Mechanistic and kinetic study of the OH + C2H5CN reaction

Chemical Physics Letters 463 (2008) 315–321

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Mechanistic and kinetic study of the OH + C2H5CN reaction Jingyu Sun, Yizhen Tang, Hao Sun, Yaru Pan, Xiujuan Jia, Xiumei Pan, Rongshun Wang * Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University, Renmin Road 5268. Changchun, Jilin 130024, PR China

a r t i c l e

i n f o

Article history: Received 7 June 2008 In final form 13 August 2008 Available online 15 August 2008

a b s t r a c t The reaction of OH radical with C2H5CN has been studied using various quantum chemistry methods. The geometries were optimized at the MP2/6-311G (d, p) and BHandHLYP/6-311G (d, p) levels. The singlepoint energies were calculated using G3(MP2) and BMC-CCSD methods. Both hydrogen abstraction and addition/elimination mechanisms have been investigated. The kinetics of this reaction were studied using the TST and multichannel RRKM methodologies over a wide temperature range of 150–3000 K. The calculated results indicate that a-H abstraction channel is the most feasible at lower temperatures. At higher temperatures, the C-addition step leading to stable intermediate C2H5C(O)NH (IM2) is apparently dominant. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction The gas-phase chemistry of cyanides is of interest not only in fundamental organic chemistry but also in interstellar [1,2] and planetary high atmosphere chemistry [3,4]. A number of studies for the reactions of HCN, CH3CN, C2H5CN, n-C3H7CN and i-C3H7CN with some free radicals (OH, O(3P), C2H, F, and Cl) have devoted to atmospheric, combustion and interstellar chemistry [5–8]. Propionitrile (C2H5CN) as an important cyanide can react with hydroxyl radical, which should be considered as possible sink for the poisonous propionitrile. Thus the mechanisms and kinetics of the reaction of OH with C2H5CN are of importance in gas-phase chemistry. Examination of the literature reveals only one earlier experimental study about this reaction [9]. In 1981, Harris and co-workers measured the rate constants by the flash photolysis–resonance fluorescence technique in the temperature range from 298 to 423 K, and obtained the expression of 2.69  1012 exp [(800 ± 176)/T] cm3 molecule1 s1. The reaction of OH with C2H5CN is similar to CH3CN with OH reaction that has been well investigated experimentally and theoretically [10– 14]. However, to our knowledge, no theoretical study for the reaction of C2H5CN with OH has been reported so far. Based on our previous work of the O(3P) reacting with C2H5CN [15] and the reaction of CH3CN with OH, we have investigated the mechanisms of the reaction of OH with C2H5CN by carefully mapping the detailed PES. The kinetics for this reaction has analyzed using the TST theory and multichannel Rice–Ramsperger– Kassel–Marcus (RRKM) theory. The aim of this work is to provide further insight into the reaction mechanism and give the reliable estimate of the rate con-

stants for practical interstellar, atmospheric and combustion applications. 2. Computational methods All the electronic structure calculations were carried out using the GAUSSIAN 03 [16]. The optimized geometries and harmonic frequencies of the reactants, products, local minima and transition states were obtained at the MP2/6-311G (d, p) level. To verify the reliability of MP2/6-311G(d, p) geometries, the optimizations of the key species were also performed at the BHandHLYP/6311G(d, p) level. The major problem in the application of the unrestricted calculation is that of contamination with higher spin states. The expectation values of S2 range from 0.940 to 0.758 before annihilation at the UMP2/6-311G(d, p) level. After annihilation, S2 is from 0.768 to 0.750, therefore, the spin contamination is not severe. Connections of the transition states between designated local minima have been confirmed by intrinsic reaction coordinate (IRC) calculations [17,18] at the same levels. Further, single-point calculations were carried out using the G3(MP2) [19] and BMC-CCSD [20] methods based on the MP2/6-311G (d, p) geometries. For BMC-CCSD method, only a brief description is given here. Single-point energy evaluations were performed at the CCSD/631B(d) and MP2/MG3 levels of theory, respectively. Finally, the energy expression for BMC-CCSD is given in

EðBMC-CCSDÞ ¼ EðHF=6-31BðdÞÞ þ cH DðHF=MG3j6-31BðdÞÞ þ c1 DðMP2jHF=6-31BðdÞÞ þ c2 DðMP2jHF=MG3j6-31BðdÞÞ þ c3 DðMP4ðDQ ÞjMP2=6-31BðdÞÞ

