1
Kinetic measurements for the reactions of ozone with crotonaldehyde and its methyl derivatives and calculations of transition-state theory

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj1

2
The rate coefficients for the reactions of O3 with six unsaturated carbonyls have been measured with the relative-rate method in the presence of a sufficient radical scavenger.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj2

3
The experiments were conducted using a 6-m3 reaction chamber combined with a long-path FTIR system.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp1

4
The rate coefficients (measured in 10−18 cm3 molecule−1 s−1) were 1.58 ± 0.23 for crotonaldehyde, 1.59 ± 0.22 for trans-2-pentenal, 1.82 ± 0.26 for 3-methyl-2-butenal, 5.34 ± 0.73 for trans-2-methyl-2-butenal, 29.5 ± 4.1 for 3-pentene-2-one and 8.3 ± 1.1 for mesityl oxide.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res1

5
Conventional transition-state theory (CTST) calculations based on ab initio molecular orbital and density functional methods were performed to evaluate the rate constants for nine unsaturated carbonyls including six compounds examined in the present experiment as well as acrolein, methacrolein, and methyl vinyl ketone.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj3

6
A log–log plot of the rate coefficients measured in the present and previous works vs. the calculated results of the rate constants, showed a linear relationship.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res2

Introduction

7
Unsaturated carbonyls are produced through the atmospheric oxidation of conjugated dienes emitted into the lower troposphere from vegetations1 and human activities such as road vehicles.2

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

8
The unsaturated carbonyls are then oxidized with OH radicals and/or O3.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

9
Thus, kinetic data for this class of molecules are often necessary in the atmospheric model calculations.

Type: Motivation | Advantage: None | Novelty: None | ConceptID: Mot1

10
For example, some unsaturated carbonyls with complex structures have recently been paid attention because these are possible intermediates of the formations of the secondary organic aerosols.3

Type: Motivation | Advantage: None | Novelty: None | ConceptID: Mot2

11
However, for complex molecules, there are only preliminarily kinetic data4–6 because of the high reactivity and difficulties in the preparation of these molecules.

Type: Motivation | Advantage: None | Novelty: None | ConceptID: Mot3

12
To predict unknown but necessary kinetic data, structure–activity relationships have often been applied to the electrophillic reactions.7,8

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

13
In this method, the logarithms of the rate coefficients are plotted as a function of the ionization potentials (IP) or the highest-occupied molecular orbital (HOMO) energies.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

14
This plot shows an almost linear correlation for the reactions of OH radical with unsaturated hydrocarbons.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

15
On the other hand, a correlation of the plot for the reactions of O3 with unsaturated hydrocarbons is much poorer than that for the reactions of OH radical.

Type: Motivation | Advantage: None | Novelty: None | ConceptID: Mot4

16
As an example of the poor correlation, Grosjean and Grosjean pointed out that the rate coefficient for 1,2-distributed alkene, e.g., trans-2-butene, is ca. 20 times larger than that for 1,1-distributed alkene, e.g., isobutene, despite these ionization potentials being close to each other.9

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

17
The poor correlation is tentatively attributed to the difference in the steric factor between 1,1- and 1,2-distributed alkenes.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

18
If this is the case, the method such as conventional transition-state theory (CTST), in which the pre-exponential factor is taken into account, must be applicable to predictions of unknown rate constants for the reactions with O3.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac7

19
In this study, the rate coefficients have been measured for the reactions of O3 with crotonaldehyde (2-butenal) and five its methyl derivatives including both 1,1- and 1,2-methyl substituted unsaturated carbonyls.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj4

20
The rate coefficients measured are compared with results of CTST calculations based on ab initio molecular orbital (MO) and density functional theory (DFT) calculations.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj5

21
The purpose of this work is to determine these rate coefficients experimentally and to check whether CTST is applicable to the evaluations of these rate constants.

