Multichannel RRKM-TST and CVT Rate Constant Calculations for

ARTICLE pubs.acs.org/JPCA

Multichannel RRKM-TST and CVT Rate Constant Calculations for Reactions of CH2OH or CH3O with HO2 S. Hosein Mousavipour* and Zahra Homayoon Department of Chemistry, College of Sciences, Shiraz University, Shiraz, Iran ABSTRACT: The kinetics and mechanism of the gas-phase reactions between hydroxy methyl radical (CH2OH) or methoxy radical (CH3O) with hydroproxy radical (HO2) have been theoretically investigated on their lowest singlet and triplet surfaces. Our investigations indicate the presence of one deep potential well on the singlet surface of each of these systems that play crucial roles on their kinetics. We have shown that the major products of CH2OH þ HO2 system are HCOOH, H2O, H2O2, and CH2O and for CH3O þ HO2 system are CH3OH and O2. Multichannel RRKM-TST calculations have been carried out to calculate the individual rate constants for those channels proceed through the formation of activated adducts on the singlet surfaces. The rate constants for direct hydrogen abstraction reactions on the singlet and triplet surfaces were calculated by means of direct-dynamics canonical variational transition-state theory with small curvature approximation for the tunneling.

’ INTRODUCTION It has been suggested that nearly all hydrocarbons convert to CO through formaldehyde (CH2O) and/or formyl radicals (HCO) by oxidation.1 The products of the initiation steps in the methanol combustion in the oxygen rich regime are hydroxy methyl radical (CH2OH), methoxy radical (CH3O) and hydroproxy radical (HO2).1,2 It has been suggested that further oxidation of CH2OH and CH3O radicals by OH, O, and HO2 produces more stable species like formaldehyde, formic acid, or hydrogen peroxide.3
6 CH2 OH þ HO2 f CH2 O þ H2 O2

ðR1Þ

CH2 OH þ HO2 f HCOOH þ H2 O

ðR2Þ

CH3 O þ HO2 f CH2 O þ H2 O2

ðR3Þ

Tsang on the basis of a literature review suggested the rate constants for reactions R1 and R3 are temperature independent and recommended values of 1.2  1010 L mol
1 s
1 and 3.0  108 L mol
1 s
1 for the rate constants of reactions R13 and R3,4 respectively. In 1998, Held and Dryer5 in a comprehensive study on the kinetic mechanism of CO, CH2O, and CH3OH combustion reported a value of 2.0  1010 L mol
1 s
1 for the rate constant of reaction R2 and suggested its rate is temperature independent. Grotheer and co-workers6 have studied the rate of consumption of the reactants in CH2OH þ HO2 system and reported a value of 3.6  1010 L mol
1 s
1 for the total rate of consumption of the reactants. To the best of our knowledge, no theoretical investigation on the mechanism of the reaction between the title radicals has been reported to date. In the present article, a comprehensive theoretical study on the reactions of hydroxy methyl radical (CH2OH) and methoxy radical (CH3O) with hydroproxy radical (HO2) on their lowest singlet and triplet surfaces to reveal detailed mechanisms is r 2011 American Chemical Society

presented. Our investigations show the presence of one deep potential well on the lowest singlet potential energy surface of each of these systems that play crucial roles in their kinetics. In the present article, we report the results of an investigation on the essential features of the potential energy surfaces of the title reactions that produced by quantum mechanical computations and the thermal rate constants for those channels proceeding through the deep potential wells on the singlet surfaces by means of multichannel RRKM and transition-state theory (TST) methods. Using the RRKM-TST method has the advantage of calculating the rate constant of each individual step in the presence of the other channels in complex systems. Also, direct-dynamics canonical variational transition-state theory calculations with small curvature approximation for tunneling were carried out to calculate the thermal rate constants of the hydrogen abstraction pathways of the title reactions on their singlet and triplet surfaces over the temperature range of 300
3000 K.

’ COMPUTATIONAL METHODS The Gaussian03 program7 was used to optimize the geometries of the stationary points and to calculate their energies. Geometries of all of the stationary points were optimized at the MPWb1K/6-31þG(d,p)8 and MP29/Aug-cc-pVTZ levels of theory. Single point calculations were carried out at the CCSD(T)10/Aug-cc-pVTZ// MP2/Aug-cc-pVTZ level of theory (coupled-cluster with single and double and perturbative triple excitations) to obtain more accurate energies of the stationary points along the PES. Harmonic vibrational frequencies were obtained at the MPWb1K/6-31þG(d,p) level of theory to characterize the stationary points as local minima or firstorder saddle points and to obtain zero-point vibration energy (ZPE). Received: December 20, 2010 Revised: February 21, 2011 Published: March 24, 2011 3291