* Corresponding author. Fax: +86 431 85099511. E-mail address: [email protected] (R. Wang). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.08.055

þ c4 DðCCSDjMP4ðDQÞ=6-31BðdÞÞ þ ESO

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where D(L2|L1/B) = E(L2/B)  E(L1/B) and D(L/B2|B1) = E(L/ B2)  E(L/B1). And cH, c1, c2, c3 and c4 take values of 1.06047423, 1.09791, 1.33574, 0.90363 and 1.55622, respectively. The high-level composite methods (CBS-QB3, ROCBS-QB3, G3(MP2)-RAD, G3X(MP2)-RAD) and various DFT procedures (BMK, MPWB1K, B3LYP, MPW1PW91, B3P86, M05-2X, M06-2X and so on) have investigated bond dissociation energies and radical stabilization energies for some test molecules including C2H5CN [21– 23]. The results indicated that composite methods, M05-2X and M06-2X have good performance. However, single point energies involved of all species are found at the BMC-CCSD level in our paper. It is in view of two aspects in the accuracy of the calculations at the BMC-CCSD level: (i) The mean unsigned error for barrier height is only 0.71 kcal/mol [20]; and (ii) The rate constant is determined mainly by the barrier height, and the calculated entrance barrier of 1.55 kcal/mol (a-H abstraction channel) is in good agreement with experimental value of 1.59 ± 0.35 kcal/mol [9]. Therefore the calculations of BMC-CCSD are more appropriate to this reaction. On the basis of PES, we calculated the rate constants for the whole reaction and the individual product channels using the transition-state theory (TST) and multichannel RRKM theory. In fact, RRKM-TST method has been successfully used to deal with many bimolecular reactions [24–26]. A modified computer program written for the C2H5CO + O2 reaction by Hou and Wang [26] was employed in the present kinetic calculations.

3. Results and discussion The MP2/6-311G(d, p) optimized structures of the reactants, products, local minima and transition states are shown in Fig. 1, along with the available experimental values and the BHandHLYP/6-311G(d, p) geometry parameters of the key species. The profile of potential energy surface for this reaction predicted by BMC-CCSD method is described in Fig. 2 in order to clarify the reaction mechanisms. The ZPE corrections and relative energies for various species are summarized in Table 1. It is shown that relative energies at G3(MP2)//MP2/6-311G(d, p) and BMC-CCSD//MP2/6-311G(d, p) levels are in good accordance. The moments of Inertia and harmonic vibrational frequencies for the key species are listed in Table 2. Compared with experimental values, the MP2/6-311G(d, p) frequencies may be more suitable than the BHandHLYP/6-311G(d, p) results for this reaction system. Thus the geometric parameters used in the discussion are the MP2/6-311G(d, p) results. The energies discussed in the present work are at the BMC-CCSD + ZPE level, unless otherwise stated.

3.1. Reaction mechanism As shown in Figs. 1 and 2, three kinds of reaction pathways in the OH + C2H5CN reaction were revealed. They are hydrogen abstraction, C-addition/elimination and N-addition/elimination. We now consider them individually.

3.1.1. Hydrogen abstraction For the reaction of C2H5CN with OH, hydrogen atom can be abstracted from a-position (CH2) and b-position (CH3). Since two a-position hydrogen atoms are equivalent and indistinguishable, only one transition state (TS1) is located along with the relative energy of 1.55 kcal/mol. The length of breaking CH bond and forming HO bond in TS1 are elongated by 0.112 and 0.319 Å when compared with the corresponding regular bond length,