Type: Goal | Advantage: None | Novelty: None | ConceptID: Goa1

Experimental

22
Experiments were conducted with a bakeable and evacuable 6-m3 photochemical chamber whose inner surface was coated with perfluoroethylene–perfluoroalkyl vinyl ether copolymer.10,11

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp2

23
The rate coefficients were determined with a relative-rate method in the presence of sufficient diethyl ether (Et2O) as a scavenger of OH radicals produced through the O3 + alkene reactions.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp3

24
Propylene and isobutene were used as reference alkenes.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp4

25
Prior to each experiment, the chamber was filled with purified air under 101 kPa.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp5

26
The desired pressures of the sample alkene, the reference alkene and Et2O were collected into calibrated bulbs.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp6

27
These gases were flushed into the chamber with N2 carrier gas.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp7

28
A diluent of O3/O2 was prepared as needed with an ozone generator (Nippon ozone, 2058) and then injected into the chamber.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp8

29
Rapid mixing was ensured using two stirring fans.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp9

30
The initial mixing ratios of the sample alkene, the reference alkene, Et2O and O3 were 0.5, 0.5, 19–84 and 1.1–2.4 ppmv, respectively.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp10

31
Under these conditions, the concentrations for the sample and reference alkenes are presented in eqn. (1), assuming that both alkenes are only consumed through the reactions with O3where [X]0 and [X]t are the concentrations of X at times 0 and t, respectively; k1 and k2 are the rate constants for the reactions of O3 with the sample alkene and reference alkene, respectively.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

32
The experimental data were analyzed according to eqn. (1).

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp11

33
The concentrations of the sample and reference alkenes were obtained from infrared absorption spectra measured by an FTIR spectrometer (Nicolet, Nexus 670) with a multi-reflection mirror system whose optical path length was 221.5 m.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp12

34
The chemicals used and their stated purities were crotonaldehyde (CA: Wako, 99%, mainly trans), 3-methyl-2-butenal (MBA32: Aldrich, 97%), trans-2-methyl-2-butenal (MBA22: Aldrich, 96%), mesityl oxide (MSO: Aldrich, 90%), 3-pentene-2-one (PO32: Aldrich, 65%, mainly trans), trans-2-pentenal (PA2: Aldrich, 95%), Et2O (Kanto, 99.5%), propylene (Takachiho, 99%) and isobutene (Takachiho, 95%).

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp13

35
The impurity of PO32 was identified to be MSO with the FTIR analysis.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res3

36
The concentration of MSO was shown to be ca.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res4

37
15% of that of the used reagent.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res4

38
All experiments were carried out at 298 ± 2 K.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp14

Method of calculations

39
The rate constants were calculated with CTST for the reactions of O3 with nine unsaturated carbonyls, i.e., six molecules examined in the present experiment as well as acrolein (AC), methacrolein (MAC) and methyl vinyl ketone (MVK).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

40
These reactions are believed to proceed on the singlet ground-state potential-energy surface via the addition of O3 to the CC double bond.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac8

41
In these reactions, O3 approaches the double bond from the directions vertical to the alkene plane, leading to the transition-state (TS) involving a five-membered ring.12

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac9

42
There are two possible TS conformers referred as syn- and anti-TS;13where Ri and X indicate the alkyl and carbonyl groups, respectively.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac10

43
Since the energies and all the bond lengths are close to each other between these TS conformers, it was assumed that the rate constants are the same between two reaction pathways via these TS conformers.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

44
The rate constants were calculated with CTST for reaction pathways viasyn-TS molecules and were then doubled to determine the overall rate constants (k1CTST);14,15where E0, L and QX represent the barrier-height energy, the statistical factor and the partition function of the internal motions for molecule X, respectively.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod4

45
The statistical factor was set to 4 because there are two configurations of ozone, i.e., O1–O2–O3 and O3–O2–O1, for each of two attack sites located in both sides of the alkene plane.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod5

46
The partition functions for the intra-molecular rotations of methyl groups in unsaturated carbonyls were calculated with a method proposed by Troe.16

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod6

47
All rate constants were calculated for temperature of 298 K.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod7

48
The vibrational frequencies, the rotational constants and the barrier-height energies necessary in the calculations of eqn. (2) were determined by ab initio MO and DFT calculations.17,18

