Article pubs.acs.org/JPCA
Mechanistic and Kinetic Study of CF3CHCH2 + OH Reaction Yunju Zhang,† Jingyu Sun,† Kai Chao,§ Hao Sun,†,‡ Fang Wang,† ShuWei Tang,† Xiumei Pan,† Jingping Zhang,† and Rongshun Wang*,† †
Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University, Renmin Road 5268., Changchun, Jilin 130024, P.R. China ‡ Institute of Theoretical Chemistry, State Key Laboratory of Theoretical and Computational Chemistry, Jilin University, Changchun, Jilin 130023, P.R. China § Ningxia Entry-Exit Inspection and Quarantine Bureau, Yinchuan, Ningxia 750001, P.R. China S Supporting Information *
ABSTRACT: The potential energy surfaces of the CF3CHCH2 + OH reaction have been investigated at the BMC-CCSD level based on the geometric parameters optimized at the MP2/6-311++G(d,p) level. Various possible H (or F)-abstraction and addition/elimination pathways are considered. Temperature- and pressuredependent rate constants have been determined using Rice−Ramsperger−Kassel− Marcus theory with tunneling correction. It is shown that IM1 (CF3CHCH2OH) and IM2 (CF3CHOHCH2) formed by collisional stabilization are major products at 100 Torr pressure of Ar and in the temperature range of T < 700 K (at P = 700 Torr with N2 as bath gas, T ≤ 900 K), whereas CH2CHOH and CF3 produced by the addition/elimination pathway are the dominant end products at 700−2000 K. The production of CF3CHCH and CF3CCH2 produced by hydrogen abstractions become important at T ≥ 2000 K. The calculated results are in good agreement with available experimental data. The present theoretical study is helpful for the understanding the characteristics of the reaction of CF3CHCH2 + OH.
1. INTRODUCTION Hydrofluorocarbons (HFCs) contain neither chlorine nor bromine atoms and thus have no potential for depleting ozone.1 Therefore, HFCs have been proposed as alternative compounds for chlorofluorocarbons (CFCs). However, HFCs still have potential contributions to the greenhouse effect because of the presence of C−F bonds, which are expected to cause absorption in the terrestrial infrared radiation region 800− 1200 cm−1.2,3 To evaluate their global warming effects and environmental impact, it is necessary to determine the lifetimes of HFCs. In general, these HFC compounds, having CH bonds, can be oxidized in the atmosphere by highly reactive radical species, such as O and OH radicals, a reaction that could contribute to degradation of HFCs.4 The CC bond of unsaturated HFCs increases the reactivity of unsaturated HFCs with radicals and decreases the atmospheric lifetimes and global warming potentials (GWPs). The unsaturated fluorinated hydrocarbons are considered good replacements.5 There are numerous experimental and theoretical studies of the reactions of the OH radical with fluorinated unsaturated compounds up to now.6−14 However, only two experimental kinetic studies have been reported for the reaction of CF3CH CH2 with the OH radical. In 1997, Orkin et al.15 investigated the kinetics of the reaction of CF3CHCH2 with OH using the flash photolysis−resonance fluorescence method. The rate constant was obtained at 100 Torr pressure of Ar and over the temperature range 252−370 K. Andersen et al.16 have also © 2012 American Chemical Society
measured the rate constant by using smog chamber/FTIR techniques, and the rate constant at 296 K is (1.36 ± 0.25) × 10−12 cm3 molecule−1 s−1. One recent paper has reported theoretical calculations of the rate constant of the addition of OH radical to CF3CHCH2 using DFT, MP2, and CCSD(T) methods,17 however, without detailed potential energy surface and kinetics investigations. Moreover, no other experimental or theoretical studies have been performed to date. Therefore, in the present article, we carried out ab intio calculations of potential energy surface for the reaction of CF3CHCH2 with the OH radical. Multichannel RRKM theory and transition state theory have been employed to calculate the rate constants over a wide range of temperatures and pressures.