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Scheme 1

The transition states were subjected to intrinsic reaction coordinate (IRC)11 calculations to facilitate connection with minima along the reaction paths. Each IRC terminated upon reaching a minimum using the default criterion. According to the previous studies and our ab initio results, the following mechanism is suggested for the title reactions. In Scheme 1, (s) or (T) stands for the singlet or triplet state of the corresponding species and w is the collisional rate constant. Channels R4 to R8 and R0 10 in CH2OH þ HO2 system and R11 to R13 in CH3O þ HO2 system proceed over the singlet surfaces and the other channels proceed over the triplet surfaces. In our suggested mechanism, two deep potential wells INT1* and INT2* are formed over the singlet surfaces of CH2OH þ H2O and CH3O þ H2O systems, respectively. There are three van der Waals complexes, vdwx, formed along the channels R7, R10, and R15. Formation of intermediate species INT1* and INT2* in some other systems are previously reported in the literature. Hydroxymethyl hydroperoxide INT1* (H2C(OH)OOH) is suggested to form as a biogenic volatile organic compound in the atmosphere.12 Vlasenko et al. predicted the formation of hydroxymethyl hydroperoxide INT1* in their study on the formaldehyde measurements by proton transfer reactions in formaldehyde oxidation.13 They have discussed about the possibility of decomposition of hydroxymethyl hydroperoxide to HCHO and H2O2 in their article. Lay and Bozzelli in 1997 reported a value of
92.8 kJ mol
1for the enthalpy of formation of energized Methyl hydrotrioxide INT2* (H3COOOH) at the G2 level.14 Plesni
car et al.15 have studied the barrier height for the decomposition of some alkyl hydrotrioxide (R 3 3 3 OOOH) compounds. They reported values of 30.9 to 44.3 kJ mol
1 for the decomposition of some alkyl hydrotrioxides compounds with different R.

’ SOME FEATURES OF THE POTENTIAL ENERGY SURFACES Figure 1 shows the optimized geometries of all the stationary points at the MP2/Aug-cc-pVTZ level of theory. The calculated relative energies at the MPWb1K/6-31þG(d,p) and CCSD(T)/ Aug-cc-pVTZ levels of theory and zero-point energies (ZPEs) are listed in Tables 1 and 2. Schematics of potential energy diagrams on the lowest singlet and triplet surfaces at the CCSD(T)/Augcc-pVTZ level are presented in Figures 2 and 3. Vibrational term values and moments of inertia for all species are listed in Table 3. ’ REACTION OF CH2OH WITH HO2 As shown in Figure 2, the association reaction of CH2OH þ HO2 by a barrierless process forms vibrationally excited intermediate INT1*, which is 303.0 kJ mol
1 more stable than the total energies of CH2OH and HO2 at the CCSD(T)/Aug-cc-pVTZ level of theory. There are three possible paths for this highly vibrationally energized intermediate to dissociate or undergoes the collisional stabilization via channel Rw4. Energized intermediate INT1* could dissociate to formic acid and water via channel R5 with a barrier height of 183.8 kJ mol
1 or to form H2O2 þ CH2O(S) via channels R6 with a barrier height of 192.8 kJ mol
1. Another possible channel for dissociation of INT1* is channel R7 to form H2OO þ CH2O(S). A van der Waals complex (vdw1) is formed along channel R7. The water oxide product undergoes isomerization process to form hydrogen peroxide via channel R8. Another possible path on the singlet surface is the formation of methanol and singlet molecular oxygen, reaction R0 10 with 22.2 kJ mol
1 barrier height. On the triplet surface, two hydrogen transfer reactions R9 and R10 occurs to form H2O2 and triplet CH2O(T) or methanol and triplet molecular oxygen, 3292

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Figure 1. Continued

Figure 1. Optimized geometries of the stationary points at the MP2/Aug-cc-pVTZ level. (a) INT1, (b) TS5, (c) TS6, (d) TS7, (e) vdw1, (f) OOH2, (g) TS8, (h) HCOOH, (i) INT2, (j) TS12, (k) TS13, (l) CH2O(S), (m) H2O2, (n) CH2O(T), (O) TS9,(P) TS14, (q) CH3OH, (r) O2(T), (s) TS10, (t) vdw2, (u) TS15, (v) vdw3, (w) CH2OH, (x) CH3O, and (y) HO2.

Table 1. Relative Energies of Various Species in CH2OHþHO2 System at Two Levels of Theory and Zero Point Energies in kJ mol
1 species

CH2OH þ O2H CH3O þ O2H

relative energy

Table 2. Relative Energies of Various Species in CH3OþHO2 System at Two Levels of Theory and Zero Point Energies in kJ mol
1

ZPE

species

relative energy

ZPE

MPWb1K/

CCSD(T)/

MPWb1K/

MPWb1K/

CCSD(T)/

MPWb1K/

6-31þG(d,p)

Aug-cc-pVTZ

6-31þG(d,p)

6-31þG(d,p)

Aug-cc-pVTZ

6-31þG(d,p)

0.0 20.5

0.0 37.6

140.5 138.1

CH3O þ O2H INT2

0.0
108.2

0.0
155.3

138.1 160.4

INT1


313.8


323.3

160.8

TS12

TS5


55.3


121.9

143.2

H2O2 þ CH2O(S)

HCOOH þ H2O


453.0


453.6

149.2

TS13

TS6


91.1


112.1

142.4

H2O2 þ CH2O(S)


210.2


240.6

TS7


83.7


112.4

vdw1 OOH2 þ CH2O(S)


87.7
20.4


117.7
47.7

152.9 143.2

H2O2 þ CH2O(T) TS15(T)

117.3

22.4

142.9


230.7


278.2

143.7

91.8

21.0

144.6

H2OO þ CH2O(S)


40.9


85.2

143.2

143.7

TS8 þ CH2O(S)


