Rice

ARTICLE pubs.acs.org/JPCA

Unimolecular Decomposition of Ethyl Hydroperoxide: Ab Initio/ Rice-Ramsperger-Kassel-Marcus Theoretical Prediction of Rate Constants Dongna Chen,† Hanfeng Jin,† Zhandong Wang,† Lidong Zhang,*,† and Fei Qi†,‡ †

National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui 230029, People's Republic of China ‡ State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China ABSTRACT: Alkyl hydroperoxides are found to be important intermediates in the combustion and oxidation processes of hydrocarbons. However, studies of ethyl hydroperoxide (CH3CH2OOH) are limited. In this work, kinetics and mechanisms for unimolecular decomposition of CH3CH2OOH have been investigated. The potential energy surface of decomposition reactions have first been predicted at the CCSD(T)/6-311þG(3df,2p)//B3LYP/6-311G(d, p) level. The results show that the formation of CH3CH2O þ OH via O-O direct bond dissociation is dominant, the branching ratio of which is over 99% in the whole temperature range from 300 to 1000 K, and its rate constant can be expressed as k1 = 9.26 1052T-11.91exp(-26879/T) s-1 at 1 atm. The rate constants of the reaction CH3CH2OOH f CH3CH2O þ OH at different temperatures and pressures have been calculated, which can help us to comprehend the reactions of CH3CH2OOH at experimental conditions.

1. INTRODUCTION As is widely known, organic peroxides are important atmospheric trace species1-3 that serve as temporary reservoirs for HOx and ROx radicals.4-9 Alkyl hydroperoxides, as the simplest species of organic peroxides, play a significant role as important intermediates in most combustion10-12 and oxidation processes of hydrocarbons,13-18 which reduce soot formation and promote the burnout process in hydrocarbon combustion.19 Further investigation on the formation and decomposition pathways of these species can offer better understanding of relevant combustion and oxidation mechanisms and, consequently, is of great importance. Alkyl hydroperoxides have been studied comprehensively. Methyl hydroperoxide (CH3OOH), as the simplest prototypical molecule in this class, is known to be a significant source of OH radicals via photodissociation,20 which has aroused wide concern with extensive studies having been carried out. In 1990, Vaghjiani et al.21 obtained the rate coefficient at 298 K for the reaction CH3OOH þ OH f CH3OO þ H2O, which is considered as an important removal mechanism for OH in the upper troposphere.7 To our knowledge, theoretical and experimental research on the dissociation of CH3OOH has been previously accomplished,22-29 from which it can be concluded that the unimolecular dissociation of CH3OOH has four dominant pathways, the bonds (O-O, O-H, C-O) fission and H2O elimination. In 2005, Matthews et al.30 completed the unimolecular dissociation and thermochemistry of CH3OOH upon summarizing previous work, in which the bond dissociation energy of the O-O bond in CH3OOH was measured to be 42.6 ( 1 kcal/mol. However, the H2O molecular r 2011 American Chemical Society

elimination channel, corresponding to more stable products, requires a barrier of about 3.4 kcal/mol higher than the simple bond fission pathway. Compared to CH3OOH, relatively fewer studies have been reported on ethyl hydroperoxide (CH3CH2OOH), which is also an important source of hydroxyl radicals (OH) in the atmosphere and combustion.16,31 As far as we know, the reaction CH3CH2 þ O2 has been studied comprehensively both experimentally and theoretically.32-34 In 1997, Ignatyev et al.32 studied the reaction of CH3CH2 þ O2, which leads to the formation of CH2CH2OOH via H atom abstraction by O2 and the formation of CH3CH2O2 followed by elimination of ethylene. In 2002, the calculations of O-H, O-O, and C-O bond energies in CH3CH2OOH were carried out by Sebbar et al.35 Carstensen et al.36 performed rate constant calculations for the abstraction reaction of CH3CH2O2 þ C2H6 in 2004. In their work, the heat of formation of CH3CH2OOH was calculated to be -39.2 kcal/mol at the CBS-QB3 level, and agreed well with the result of -39.5 ( 0.7 kcal/mol found by Blanksby et al.37 from a combined experimental and ab initio study. Bond dissociation energies (BDEs) of O-O and O-H bonds were reported to be 44.4 and 86.0 kcal/mol, respectively, compared to the O-O bond in H2O2 (BDE = 50.3 kcal/mol) and O-O bond (BDE = 44.8 kcal/mol), O-H bond (BDE = 86.2 kcal/mol) in CH3OOH. It was concluded that CH3CH2OOH required less energy to dissociate than H2O2, and Received: October 15, 2010 Revised: December 12, 2010 Published: January 5, 2011 602