respectively. On the reactant and product sides, two complexes (CR1 and CP1) were found. The hydrogen bonds of OH and NH bond in CR1 are 2.945 and 2.362 Å, respectively. The hydrogen bond in CP1 is located between N and the abstracted H with the bond length being 2.432 Å. Then P1 (CH3CHCN + H2O) is generated with the relative energy of 25.62 kcal/mol. Three hydrogen atoms in methyl group are unequivalent, namely, in-plane H-abstraction (denoted as Ha) and out-plane Habstraction (one denoted as Hb). The corresponding two saddle points, TS2 and TS3, are located, and their relative energies are 2.77 and 1.90 kcal/mol, respectively, which are higher than TS1. In TS2 and TS3 structure, the breaking CHa and CHb bond and the forming HaO and HbO bond are stretched by 0.103 Å, 0.110 Å, 0.346 Å and 0.333 Å compared with the corresponding regular bond length, respectively. The complexes at the entrance valleys are labeled as CR2 and CR3, and there are no product complexes. The lengths of hydrogen bond HaO in CR2 and HbN in CR3 are 2.774 and 2.222 Å, respectively. P2 (CH2CH2CN + OH) is produced, along with the energy of 16.98 kcal/mol lower than reactants. Seen from Fig. 2, the barrier height of TS1 is lower than that of TS2 and TS3, and P1 is more stable than P2, so P1 is predominantly formed.

3.1.2. C-addition/elimination The OH radical can add to the C atom of the CN group in C2H5CN via a transition state TS4 with the formation of the intermediate C2H5C(OH)N (IM1). The forming CO bond in TS4 is 1.836 Å, and the barrier height of TS4 is 2.91 kcal/mol. The newly formed CO bond in IM1 is 1.359 Å, and the C„N triple bond becomes double bond gradually. IM1 is chemically activated since the association is exothermic by 23.32 kcal/mol. Subsequently, IM1 decomposes to form the final product P3 (C2H5 + HOCN) via TS5. This is a CC bond scission process. The breaking CC bond length in TS5 is stretched by 0.577 Å, and the barrier height of TS5 is 32.80 kcal/ mol with respect to IM1. IM1 is apparently hard to climb TS5 to form unstable P3 which lies 1.96 kcal/mol higher than the reactants. Starting from IM1, H-migration channel is found. It is 1, 4H shift from the O atom to terminal N atom leading to the C2H5 C(O)NH (IM2) via TS6. The breaking OH and the forming HN bond are 1.280 Å and 1.284 Å, respectively. The barrier height of TS6 is 33.94 kcal/mol, which is 1.14 kcal/mol higher than that of TS5. Subsequently, IM2 can decompose to form P4 (C2H5 + HNCO) via TS7. The breaking CC bond length in TS7 is elongated by 0.253 Å. The corresponding barrier height is 8.71 kcal/mol. P4 lies 22.02 kcal/mol lower than the reactants. As can be seen from Fig. 2, IM1 is stable on PES, and the barrier height of TS3 and TS4 with respect to IM1 seems a bit high. Therefore, the stabilization of the IM1 (C2H5C(OH)N) should be important in the lower temperatures. However, with the temperatures increasing, IM1 has enough energy to climb TS4 to form IM2 instead of P3 because P3 is unstable than IM2.

3.1.3. N-addition/elimination The terminal N site of the C2H5CN molecule can be attacked by the OH radical. This initial addition reaction takes place stereospecifically, that is, only cis-C2H5CNOH (IM3) can be created. The corresponding transition state is TS8. The forming NO bond in TS8 is 1.576 Å. The energy barrier of TS8 is 22.14 kcal/mol. Surprisingly, the energy of IM3 is 23.35 kcal/mol. However, TS8 connects IM3 in the forward path indeed. It is indicated that IM3 is not enough stable to form. Starting from IM3, the CC bond scission process is possible. The corresponding transition state is TS9 as shown in Fig. 1. The breaking CC bond is 2.289 Å, and the barrier height is exceedingly high, 65.27 kcal/mol. Moreover the product of P5

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Fig. 1. Optimized geometries (in Å and degree) of the reactants, products, complexes, intermediates and transition states for the reaction of OH with C2H5CN at the MP2/6311G(d, p) level. The experimental values are indicated by asterisks [33]. The values in italics correspond to the BHandHLYP/6-311G(d, p) level.

(C2H5 + HONC) is produced via TS9, and P5 lies 61.33 kcal/mol above the reactants on PES. These results indicate that N-addition step is hard to occur because of higher reaction barrier and unstable products. Thus the N-addition/elimination channel can be negligible for the whole reaction.