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod8

49
Prior to the calculations, a conformer with the lowest energy was found with an RHF/6-31G(d) method for each reactant.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod9

50
For the conformers found, the geometries for the reactant and the TS were optimized by the RHF/6-31G(d) method and the hybrid density functional consisting of Becke's three parameter nonlocal hybrid exchange potential with the nonlocal correlation functional of Lee, Yang, and Parr (B3LYP) method19 with the 6-31G(d,p) basis set.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod10

51
Harmonic vibrational frequencies were calculated at the optimized geometries by the respective methods.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod11

52
The results of vibrational frequencies were scaled with factors of 0.89 and 0.96 for the results of the RHF and B3LYP methods, respectively.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod12

53
The single-point energies were calculated by the fourth order Møller–Plesset perturbation theory (MP4) with the 6-31G(d,p) basis set and the coupled-cluster singles and doubles including a perturbational estimate of triple excitations (CCSD(T)) method20 with the 6-311G(d,p) basis set for the geometries optimized by the RHF/6-31G(d) and B3LYP/6-31G(d,p) methods, respectively.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod13

54
In order to examine validities of the basis sets used in the above calculations, geometry optimizations were also carried out at by the B3LYP/6-311G(d,p) method for the reactants and TS for the O3 + ACR reaction, and the single-point energies were also calculated at the CCSD(T) level with 6-311G(d,p), 6-311++G(d,p), 6-311G(2d,2p) and 6-311++G(2d,2p) basis sets.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod14

55
The HOMO energies of unsaturated carbonyls were calculated by the B3LYP/6-31+G(d,p) method for the geometries optimized at the RHF/6-31G(d) level of theory.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod15

Results and discussion

Experimental results of rate coefficient k1

56
The concentrations of the sample and the reference alkenes were determined from the infrared spectra measured as follows: A contribution of Et2O to the infrared spectrum measured was subtracted prior to each analysis.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp15

57
The concentration of the reference alkene was then determined with an absorption line peaked at 912 cm−1 for propylene or 890 cm−1 for isobutene.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp16

58
The concentration of the sample alkene was determined with an absorption line attributed to the CC stretching mode at around 1640 cm−1.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp17

59
For PO32, the CC absorption line contained a contribution of the MSO impurity of ≤25% in the absorbance.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs1

60
This component was subtracted with an absorption line at 968 cm−1 before the evaluation of the concentration of PO32.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp18

61
All the concentrations could be determined without interference from any product absorption.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs2

62
The concentrations of the sample and reference alkenes are plotted in Fig. 1 in accordance with eqn. (1) for the measurements with propylene as the reference alkene.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs3

63
Since the plots for all measurements examined were almost linear, the relative rate coefficients (k1/k2) were obtained from the slopes with the linear least-squares analysis.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp19

64
The results of k1/k2 are listed in Table 1 along with initial experimental conditions.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs4

65
The initial conditions were varied to check validities of k1/k2 obtained as follows: First, k1/k2 of each compound were measured at both [Et2O]0 ≈ 80 and ≈ 20 ppmv to confirm that OH radicals were entirely scavenged.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp20

66
For example, for CA, k1/k2 obtained at 18.9 ppmv (0.152 ± 0.016) shows good agreement with that obtained at 82.6 ppmv (0.152 ± 0.008).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res5

67
Similar results were obtained for all the other compounds examined as listed in Table 1.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs5

68
These results indicate that OH radicals are entirely scavenged even at [Et2O]0 ≈ 18 ppmv.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res6

69
Next, if the decay rate of the sample alkene due to the reaction with O3 (k1[O3]t) was comparably as low as that due to the wall loss, k1/k2 obtained would be overestimated.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp1

70
To check that there is no such overestimation, a dependence of k1/k2 upon [O3]0 was measured for MBA32.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj6

71
As shown in Table 1, k1/k2 is almost independent of [O3]0 between 1.21 and 2.38 ppmv.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs6