dx.doi.org/10.1021/jp1099305 | J. Phys. Chem. A 2011, 115, 602–611

The Journal of Physical Chemistry A

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the size of the alkyl group affection to either O-O or O-H bond strength is limited. In order to further understand the atmospheric chemistry of CH3CH2OOH, Wang et al.38 completed an experimental study on rate constants for the reaction of CH3CH2OOH with OH, O3, NO2, and NO in 2008. Recently, Kato et al.39 reported their research on kinetics and dynamics of the HO- þ CH3CH2OOH reaction, and proposed that ethyl hydroperoxide reacted with HO- via different channels, leading to the formation of CH3CHO, CH3CH2OO-, and CH2CH2, respectively. In 2005, Hou et al.40 accomplished a theoretical study on the reaction of CH3CH2OO þ HO2. In this work, they proposed the mechanistic pathways for the reaction, one was the channel forming various radical products via an addition-elimination mechanism on a singlet potential energy surface (PES), and the other was forming CH3CH2OOH þ O2 on the triplet PES, which subsequently decomposed to CH3CH2OO þ H (þ O2), CH3CH2 þ HO2 (þ O2), CH3CH2O þ OH (þ O2), and CH3CHO þ H2O (þ O2). They asserted that the simple O-O bond cleavage channel of CH3CH2OOH was the most favorable reaction mechanism, which produced CH3CH2O and OH with an endothermicity of 41.6 kcal/mol. Alkylperoxy is important for the oxidation of hydrocarbons at low temperatures.41 In a recent work, hydroperoxides were detected during the low temperature oxidation of organic compounds.42 Thus, detailed theoretical studies can help to comprehend the reactions at different temperatures and pressures. In this work, we provide comprehensive quantum chemistry and rate constant calculations for the unimolecular dissociation of CH3CH2OOH. Fifteen reaction pathways are proposed. A detailed mapping of the PES of the system was calculated at the CCSD(T)/ 6-311þG(3df,2p)//B3LYP/6-311G(d,p) level. The energies and rate constants of these reaction channels are obtained based on our ab initio calculations. This will help to further understanding of the combustion and oxidation mechanism.

calculations using the Boltzmann probability distribution of the complex. The eigenvalue-solver is used for the master equation based approach for the dissociation processes.53,54 In order to achieve convergence in the integration over the energy range, an energy grain size of 100 cm-1 is used, and the energy span ranges from -13955.2 to 65944.8 cm-1. We also calculated with two more energy sizes of 50 and 200 cm-1, which show they have little influence on the results. Therefore, our option of 100 cm-1 is reasonable and the following section will only be discussed with 100 cm-1. The total angular momentum J ranges from 1 to 241 with a step length of 10 in the course of J-resolved calculation. Lowfrequency vibrational modes corresponding to internal rotation are treated as hindered rotors from B3LYP/6-31G(d) rotor potentials.55 For the barrierless channels, the Morse potential V(R) = De{1 - exp[-β(R - Re)]}2 is used to simulate the potential energy along the individual reaction coordinate. Here, De is the electronic binding energy with ZPE, and Re is the equilibrium bond length. Moreover, we have compared the Varshni potential with the Morse potential, and concluded that these have little difference. Reactions with tight transition states are treated with the canonical nonvariational transition state theory,56 and the numbers of states are evaluated based on the rigid-rotor harmonic-oscillator assumption. The rate constants are corrected using the quantum tunneling according to the Eckart theory.57

3. RESULTS AND DISCUSSION 3.1. Potential Energy Profile and Reaction Mechanism. The optimized geometries of the reactant, intermediates, transition states, and products including the bond distances and angles are presented in Figure 1, and the potential energy diagram obtained at the CCSD(T)/6-311þG(3df,2p) level is shown in Figure 2. Fifteen possible reaction pathways are listed as follows:

2. COMPUTATIONAL METHODS 2.1. Ab Initio Calculations. The hybrid density functional

B3LYP method combined with the 6-311G(d,p) basis set43-47 has been employed in our work to optimize the geometries of the reactant, transition states, and products. The further frequency calculation at the same level for all of the stationary points is to get zero-point energy (ZPE) and to identify the local minima and transition states. Also, the intrinsic reaction coordinate48 (IRC) calculations were used to confirm the connection between the designated transition states and the reactants or products. To achieve more accurate energetic information, we carried out the singlepoint energy calculations with the CCSD(T)/6-311þG(3df,2p) method.49 We employed the multireference methods CASSCF and CASPT2 to scan the Potential Energy Surface (PES) for the O-O bond dissociation processes, which have been proven to be effective by Harding et al.50 In our work, the active space was chosen as a bonding orbital σ and an antibonding orbital σ* for the breaking bond. All quantum chemistry calculations were performed with Gaussian 03 program.51 2.2. Rate Constant Calculations. The rate constants for the main product channels have been computed with variable reaction coordinate-transition state theory (VRC-TST) and RiceRamsperger-Kassel-Marcus (RRKM) theory based on the PES using the VARIFLEX code.52 The rates are evaluated at the E/J-resolved level, for which the pressure dependence of the rate constant is treated by one-dimensional (1D) master equation 603