0.6


55.0

132.2

151.5

TS14

75.2

194.6

131.9

50.4
24.7

27.2
25.5

131.2 139.2

TS8 þ CH2O(S)

19.9


17.5

132.2

vdw3(T)


33.1


34.4

142.6

TS9

96.0

101.7

130.3

CH3OH þ O2(T)


228.8


241.4

149.7

H2O2 þ CH2O(T)

70.9

64.8

131.2


25.0


18.5

139.3

TS 10(S)

93.6

23.8

138.9

vdw2(T)


36.5


35.6

150.4

CH3OH þ O2(T) CH3OH þ O2(S)


207.1
82.5


203.9
79.3

149.7 149.7

TS10(T) 0

respectively. The barrier height for channel R9 was found to be 91.6 kJ mol
1 at the CCSD(T)/Aug-cc-pVTZ level of theory while channel R10 is a barrierless reaction. A van der Waals complex vdw2 as shown in Figure 2 is formed along channel R10.

’ REACTION OF CH3O WITH HO2 As shown in Figure 3, the association reaction of CH3O and HO2 radicals on the singlet surface by a barrierless process forms vibrationally excited intermediate INT2*, which is 100.4 kJ mol
1

more stable than the total energies of CH3O and HO2 at the CCSD(T)/Aug-cc-pVTZ level of theory. There are two possible dissociative paths for this vibrationally energized intermediate INT2*. It may dissociate into H2O2 þ CH2O(S) via channel R12 with a barrier height of 127.6 kJ mol
1 or into H2OO þ CH2O(S) via channel R13 with a barrier height of 127.9 kJ mol
1 or undergoes stabilization process under collision via channel Rw11. The produced water oxide in reaction R13 furthermore undergoes isomerization process to form H2O2 via channel R8. On the triplet surface, two hydrogen transfer reactions R14 and R15 occur to form H2O2 and CH2O(T) or methanol and triplet molecular oxygen, respectively. The barrier height of channel R14 was found to be 188.5 kJ mol
1 at the CCSD(T)/Aug-cc-pVTZ level of theory, whereas channel R15 is a barrierless reaction. A van der Waals complex vdw3 is formed along channel R15. We were not able to reach a reasonable 3294

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Figure 2. Relative energies of the stationary points of CH2OH þ HO2 system in kJ mol
1 on both singlet and triplet surfaces at the CCSD(T)/Aug-ccpVTZ level. All values are corrected for the zero-point energies.

Figure 3. Relative energies of the stationary points of CH3O þ HO2 system in kJ mol
1 on both singlet and triplet surfaces at the CCSD(T)/Augcc-pVTZ level. All values are corrected for the zero-point energies. 3295

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17.2 16.5 22. 9 14.5 319.0 28.2 15.4 28.5

184.2, 285.5, 381.9, 489.5, 602.4, 846.9, 1010.4, 1087.7, 1107.4, 1307.5, 1342.5, 1411.0, 1467.01, 1547.1, 3023.7, 3132.6, 3793.7, 3848.9

1649.4 i, 173.5, 297.3, 349.5, 515.6, 592.5, 680.5, 1007.6, 1086.6, 1172.9, 1253.8, 1280.1, 1324.3, 1473.2, 1863.1, 3127.9, 3776.5, 3950.8

1675.5 i, 156.9, 263.0, 323.4, 532.1, 636.9, 898.4, 964.0, 1201.2, 1259.5, 1326.9, 1369.9, 1389.1, 1624.9, 2002.8, 2982.2, 3067.9, 3793.5

180.7 i, 117.1, 256.8, 293.1, 355.9, 497.9, 869.2, 1044.5, 1200.9, 1247.8 1292.7, 1564.6, 1658.9, 1731.7, 3019.4, 3119.1, 3242.4, 3797.9 1300.3 i, 730.1, 1023.8, 1389.8, 3024.9, 3925.5

2052.9 i, 52.48, 133.4, 206.2, 282.2, 418.4, 557.3, 703.0, 1060.4, 1098.8, 1166.4, 1342.7, 1422.6, 1453.6, 1592.9, 3136.4, 3258.2, 3888.1

663.0 i, 123.3, 142.1, 270.3, 400.4, 604.3, 792.6, 989.0, 1094.2, 1148.0, 1213.2, 1367.2 1413.9, 1485.9, 1586.1, 3051.1, 3198.8, 3729.7

892.8i, 140.9, 156.2, 337.4, 479.6, 642.6, 848.3, 1074.9, 1082.7, 1272.9, 1330.9, 1395.0, 1479.9, 1508.5, 2252.9, 3000.5, 3339.0, 3946.3

INT1

TS5

TS6

TS7 TS8

TS9

TS10

TS 10

3296

1235.0, 1285.4, 1557.9, 1817.3, 3005.8, 3089.5

489.6, 731.1, 1160.1, 1339.5, 3028.4, 3131.3

547.8, 941.7, 1377.5, 1487.1, 3834.1, 3837.1 657.3, 839.5, 1113.1, 1154.8, 1354.7, 1436.9, 1798.4, 3098.1, 3655.3

316.2, 1066.1, 1021.0, 1108.9, 1285.6, 1398.3, 1429.5, 1439.3, 2864.5, 2931.3, 2984.4, 3616.4

CH2O(S)

CH2O(T)