2. COMPUTATIONAL METHODS All the electronic structure calculations are carried out using the GAUSSIAN 03 suit of programs.18 The optimized geometries and harmonic frequencies of all the reactants, products, intermediates, transition states, and complexes are obtained at the restricted or unrestricted second-order Moller−Plesset perturbation theory (MP2)19 with the 6-311++G(d,p) basis set. The number of imaginary frequencies (0 or 1) indicates whether a minimum or a transition state has been located. Received: August 10, 2011 Revised: February 28, 2012 Published: March 2, 2012 3172
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The rate constants for the important product channels have been calculated statistically using the transition-state theory (TST) and the multichannel RRKM theory34 that had been successfully used to deal with the complex reactions.35−37
The connections of the transition states between designated reactants and products have been confirmed by intrinsic reaction coordinate (IRC) calculations.20,21 The geometries optimized at the MP2/6-311++G(d,p) level are used to perform single-point energy calculations for all the species using BMCCCSD22 method. The energy of expression for BMC-CCSD is given in
3. RESULTS AND DISCUSSION The optimized geometries of the reactants and products along with the available experimental values are shown in Figure 1. Intermediates, transition states, and complexes are depicted in Figure 2. It can be seen from Figure 1 that the calculated bond lengths and angles at the MP2/6-311++G(d,p) level are in good agreement with experimental values. The schematic potential energy surfaces (PESs) of the OH + CF3CHCH2 reaction at the BMC-CCSD//MP2/6-311++G(d,p) + ZPE level are presented in Figure 3a,b. The moment of inertia and rotational symmetry numbers of the major species involved in this reaction are deposited in Table S1 as Supporting Information. The Z-matrix (Cartesian coordinates) and harmonic vibrational frequencies of the major species found on the PES are shown in Table S2 and S3 (Supporting Information), respectively. The geometric parameters used in the following discussion are the MP2/6-311++G(d,p) results. The energies discussed in this work are at the BMC-CCSD + ZPE level, unless otherwise stated. As shown in Figures 3a,b, two kinds of reaction pathways in the OH + CF3CHCH2 reaction are revealed. They are the H (or F)-abstraction mechanism and addition−elimination mechanism. We now consider them individually. 3.1. H-Abstraction and F-Abstraction Reactions. Figure 3a shows five abstraction possible pathways. For CF3CH CH2, three different H-abstraction channels have been found. The OH radicals can abstract one of the H atoms in the end CH2 group directly to form products of P1 (CF3CHCH(I) + H2O) or P2 (CF3CHCH(II) + H2O) via TS1 and TS2, respectively. The corresponding barrier heights are calculated to be 6.58 and 6.98 kcal/mol, respectively. The OH radical can also attack the H atom in the CH group to form P3 (CF3CCH2 + H2O) via TS3 after clearing a barrier of 6.21 kcal/mol. In the Cs symmetry CF3CHCH2 molecule, the three F atoms in the −CF3 group rotated on the time scale of the chemical reaction and can be divided into two types: the inplane F atom, and the two out-of-plane F atoms. Therefore, there are two F-abstraction pathways (in-plane and out-of-plane F-abstraction) via TS4 and TS5 to form P4 (CF2CHCH2(I) + HOF) and P5 (CF2CHCH2(II) + HOF). As shown in Figure 2, in saddle points TS4 and TS5, the elongation of the breaking bond is greater than that of the forming bond. Thus, TS4 and TS5 are product-like, and the two channels will proceed via an early transition state, respectively. The relative energies of TS4 and TS5 are 87.19 and 79.66 kcal/mol, respectively. In comparison with hydrogen elimination, the fluorine abstraction is a strongly endothermic route and has a higher barrier. Thus the fluorine abstraction channels are of no important for the title reaction. 3.2.1. Addition−Elimination Mechanism. Initial Association. The OH radical and CF3CHCH2 approach each other forming a weakly bound complex CR1. Complex CR1 contains two C−O bonds that are very long (i.e., 3.179 and 3.300 Å); thus CR1 is a loosely bound van der Waals complex. The energies of CR1 are −4.70 kcal/mol relative the reactant R (CF3CHCH2 + OH). This addition process is a barrierfree association. Subsequently, the reaction bifurcates into two different pathways. The O atom of the OH radical attacks the