CH3 CH2 OOH f CH3 CH2 O þ OH

ð1Þ

f CH3 CHO þ H2 O

ð2Þ

f CH2 CH2 þ H2 O2

ð3Þ

f CH3 CHO2 þ H2

ð4Þ

f CH3 CH2 þ HO2

ð5Þ

f HCOOH þ CH4

ð6Þ

f CH2 O2 þ CH4

ð7Þ

f CH3 OH þ HCOH

ð8Þ

f CH3 CH2 OO þ H

ð9Þ

f CH2 OOH þ CH3

ð10Þ

f INT1 f CH3 CH2 OH þ O

ð11Þ

f CH2 O2 CH2 þ H2

ð12Þ

f CH3 CHOOH þ H

ð13Þ

f CH2 CH2 OOH þ H

ð14Þ

dx.doi.org/10.1021/jp1099305 |J. Phys. Chem. A 2011, 115, 602–611


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Figure 1. Optimized geometries of the reaction, transition states, products, and intermediates at the B3LYP/6-311G(d,p) level. The units for bond lengths and bond angles are Å and degrees, respectively. The optimization of INT2 and TS2-2 are performed at the CAS(4,4)/6-311G(d,p) level. 604



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Figure 2. Potential energy diagram for decomposition of CH3CH2OOH at the CCSD(T)/6-311þG(3df,2p)//B3LYP/6-311G(d,p) level. The optimization of INT2 and TS2-2 are performed at the CAS(4,4)/6-311G(d,p) level.

Among them, there are two reactions (via TS1 and TS2) for formation of CH3CHO þ H2O (channel 2). Here, we will only discuss five major channels (1-5) for the decomposition of CH3CH2OOH below. Table 1 lists the detailed vibrational frequencies and rotational constants of important species used in the rate constant calculations. 3.1.1. CH3CH2O þ OH Channel. This is a direct peroxy bond dissociation process. The calculated dissociation energy is 39.9 kcal/mol, which is the lowest energy pathway. This result is in accord with previous work.29 The reaction coordinate path (DCP) for the bond dissociation was computed at the CASPT2//CAS(2,2)/6-311G(d,p) level,58,59 scanning along the dissociation bond length in 0.2 Å intervals (shown in Figure 3). We employed the active space including the O-O bond σ and σ* orbitals for CASPT2 calculations. The same method was used to calculate the DCP of the channel CH3CH2 þ HO2. From the calculations, the Morse potential energy function for the dissociation process from reactant to CH3CH2O þ OH was obtained with De = 36.4 kcal/mol, β = 2.455 Å-1 and Re = 1.493 Å. The potential for the dissociation process was used in all subsequent rate constant calculations. The calculated dissociation energy CH3CH2OOH is 41.48 kcal/mol, which is approximately equivalent with CH3OOH (the calculated dissociation energy is 41.5 kcal/mol at the same level). 3.1.2. CH3CHO þ H2O Channel. There are two reaction pathways to form CH3CHO and H2O (Figure 2). Among them, the pathway with a four-member-ring transition state (TS1) is dominant, and the calculated barrier is 46.5 kcal/mol. This reaction includes the O1;O2 and C1;H bond dissociation and O1; H(C1) bond formation. The O1;O2, O1;H(C1), and C1;H bond lengths in TS1 are 1.922, 1.491, and 1.238 Å, respectively. The C1;O2 bond changes from single bond to double bond in this reaction process, and the C1;O2 bond lengths in RC, TS1, and CH3CHO are 1.426, 1.308, and 1.204 Å, respectively. It is