H2O2 HCOOH

CH3OH

16.4

451.8 i, 98.2, 182.7, 204.4, 300.2, 675.3, 973.4, 1038.5, 1196.9, 1296.5, 1383.6, 1399.2, 1543.3, 1614.8, 2288.2, 2853.2, 3090.0, 3163.5

TS15

128.4

300.5 76.7

259.6

286.2

287.4

2026.9 i, 88.8, 113.0, 252.9, 413.6, 488.9, 598.8, 915.4, 1093.5, 1103.6, 1238.1, 1327.6, 1351.9, 1448.1, 1588.3, 3022.2, 3110.5, 3896.9

TS14

101.7,142.3,177.7,204.9,254.3,512.5,625.8, 1100.9,1230.8, 625.9, 1100.9,1230.7, 1319.4, 1378.5,1438.5, 1531.4,1598.1,2936.1,3067.5,3182.8, 3248.8

15.6 16.7

1010.2 i, 206.1, 414.5, 442.3, 568.2, 621.3, 712.4, 1090.5, 1109.9, 1239.0, 1272.9, 1398.1, 1457.6, 1563.8, 1830.7, 3049.2, 3145.4, 3854.3 1248.7 i, 203.5, 475.7, 523.3, 570.9, 649.1, 862.8, 1108.8, 1210.9, 1237.4, 1331.1, 1381.5, 1483.1, 1549.4, 1648.3, 3024.9, 3119.7, 3779.3

TS12 TS13

811.4, 949.1, 1000.2, 1644.1, 3699.8, 3824.5

30.5 16.1

170.6, 228.5, 393.9, 460.9, 607.7, 916.9, 1001.2, 1101.9, 1210.3, 1252.4, 1452.5, 1487.5, 1510.0, 1542.9, 3123.7, 3218.2, 3240.4, 3891.6

INT2

H2OO

15.8 19.9

106.5, 152.9, 183.2, 234.7, 333.7, 588.8, 657.4, 848.0, 1107.7, 1305.3, 1322.6, 1405.1, 1526.9, 1574.9, 3188.7, 3321.5, 3343.5, 3923.0

vdw2

vdw3

15.3

184.2, 217.4, 246.5, 270.5, 337.3, 660.2, 783.2, 1084.5, 1264.0, 1277.7 1307.0, 1516.7, 1687.7, 1710.3, 2942.9, 3076.2, 3210.6, 3771.5

vdw1

0

619.3

1240.8, 1507.9, 3698.7

O2H

159.1

1006.9, 1140.6, 1188.7, 1234.8, 1410.1, 2996.6, 3044.6, 3070.8, 4750.5

193.4

513.8, 624.5, 1088.7, 1222.7, 1394.2, 1516.5, 3224.2, 3375.5, 3897.5

CH3O

term values (cm
1)

CH2OH

species

Table 3. Vibrational Term Values and Moments of Inertia of Different Species Calculated at the MPWb1K/6-31þG(d,p) Level

24.9

26.4 11.9

34.9

38.5

24.8

3.9

4.11

3.9

3.9 6.0

5.9

3.8

4.0

3.3

4.1

3.1

4.6 23.6

4.6

5.2

5.9

34.5

28.1

29.9

Ii (a.u.)

24.1

25.6 10.3

31.6

33.9

23.9

3.2

3.38

3.3

3.6 4.6

5.2

3.4

3.2

3.1

3.5

2.9

3.6 23.1

4.4

4.5

4.9

32.7

28.1

26.2

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Table 4. Microcanonical Variational RRKM Results for Unimolecular Dissociation Reaction R4 N d(v,j)  #

R (Å)

a

E(ν,j)

b

E0c

10

10

Ge(E#)  10

7

Table 5. Microcanonical Variational RRKM Results for Unimolecular Dissociation Reaction R11

k (E) 

N d(v,j) 

8

#

R (Å)

10 (1/s)

a

E(ν,j)

b

E0c

Ge(E#) 

k (E) 

10

107

108 (1/s)