Mechanism II a

2

C2 H5 CN þ OH C2 H5 CðOHÞN ðIM1 Þ ! P3 ðC2 H5 þ HOCNÞ 1

ðR4Þ

½M

! C2 H5 CðOHÞNðIM1Þ w

3

C2 H5 CðOÞNH ðIM2 Þ ðR5Þ

3.2. Kinetic calculation

4

5

We choose the most important reaction channels: two kinds of hydrogen abstraction and C-addition/elimination. The following reaction paths are included in the calculations: Mechanism I TS1

C2 H5 CN þ OH ! P1 ðCH3 CHCN þ H2 OÞ TS2

C2 H5 CN þ OH ! P2 ðCH2 CH2 CN þ H2 OÞ TS3

! P2 ðCH2 CH2 CN þ H2 OÞ

ðR1Þ ðR2Þ ðR3Þ

! P4 ðC2 H5 þ HNCOÞ

ðR6Þ

½M

! C2 H5 CðOÞNHðIM2Þ w

The conventional transition state theory (CTST) [27] is employed to estimate the rate constants for mechanism I. For mechanism II, the multichannel RRKM-TST theory is used [28]. The tunneling effect was considered using the Eckart potential [29]. The microcannonical rate constant is calculated using RRKM theory as follows:

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lision frequency. However, the Lennard–Jones parameters for the intermediates are not available, which are estimated using the Lennard–Jones potential (V(r) = 4e[(r/r)12  (r/r)6]) in which the potential well (e = 90 K) and the collisional diameter (r = 3.39 Å) were estimated with performing potential-energy surface scan at the MP2/6-311G(d, p) level for IM1N2. [M] is the concentration of the bath gas M (N2). The weak collision approximation is used for the intermediate. The individual rate constants for various product channels are

80

TS 9

P5 C 2H5+HONC

60

E (kcal/mol)

40

TS 8

20

R

R

0

IM3

TS5 TS6 TS 4 TS 2 TS1 CR 2 TS3 CR 1 CR 3

P3 C 2H5+HOCN TS 7 IM2

P2 CH2CH 2CN+H2O P4 C 2H5+HNCO

-20

IM1

kP3 ðTÞ ¼

CP1 P1 CH3CHCN+H2O

-40

kP4 ðTÞ ¼ -60

Fig. 2. The profile of potential energy surface for the OH + C2H5CN reaction. The relative energies are calculated at the BMC-CCSD + ZPE level of theory.

Q 6¼t Q 6¼r eEa =RT h Q OH Q C2 H5 CN

a

Q 6¼t Q 6¼r eEa =RT h Q OH Q C2 H5 CN

a

kIM1 ðTÞ ¼ kIM2 ðTÞ ¼

Table 1 ZPE corrections and relative energies (in kcal/mol) for various species at the three different methods Species

ZPE

ER(MP2)

R: C2H5CN + OH CR1 CR2 CR3 CP1 IM1 IM2 IM3 TS1 TS2 TS3 TS4 TS5 TS6 TS7 TS8 TS9 P1: CH3CHCN + H2O P2: CH2CH2CN + H2O P3: C2H5 + HOCN P4: C2H5 + HNCO P5: C2H5 + HONC

52.50 53.75 52.98 53.87 54.20 57.65 56.51 57.52 52.14 50.92 51.08 55.29 54.56 54.28 54.77 55.44 52.99 52.70 51.31 51.36 51.33 50.76

0.00 4.01 1.89 4.50 19.82 14.99 5.25 35.30 8.08 7.29 6.35 17.55 21.13 17.40 3.31 39.21 73.51 14.04 13.66 2.57 21.58 66.08

a b c

a

b

ER(G3(MP2))

ER(BMC-CCSD)

0.00 3.04 1.26 3.40 25.97 21.86 13.35 25.48 4.18 5.27 4.42 4.71 12.26 11.96 3.29 24.96 66.61 23.12 14.75 3.81 20.91 62.50