worth noting that this H2O-elimination is highly exothermic by about 60.6 kcal/mol and has a barrier of 46.5 kcal/mol, which agrees well with previous data of 59.8 and 47.7 kcal/mol, respectively, in Hou’s report.29 Another pathway is the reaction with a five-member-ring transition state (TS2). Compared to the first pathway, the H atom of the eliminated H2O comes from the C2 atom. The calculated barrier is 56.2 kcal/mol, which is 9.7 kcal/mol higher than TS1. Due to the instability of CH2CH2O intermediate (INT2), it changes to CH3CHO through an H atom transformation with a small barrier TS2-2 of 17.4 kcal/mol in this reaction process. The geometies of INT2 and TS2-2 cannot be obtained at the B3LYP/6-311G(d,p) level, and they were optimized at the CASSCF(4,4)/6-311G(d,p) level, in which the active space includes the single-electron occupied orbital and the C-H bond σ and σ* orbital. The lowest barrier for the channel CH3CHO þ H2O is 6.6 kcal/mol higher than that of the channel CH3CH2O þ OH, which is different from the reactions of ethanol (the lowest energy channel is the H2O-elimination reaction).60 3.1.3. CH2CH2 þ H2O2 Channel. As shown in Figure 1, H2O2 eliminates from CH3CH2OOH via a planar four-memberring transition state TS3. The breaking C2;H and C1;O bonds in TS3 are 1.354 and 2.004 Å, which are 0.261 and 0.578 Å longer than those in CH3CH2OOH, respectively. The imaginary frequency of TS3 is 1335i cm-1, whose vibration model is relative to the reactant and products, and the energy of TS3 lies above CH3CH2OOH by 62.0 kcal/mol, representing a well-defined transition state, leading to the formation of ethylene and hydrogen peroxide from CH3CH2OOH. 3.1.4. CH3CHO2 þ H2 Channel. As shown in Figure 1, the process of the H2 molecule formation occurs via a five-member-ring transition state TS4 with a barrier of 65.9 kcal/mol, involving the H atom in the CH2 group and another H atom in the OOH group attached together. The product CH3CHO2 (singlet) can be formed to a more stable cyclic geometry product (c-CH3CHO2) via the 605



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Table 1. Vibrational Frequencies and Rotational Constants of Important Species Used in the Rate Constant Calculationsa species

νj (cm-1)

Ii (a.u.)

CH3CH2OOH

116.4, 329.6, 390.8

154.7, 200.1, 236.9, 349.0, 486.3, 768.6, 831.4,882.7, 1007.4, 1070.2, 1144.7, 1266.5, 1322.6, 1340.0,

CH3CH2O2

101.5, 320.5, 371.7

113.1, 227.2, 346.1, 512.4, 773.4, 816.0, 960.0, 1061.5, 1112.8, 1162.1, 1264.6, 1332.3, 1363.2,

CH3CHOOH

47.9, 432.9, 460.0

75.4, 151.8, 209.8, 292.0, 476.6, 632.3, 832.4, 906.9, 991.0, 1083.8, 1148.6, 1300.3, 1319.7, 1363.2,

CH2CH2OOH

111.7, 315.2, 371.6

111.2, 156.6, 213.7, 345.1, 453.4, 552.0, 806.3, 833.4, 921.4, 1021.9, 1099.3, 1230.7, 1317.7,

CH3CH2O

45.4, 189.2, 212.6

1325.5, 1399.0, 1411.5, 2884.0, 2955.5, 3034.8, 3141.1, 3641.0 76.4, 266.8, 418.6, 838.2, 857.6, 1033.5, 1061.5, 1198.8, 1298.4, 1342.9, 1364.2, 1435.7, 1446.3,

1364.2,1425.1, 1436.7, 1458.9, 2924.6, 2932.3, 2971.0, 2994.2,3011.6, 3656.4 1432.8, 1437.6, 1456.0, 2939.1, 2963.2, 3002.9, 3009.6, 3029.0 1414.4, 1440.5, 2864.6, 2949.7, 2998.0, 3040.6, 3612.9

2789.2, 2797.9, 2929.4, 2994.2, 3003.8 CH3CH2

17.4, 79.4, 85.7

109.2, 459.2, 787.0, 947.5, 1027.7, 1152.4, 1354.5, 1416.4, 1433.8, 1433.8, 2844.3, 2932.3,

CH2O2H

33.9, 161.9, 187.8

151.8, 230.1, 464.1, 632.3, 813.1, 1096.4, 1152.4, 1317.7, 1384.5, 3011.6, 3150.8, 3619.7

TS1

117.7, 388.7, 443.0

1418.3i, 161.5, 194.3, 234.9, 433.1 487.3, 606.2, 759.9, 876.9, 1030.6, 1050.9, 1084.7,

TS2

126.9, 330.6, 402.7

1143.7i, 125.7, 234.9, 299.7, 431.2, 642.0, 781.2, 829.5, 929.1, 990.0, 1106.0, 1155.3, 1269.4, 1343.9, 1369.0, 1432.8, 1436.7, 1461.8, 2844.3, 2934.2, 2955.5, 2992.2, 3015.4, 3035.8

TS2-2

33.2, 176.6, 198.5

1375.9i, 449.7, 560.2, 734.9, 957.8, 994.4, 1187.9, 1312.5, 1400.7, 1505.8, 1587.3, 2391.1,

TS3

77.6, 508.9, 556.2

1290.7i, 155.7, 224.3, 361.6, 438.9, 452.5, 583.0, 758.9, 783.1, 808.2, 968.7, 982.3, 1136.0, 1201.7,