72
This overestimation is negligible even at [O3]0 = 1.21 ppmv.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res7

73
Finally, for MSO, both propylene and isobutene were employed as the reference alkene. k1/k2 obtained for isobutene was 0.767 ± 0.011.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp21

74
Multiplying this value to a literature value of k2 of isobutene,21 the rate coefficient k1 is determined to be (8.82 ± 0.35) × 10−18 cm3 molecule−1 s−1.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp22

75
The result of k1 agrees with that obtained from propylene data, (8.3 ± 1.1) × 10−18 cm3 molecule−1 s−1, which is described later.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs7

76
This suggests that a systematic error due to the use of propylene is negligible.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res8

77
Since the possible systematic errors could be ruled out for all the results of k1/k2, the results of k1/k2 for each compound were averaged.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp23

78
The results of averaged values are listed in Table 1.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs8

79
The rate coefficients k1 were calculated with the averaged values of k1/k2 and a literature value of k2 for propylene,22 (1.04 ± 0.14) × 10−17 cm3 molecule−1 s−1.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp24

80
The rate coefficients k1 determined are listed in Table 2 along with previous data.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs9

81
To our knowledge, the previous kinetic data are available for CA and PO32.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac11

82
For CA, two literature values have been reported.23,24

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac12

83
Both data were measured by monitoring the O3 decay curves with UV absorption methods in the presence of excess CA.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac13

84
A literature value,21 (1.74 ± 0.20) × 10−18 cm3 molecule−1 s−1, is consistent with the present result, (1.58 ± 0.23) × 10−18 cm3 molecule−1 s−1, within the experimental uncertainties.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res9

85
However, another literature value,24 (0.90 ± 0.18) × 10−18 cm3 molecule−1 s−1, is a factor of 0.57 lower than the present result.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res10

86
For PO32, two literature values are available.24,25

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac14

87
A literature value,25 (35.0 ± 8.9) × 10−18 cm3 molecule−1 s−1, was measured with a relative-rate method.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac15

88
This data agrees with the present result, (29.5 ± 4.1) × 10−18 cm3 molecule−1 s−1.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res11

89
Another literature value, (21.3 ± 3.9) × 10−18 cm3 molecule−1 s−1, which is taken from ref. 24 is again slightly lower than the present data.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res12

90
The rate coefficients measured in the present and previous works for unsaturated carbonyls were compared with those for unsaturated hydrocarbons to study the substituent effects on the rate coefficients.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj7

91
Fig. 2 shows the available data of the rate coefficients plotted as a function of a series of five molecular structures, i.e., CH2CHX, CH3CHCHX, (CH3)2CCHX, C2H5CHCHX and CH3CHC(CH3)X, and compares the kinetic data for molecules with XH (kHC), CHO (kALD) and COCH3 (kKET).

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp25

92
The previous kinetic data plotted in the figure for ACR, MAC and MVK are listed in Table 2,12,23,24,26,27 and these for hydrocarbons, in units of 10−18 cm3 molecule−1 s−1, are 1.43 ± 0.19 for ethylene,22 10.4 ± 1.4 for propylene,22 11.5 ± 4.6 for isobutene,21 9.80 ± 0.29 for 1-butene21 and 129 ± 9 for cis-2-butene.21

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs10

93
Fig. 2 shows that the ratio of kALD to kHC was kept almost constant among all five structures.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs11

94
An averaged value of kALD/kHC with an error of one standard deviation was 0.14 ± 0.06.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs12

95
This means that the rate coefficient for unsaturated hydrocarbon is suppressed with a substitution of the H atom in the unsaturated hydrocarbon with an electron-withdrawing CHO group.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res13

96
An averaged value of kKET/kALD was also calculated to be 14 ± 9.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs13

97
In contrast to the result of kALD/kHC, the rate coefficient for unsaturated aldehyde is enhanced with a substitution of the H atom in the CHO group with an electron-releasing methyl group.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res14

98
The results of the substituent effects suggest that the reactions of O3 with alkenes are electrophillic reactions.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res15

Conventional structure–activity relationships

99
Assuming that the reactions of O3 with alkenes are electrophillic, a relationship of the present and previous experimental results of the rate coefficients with –EHOMO was studied.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj8