0.00 3.12 1.42 3.53 28.67 23.32 13.76 23.35 1.55 2.77 1.90 2.91 9.48 10.62 5.05 22.14 65.27 25.62 16.98 1.96 22.02 61.33

c

i ¼ 1; 2; 3; 4; j ¼ 1; 2

Z

Q 6¼t Q 6¼r eEa =RT h Q OH Q C2 H5 CN

a

Q 6¼t Q 6¼r eEa =RT h Q OH Q C2 H5 CN

a

1 0 1 0

Z

k2 ðEÞ N2 ðE6¼ Þe X 1 ðEÞ

k5 ðEÞk3 ðEÞ N2 ðE6¼ Þe X 1 ðEÞX 2 ðEÞ

1

x X 1 ðEÞ

0

Z

1

0

E6¼ =RT

N2 ðE6¼ Þe

dE6¼ E6¼ =RT

E6¼ =RT

k3 ðEÞx N2 ðE6¼ Þe X 2 ðEÞ

ð2Þ dE6¼ ð3Þ

dE6¼

E6¼ =RT

dE6¼

ð4Þ ð5Þ

with the following definitions

X 1 ðEÞ ¼ k1 ðEÞ þ k2 ðEÞ þ k3 ðEÞ þ x

ð6Þ

X 2 ðEÞ ¼ k4 ðEÞ þ k5 ðEÞ þ x

ð7Þ

In the above equations, a is the statistical factor (degeneracy) for the association step a; Ea is the energy barrier of TS4 for the reaction step a. QOH and Q C2 H5 CN are the total partition function of 6¼ OH and C2H5CN, respectively; Q 6¼ t andQ r are the translational and rotational partition functions of the transition state TS4 for the association. N2(E6¼) is the number of state for the association transition state (TS4) with excess energy E6¼ above the association barrier. The rate constants for hydrogen abstraction can be readily obtained using the conventional transition-state theory.

kabs ðTÞ ¼ j

At the low-level MP2/6-311G(d, p) method including ZPE corrections. The relative energies calculated at the G3(MP2)//MP2/6-311G(d, p) level. At the BMC-CCSD + ZPE level.

qffiffiffiffiffiffiffiffiffiffiffiffiffi Ni ðE  E6¼i Þ ki ðEÞ ¼ ai j I6¼i =IIM ; j hqj ðEÞ

Z

ð1Þ

where ki(E) is the energy-specific rate constant for the ith channel; ai is the statistical factor for reaction path degeneracy; j is the tunIM neling factor; I6¼ i , I j is the moments of inertia (IaIbIc, i.e. the product of Ia, Ib and Ic) of the transition state i and the intermediate j; h is Planck’s constant; qj(E) is the density of states at energy E of the intermediate j; Ni ðE  E6¼ i Þ is the number of states at the energy above the barrier height for transition state i; The density of states and the number of states are calculated using the extended Beyer– Swinehart algorithm [30,31]. The collision deactivation rate x = bcZLJ[M], in here, bc is the collision efficiency calculated using Troe’s weak collision approximation [32] with the energy transfer parameter –hDEi. The –hDEi is unknown and cannot be calculated quantitatively. In consideration of the experimental rate constants, it is found that the values around 20 cm1 for –hDEi should be reasonable to calculate the rate constants. ZLJ is the Lennard–Jones col-

kB T Q 6¼TS eE=ðRTÞ h Q OH Q C2 H5 CN

ð8Þ

where j is the tunneling factor, kB and h are Boltzmann and Planck constants, respectively. Q 6¼ TS ; Q OH ; andQ C2 H5 CN are the transition states (TS1, or TS2, or TS3), OH and C2H5CN partition functions. E is the energy barrier of the transition states (TS1, or TS2, or TS3). For the multiple-channel reaction of OH with C2H5CN, the calculated rate constants for H abstraction from CH2 group, Ha and Hb abstractions from CH3 position are denoted as k1, k2 and k3, respectively, and the overall C-addition reaction rate constant is denoted as k4. The total second-order rate constant for the OH + C2H5CN reaction is noted as k, k = k1 + k2 + k3 + k4. The branching ratios for the whole reaction are k1/k, k2/k, k3/k, and k4/k, respectively. For C-addition channel, kIM1, kIM2, kP3, kP4 represent the rate constants of IM1, IM2, P3, and P4, respectively, k4 = kIM1 + kIM2 + kP3 + kP4, and the product branching ratios are kIM1/k4, kIM2/k4, kP3/k4, kP4/k4, respectively. Fig. 3 and Table 3 present the total and individual rate constants over the temperature range of 150–3000 K and at a pressure of 50 Torr in order to compare with the previous experimental results. It is indicated that the total rate constants show strong positive temperature dependence. The calculated rate constants are in excellent with available experimental value, with the maximum relative deviation less than 4 times. For example, at 298 K, the calculated total rate constant is 2.68  1013 cm3 molecule1 s1, which is in good agreement with the experimental value of 1.94  1013 cm3 molecule1 s1. At 150–600 K, the value of k1 is much higher than that of k2, k3, and k4. The branching ratios shown in Fig. 4 indicate that the k1/k is approximately from 91% to 51% between 150 and 600 K.