TS4

116.4, 300.4, 361.8

1045.1i, 176.9, 307.4, 466.0, 644.9, 686.4, 779.2, 846.0, 926.2, 940.7, 1066.4, 1124.4, 1171.8,

TS4-2

109.5, 250.9, 327.8

653.6i, 259.2, 368.5, 492.3, 722.8, 874.6, 907.7, 1076.1, 1138.4, 1354.1, 1397.0, 1432.2, 1462.7, 1570.2, 2996.9, 3030.4, 3065.7, 3166.1

TS5

155.2, 368.1, 467.7

1128.3i, 145.0, 174.0, 200.1, 292.0, 326.8, 439.9, 508.5, 792.8, 833.4, 913.6, 965.8, 1137.9,1170.8,

TS6

160.8, 283.8, 395.8

1289.7i, 88.0, 272.6, 350.0, 505.6, 608.1, 719.3, 785.0, 826.6, 906.9, 1074.1, 1172.7, 1208.5, 1244.3,

TS6-2

40.9, 117.3, 151.6

698.7i, 743.8, 777.9, 1014.3, 1200.0 1406.8, 1555.9, 3052.9, 3209.1

TS7

203.0, 261.7, 438.4

767.6i, 86.0, 201.1, 266.8, 292.9, 322.9, 417.7, 656.5, 761.8, 806.3, 940.7, 987.1, 1085.7, 1197.9,

TS8

92.3, 410.3, 428.7

1367.1, 1379.6, 1427.0, 1502.4, 2848.2, 2926.5, 3009.6, 3144.0, 3184.6, 3473.7 935.9i, 109.2, 240.7, 293.9, 409.9, 717.4, 792.8, 834.3, 859.5, 952.3, 1067.3, 1124.4, 1149.5, 1160.2,

TS9

118.8, 317.5, 370.7

462.1i, 174.0, 321.0, 362.6, 439.9, 582.0, 604.3, 667.1, 746.4, 783.1, 815.0, 832.4, 1012.2, 1119.6,

INT1

125.3, 323.6, 391.4

154.7, 217.5, 304.5, 433.1, 657.4, 770.5, 797.6, 855.6, 965.8, 1047.0, 1093.5, 1218.2, 1292.6, 1341.9,

INT2(CH2CH2O) CH3CHO

39.3, 175.9, 203.6

1368.0, 1428.9, 1434.7, 1460.8, 2928.4, 2957.4, 2991.3, 3033.8, 3055.1, 3616.8 191.4, 410.9, 461.8, 700.4, 944.9, 1114.3, 1184.9, 1204.2, 1476.0, 1492.3, 1564.1, 2941.1, 3146.4, 3282.7, 3392.2

31.5, 178.1, 198.5

HCOOH

29.1, 185.6, 214.7

152.8, 319.0, 414.8, 796.6, 885.6, 998.7, 1764.4, 2889.8, 3654.5

CH2O2

62.6, 70.5, 120.7

806.3, 895.8, 1024.2, 1181.8, 1252.1, 1312.8, 1550.0, 3052.4, 3146.3

CH3CHO2

97.2, 246.8, 289.5

211.1, 384.6, 458.4, 774.5, 845.2, 934.2, 1032.2, 1133.5, 1207.8, 1304.7, 1400.3, 1450.4, 1477.4,

CH2O2CH2

12.3, 59.7, 72.0

CH3CH2OH

51.5, 192.7, 221.6

2974.8, 3033.8, 3131.5

1214.3, 1224.0, 1344.8, 1355.5, 1432.8, 1443.4, 1754.7, 2845.3, 2929.4, 2991.3, 3015.4, 3489.2

3179.9, 3270.5, 3380.7, 1226.9, 1282.9, 1419.3, 1498.5, 1636.8, 3004.8, 3058.0, 3084.1, 3148.9, 3631.3 1251.0, 1345.8, 1366.1, 1401.9, 1436.7, 1457.9, 2352.2, 2913.9, 2997.1, 3029.0, 3067.7

1321.6, 1382.5, 1428.9, 1457.0, 2294.2, 2954.5, 3040.6, 3074.4, 3101.5, 3671.9 1295.5, 1405.7, 1437.6, 1469.5, 1709.3, 2906.2, 2977.7, 3005.8, 3022.2, 3128.6

1255.9, 1347.7, 1419.3, 1450.2, 2044.8, 2869.5, 2931.3, 2959.4, 2971.9, 3592.6 1149.5, 1210.4, 1262.6, 1419.3, 1454.1, 2978.7, 3059.0, 3076.4, 3188.5, 3591.7

154.7, 491.1, 751.2, 853.7, 1088.6, 1097.3, 1329.4, 1378.7, 1411.5, 1422.2, 1763.4, 2761.2, 2920.7, 2973.9, 3031.9