E(BMC‐CCSD) = E(HF/6‐31B(d)) + cHΔ (HF/MG3|6‐31B(d)) + c1Δ(MP2|HF/6‐31B(d)) + c 2Δ(MP2|HF/MG3|6‐31B(d)) + c3Δ(MP4(DQ)|MP2/6‐31B(d)) + c4Δ(CCSD|MP4(DQ)/6‐31B(d)) + ESO
where Δ(L2|L1/B) = E(L2/B) − E(L1/B) and Δ(L/B2|B1) = E(L/B2) − E(L/B1) and Δ(L2|L1/B2|B1) = E(L2/B2) + E(L1/B1) − E(L1/B2) − E(L2/B1). Also, the scaling coefficients cH, c1, c2, c3, and c4 take values of 1.06047423, 1.09791, 1.33574, 0.90363, and 1.55622, respectively, as given in ref 22. To test the accuracy of BMC-CCSD energies and the predicted heats of reactions, we have also carried out the calculations using G3(MP2)23 and CCSD(T)24/6-311++G(d,p) levels. It appears that the entrance barriers of the main reaction pathways at BMC-CCSD level are smaller than those at the other two levels and release the most energy, but there is a very good linear correlation among the three sets of data for relative energies and relative enthalpies, respectively. Our calculated results indicate that the BMC-CCSD method is appropriate for the calculations of the OH + CF3CHCH2 reaction because (1) the mean unsigned error for barrier height is only 0.71 kcal/mol22 and (2) the rate constant is determined mainly by the entrance barrier height and the calculated entrance barrier of 4.43 (TS6) and 4.47 (TS7) kcal/mol, which are smaller than the two latter methods, respectively. Moreover, it has been shown that the BMC-CCSD method gives accurate energies for many reactions.25−27 To gain an insight on the multireference feature for the stationary points, the T1-diagnostic28,29 values of the CCSD(T) wave functions are monitored for each point. For closed and open shell systems, values exceeding 0.02 and 0.045 are suspect.28−31 Evidently, the T1 values of closed-shell and open-shell species calculated at the CCSD(T)/ 6-311++G(d,p) level are smaller than 0.02 and 0.045, which indicates multireference character in the CCSD(T) wave functions is not a problem. The major problem in the application of unrestricted single determinant reference wave function is that of contamination with higher spin states. The severe spin contamination could lead to a worse estimate of the barrier height.32,33 We examine the spin contamination before and after annihilation for the radical species and transition states involved in the title reaction. The expectation values of ⟨S2⟩ range from 0.75 to 0.96 before annihilation expect TS4 (1.02) and TS5 (1.19), and after annihilation, ⟨S2⟩ is 0.75−0.76 (the exact value for a pure doublet is 0.750) except TS5 (0.875). Fortunately, the two species are not important on the potential energy surface, which would not affect reaction mechanism. 3173
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Figure 1. Optimized structures of the reactants and products for the reaction of OH with CF3CHCH2 at the MP2/6-311++G(d,p) level. Distances are given in angstroms and angles are in degrees. The values in italics are experimental data from ref 46.
2.75 kcal/mol with the barrier of 32.62 kcal/mol. In the second channel, the H atom in the CH group of IM2 can be eliminated to form product P9 (CF3COHCH2 +H) via transition TS11 after clearing a barrier of 37.87 kcal/mol. The last pathway is that IM2 dissociates to product P10 (c-CF2OCHCH2 + HF) via five-membered ring transition state TS12 after overcoming a barrier of 72.25 kcal/mol. Due to the higher barrier height, the production of P10 is expected to be negligible at low and moderate temperatures. 