J. Sun et al. / Chemical Physics Letters 463 (2008) 315–321

319

Table 2 Moments of Inertia (Ia, Ib, Ic, in a.u.) and harmonic vibrational frequencies (in cm1) of the key species for the important channels through the OH with C2H5CN reaction at the MP2/6-311G (d, p) level along with the experimental values and BHandHLYP/6-311G(d, p) results Species

Ia, Ib, Ic

Frequencies

C2H5CN

65.4, 385.7, 428.7

208(224)a [206],b 231(227), 382(416), 539(576), 799(818)[798], 854(870), 1043(1054)[1075], 1111(1137), 1128(1159), 1307(1339), 1366(1407)[1326], 1434(1473)[1465], 1496(1530), 1521(1550), 1526(1558), 2204(2480)[2264], 3091(3132)[3004], 3104(3139), 3152(3174), 3186(3206), 3191(3211)

OH

0.0, 3.2, 3.2

3852(3880)[3650]

CH3CHCN

48.2, 388.3, 425.2

69, 232, 372, 565, 610, 874, 1005, 1118, 1151, 1386, 1430, 1498, 1505, 2790, 3057, 3143, 3192, 3278

CH2CH2CN

63.3, 365.6, 405.2

113, 236, 355, 485, 601, 788, 913, 1095, 1105, 1301, 1327, 1487, 1496, 2199, 3100, 3154, 3213, 3336

H2O

2.3, 4.0, 6.3

1667(1683)[1595], 3906(3981)[3657], 4014(4077)[3756]

C2H5

17.5, 79.7, 85.8

160, 460, 820, 999, 1091, 1218, 1421, 1496, 1510, 1511, 3039, 3123, 3168, 3208, 3320

HOCN

2.8, 172.7, 175.5

433, 478, 1081, 1269, 2265, 3854

HNCO

2.2, 164.7, 166.9

558, 628, 781, 1306, 2360, 3731

IM1

169.6, 473.3, 620.5

69, 245, 251, 456, 481, 529, 597, 825, 853, 1045, 1112, 1133, 1197, 1299, 1333, 1401, 1440, 1484, 1519, 1525, 1991, 3094, 3098, 3149, 3185, 3191, 3827

IM2

183.6, 451.9, 613.3

20, 227, 267, 390, 513, 539, 792, 826, 826, 1027, 1076, 1120, 1130, 1284, 1301, 1391, 1434, 1489, 1510, 1521, 1640, 3091, 3095, 3138, 3187, 3199, 3497

TS1

353.5, 499.9, 780.6

1866i,c 89, 113, 132, 216, 221, 422, 560, 716, 806, 845, 898, 1074, 1122, 1151, 1243, 1347, 1429, 1482, 1512, 1517, 3086, 3125, 3160, 3178, 3197, 3832

TS2

79.6, 1060.7, 1109.5

1816i, 63, 87, 121, 195, 350, 407, 524, 758, 819, 863, 941, 1067, 1128, 1140, 1307, 1325, 1364, 1466, 1489, 1493, 2240, 3111, 3135, 3163, 3219, 3842

TS3

305.7, 515.2, 747.6

1940i, 86, 125, 208, 233, 354, 415, 535, 694, 840, 896, 940, 1045, 1118, 1134, 1273, 1323, 1374, 1476, 1486, 1492, 2245, 3099, 3133, 3157, 3222, 3827

TS4

184.0, 541.2, 702.8

945i, 76, 215, 231, 242, 329, 472, 494, 812, 861, 904, 1049, 1114, 1149, 1301, 1359, 1436, 1491, 1519, 1526, 2495, 3093, 3130, 3177, 3188, 3197, 3812

TS5

198.8, 522.0, 697.5

895i, 43, 185, 211, 305, 305, 457, 527, 678, 845, 859, 1035, 1098, 1113, 1241, 1283, 1419, 1498, 1500, 1509, 2386, 3066, 3157, 3168, 3196, 3273, 3805