1493.5, 3036.4, 3084.6, 3097.8, 3136.3

a

CH3CH

14.8, 67.7, 72.1

807.3, 940.7, 941.7, 1031.6, 1197.9, 1334.2, 1423.1, 1635.8, 3018.3, 3032.9, 3087.0, 3114.1 243.6, 280.4, 403.2, 798.6, 872.1, 1000.6, 1070.2, 1140.8, 1235.6, 1258.8, 1359.3, 1411.5, 1431.8, 1453.1, 1480.2, 2868.5, 2891.7, 2933.3, 2998.0, 3002.9, 3710.6 461.2, 593.6, 927.2, 1080.9, 1224.0, 1260.7, 1305.2, 1462.8, 2736.0, 2804.7, 2888.8, 2976.8

The optimization of INT2 and TS2-2 are performed at the CAS(4,4)/6-311G(d,p) level.

transition state (TS4-2, 69.5 kcal/mol). The CH2O2 þ CH4 channel has a similar reaction process with transition states (TS6 and TS6-2). The final products c-CH2O2, c-CH3CHO2, and

c-CH2O2 are the most stable products. The relative energies are listed in Table 2. In another H2-elimination pathway (TS9), the H atoms come from the CH3 and OOH groups. And the barrier 606



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Figure 3. The dissociation curve for the reactions (a) CH3CH2OOH f CH3CH2O þ OH and (b) CH3CH2OOH f CH3CH2 þ HO2 at the CASPT2//CAS(2,2)/6-311G(d,p) level.

Table 2. Relative Energies for CH3CHO2 and CH2O2 at the CCSD(T)/6-311þG(3df,2p)//B3LYP/6-311G(d,p) Level (kcal/mol) species

ΔE

species

ΔE

CH3CHO2 (singlet) c-CH3CHO2 (singlet)

0 -22.9

CH2O2 (singlet) c-CH2O2 (singlet)

0 -25.5

CH3CHO2 (triplet)

33.3

CH2O2 (triplet)

28.7

is obviously higher (90.2 kcal/mol). The C1;H and O1;H bond lengths in TS4 are 1.751 and 1.467 Å, respectively. They are 0.655 and 0.501 Å longer than those in CH3CH2OOH. The forming H-H bond 0.881 Å (in TS4) is a little longer than the H2 molecular equilibrium bond length 0.744 Å calculated at the same level of theory. The imaginary frequency associated with TS4 is calculated to be 1081i cm-1. Analysis of the atomic motion along this vibration indicates that this transition state is mainly associated with the motion of the two H atoms. 3.1.5. CH3CH2 þ HOO Channel. CH3CH2OOH dissociates into species CH3CH2 and HO2 without a well-defined transition state. From the DCP calculations, we acquired an even and fair potential curve and made use of it to fit the Morse potential energy function with the parameters De = 68.9 kcal/mol, β = 2.579 Å-1, and Re = 1.429 Å. The potential for the dissociation process was used in all subsequent rate constant calculations based on the RRKM and VTST theory. At the CCSD(T)/6-311þG(3df,2p) level, the decomposition energy for this channel was calculated to be 68.1 kcal/mol, which proves it to be highly endothermic, in accordance with previous results. The other direct bond dissociation channels include the O-H, C-C ,and C-H bond cleavage, and their dissociation energies are relatively higher. The orders of the dissociation energies are O-H < C-C < C1;H < C2;H, which are 81.3, 85.2, 92.9, and 98.7 kcal/mol, respectively. As shown in Figure 2, we also calculated other reaction channels consisting of CH4-elimination, CH3OH þ CH2O, and CH3CH2OH þ O channels. Among them, the channel CH3CH2OH þ O includes two steps. The first step is an isomerization process with a lower barrier (TS8, 49.3 kcal/mol). The intermediate INT1 can further dissociate to the products CH3CH2OH þ O with the dissociation energy 45.9 kcal/mol. However, the overall barrier 89.0 kcal/mol is much higher than that of the H2O-elimination channel. The calculated barriers of the channels HCOOH þ CH4, CH2O2 þ CH4 and CH3OH þ CH2O are 71.6, 72.1, and 74.6