3.2.3. Isomerization of IM1 (CF3CHCH2OH) and IM2 (CF3CHOHCH2). The H atom in the OH group of IM1 migrates to the middle C atom to give IM3 (CF3CH2CH2O) via afour-membered-ring transition state TS13 with a barrier of 34.15 kcal/mol. In TS13, the broken OH bond is 1.253 Å and the formed CH bond is 1.307 Å, which are 30.2% and 19.7% longer than the corresponding equilibrium bond lengths of OH in isolated IM1 and CH in IM3. The elongation of the breaking bond is greater than that of the forming bond. Thus, TS13 is a later transition state. IM3, lying 22.11 kcal/mol below the initial reactant, can decompose to product P11 (CF3CH2 + CH2O) by CC rupture via TS14 facing a barrier of 18.75 kcal/mol. Alternatively, IM1 can isomerize to IM4 (CF3CH2CHOH) by a 1,2-H shift via TS15 with a high barrier of 38.08 kcal/mol, followed by C−C cleavage to product P8 (CH2CHOH + CF3) via TS16 surmounting a barrier of 34.73 kcal/mol. Similar to the channel of IM1, IM2 can rearrange to isomer IM5 (CF3CH(O)CH3) by a 1,3-H shift via a four-membered ring transition state TS17, which faces a barrier height of 33.65 kcal/mol. IM5, −17.64 kcal/mol relative to the initial reactant, by breaking the CC bond, either gives rise to P12 (CF3CHO + CH3) via TS18 or yields P13 (CH3CHO + CF3) via TS19. The barrier heights are 12.15 and 12.79 kcal/mol, respectively. The relative energies of TS18 and TS19 are
terminal C of CF3CHCH2, forming the intermediate IM1 (CF3CHCH2OH) via TS6 after overcoming a barrier of 4.43 kcal/mol. On the other hand, the O atom of the OH radical can also add to the central unsaturated carbon atom of CF3CHCH2 via TS7, forming the intermediate IM2 (CF3CHOHCH2) after clearing a barrier height of 4.77 kcal/mol. The relative energy of TS6 is only 0.34 kcal/mol lower than that of TS7. In TS6 and TS7, the forming C−O bond is 2.019 and 2.042 Å, respectively, and the geometries of the CF3CHCH2 moiety of IM1 and IM2 are nearly the same as those of the CF3CHCH2, namely, both TS6 and TS7 are early transition states. As shown in Figure 3b and Table 1, IM1 and IM2 are chemically activated because the association is exothermic by 28.22 and 30.87 kcal/mol, respectively, which means that the initial association provides IM1 and IM2 with enough energy to undergo decomposition and intramolecular rearrangement. In the following part, we will focus on the formation pathways of various products proceeding via IM1 and IM2, respectively. 3.2.2. Decomposition of IM1 (CF3CHCH2OH) and IM2 (CF3CHOHCH2). Two decomposition pathways for IM1 and three for IM2 have been investigated, and the energies are shown in Table 1. Starting from IM1, the first pathway is that IM1 eliminates an H atom to form the product P6 (CF3CHCHOH +H) via the transition state TS8 with the barrier height of 32.92 kcal/mol. The other channel involves the H atom of the OH group migrating to the end F atom, while, the C−F bond breaks to give P7 (CF2CHCH2O + HF) via TS9, a six-membered ring transition state. The barrier height, 44.69 kcal/mol, is rather high. Moreover, product P7 is the most unstable product on the PES. Apparently, the pathway of product P7 is not important to the overall reaction. As for IM2, three decomposition channels are taken into account. In the first pathway, IM2 directly eliminates the CF3 radical to form product P8 (CH2CHOH + CF3) via transition state TS10 lying above the recants by 3174
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Figure 2. Optimized structures of intermediates and transition states for the reaction of OH with CF3CHCH2 at the MP2/6-311++G(d,p) level. Distances are given in angstroms and angles are in degrees.
1,2-H shift via TS20 with a higher barrier of 39.00 kcal/mol. Subsequently, the intermediate IM6 can dissociate to P14 (CH3COCF3 + H) by CH bond cleavage via TS21, needing
5.49 and 4.85 kcal/mol below the reactant. The products P12 and P13 are about 10.08 and 9.77 kcal/mol lower than the reactant. IM2 can also isomerize to IM6 (CF3COHCH3) by a 3175
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Figure 3. (a) Schematic energy diagram of the hydrogen abstraction channels in the reaction of OH + CF3CHCH2. (b) Schematic energy diagram of the addition/elimination channels in the reaction of OH + CF3CHCH2. All relative energies are calculated at the BMC-CCSD//MP2/6-311++ G(d,p) level.
normal modes of IM1 or IM2 using the following exponential expression:
