ07 9.43Eþ06 1.68Eþ06 3.58Eþ05 8.93Eþ04 2.56Eþ04 1.79Eþ03 2.08Eþ02 3.52Eþ01 7.94Eþ00 2.21Eþ00 7.35E01 2.81E01 1.20E01
2.62Eþ18 1.55Eþ16 2.14Eþ14 5.64Eþ12 2.47Eþ11 2.06ED10 1.62Eþ10 1.48Eþ09 1.77Eþ08 2.67Eþ07 4.86Eþ06 1.04Eþ06 3.88Eþ04 2.70Eþ03 2.95Eþ02 4.54Eþ01 9.08Eþ00 2.24Eþ00 6.55E01 2.19E01
4.57Eþ13 7.58Eþ10 3.66Eþ08 4.02Eþ06 8.40Eþ04 3.91ED03 2.92Eþ03 1.55Eþ02 1.17Eþ01 1.17Eþ00 1.49E01 2.34E02 4.69E04 1.44E10 2.85E11 1.92E11 1.37E11 1.03E11 8.00E12 6.41E12
4.78Eþ21 2.61Eþ21 1.41Eþ21 7.58Eþ20 4.05Eþ20 2.30ED20 2.17Eþ20 1.16Eþ20 6.25Eþ19 3.40Eþ19 1.86Eþ19 1.03Eþ19 2.48Eþ18 6.45Eþ17 1.84Eþ17 5.71Eþ16 1.95Eþ16 7.04Eþ15 3.23Eþ15 1.55Eþ15
5.98Eþ10 1.98Eþ09 1.13Eþ08 9.95þ06 1.22þ06 2.28D05 1.94þ05 3.85þ04 9.12þ03 2.51þ03 7.85þ02 2.73þ02 2.84þ01 4.47þ00 9.4901 2.5401 8.0902 2.9802 1.2202 5.5503
Bold values are examples that have been discussed at the temperature of 298.15 K. a O3 concentration is about 2.688 1011 molecule cm3. b H2O concentration is about 5.375 1017 molecule cm3.
O1eO2 bonds in the TSa5 are elongated by 22.7% and 38.5%, respectively. Since ERa(2) has a lower potential barrier than ERa(5), it occurs more easily. IMa3 is an oxygenated free radical with high activity which would further react easily in the atmosphere. For example, intramolecular hydrogen migration takes place in IMa3 in the ERa(3), i.e., the H1 atom of the C4eH1 bond transfers to O1 atom to form five-member ring via transition state TSa3, and generates IMa4. In the TSa3, the breaking of the C4eH1 bond and the formation of the O1eH1 bond occur simultaneously. The O2eO1, C4eH1, O1eH1 bond lengths are 1.375, 1.324 and 1.329 Å, respectively. The reaction barrier is 18.69 kcal mol 1 and the reaction heat is 14.00 kcal mol1. Similar to IMa3, IMa6 also undergoes intramolecular hydrogen migration, labeled as ERa(8). The H8 atom of the C6eH8 migrates to the O1 atom to form a five-member ring and generate IMa9 via transition state TSa8 with a barrier of 35.86 kcal mol1. The lengths of the O3eO1, C6eH8 and O1eH8 bond are 1.474, 1.347 and 1.468 Å in the TSa8, respectively. This process is strongly exothermic by up to 30.23 kcal mol1. 3.1.2. Reaction channel B The reaction channel B is similar to the reaction Channel A. IMb1 is produced from O3 addition to the C7]C8 double bond of ocimene. Then the subsequent elementary reactions are listed as follows. The DEb is the potential barrier and the DEr is the reaction heat in the elementary reaction.