Figure 4. Comparison of the calculated rate constant of channel 1 with the experimental measurement63 and the modeling data.61

kcal/mol, respectively, which are above 30 kcal/mol higher than the dissociation energy of channel CH3CH2O þ OH. 3.2. Rate Constant Calculations. As mentioned above, there are 15 possible channels for the unimolecular decomposition of CH3CH2OOH. However, channels 6-14 are less important kinetically, because of their much larger barriers. Therefore, we carried out the VTST and RRKM calculations for the major competitive channels 1-5 utilizing the VARIFLEX code developed by Klippenstein et al.52 through the temperature range of 3001000 K and the pressure from 0.001 to 1000 atm with Ar as bath gas. The Lennard-Jones (L-J) pairwise potential for ethanol (σ = 4.317 Å, ε/k = 450.2 K) are used as an approximation to the L-J parameters of CH3CH2OOH.61 The L-J parameters of Ar is employed in this calculation with σ = 3.465 Å, ε/k = 113.5 K, respectively. An exponential-down model is used for the collisional energy transfer, where the average downward transfer parameter ÆΔEdownæ was assumed to be 400 cm-1 in Ar, which comes from the parameter of CH3CH2OOH.61 On the basis of the data in Figure 2 and Table 1, the calculated rate constants at different temperatures and pressures are shown in Figures 4-7 and presented in Table 3. Moreover, we also calculated the rate constant with Varshni potential, and two more energy grain sizes of 50 cm-1 and 200 cm-1. The results are listed in Table 4, which shows a small variation from the previous one obtained with 100 cm-1. As a 607



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Table 3. Equations for Rate Constants (s-1) at Different Pressures in the Temperature Range 300-1000 K

k1

0.1 atm

1 atm

100 atm

6.05 1058T-14.05exp(-27258/T)

9.26 1052T-11.91exp(-26879/T)

1.38 1033T-5.27exp(-24521/T)

38 -9.32

3.56 10 T

k2

2.76 10 T 6.07 10 T 2.43 10

k5

-22 7.87

T

4.16 1026T-5.40exp(-30547/T)

exp(-27468/T)

1.89 1022T-4.58exp(-31052/T)

exp(-27894/T)

5.27 1019T-1.78exp(-29734/T)

14 -2.59

7.77 10 T

exp(-21918/T)

1.68 107T1.47exp(-20801/T)

14 -4.45

2.49 10 T

exp(-34534/T)

exp(-23630/T)

47 -13.88

3.24 10 T

exp(-27142/T)

45 -14.88

k4

9.54 10 T

exp(-23966/T)

30 -9.65

k3

31 -6.87

exp(-31564/T)

Table 4. Rate Constants with Different Parameters at 1 Atm for the Channel 1 Varshni