to surmount a barrier of 38.90 kcal/mol. The isomerization and dissociation barrier heights are so high that this pathway is not important for the title reaction. 3.3. Rate Constants Calculation. To understand the reaction kinetics and compare the rate constants with available experimental values, the rate constants for the CF3CHCH2 + OH reaction are carried out by using the multichannel RRKM theory and transition state theory. For the two essentially barrierless pathways, namely, OH + CF3CHCH2 → CR1 → IM1 or IM2, the rate constants are calculated using the variational transition state theory. The energies along the reaction coordinate (RCO) are calculated at the BMC-CCSD level of theory (Figure S1, Supporting Information). The variation of the dividing surface of the transition state was carried out in the range RCO = 1.4−3.2 Å with the step size of 0.1 Å. The vibrational frequencies for the variational transition state are considered to be those of the reactant (CF3CHCH2 and OH), together with four “intermolecular frequencies” after excluding the C−O stretch vibration along the reaction coordinate, which are calculated by extrapolating the corresponding
v(R ) = v(R e)e−α(R − R e)
where Re is the equilibrium C−O bond length in IM1 or IM2 and the parameter α is set to 1. The following reaction paths are included in the calculation:
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Table 1. ZPE Corrections, T1 Diagnostic Values and Relative Energies for Various Species as Well as Relative Enthalpies of Intermediates and Products at 298 K (Energies in kcal/mol) species
ZPE
T1a
ΔEb
ΔEc
ΔEd
ΔHe
ΔHf
ΔHg
R: CF3CHCH2 + OH P1: CF3CHCH(I) + H2O P2: CF3CHCH (II) + H2O P3: CF3CCH2 + H2O P4: CF2CHCH2(I) + HOF P5: CF2CHCH2(II) + HOF P6: CF3CHCHOH + H P7: CF2CHCH2O + HF P8: CH2CHOH + CF3 P9: CF3COHCH2 + H P10: c-CF2OCHCH2 + HF P11: CF3CH2 + CH2O P12: CF3CHO + CH3 P13: CH3CHO + CF3 P14: CH3COCF3 + H IM1 IM2 IM3 IM4 IM5 IM6 CR1 TS1 TS2 TS3 TS4 TS5 TS6 TS7 TS8 TS9 TS10 TS11 TS12 TS13 TS14 TS15 TS16 TS17 TS18 TS19 TS20 TS21
41.42 38.91 41.42 42.04 44.55 41.42 39.74 42.67 43.30 38.90 41.42 40.79 40.16 42.67 38.90 45.98 45.17 46.09 46.26 45.95 45.91 44.24 40.98 41.03 41.02 45.14 44.15 44.15 44.12 41.62 43.53 43.94 40.97 41.80 43.57 43.81 42.93 44.35 43.18 43.34 44.09 42.66 40.21
0.012, 0.010 0.024, 0.010 0.024, 0.010 0.025, 0.010 0.015, 0.014 0.024, 0.014 0.014, 0.000 0.017, 0.011 0.013, 0.015 0.013, 0.000 0.015, 0.011 0.013, 0.017 0.015, 0.008 0.016, 0.015 0.014, 0.000 0.014 0.013 0.014 0.014 0.015 0.015 0.012 0.025 0.018 0.021 0.028 0.034 0.024 0.024 0.021 0.023 0.022 0.022 0.023 0.017 0.022 0.015 0.022 0.016 0.021 0.023 0.015 0.022
0.00 −2.22 −1.92 −1.43 80.86 71.94 3.52 6.15 3.48 5.46 −2.35 −10.67 −9.02 −8.49 −5.82 −23.58 −25.74 −21.09 −29.09 −16.64 −31.53 −0.25 10.52 11.31 10.68 91.70 85.89 3.20 3.61 11.83 22.80 8.42 14.78 47.01 10.35 0.25 16.94 6.33 7.44 −1.33 0.32 15.77 8.00
0.00 −3.91 −3.73 −3.23 82.82 69.51 0.31 6.89 0.99 1.91 −2.87 3.62 −9.09 −8.62 −7.23 −23.38 −27.05 −21.03 −30.54 −22.14 −33.10 −0.16 10.05 10.51 9.80 91.22 85.23 2.11 2.76 8.18 20.16 5.48 11.17 44.78 9.48 −0.88 14.21 3.74 6.27 −3.26 −1.50 12.84 5.86
0.00 −7.05 −6.95 −6.74 83.22 67.46 −1.06 5.51 −0.89 1.04 −5.03 −11.38 −10.08 −9.77 −7.30 −27.26 −29.87 −22.11 −33.53 −17.64 −36.08 −4.70 6.58 6.98 6.21 87.19 79.66 −0.27 0.07 5.66 17.43 2.75 8.00 42.38 6.89 −3.36 10.82 1.20 3.78 −5.49 −4.85 9.13 2.82
0.00 −1.58 −1.43 −0.78 83.88 71.70 3.58 6.32 2.96 5.51 −2.27 −10.68 −8.66 −8.89 −5.54 −22.47 −24.66 −20.39 −28.15 −15.84 −30.45 1.66 11.98 12.62 12.08 93.46 86.56 4.35 4.66 12.62 23.22 9.66 15.56 48.11 10.86 1.19 17.93 7.63 7.94 −0.23 1.35 16.68 9.31
0.00 2.49 2.69 3.23 88.92 75.64 6.56 13.24 6.65 8.13 3.38 9.78 −2.55 −2.85 −0.77 −18.16 −21.86 −16.22 −25.48 −17.22 −27.91 5.86 15.62 15.93 15.32 97.08 90.01 7.37 7.93 13.08 24.68 10.83 16.05 49.99 14.09 4.17 19.30 9.16 10.88 1.95 3.64 17.87 11.26
0.00 −6.83 −6.72 −6.45 83.11 67.41 −1.09 5.68 −1.42 1.08 −4.96 −11.39 −9.72 −10.18 −7.02 −28.22 −30.87 −23.48 −34.66 −18.91 −37.08 −4.86 5.97 6.21 5.54 86.87 78.26 −1.19 −0.95 4.36 15.78 1.91 6.68 41.42 5.32 −4.49 9.73 0.43 2.21 −6.47 −5.89 7.97 2.05
a
T1 diagnostic values are calculated at the CCSD(T)/6-311++G(d,p) level. bAt the CCSD(T)/6-311++G(d,p) + ZPE level. cAt the G3(MP2) + ZPE level. dAt the BMC-CCSD + ZPE level. eThe calculated heats of reaction at 298 K at the CCSD(T)/6-311++G(d,p) level. fThe calculated heats of reaction at 298 K at the G3(MP2) level. gThe calculated heats of reaction at 298 K at the BMC-CCSD level.