8

3.50 3.24

312.3 316.5

313.5 308.4

0.28210 0.32830

0.00011 0.00052

0.00012 0.00047

2.74 2.74

106.0 114.3

100.7 100.7

0.000245 0.000465

0.000002 0.000023

0.26120 1.45800

3.23

320.7

308.3

0.38140

0.00180

0.00141

2.74

118.5

100.7

0.000634

0.000057

2.69100

3.22

324.9

308.2

0.44250

0.00521

0.00353

2.73

122.7

100.7

0.000858

0.000130

4.54400

3.21

329.1

308.1

0.51280

0.01335

0.00781

2.73

131.0

100.6

0.001544

0.000557

10.82000

3.21

337.5

308.0

0.68570

0.06803

0.02974

2.73

135.2

100.6

0.002053

0.001070

15.63000

3.20

341.6

307.9

0.79140

0.14000

0.05302

2.72

143.6

100.6

0.003572

0.003531

29.64000

3.20

350.0

307.9

1.05000

0.51730

0.14770

2.72

147.8

100.5

0.004676

0.006128

39.29000

3.20 3.19

354.2 366.8

307.9 307.9

1.20800 1.82300

0.94120 4.78700

0.23360 0.78700

2.72 2.72

156.1 160.3

100.4 100.4

0.007899 0.010250

0.017140 0.027750

65.03000 81.21000

3.19

370.9

307.7

2.08700

7.85800

1.12900

2.71

164.5

100.4

0.013180

0.044120

100.40000

2.72

379.3

293.7

2.72500

18.8600

2.07500

2.71

172.8

100.3

0.021540

0.106200

147.70000

2.70

383.5

293.6

3.10900

27.9700

2.69700

2.71

177.0

100.3

0.027380

0.161100

176.40000

2.51

387.7

281.0

3.54300

39.0000

3.30000

2.70

185.4

100.2

0.043730

0.357000

244.70000

2.50

391.9

280.9

4.03300

55.0500

4.09100

2.70

189.6

100.1

0.054970

0.522200

284.80000

2.70

197.9

100.0

0.086000

1.083000

377.60000

2.70 2.69

202.1 206.3

100.0 99.9

0.107000 0.132800

1.538000 2.164000

430.60000 488.40000

2.69

214.6

99.8

0.202800

4.183000

618.40000

2.69

223.0

99.7

0.306000

7.847000

768.80000

a

Position of the bottleneck in angstrom. b Total energy available to the system in kJ mol
1. c Classical energy difference between the reactant and the transition state. d Density of states in cm
1. e Sum of states.

path for the formation of methanol and singlet molecular oxygen from CH3O þ HO2.

’ RATE CONSTANT CALCULATIONS Depends on the shape of potential energy surface of the different channels, two methods were used to calculate the rate constants. The rate constants for those channels proceed through the formation of energized intermediates were calculated by means of the multichannel RRKM-TST method and the CVT method was used to calculate the rate constants for those channels passing over saddle point or barrierless bimolecular reactions. The results from CCSD(T)/Aug-cc-pVTZ calculations were used to calculate the RRKM-TST rate constants. To calculate the CVT rate constants, the MPWb1K/6-31þG(d,p) for low level and the CCSD(T)/Aug-cc-pVTZ method for high level corrections was used. For the formation of energized intermediates INT1* and INT2* no saddle point was found. Microcanonical variational RRKM method16 was used to locate the positions of the bottlenecks for barrierless channels R4 and R11. Tables 4 and 5 show the results of microcanonical variational RRKM calculations for the entrance channels of INT1* and INT2* formation, channels R4 and R11, respectively. Standard RRKM program from Zhu and Hase17 was used to obtain the sum and density of states. To locate the position of the bottlenecks, the RRKM program searches for the minimum in the sum of states versus reaction coordinate as a function of available energy (temperature).18 In the RRKM calculations, a step size of ΔEþ= 0.8 kJ mol
1 was used. In the RRKM calculations, the external rotations were treated as being adiabatic. The ratio of the electronic partition functions was assumed to be equal 0.25. N2 was chosen as bath gas and a value of 0.5 was selected for the collision efficiency from ref 19. Sums of states was calculated according to Tardy et al.20 method, in which only a fraction of the zero-point energy (aEz) is included in the classical energy at each point along the reaction coordinate.

a

Position of the bottleneck in angstrom. b Total energy available to the system in kJ mol
1, c Classical energy difference between the reactant and the transition state. d Density of states in cm
1. e Sum of states.

A method suggested by Dean,21 which is based on the RRKM method was used to calculate the rate constants for those channels passing through INT1* and INT2* wells. Steady-state assumption for the energized intermediates leads to the following expressions for the second order rate constants of channels Rw4 to R8 and Rw11 to R13. !
Eþ þ fGðEV Þg exp w ¥ RT σBe Q1 kbi ðRw4Þ ¼ hQHO2 QCH2 OH E0 F1
F2

∑

σBe Q1 kbi ðR5Þ ¼ hQHO2 QCH2 OH

σBe Q1 kbi ðR6Þ ¼ hQHO2 QCH2 OH

kbi ðR7Þ ¼ 3297

σBe Q1 hQHO2 QCH2 OH

¥

∑E

fGðEþ V Þg exp

F1
F2

0

fGðEþ V Þg ¥

∑E

exp

!
Eþ k6 ðEÞ RT

F1
F2

0

fGðEþ V Þgexp ¥

∑E ðF1
F2Þðk 0

!
Eþ k5 ðEÞ RT

!
Eþ kvdw1 ðEÞk7 ðEÞ RT


vdw1 ðEÞ þ k7 ðEÞ þ wÞ

dx.doi.org/10.1021/jp112081r |J. Phys. Chem. A 2011, 115, 3291–3300

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ARTICLE

Figure 4. Arrhenius plot of the calculated rate constants for various channels of CH2OH þ HO2 reaction at 760 Torr pressure of N2. Solid line, dashed line, and dotted line represent the results for reaction R1 from ref 3 and for reaction R2 from ref 5 and total rate of consumption of the reactants from ref 6, respectively. Symbols are defined as (black square) R5, (green circles) R6, (light-blue triangle) R7, (magenta diamond) Rw4, (dark-blue triangle) R0 10, (dark-green triangle) R10, and (þ) R9 from the present study.