Morse T 300

50 cm-1

100 cm-1

200 cm-1

100 cm-1

4.41 10-16

4.20 10-16

4.30 10-16

2.80 10-16

-13

-13

-13

325 350

1.38 10 1.87 10-11

1.31 10 1.78 10-11

1.34 10 1.82 10-11

9.00 10-14 1.26 10-11

375

1.29 10-9

1.24 10-9

1.26 10-9

8.95 10-10

-8

4.97 10

-8

5.07 10

-8

3.67 10-8

1.27 10

-6

1.29 10

-6

9.57 10-7

2.21 10

-5

2.25 10

-5

1.70 10-5

2.80 10

-4

2.83 10

-4

2.18 10-4

2.69 10

-3

2.71 10

-3

2.13 10-3

-2

2.04 10 0.125

-2

1.63 10-2 0.102

400 425 450 475 500

5.19 10

-6

1.32 10

-5

2.30 10

-4

2.90 10

-3

2.78 10

-2

525 550

2.10 10 0.129

2.03 10 0.125

561

0.269

0.262

0.262

0.214

575

0.658

0.641

0.639

0.527

600

2.88

2.81

2.79

2.33

625

10.9

10.7

10.6

650

36.6

35.9

35.5

30.4

653

42

40.7

35

41.2 108 294

106 289

92.4 254

725 741

732

717

637

750

1.70 103

1.68 103

1.64 103

1.47 103

775

3.63 10

3.59 10

3.50 10

3

3.17 103

800

7.24 103

7.19 103

6.99 103

6.39 103

825

1.36 104

1.35 104

1.31 104

1.21 104

850

2.42 104

2.41 104

2.34 104

2.17 104

875 900

4.11 104 6.65 104

4.10 104 6.64 104

3.96 104 6.40 104

3.71 104 6.05 104

925

1.03 105

1.03 105

9.94 104

9.46 104

950

1.54 105

1.55 105

1.49 105

1.42 105

975

2.23 105

2.24 105

2.14 105

2.07 105

1000

3.12 105

3.13 105

3.00 105

2.91 105

3

rate constant of k1 is obviously larger than the other channels due to the lower dissociation energy. The orders of the barriers for channels 2-4 are TS1 < TS3 < TS4, which is consistent with rate constants. Thus the enthalpies of the transition states have a main contribution to the rate constants. The dissociation energy of channel 5 (CH3CH2OOH f CH3CH2 þ HOO) is highest among the five channels, while k5 and k3 are close at the lower temperatures and k5 becomes slightly larger than k3 with the increase in temperature. Because the entropies of the transition states have a larger effect on the rate constants for the direct bond dissociation channels. The calculated rate constants for the five channels at 0.01 atm are shown in Figure 6. Compared to the rate constants at 1 atm, the rate constants decrease, especially at high temperature. The relative orders of channels 1, 2, and 4 are consistent with the that at 1 atm. The inequality k1 > k2 > k4 holds across the temperature range of 300-1000 K. For k3 and k5, they are between k2 and k4 in the temperature range of 3001000 K. Comparing to the rate constants at 1 atm, there is an intersection for k3 and k5. For these two channels, over 600 K, k5 > k3, while under 600 K, k5 < k3. For CH3CH2OOH unimolecular decomposition reactions, channel 1 CH3CH2OOH f CH3CH2O þ OH is dominant with branching ratio over 99% throughout the whole temperature range and at 0.001 and 1000 atm. Because the dissociation energy of the channel is lowest and this reaction is the favorable enthalpy reaction. Figure 7 shows a 3D plot of the rate constants for channel 1 as a function of temperature and pressure. Figure 8 presents the rate constant ratios at different pressures. The results show that below 500 K, the dissociation rate constant for channel 1 at 1 atm already reaches the rate constant value at 1000 atm; as expected, at higher temperatures, it shows a tendency of pressure dependence. On the basis of the PES and rate constant

8.97

675 110 700 298

3

Figure 5. Temperature dependence of rate constants at 1 atm for channels 1-5.

result, the option of 100 cm-1 and Morse potential is reasonable, and the discussion in this work is done with these two parameters only. Figure 4 compares our calculated rate constant for channel 1 at 1 atm to the experimental results and the modeling data at 400-800 K.62,63 The experimental data from the work of Kirk and Knox64 obtained in the temperature range of 561-653 K. Our calculated results are in good agreement with the experimental measurement and modeling data. Figure 5 presents the rate constants for channels 1-5 at 1 atm. For channels, k1 > k2 > k5 ≈ k3 > k4 across the temperature range of 300-1000 K. Among them, the 608



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Figure 6. Temperature dependence of rate constants at 0.01 atm for channels 1-5.

Figure 9. The rate constants for the reaction CH3OOH f CH3O þ OH62 and C2H5OOH f C2H5O þ OH in the temperature range 400-800 K at 1 atm.

decomposition at various temperatures and pressures are collected in Table 2 for detailed kinetic modeling applications in the future. Moreover, we made a comparison of the rate for the reaction CH3OOH f CH3OþOH62 and CH3CH2OOH f CH3CH2O þ OH in the temperature range of 400-800 K, as listed in Figure 9, which shows similar tendency in the two curves. It can be easily concluded that the size of the alkyl group affection to the reactivity of alkyl hydroperoxides is limited.

4. CONCLUSIONS The kinetics and mechanisms for the unimolecular decomposition of CH3CH2OOH have been studied by high-level ab initio theories and variational RRKM calculations. The PES was calculated at the CCSD(T)/6-311þG(3df,2p) level based on the geometry optimizations and frequency computations at the B3LYP/6-311G(d,p) level, followed by successive rate constant calculations with the microcanonical RRKM and VTST theory. The primary unimolecular decomposition of CH3CH2OOH consists of direct bond dissociation and different types of H2-, H2O2-, H2O2-, and CH4-molecular elimination processes, but some of them with much high barriers (or dissociation energies) are considered to be kinetically unimportant. Thus, the rate constants of the five main channels were computed. The calculations show that the formation of CH3CH2O þ OH is dominant, with a product branching ratio over 99% through the whole temperature range from 300 to 1000 K at 0.001 and 1000 atm. So the decomposition of CH3CH2OOH to CH3CH2O þ OH through direct bond fission is more favorable than the other four channels for its lowest barrier. The three-parameter fittings of the calculated rate constants for this channel are expressed as k1 = 9.26 1052T - 11.91exp(-26879/T) s-1 in the temperature range T = 300-1000 K at 1 atm. Thus, the detailed theoretical studies can help us to comprehend the reactions of CH3CH2OOH at different temperatures and pressures. In the long term, it would be significant to study the unimolecular decomposition of several special hydroperoxides such as branched ones, ketohydroperoxides, and so on, which will exhibit structure-reactivity relationships and help to establish more detailed kinetic models in further combustion and oxidation studies.

Figure 7. Calculated rate constants for channel 1 as a function of temperatue and pressure.

Figure 8. The ratios of the rate constants at different pressures with the rate constants at infinite pressure.

calculations, the dominant channel for the CH3CH2OOH dissociation is the reaction CH3CH2OOH f CH3CH2O þ OH. The predicted individual rate constants for CH3CH2OOH 609



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’ AUTHOR INFORMATION

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Corresponding Author

*E-mail: [email protected].

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