where “*” represents the vibrational excitation of the intermediates (IM1 and IM2). The steady-state approximations for energized intermediates (IM1* and IM2*) lead to the following expressions, which were previously derived for bimolecular reactions taking place via a long-lived intermediate:38
kP6(E) =
kP8(E) =
3
×
Q t⧧Q r⧧ αa e−Ea / RT h Q OHQ CF CHCH 3
×
∫0
Q t⧧Q r⧧ αb e−Ea / RT h Q OHQ CF CHCH
kIM1(E) =
∫
3
2
× (1) 3177
(2)
Q t⧧Q r⧧ αa e−Ea / RT h Q OHQ CF CHCH
⧧
∞ k2(E) N2(E ) −E⧧ / RT e dE ⧧ k1 + k2 + w
2
∞ k4(E) N2(E⧧) −E⧧ / RT e dE ⧧ k3 + k4 + w 0
∫0
2
⧧
∞ w1(E) N2(E ) −E⧧ / RT e dE ⧧ k1 + k2 + w
(3)
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Article IM1 IM2 for IM1···N2 and IM2···N2; (εAr = 92.12 K, εAr = 89.16 K, IM1 IM2 σAr = 3.22 Å, σAr = 3.21 Å) for IM1···Ar and IM2···Ar. The weak collision approximation is used for the intermediate. The rate constants for direct hydrogen abstraction can be readily obtained using the conventional transition-state theory.
Q t⧧Q r⧧ α kIM2(E) = b e−Ea / RT h Q OHQ CF CHCH 3
×
kII(E) =
2
∞ w2(E) N2(E⧧) −E⧧ / RT e dE ⧧ k3 + k4 + w 0
∫
(4)
⧧ QTS k T kabs(T ) = κ1 B e−E1/(RT ) h Q CF CHCH Q OH 3 2
Q t⧧Q r⧧ αa e−Ea / RT h Q OHQ CF CHCH 3
×
∫0
where κ1 is the tunneling factor, kB and h are Boltzmann and ⧧ Planck constants, respectively. QTS , QCF3CHCH2, and QOH are the TS1 (or TS3), CF3CHCH2, and OH partition functions, respectively. E1 is the energy barrier of TS1 (or TS3). For the reaction of OH + CF3CHCH2, the calculated rate constants for direct hydrogen abstraction are denoted kP1 and kP3, and the rate constants for P6, P8, IM1, and IM2 by addition step are denoted kP6, kP8, kIM1, and kIM2 at the bath gas of Ar, respectively. The total second-order rate constant is noted as ktot, ktot = kP1 + kP3 + kP6 + kP8 + kIM1 + kIM2. The branching ratios are kP1/ktot, kP3/ktot, kP6/ktot, kP8/ktot, kIM1/ktot, and kIM2/ktot. To distinguish the results of N2, the superscript “N2”is applied, i.e., N2 2N N2 N N2 2 N N2 kP1 kP3 , kP6 , k2P8 , kIM1 , kIM2 , and ktot . The following results discussed are based on the conditions of bath gases of Ar and N2. The temperature dependence of the total and important individual rate constants are plotted in Figure 4a,b at the
2
∞ (k2 + k4 + w)(E) N2(E ⧧) −E⧧ / RT
k1 + k2 + k3 + k4 + w
e
dE ⧧ (5)
The microcanonical rate constant is calculated using the RRKM theory as follows: k i(E) = αik
Ii⧧ Ni(E − Ei⧧) I jΙΜ
hρj(E)
i = 1, 2, 3; j = 1, 2 (6)
In eqs 1−6, αa and αb are the statistical factor for the reaction paths a and b, and αi is the statistical factor (degeneracy) for the ith reaction path. Ea represents the energy barrier of TS6 and TS7 for the reaction steps a and b. QOH and QCF3CHCH2 are the total partition functions of OH and CF3CHCH2, respectively, and Qt ⧧ and Qr⧧ are the translational and rotational partition functions of the transition state TS6 and TS7 for the association. N2(E⧧) is the number of states for the association transition state (TS6 and TS7) with excess energy E⧧ above the association barrier. ki(E) is the energy-specific rate constant for the ith channel. κ is the tunneling factor; Ii⧧ and IjIM are 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; ρj(E) is the density of states at energy E of the intermediate j; Ni(E − Ei⧧) is the number of states at the energy above the barrier height for transition state i; and the density of states and the number of states are calculated using the extended Beyer−Swinehart algorithm.39,40 The collision deactivation rate ω = βcZLJ[M]; in here, βc is the collision efficiency calculated using Troe’s weak collision approximation41 with the energy transfer parameter −⟨ΔE⟩. The simple expression for collisional energy transfer (−⟨ΔE⟩)42,43 is βc 1 − βc1/2
≅
−⟨ΔE⟩ FEkT