σBe Q2 kbi ðRw11Þ ¼ hQHO2 QCH3 O

σBe Q2 kbi ðR12Þ ¼ hQHO2 QCH3 O

σBe Q2 kbi ðR13Þ ¼ hQHO2 QCH3 O

¥

∑E k

fGðEþ V Þg

∑E k 0

¥

exp

!
Eþ k12 ðEÞ RT


11 ðEÞ þ k12 ðEÞ þ k13 ðEÞ þ w

fGðEþ V Þg exp

∑E k 0

exp

!
Eþ w RT


11 ðEÞ þ k12 ðEÞ þ k13 ðEÞ þ w

0

¥

fGðEþ V Þg

!
Eþ k13 ðEÞ RT


11 ðEÞ þ k12 ðEÞ þ k13 ðEÞ þ w

where F1 and F2 are defined as: F1 ¼ k
4 ðEÞ þ k5 ðEÞ þ k6 ðEÞ þ kvdw1 ðEÞ þ w F1 ¼

kvdw1 ðEÞk
vdw1 ðEÞ k
vdw1 ðEÞ þ kvdw1 ðEÞ þ w

where kbi(Rw4) and kbi(Rw11) are the rate constants for the stabilization of energized intermediates INT1* and INT2* under collision at 760 Torr N2 pressure, respectively. kbi(R5) to kbi(R13) are the rate constants for the corresponding channels. Be is the ratio of the electronic partition functions for association reactions R4 and R11 that was set to a value of 0.25 (association of two radicals), h is the Planck constant, Q#1 and Q#2 are the products of translational and rotational partition functions of the bottlenecks for the entrance channels of INT1* and INT2* intermediates respectively, QHO2, QCH3O, and QCH2OH are the partition functions of the reactants, G(Eþ V ) is the sum of the vibrational states of the corresponding transition states at internal energy Eþ V , w(∼Zβc[A]) is the collisional stabilization for

Figure 5. Arrhenius plot of the calculated rate constants for various channels of CH3O þ O2H reactions at 760 Torr pressure of N2. Solid line represents the result for reaction R3 from ref 4. Symbols are defined as (red circle) R12, (blue triangle) R13, (light-blue diamond) R15, (green triangle) Rw11, and (þ) R14 from the present study.

energized intermediates INT1* and INT2*, in which βc is the collision efficiency, and kx(E) is the microcanonical rate coefficient for the corresponding step in the energy range of E to E þ dE, which is calculated from the quotient of the sum of states to the density of states of the corresponding step. The Arrhenius plots for reactions Rw4 to R7 are shown in Figure 4 and for reactions Rw11 to R13 are shown in Figure 5, which are compared with the available data in the literature. As shown in Figure 4, channels R5, R6, and R7 are the major channels in the reaction of CH2OH þ HO2 with the HCOOH, H2O, H2O2, and CH2O(s) as the major products. Our calculated rate constants for these channels are in good agreement with the results reported by Tsang3,4 and Held and Dryer.5 In Figure 5, we have compared our calculated rate constants for different channels of CH3O þ HO2 reaction with the reported data by Tsang and Hampson for reaction R3.4 Our calculated rate constants for those channels proceeds over the singlet surface, reactions R12 and R13, that lead to the formation of H2O2, H2OO, and CH2O(S) are much slower than the reported rate constant by Tsang and Hampson4 at lower temperatures. Our calculations indicated there are 27.2 and 27.5 kJ mol
1 barriers for reactions R12 and R13 respectively, whereas Tsang and Hampson suggested no barrier for reaction R3. Our results in Figure 5 indicate that the rate constant for the stabilization process Rw11 on the singlet surface is more important than the rate of reactions R12 and R13 in CH3O þ HO2 system. Nonlinear least-squares fitting to the calculated rate constants at the CCSD(T)/Aug-cc-pVTZ level in Figures 4 and 5 gave the following rate expressions in L mol
1 s
1 unit. kW4 ¼ 9:7  109 T
1:85 exp ð1:9kJ mol-1 =RTÞ k5 ¼ 3:6  109 T 0:12 exp ð
1:9kJ mol-1 =RTÞ k6 ¼ 6:3  108 T 0:28 exp ð3:4kJ mol
1 =RTÞ k7 ¼ 6:8  108 T 0:21 exp ð1:9kJ mol
1 =RTÞ 3298

dx.doi.org/10.1021/jp112081r |J. Phys. Chem. A 2011, 115, 3291–3300

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ARTICLE

kw11 ¼ 2:6  1012 T
3:50 exp ð0:2 kJ mol
1 =RTÞ k12 ¼ 9:1  T 1:53 expð
26:72 kJ mol
1 =RTÞ k13 ¼ 7:6  T 1:4 expð
25:72 kJ mol
1 =RTÞ As shown in Scheme 1, the produced water oxide in channel R7 isomerizes to hydrogen peroxide via channel R8. The highpressure rate constant expression for reaction R8 according to RRKM calculations at the CCSD(T)/Aug-cc-pVTZ level was found as; k8 ¼ 1:6  10 T 12