TS6

153.5, 492.6, 623.8

1828i, 57, 220, 222, 472, 480, 738, 783, 812, 980, 1060, 1108, 1134, 1298, 1298, 1426, 1450, 1486, 1520, 1525, 1818, 2370, 3092, 3100, 3146, 3186, 3186

TS7

221.9, 426.8, 573.0

880i, 53, 226, 284, 382, 512, 595, 678, 789, 935, 947, 1030, 1091, 1139, 1251, 1261, 1411, 1490, 1495, 1518, 1865, 3070, 3151, 3163, 3211, 3254, 3508

a b c

The values in the parentheses are obtained from the BHandHLYP/6-311G(d, p) results. The experimental vibrational frequencies are listed by italics in square brackets [34–36]. i represents imaginary frequency.

And the k2/k, k3/k, and k4/k are much smaller than k1/k. It is mainly because the entrance barrier height (TS1) for a-H abstraction channel is only 1.55 kcal/mol. Thus the title reaction is dominated by a-H abstraction channel and the major products are CH3CHCN and H2O at lower temperatures. It is consistent with the experimental expectation [9] that the reaction proceeds largely or entirely by abstraction of a hydrogen atom at atmospheric conditions. However when temperatures are greater than 700 K, the total rate constants increase strongly with the increase in the temperatures. The values of k4 increase evidently when temperatures are greater than 700 K, whereas k1 increases slowly. The result indicates that the C-addition/elimination mechanism dominates the whole reaction at higher temperatures. For example, at T = 1000 K, the branching ratio of k4/k is increasing largely and about 96%. The yield of H2O and CH3CHCN decreases rapidly. In order to confirm the products of C-addition step, the branching ratios of IM1, IM2, P3 and P4 are shown in Fig. 5. The kIM1/k4 is much higher than kIM2/k4, kP3/k4 and kP4/k4 at 150–384 K. The branching ratio of kIM1/k4 is 99.7% at 298 K. The rate constants for IM2, P3 and P4 are always a few orders of magnitude lower and thus are negligible. Therefore, at temperatures below 500 K, the reaction is dominated by the stabilization of the IM1 (C2H5C(OH)N). At temperatures greater than 500 K, the yield of IM2 (C2H5C(O)NH) increases rapidly. At T = 600 and 1000 K, the kIM2/k4 is 66.2% and 99.8%, respectively. The contribution of IM1, P3 and P4 can be negligible. It is shown that IM2

(C2H5C(O)NH) becomes important at higher temperatures. Thus at higher temperatures, the stabilization of IM2 (C2H5C(O)NH) is the dominant channel. Based on PES, IM2 (C2H5C(O)NH) is a stable intermediate. 3.3. Comparison with the OH + CH3CN and O(3P) + C2H5CN reactions It is of interest to compare the reaction mechanism and kinetics of the OH + C2H5CN reaction with those of the analogous ones OH + CH3CN and O(3P) + C2H5CN. Theoretically, the detail mechanism and kinetics of OH + CH3CN was reported by two studies [14,13]. Compared with Ref. [14], it is readily found that the initial attack of the OH radical to R–CN (R@CH3, C2H5) molecules is almost in parallel: (a) the hydrogen abstraction; (b) the addition to the C atom in the –C„N group; (c) the addition to the N atom. Furthermore, Li et al. calculated the rate constant of the direct hydrogen abstraction using the conventional transition state theory (TST) and canonical variational transition state theory (CVT). Moreover, the RRKM-TST theory was employed to calculate the rate constants of addition and hydrogen abstraction channels in our investigation. On the other hand, compared with our previous study for O(3P) + C2H5CN reaction, the similar mechanisms are found, namely, hydrogen abstraction, C-addition and N-addition. The comparisons of the two reactions indicate that H-abstraction channel from methylene (CH2) group dominates the whole reaction for O(3P) + C2H5CN reaction, however, for the OH + C2H5CN

320

J. Sun et al. / Chemical Physics Letters 463 (2008) 315–321 1E-6 1.0 1E-7

k k1 k2 k3 k4 ref 9

1E-10

0.8

Branching Ratio

1E-9

1E-11 1E-12

3

-1 -1

k (cm molecule s )

1E-8

1E-13

kIM1/k4 kIM2/k4 kp3/k4 kp4/k4

0.6

0.4

0.2

1E-14 1E-15

0.0

1E-16 1E-17 0

1

3

2

5

4

0

7

6

1

Fig. 3. The total and individual rate constants along with the experimental values for the OH + C2H5CN reaction at the pressure of 50 Torr and the temperatures from 150 to 3000 K.