Table 3 Arrhenius formulas (units are s1 and cm3 molecule1 s1 for unimolecular and bimolecular reactions, respectively) for elementary reactions involved in the reaction channel A over the temperature range of 200e800 K. ERa(1) ERa(2) ERa(3) ERa(4) ERa(5) ERa(6) ERa(7) ERa(8) ERa(9)
k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T)
¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼
4.18 9.05 4.29 1.20 1.80 5.98 1.26 7.48 4.44
1015 exp(511.26/T) 105 exp(9486.72/T) 1011 exp(7559.32/T) 1011 exp(11,710.67/T) 1021 exp(16,692.89/T) 101 exp(4176.44/T) 1014 exp(4147.90/T) 1011 exp(16,698.18/T) 1012 exp(8005.20/T)
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IMb1/TSb1/IMb2
DEb ¼ 1:66 kcal mol1
DEr ¼ 73:08 kcal mol1
ERb(1)
IMb2/TSb2/IMb3 þ C3 H6 O
DEb ¼ 27:89 kcal mol1
DEr ¼ 2:21 kcal mol1
ERb(2)
IMb3/TSb4/IMb4
DEb ¼ 18:62 kcal mol1
DEr ¼ 23:33 kcal mol1
ERb(4)
IMb2/TSb6/Pb1 þ C3 H6 O2
DEb ¼ 23:89 kcal mol1
DEr ¼ 6:95 kcal mol1
ERb(6)
3.1.3. Reaction channel C The third addition fashion is O3 addition to the C1]C2 double bond in Ocimene, which is labeled as Channel C. After IMc1 is formed, it isomerizes to IMc2 which contains a five-member ring via TSc1. Similar to the above two reaction pathways, there are also two competitive reactions with IMc2, ERc(2) and ERc(5). The reaction pathways are described as follows.
IMa5, the O4eH2 and O2eO1 bonds break up while the C4eO4 and O1eH2 bonds are formed simultaneously. The length of C4eO4, O2eO1, O1eH2 and O4eH2 bond in the TSa4 is 2.040, 1.808, 1.485 and 1.020 Å. This process is strongly exothermic by up to 67.06 kcal mol1. The reaction of IMa6 is similar to that of IMa4, and another Van der Waals complex IMa7 is formed. The main difference is that a five-member ring is formed in IMa7 which includes
IMc1/TSc1/IMc2
DEb ¼ 2:22 kcal mol1
DEr ¼ 64:61 kcal mol1
ERc(1)
IMc2/TSc2/IMc3 þ CH2 O
DEb ¼ 22:08 kcal mol1
DEr ¼ 1:37 kcal mol1
ERc(2)
IMc2/TSc5/Pc2 þ CH2 O2
DEb ¼ 24:75 kcal mol1
DEr ¼ 2:69 kcal mol1
ERc(5)
The above three channels share some common properties. For example, the O3 addition to form five-member ring, the H migration. As for the adducts of ocimene with O3, the Criegee biradicals would be generated when the five-member ring ruptured, for example, IMa3 and Pa2, IMa6 and Pa5, Pb1 and C3H6O2, IMb3 and C3H6O, IMc3 and CH2O, Pc2 and CH2O2. The polarities for most of them are higher than that of ocimene, which results in the decrease in volatility. These intermediates can be oxidized continuously into the semi-volatility compounds, which are highly potential to form the SOA through the hydration or absorption on the aerosol surface the same as the D-limonene with O3.
the O5, H6 atoms in H2O molecule and C5, O3 and O1 atoms in IMa6. With a potential barrier of 7.69 kcal mol1, the O5eH6 bond of the H2O breaks and the O5eC5 and H6eO1 bonds of IMa7 is produced via TSa6, and IMa8 is obtained in ERa(6). In TSa6, the length of C5eO5, O5eH6 and O1eH6 bond is 1.980 Å, 1.048 Å and 1.475 Å. The reaction heat is 37.87 kcal mol1. Finally, IMa8 is isomerized to Pa3 and H2O via a four-member ring transition state TSa7. As for other reaction involved with H2O molecule, for example, the ERa(9) in channel A, ERb(5) in channel B, and ERc(4) in the channel C, the mechanisms are the same as ERa(4). The H2O molecule can be regenerated and act as an activator which plays an important role in the formation of SOA in atmosphere.