0:42


1


1

exp ð
7:9kJ mol =RTÞs

Channels R9 and R14 on the triplet surfaces and R0 10 on the singlet surface proceed through the corresponding saddle points TS9, TS14, and TS0 10, respectively. Canonical variational transition-state theory (CVT)22,23 calculations were performed to calculate the rate constants for these channels. GAUSSRATE9.1 program,24 which is an interface between POLYRATE9.3.125 and Gaussian 03 program, was employed in our CVT calculations. The CVT rate constant, kCVT, can be calculated at temperature T, by minimizing the generalized TST rate constant, kGT(T,s), as a function of s: " # kB T Q GT ðT, sCVT Þ
VMEP ðsCVT Þ CVT exp k ðTÞ ¼ σ h Q R ðTÞ kB T where s is the arc length along the MEP measured from the saddle point; sCVT is the value of s at which kGT(T,s) has a minimum, σ is the reaction path degeneracy; kB and h are the Boltzmann and Planck constants respectively, VMEP (sCVT) is the classical MEP potential at s = sCVT, and QGT(T, sCVT) and QR(T) are the internal (rotational, vibrational, and electronic) partition functions of the generalized transition state at s = sCVT and reactants, respectively. The Page
McIver algorithm was used to follow the minimum energy path (MEP).26 We performed a generalized normal-mode analysis projecting out frequencies at each point along the path.27 With this information, we can calculate both the vibrational partition function along the MEP and the ground state vibrationally adiabatic potential curve VaG ðsÞ ¼ VMEP ðsÞ þ εGint ðsÞ where εintG(s) is the zero-point energy at s from the generalized normal mode vibrations orthogonal to the reaction coordinate. A step size of 0.02 (amu)1/2 bohr was used to calculate each individual point along the MEP, and a Hessian calculation was performed at each 0.06 (amu)1/2 bohr. To account for the quantum effects on the motion along the reaction coordinate, kCVT (T) is multiplied by a ground-state transmission coefficient, κCVT/G (T), which accounts for tunneling and nonclassical reflection effects.22,28 kCVT=G ðTÞ ¼ kCVT=G ðTÞkCVT ðTÞ Small curvature tunneling approximation was used to calculate the rate constants.22,29 In performing the dynamics calculations for reactions R9, R14, and R0 10 the geometries of all the stationary points were optimized at the MPWb1K level of theory along with the 6-31þG(d,p) basis set. The intrinsic reaction coordinate or MEP was constructed at the MPWb1K/6-31þG(d,p) for low

level calculations and at the CCSD(T)/Aug-cc-pVTZ level for high level corrections. The CVT rate constants for channels R9, R0 10, and R14 are shown in Figures 4 and 5. The following expressions for the rate constants of reactions R9, R0 10, and R14 were obtained from nonlinear least-squares fitting to the corresponding data in Figures 4 and 5. k9 ¼ 1:3  106 ðT=298Þ5:31 exp ð
60:1kJ mol
1 =RTÞL mol
1 s
1 k010 ¼ 5:7  104 ðT=298Þ3:2 exp ð
6:8kJ mol-1 =RTÞL mol
1 s
1 k14 ¼ 1:9 101 ðT=298Þ10:67 exp ð
106:1kJ mol
1 =RTÞL mol
1 s
1

To the best of our knowledge, no data are reported for the rate constants of reactions R9, R0 10, and R14 in the literature. The formation of methanol and molecular oxygen on the triplet surfaces (reactions R10 and R15) are bimolecular barrier less reactions. We have ignored the possible effect of the formation of van der Waals complexes vdw2 and vdw3 on the rate of reactions R10 and R15 because of the shape of their potential energy surfaces. The transition-state theory was used to calculate their rate constants. The Arrhenius plot for channels R10 and R15 are shown in Figures 4 and 5. As shown in Figure 4, the calculated rate constants for channels R10 and R0 10 are not important in CH2OH þ HO2 system. In Figure 5, our calculated rate constant for reaction R15 to form methanol and triplet molecular oxygen was found to be comparable with the rate constant of reaction R3 reported by Tsang and Hampson.4 Tsang and Hampson ignored the formation of methanol in their study on the kinetics of reaction of CH3O þ HO2. It seems they reported the total rate constant for the consumption of the reactants CH3O and HO2 instead of reporting the rate constant just for reaction R3. Our results indicated reaction R15 to form methanol and molecular oxygen is the major channel in the reaction of CH3O with HO2. The rate constants for reactions R10 and R15 were found to be independent to the temperature with values of; k10 = 2.0 108 L mol
1 s
1 and k15 = 1.4  108 L mol
1 s
1.

’ CONCLUSIONS The first thorough study on the mechanism and kinetics of the reactions between hydroxy methyl radical (CH2OH) or methoxy radical (CH3O) with hydroproxy radical (HO2) has been theoretically investigated on the lowest singlet and triplet surfaces. To calculate the potential energy surfaces, the CCSD(T) method along with the Aug-cc-pVTZ basis set was used that is accepted as a relatively good method in constructing the PESs.30 Two energized intermediates INT1* and INT2* on the singlet surfaces are involved in the kinetics of the title reactions. Although the formation of INT1* and INT2* are not reported for the title reactions yet, their formation in some other systems are reported in the literature.12
15 The nonadiabatic transitions between singlet and triplet potential energy surfaces are often important in some dissociation-association reactions. We were not able to detect any intersection point between the singlet (channels R6 and R8) and triplet (channel R9) potential energy surfaces. The reason could be due to the large energy gap between the potential energy surfaces of these channels. 3299