100
Prior to this analysis, validities of the present results of –EHOMO were checked with previous experimental data of IP.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj9

101
The results of –EHOMO calculated for nine compounds, i.e. six molecules examined in the present experiment as well as ACR, MAC and MVK are listed in Table 2 together with the available data of IP.28

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs14

102
Fig. 3 shows the data of IP plotted as a function of the results of –EHOMO.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs15

103
With the linear least-square analysis, the data plotted can be approximated with a straight line, IP = (1.43 ± 0.08) × (–EHOMO) − 0.50 ± 0.59.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod16

104
The errors quoted for the slope and the intercept are two standard deviations.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod17

105
The correlation coefficient (R2) was 0.994 and was nearly the same as unity.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs16

106
This suggests that the results of –EHOMO can be used instead of the experimental data of IP.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res16

107
Fig. 3b shows the experimental rate coefficients for the reactions of O3 with nine unsaturated carbonyls plotted as a function of −EHOMO.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp26

108
The data plotted in the figure are taken from Table 2.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs17

109
All the data plotted in Fig. 3b were fitted with the linear least-squares analysis.

Type: Experiment | Advantage: None | Novelty: None | ConceptID: Exp27

110
The line fitted was represented as log10k1 = −(2.83 ± 0.80) × (−EHOMO) + 2.50 ± 5.72.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod18

111
The errors for the slope and the intercept are two standard deviations.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod19

112
The correlation coefficient was 0.723 and was smaller than unity.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs18

113
This indicates that the correlation of log10k1 with −EHOMO was so poor that the plot cannot be used for the predictions.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res17

114
The data for seven compounds, i.e., PO32, MBA22, MVK, MAC, PA2, CA and ACR, can be approximated with a single straight line as shown in Fig. 3b with a dotted line.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs19

115
The rate coefficients for 1,1-dimethyl alkenes, i.e., MBA32 and MSO, are lower than those predicted with the dotted line.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs20

116
This result would be consistently attributed to the steric hinderance of 1,1-distributed substituents, as described by the previous workers.9

Type: Result | Advantage: None | Novelty: None | ConceptID: Res18

117
However, the data for 1-methyl-1-carbonyl alkenes, i.e., MBA22 and MAC, are fitted with a single line together with the data for 1,2-distributed alkenes, PO32, PA2 and CA.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs21

118
This suggests that the present results of the scattered plot cannot simply be interpreted with the steric hinderance of the 1,1-distributed substituents.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res19

Results of ab initio and DFT calculations

119
In order to study the reaction dynamics of O3 with unsaturated carbonyls and check whether accurate rate constants can be predicted, the calculations of the rate constants were performed with CTST based on the ab initio MO and DFT calculations.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj10

120
In the previous theoretical studies on the reactions of O3 with alkenes, the barrier heights have been successfully predicted by employing the MP4/6-31G(d,p)//MP2/6-31G(d,p) method29 and the CCSD(T)/6-31G(d)//B3LYP/6-31G(d,p) method.30

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac16

121
In this work, we have employed the MP4(SDQ)//RHF/6-31G(d) and CCSD(T)/6-311G(d,p)//B3LYP/6-31G(d,p) methods for the reactions of O3 with nine unsaturated carbonyls.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod20

122
The results of the energies and the zero-point energies (ZPE) calculated at the RHF/6-31G(d) level are listed in Table 3.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs22

123
Table 4 shows the barrier-height energies (E0) for the respective reactions, calculated from the single-point energies and the ZPEs, as well as the available experimental data for MAC and MVK.27

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs23

124
For MAC, the barrier-height energies were evaluated as 23.9, 21.5, and 10.8 kJ mol−1 for the MP4(SDQ), CCSD, and CCSD(T) methods, respectively.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs24

125
These values are close to the experimental activation energy of 17.5 kJ mol−1 and distribute within a range of ±8.4 kJ mol−1 (= ±2 kcal mol−1).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs25