This expression holds nearly exactly at the weak collision limit −⟨ΔE⟩ ≪ FEkT for all collision models.43,44 The factor FE is set to 1.0 empirically. Because there is no experimental value of −⟨ΔE⟩ for our system, n consideration of the experimental rate constants, argon and nitrogen are employed as bas gases with the −⟨ΔE⟩ value of 200 cm−1 for the energy transfer in N2 and 100 cm−1 for Ar, respectively. ZLJ is the Lennare-Jones collision frequency and [M] is the concentration of the base gas M. But the Lennard-Jones parameters for the intermediate are not available, so the collision efficiency is estimated using the Lennard-Jones potential (V(r) = 4ε[(σ/r)12 − (σ/r)6]) by fitting the interaction energies calculated at the MP2/6-311++ G(d,p) level for IM1···N2 and IM1···Ar. It is estimated that (εNIM1 = 376 K, 2εN IM2 = 111.81 K, σNIM1 = 2.74 Å, 2σN IM2 = 2.94 Å) 2 2
Figure 4. Temperature dependence of the total and individual rate constants for the OH + CF3CHCH2 reaction. (a) At 100 Torr Ar and (b) at 700 Torr N2. 3178
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pressure of 700 Torr of N2 and 100 Torr Ar, respectively. For comparison, the available experimental data are also included. N is in good agreement with the relevant The calculated k2tot experiment data, but the trend of ktot in Ar is opposite at 252− 370 K relative to the data reported by Orkin et al.15 Fortunately, the rate difference between theoretical and experimental values is very small. The difference of the above results may be due to the bath gas, experimental conditions, and measuring technique. However, it can be seen from Table S4 (Supporting Information) that the calculated overall rate constant is insensitive to the bath gas and different pressures in the entire N2 = 1.64 × 10−12 cm3 molecule−1 s−1 temperature range (at 298 K, ktot Ar at 760 Torr N2 and ktot = 1.65 × 10−12 cm3 molecule−1 s−1 at 100 Torr Ar). The similarities are also found in Figure 4a,b, which are reflected in the variational trend of the overall and branching rate constants. The overall rate constants are almost a constant at first and then exhibit positive temperature dependence with the increasing temperatures. The rate constant for direct hydrogen abstraction and those for P6 and P8 channels increase monotonically, and the rate constants of IM1 and IM2 collisional stabilization channels are almost the same at first but decrease rapidly with rising temperatures. The branching ratios for the important products are also shown in Figure 5a,b. Under 100 Torr of Ar, first the yield of stabilized IM1 and IM2 radicals are almost unchanged with increasing temperatures and then sharply drop with increasing temperatures (e.g., 74.8% at 200 K
down to 48.7% at 700 K, and 0.4% at 1400 K for IM1), whereas the yield of product P8 almost becomes a constant at 200−400 K, sharply rises with increasing temperatures (at 400−1000 K), from 0.1% at 400 K to a maximal point of 62.4% at 1000 K, and drops with increasing temperatures (T ≥ 1200 K), from 57.9% at 1200 K to 11.8% at 3000 K. It can be seen from Figure 5a that P1 and P3 are the major products at T ≥ 2000 K, 47.7% for P1 and 35.3% for P3 at 3000 K. Similar changes occur for the 700 Torr N2 as shown in Figure 5b, whereas the results for 700 Torr N2 have differences, the major products are IM1 and IM2 at T ≤ 900 K, and P8 plays an important role during the temperature range 1000−1600 K, from 38.1% at 1000 K up to 48.5% at 1200 K then down to 11.8% at 3000 K. It implies that temperature, pressure, and bath gas will affect the yield of products. The calculated high-pressure limit rate constants (kinf) at P = 1010 Torr are shown in Figure 6 and Figure S2 (Supporting
Figure 6. High-pressure limit rate constants for the addition/ elimination channels of the OH + CF3CHCH2 reaction in the temperature range 200−300 K at 1010 Torr Ar.