3.2. Secondary reactions In the reaction channel A, B and C, those Criegee biradicals are important intermediates produced in the oxidation process of ocimene with O3. As their removal from the troposphere, these radical intermediates could further react with H2O or NO, because NO or H2O are abundant in atmosphere. Bonn focused on the investigation of the influence of water vapor on the size distribution of the newly formed aerosol particles during the reaction of monoterpenes and ozone measured by a scanning mobility particle sizer (Bonn et al., 2002). The secondary reactions about these intermediates are discussed in the following. 3.2.1. The reaction in the presence of H2O In the channel A, the profile of the potential energy surface shows that the reaction of IMa4 with H2O is a barrierless association to produce a Van der Waals complex IMa5. Then IMa5 will form Pa1 and H2O via TSa4 with a barrier of 32.08 kcal mol1. The detailed process is as follows: the O4 and H2 atoms in the H2O and the O1, O2, C3, C4 atoms in IMa4 constitute a six-member ring in
3.2.2. The reaction in the presence of NO and O3 It is widely accepted that the O abstraction by NO radical takes place easily once the peroxy-hydrocarbon exists in atmosphere. Take ERb(3) in the reaction channel B for example, the O1 atom of IMb3 can be extracted by NO to obtain products Pb1 and NO2 via the transition state TSb3. In the TSb3, the length of O3eO1 and NeO1 bond is 1.434 and 1.363 Å. The potential barrier, reaction enthalpy and Gibbs free energy are 1.94 kcal mol1, 69.59 kcal mol1 and 69.82 kcal mol1, respectively. The reaction barrier of NO extraction O is very low and the Gibbs free energy is a large negative value which indicates that this reaction is controlled both thermodynamically and kinetically. Since the intermediates or products still have C]C double bonds, they can react with O3 sequentially. For example, Pc2 can react with O3 to form a Van der Waals complex IMc6, and then to form IMc7 via TSc6 with a small barrier of 1.85 kcal mol1. The process is O3 addition to the C7]C8 double bond of the Pc2. The C7eO3 bond and the C8eO2 bond length is 2.323 and 2.309 Å in the TSc6, and a carboneoxygen five-member ring is formed in IMc7. The reaction heat
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of this step is 70.81 kcal mol1. Subsequently, the C7eC8 and O1eO3 bonds in the five-member ring of IMc7 break simultaneously via TSc7 to produce new Criegee biradicals Pc3 and C3H6O2. The C7eC8 and O1eO3 bond length in the TSc7 elongates by 21.0% and 39.2% compared with the IMc7. The potential barrier is 23.10 kcal mol1 and the reaction heat is 7.04 kcal mol1 in ERc(7).
3.3. Rate constants Since the mechanisms of these three reaction channels are very similar, the elementary reactions in Channel A are chosen as examples to discuss. The RiceeRamspergereKasseleMarcus (RRKM) theory modified by Hou (Hou and Wang, 2007) and the canonical variational transition state theory (CVT) with small-curvature tunneling (SCT) effect (Qu et al., 2009; Zhang et al., 2008, 2009) are used to calculate the rate constants. The results are listed in Table 2. For the dimolecular reaction or the unimolecular dissociation reaction, the RRKM theory is used to calculate the rate constants of elementary reactions as follows:
C10 H16 þ O3 /IMa1/TSa1/IMa2
ERa(1)
IMa2/TSa2/IMa3 þ Pa2
ERa(2)
IMa4 þ H2 O/IMa5/TSa4/Pa1 þ H2 O
ERa(4)
IMa2/TSa5/IMa6 þ Pa5
ERa(5)
IMa6 þ H2 O/IMa7/TSa6/IMa8
ERa(6)
IMa8/TSa7/Pa3 þ H2 O
ERa(7)
IMa9 þ H2 O/IMa10/TSa9/Pa4 þ H2 O
ERa(9)
The elementary reaction IMa8 / TSa7 / Pa3 þ H2O ERa(7) is taken as an example to consider the pressure effect. From 0.5 atm to 1 atm, the rate constants changed from 8.71E21 to 4.35E21. The rate constants of other elementary reactions do not vary with pressure. So it can be found that the pressure has little effect on the rate constants in the present case which is inconsistent with Drozd’s result, since the excess energy is disregarded and all species is assumed to be thermalized (Drozd and Donahue, 2011). Then the 1 atm pressure is chosen to discuss the rate constants under the temperature from 200 K to 800 K. As for the unimolecular isomerization reaction, such as ERa(3) and ERa(8), the CVT/SCT method is used to calculate the rate constants. The pressure effect can be ignored since the molecular number of the reactants and products is the same.