126
It is noted that an estimation of the barrier height with an error smaller than ±4.2–8.4 kJ mol−1 may be difficult even at a higher level of theory.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res20

127
The higher the level of theory, the lower the result of the barrier height.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res21

128
The difference in E0 between the CCSD and CCSD(T) methods are larger than that between the MP4(SDQ) and CCSD methods.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs26

129
The similar tendency can be seen for the other reactions, as listed in Table 4.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs27

130
This suggests that contributions of highly electronic excited configurations are important in the present reaction systems.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res22

131
To check the dependence of the results of E0 upon the basis sets, CCSD(T) calculations were carried out for the O3 + ACR reaction, with 6-311G(d,p), 6-311++G(d,p), 6-311G(2d,2p), and 6-311++G(2d,2p) basis sets for geometries optimized by the B3LYP/6-311G(d,p) method.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj11

132
The results are listed in Table 4.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs28

133
The barrier-height energies determined by CCSD(T)/6-311G(d,p)//B3LYP/6-31G(d,p) and CCSD(T)/6-311G(d,p)//B3LYP/6-311G(d,p) are 20.1 and 22.9 kJ mol−1, respectively, and their difference is just 2.8 kJ mol−1.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod21

134
For the same B3LYP/6-311G(d,p) geometries, the CCSD(T) barrier-height energies were evaluated as 22.9, 22.5, 15.8 and 20.4 kJ mol−1 with the 6-311311G(d,p), 6-311++G(d,p), 6-311G(2d,2p), and 6-311++G(2d,2p) basis sets, respectively.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod22

135
As shown in these results, no systematic trend is seen as to the basis sets.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res23

136
The width of the distribution of the results of E0 is ca. ±4.2 kJ mol−1.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs29

137
This value is used as an uncertainty of the results of E0 in the present CTST calculations described in the next section.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod23

Rate constants calculated with CTST method

138
The CTST calculations were performed using the results of E0 obtained at the MP4(SDQ), CCSD and CCSD(T) levels.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj12

139
The pre-exponential factors, ACTST and k1CTST, were calculated following eqn. (2) for nine unsaturated carbonyls.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod24

140
These results are listed in Table 4 together with results of the ab initio calculations of E0.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs30

141
Fig. 4a shows the experimental results of the rate coefficients plotted as a function of k1CTST calculated with the results of E0 for the MP4(SDQ) method.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs31

142
In Fig. 4a, the errors of the experimental data represent the experimental uncertainties, whereas the errors of k1CTST represent those evaluated taking into account the uncertainties of the results of E0, as described previously.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod25

143
With the linear least-squares analysis, the data plotted in Fig. 4a were fitted with a straight line:log10k1 = a log10k1CTST + b,where a and b are fitting parameters.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod26

144
Fit results of the parameters with errors of two standard deviations were a = 0.585 ± 0.107 and b = –7.04 ± 1.93.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod27

145
The correlation coefficient was 0.863.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs32

146
Figs. 4b and 4c show similar plots with E0 obtained with the CCSD and CCSD(T) methods, respectively.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs33

147
These plots were also fitted with eqn. (3).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod28

148
The parameters fitted were a = 0.352 ± 0.107 and b = −11.6 ± 1.8 for the CCSD method, and these were a = 0.395 ± 0.097 and b = −11.6 ± 1.5 for the CCSD(T) method.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod29

149
The correlation coefficients were 0.692 and 0.778 for the CCSD and CCSD(T) methods, respectively.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs34

150
The slopes of the fitted lines for Figs. 4a–c are smaller than unity.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs35

151
This is because the results of E0 still contain errors even for the CCSD(T)/6-311G(d,p)//B3LYP/6-31G(d,p) method.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res24

152
However, all the plots for the MP4(SDQ), CCSD and CCSD(T) methods show linear relationships within the errors of k1CTST.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res25

153
Especially the correlation coefficients for the MP4(SDQ) and CCSD(T) methods are larger than that for the plot of log10k1vs. of −EHOMO (0.723).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res26

154
CTST calculations combined with an ab initio MO and DFT methods can predict the relative values of the rate constants with a higher accuracy than those predicted with the conventional structure–activity relationships.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con1