dx.doi.org/10.1021/jp112081r |J. Phys. Chem. A 2011, 115, 3291–3300

The Journal of Physical Chemistry A A method based on the RRKM and TST was used to calculate the rate constants for those channels that proceed through the formation of energized intermediates INT1* and INT2*. Strong collision assumption was used in our RRKM-TST calculations. Canonical variational transition-state theory along with the smallcurvature tunneling approximation was used to calculate the rate constants of direct H abstraction channels. The major products in CH2OH þ HO2 reaction are CHOOH, H2O, CH2O(S), and H2O2 via the formation of H2OO on the singlet surface, while the major products of CH3O þ HO2 reaction are methanol and molecular oxygen. To the best of our knowledge, the only reported study on the kinetics of reaction of CH3O þ H2O is a literature review by Tsang and Hampson (reaction R3).4 As shown in Figure 5, our calculated rate constant for the formation of methanol, reaction R15, is in good agreement with the rate constant reported by Tsang and Hampson for reaction R3 to form H2O2 and CH2O. It seems they reported the total rate of consumption of the reactants instead of rate constant for the formation of H2O2 and CH2O.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

ARTICLE

(22) Truhlar, D. G.; Isaacson, A. D.; Garrett, B. C. In Theory of Chemical Reaction Dynamics; Baer, M., Ed.; CRC Press: Boca Raton, 1985; Vol. 4,p 65. (23) Truhlar, D. G.; Garrett, B. C. Annu. Rev. Phys. Chem. 1984, 35, 159. (24) Corchado, J. C.; Chuang, Y.-Y.; Coitino, E. L.; Truhlar, D. G. GAUSSRATE, version 9.1/P9.1-G03/G98/G94; Department of Chemistry and Supercomputer Institute, University of Minnesota: Minneapolis, MN, 2003. (25) Corchado, J. C.; Chuang, Y.-Y.; Fast, P. L.; Villa, J.; Hu, W.-P.; Liu, Y.-P.; Lynch, G. C.; Nguyen, K. A. F. Jackels, C. F.; Melissas, V. S.; Lynch, B. J.; Rossi, I.; Coitino, E. L.; Fernandez Ramos, A.; Pu, J.; Albu, T. V.; Steckler, R.; Garrett, B. C.; Isaacson, A. D.; Truhlar, D. G. POLYRATE, version 9.3; Department of Chemistry and Supercomputer Institute, University of Minnesota: Minneapolis, MN, 2003. (26) Page, M.; McIver, J. W. J. Chem. Phys. 1988, 88, 922. (27) Miller, W. H.; Handy, N. C.; Adams, J. E. J. Chem. Phys. 1980, 72, 99. (28) Garrett, B. C.; Truhlar, D. G.; Grev, R. S.; Magnuson, A. W. J. Phys. Chem. 1980, 84, 1730. (29) Truhlar, D. G.; Kuppermann, A. J. Am. Chem. Soc. 1971, 93, 1840. Liu, Y.-P.; Lynch, G. C.; Truong, T. N.; Lu, D.-h.; Truhlar, D. G.; Garrett, B. C. J. Am. Chem. Soc. 1993, 115, 2408. Liu, D.-h.; Truong, T. N.; Melissas, V. S.; Lynch, G. C.; Liu, Y.-P.; Garrett, B. C.; Steckler, R.; Isaacson, A. D.; Rai, S. N.; Hancock, G. C.; Lauderdale, J. C.; Joseph, T.; Truhlar, D. G. Comput. Phys. Commun. 1992, 71, 235. (30) Crittenden, D. L. J. Phys. Chem. A 2009, 113, 1663.

’ ACKNOWLEDGMENT The financial support from the Research Council of Shiraz University is acknowledged. ’ REFERENCES (1) Li, J.; Zhao, Z.; Kazakov, A.; Chaos, M.; Dryer, F. L.; Scire, J. J., Jr. Int. J. Chem. Kinet. 2007, 39, 109. (2) Abou-Rachid, H; El Marrouni, K.; Kaliaguine, S. J. Mol. Struct. (Theochem). 2003, 631, 241; 2003, 621, 293. (3) Tsang, W. J. Phys. Chem. Ref. Data 1987, 16, 471. (4) Tsang, W.; Hampson, R. F. J. Phys. Chem. Ref. Data 1986, 15, 1087. (5) Held, T, J.; Dryer, F. L. J. Int. J. Chem. Kinet. 1998, 30, 805. (6) Grotheer, H. H.; Riekert, G.; Meier, U.; Just, T. Ber. Bunsenges. Phys. Chem. 1985, 89, 187. (7) Frisch, M. J. et al. Gaussian 03, revision B.01; Gaussian, Inc.: Pittsburgh, PA, 2003. (8) Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2004, 108, 6908. (9) Møller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618. (10) Scuseria, G. E.; Schaefer, H. F., III J. Chem. Phys. 1989, 90, 3700. Pople, J. A; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968. (11) Gonzales, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154. Gonzales, C.; Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523. (12) Belgian Institute for Space Aeronomy, http://tropo. aeronomie.be/. (13) Vlasenko, A.; Macdonald, A. M.; Sjostedt, S. J.; Abbatt, J. P. D. Atmos. Meas. Tech. 2010, 3, 1055. (14) Lay, H. T.; Bozzelli, J. W. J. Phys. Chem. 1997, 101, 9505. (15) Plesni
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dx.doi.org/10.1021/jp112081r |J. Phys. Chem. A 2011, 115, 3291–3300