IMa3/Tsa3/IMa4
ERa(3)
IMa6/Tsa8/IMa9
ERa(8)
From the rate constants of elementary reactions, the ERa(3) and ERa(6) have large rate constants, and ERa(3) is the largest one. The ERa(1), ERa(2) and ERa(5) have the medium values. The ERa(4), ERa(7), ERa(8) and ERa(9) have smaller values, and the ERa(4), is the smallest one. It is obvious that the calculated rate constants exhibit typical nonArrhenius behavior, i.e., k(T) ¼ a 10bTc exp(d/T). The arrhenius formulas for elementary reactions involved in the reaction channel A over the temperature range are listed in Table 3. The formula of the rate constants with temperature are helpful for the atmospheric aerosol model study.
According to the rate constants of elementary reaction, the atmospheric lifetime of the reactants can be calculated. For the first order reaction, such as monomolecular pyrolysis or photolysis reaction, the lifetime s is the reciprocal of the rate constant k, i.e., s ¼ 1=k. In Drozd’s discussions, the reactions of Criegee Intermediates with much excess energy are influenced by pressure (Drozd and Donahue, 2011). So the lifetime of Criegee Intermediates as IMa3 and IMa6 is not reported in order to avoid misleading. Then the lifetime of the reactants in ERa(1), ERa(2), ERa(4), ERa(5), ERa(7) and ERa(9) can be obtained at the range of 200e800 K and listed in Table 2. Those lifetime at the room temperature is taken as example to discuss. The lifetimes of C10H16 was 86 min. It belongs to short lifetime species. In comparison, IMa2 (2.56 d) and IMa9 (2.60 d) are belonging to middle lifetime species. Because of high barriers, IMa4 and IMa8 belong to long lifetime species. 4. Conclusion In this paper, a theoretical study on ocimene ozonolysis reaction is performed at the MPWB1K/6-311þG(3df,2p)//MPWB1K/6-31G(d,p) level. A detailed description of the possible oxidation mechanism in the presence of H2O or NO is provided. The rate constants are calculated using the RRKM theory and the CVT/SCT method. Some valuable results are found. (1) The information of the stationary points including the reactants, intermediates, transition states and products are calculated, which are useful to further understand the chemical formation process of SOA. There exist three reaction channels, all of which can take place. The potential barriers of three intramolecular reaction sites in ocimene with the O3 have little in common. The C]C(CH3)2 site accounts for a large proportion of the reaction, which is consistent with the experimental results. (2) In the subsequent reaction, H2O molecule acts as an activator of OH transfer in ERa(4), ERa(6) and ERa(9) which promotes the chemistry process. The O abstraction reactions from peroxy hydrocarbons with NO molecule are favorable in both thermodynamics and dynamics. (3) The oxidation process occurs spontaneously once it is initiated by O3. Most of the obtained products have high polarity and water-solubility, which contributes to the formation of SOA through the hydration or absorption reaction on aerosol surface. (4) According to values of the lifetime, the C10H16 belongs to the short lifetime species, and IMa2 and IMa9 belong to middle lifetime species while the IMa4 and IMa8 belong to long lifetime ones. Acknowledgments This work is supported by National Natural Science Foundation of China (No. 20903062, No. 20873074 and No. 20737001), Natural Science Foundation of Shandong Province (No. Q2008B07), Independent Innovation Foundation of Shandong University (No. 2010TS064) and Open Project from State Key Laboratory of Environmental Chemistry and Ecotoxicology, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences (No. KF2009-10). The authors thank Professor Donald G. Truhlar for providing the POLYRATE 9.7 program and Professor Baoshan Wang for providing the RRKM program. Appendix. Supplementary information Supplementary information associated with this article can be found, in the online version, at doi:10.1016/j.atmosenv.2011.08.010.
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