155
Finally, the difference in the rate coefficient between 1,2-methyl substituted alkene (MBA22) and 1,1-methyl substituted alkene (MBA32) is discussed using the present results of ACTST and E0.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj13

156
The rate coefficients for the reaction of MBA22, (5.34 ± 0.73) × 10−18 cm3 molecule−1 s−1, is 2.9 times larger than that for the reaction of MBA32, (1.82 ± 0.26) × 10−18 cm3 molecule−1 s−1, as listed in Table 2.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs36

157
If this is caused by the steric hindrance of 1,1-methyl substituents, the potential energy curves for the TS for the reaction of MBA32 should be tighter than those for the reaction of MBA22, and thus the result of ACTST for MBA32 should be smaller than that for MBA22.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp2

158
However, the results of ACTST obtained at the B3LYP level for MBA32 (9.63 × 10−15 cm3 molecule−1 s−1) is very close to that for MBA22 (1.02 × 10−14 cm3 molecule−1 s−1) as listed in Table 4.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs37

159
In addition, ACTST for MBA32 is also close to those for the other two isomers, PO32 (1.04 × 10−14 cm3 molecule−1 s−1) and PA2 (2.77 × 10−14 cm3 molecule−1 s−1).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs38

160
These results indicate that the pre-exponential factor is almost independent of the molecular structure.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res27

161
On the other hand, the result of E0 obtained at the CCSD(T) level for MBA32 (11.7 kJ mol−1) is higher than that for MBA22 (2.6 kJ mol−1), i.e., E0 depends on the molecular structure.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res28

162
This suggests that the rate constant is determined by E0 rather than the pre-exponential factor.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res29

163
Fig. 5 shows the geometries optimized with the B3LYP/6-31G(d,p) method for MBA32 and MBA32-TS molecules.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod30

164
The reactant alkene has a structure with Cs symmetry.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs39

165
In contrast, the methyl and carbonyl substituents in the TS move out of the original Cs plane into the opposite side of the O3 group.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs40

166
The methyl groups move further from the original geometry via the intramolecular rotations.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs41

167
These results suggest that motion of the TS along the intrinsic reaction coordinate consists of the relative translation between the O3 and alkene groups as well as the symmetric out-of-plane vibration of the alkene group and the intramolecular rotations of the methyl groups.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res30

168
Since the geometry change of the alkene group is necessary for the formation of the TS, there is a substantial barrier for the reactions of O3 with alkenes.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res31

169
The normal mode frequency assigned to the methyl rotation for MBA32 (127 cm−1) is larger than that for MBA22 (90 cm−1).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs42

170
Since the tightness of the potential energy curves for the internal motions of alkene depends on the combination of the substituted sites, the barrier-height energy depends on the molecular structure.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res32

Conclusion

171
In summary, the rate coefficients of the reactions of O3 with six unsaturated carbonyls were measured with a relative-rate method in the presence of sufficient diethyl ether.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj14

172
Using the present and previous experimental results of the rate coefficients, the correlation of the rate coefficients with the HOMO energies was investigated, and it was found that the linearity of the plot is poor.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res33

173
To evaluate the rate constants taking into account the reaction dynamics, conventional transition-state theory calculations based on ab initio molecular orbital and DFT methods were performed.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj15

174
A log–log plot of the experimental rate coefficients vs. the results of the calculated rate constants show linear relationships for the results with the MP4(SDQ), CCSD and CCSD(T) barrier-height energies.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res34

175
Among four isomers of MBA32, the result of the pre-exponential factor is almost independent of the reactant, while the result of the barrier-height energy depends on the reactant.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2

176
These results suggest that the rate constant is determined by the barrier-height energy rather than the pre-exponential factor.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con3

177
In future works, both theoretical and experimental studies of the rate coefficients are necessary for the reactions of O3 with unsaturated carbonyls, which are considered to be possible intermediates of the secondary organic aerosols, such as cyclic carbonyl alkenes, dicarbonyl alkenes and carbonyl dienes.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4