Table 3 The rate constants of k1, k2, k3, k4 and total rate constants k (in cm3 molecule1 s1) calculated using the TST and multichannel RRKM methodologies for the title reaction between 150 and 3000 K together with available experimental values T (K)

k1

k2

k3

k4

k

Ref. [9]

150 200 298 350 384 423 500 600 700 800 900 1000 1200 1500 1800 2000 2200 2500 2800 3000

8.28E-14 1.19E-13 2.33E-13 3.20E-13 3.89E-13 4.81E-13 7.09E-13 1.11E-12 1.65E-12 2.35E-12 3.24E-12 4.32E-12 7.17E-12 1.33E-11 2.22E-11 2.97E-11 3.86E-11 5.48E-11 7.47E-11 9.02E-11

8.27E-16 1.73E-15 6.62E-15 1.23E-14 1.78E-14 2.63E-14 5.23E-14 1.11E-13 2.08E-13 3.56E-13 5.69E-13 8.61E-13 1.74E-12 3.99E-12 7.69E-12 1.11E-11 1.54E-11 2.37E-11 3.44E-11 4.31E-11

7.14E-15 1.09E-14 2.50E-14 3.75E-14 4.81E-14 6.30E-14 1.03E-13 1.79E-13 2.91E-13 4.47E-13 6.56E-13 9.26E-13 1.68E-12 3.48E-12 6.24E-12 8.72E-12 1.18E-11 1.75E-11 2.47E-11 3.04E-11

2.85E-17 3.30E-16 3.67E-15 8.10E-15 1.30E-14 2.34E-14 9.86E-14 7.46E-13 4.10E-12 1.63E-11 5.09E-11 1.32E-10 6.04E-10 3.16E-9 1.05E-8 1.96E-8 3.33E-8 6.12E-8 9.11E-8 1.06E-7

9.08E-14 1.32E-13 2.68E-13 3.78E-13 4.68E-13 5.94E-13 9.63E-13 2.15E-12 6.25E-12 1.95E-11 5.54E-11 1.38E-10 6.15E-10 3.18E-9 1.05E-8 1.96E-8 3.34E–8 6.13E-8 9.12E-8 1.06E-7

– – 1.94E-13 2.33E-13 3.62E-13 4.14E-13 – – – – – – – – – – – – – –

2

3

4

5

6

7

1000/T

1000/T

Fig. 5. The calculated branching ratios of the products for C-addition step versus 1000(K)/T between 150 and 3000 K at the pressure of 50 Torr.

reaction, the a-H abstraction channel is the most feasible at lower temperatures; while at higher temperatures, the C-addition channel is apparently dominant. 4. Conclusion In this Letter, the mechanisms and kinetics of OH + C2H5CN were investigated employing quantum chemistry methods and RRKM theory. The hydrogen abstraction and addition/elimination channels are involved. The results show that a-H abstraction channel is important at lower temperatures, however, at higher temperatures, the C-addition/elimination channel becomes dominant and IM2 (C2H5C(O)NH) is the dominant product. The rate constant calculations show that the overall rate constants have positive temperature dependence. The calculated overall rate constant is in good agreement with the experimental value. Acknowledgements The authors thank Professor Baoshan Wang for providing the computer program. This work is supported by the National Natural Science Foundation of China (No. 20773021) and the Science Foundation for Young Teachers of Northeast Normal University (No. 20070315). The authors are thankful for the reviewer’s invaluable comments. References

1.0

Branching Ratio

0.8 k1/k k2/k k3/k k4/k

0.6

0.4

0.2

0.0 0

1

2

3

4

5

6

7

1000/T Fig. 4. The branching ratios of methylene-H abstraction (k1/k), methyl-Ha and Hb abstraction (k2/k and k3/k) and C-addition/elimination (k4/k) channels over the temperature range of 150–3000 K and at the pressure of 50 Torr.

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