Information). As for the hydrogen abstraction channels, the rate constants are independent of pressure. Therefore, only highpressure limit rate constants for the addition/elimination channel were calculated in the temperature range 200−3000 K. kinf(IM1), kinf(IM2), kinf(P6) ,and kinf(P8) decrease with rising temperatures (e.g., negative temperature dependence). It can be seen that IM1 and IM2 deactivation is dominant for the addition/elimination channel, whereas the formation of P6 and P8 can be negligible. The rate constants of IM1 and IM2 deactivation are always a few orders of magnitude higher than rate constants of P6 and P8. Similar conclusions are found in N2. We also select the temperature of 298 K and perform the pressure dependence of the rate constants for the addition channel (Figure 7 and Figure S3, Supporting Information). The rate constant kII is pressure independent in the pressure ranges 10−10−10−5 and 101−1010 Torr, respectively, and is pressure dependent in the pressure range 10−4−100 Torr. The individual rate constants are also sensitive to pressure. In Figure 7, it is apparent that the IM1 and IM2 deactivation can compete with each other at the entire pressure range investigated. Moreover, IM1 and IM2 deactivation is dominant at P > 10−2 Torr. Figure 7 shows that kIM1 and kIM2 exhibit positive pressure dependence when the pressure is lower than 10−2 Torr, and they are constant above 10−1 Torr. Different from kIM1 and kIM2, kP8 has negative
Figure 5. Branching ratios of the important product channels for the OH + CF3CHCH2 reaction in the temperature range 200−3000 K. (a) At 100 Torr pressure of Ar and (b) at 700 Torr pressure of N2. 3179
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reactivity of C atom of the CC double bond attack on the O atom of OH. Thus, theoretically, the trend of the reaction rate constant is k(CH3CHCH2) > k(CF3CHCH2), which is quantitatively in line with the experimental results. The experimental rate constant (298 K) is 3.46 × 10−11 cm3 molecule−1 s−1 for CH3CHCH2 with OH and (1.54 ± 0.05) × 10−11 cm3 molecule−1 s−1 for CF3CHCH2 with OH, respectively. Hydrogen abstraction channels cannot be ignored because they are dominant at higher temperatures.
4. CONCLUSIONS A detailed theoretical survey on the complicated doublet PESs of the reaction of CF3CHCH2 with the OH radical has been performed at the MP2 and BMC-CCSD levels of theory. The rate calculations, to quantitatively predict the major products have been performed in the temperature range 200−3000 K using RRKM theory. The calculated results revealed that the tunneling effect is significant only for hydrogen abstraction at lower temperatures. However, the strong tunneling effect at the lowest temperature considered cannot influence our kinetic calculations. Two possible products channels including the H (or F)-abstraction and the addition/elimination reaction pathways have been found on the doublet potential energy surfaces. The addition adducts IM1 and IM2 are the dominant products below 700 K in bas gas Ar (below 900 K for N2). A significant fraction of the total reaction leads to enols at high temperatures. When the temperatures are above 2000 K, the hydrogen abstraction channel becomes important. The present work will provide useful information for understanding the process of OH radical with other halogen substituted unsaturated hydrocarbons.
Figure 7. Pressure dependence of the rate constants for addition/ elimination channels of the OH + CF3CHCH2 reaction at 10−10− 10−10 Torr with Ar at 298 K.
pressure dependence above 10−2 Torr, and it also becomes a constant below 10−4 Torr when it is close to the kII. Similar to the case for kP8, one can make the same conclusions for kP6. At P = 10−3 Torr, the rate constant for IM1, IM2 and P8 almost take the same value. These results indicate that stabilization of IM1 and IM2 are dominant at P > 10−2 Torr and P8 plays an important role P < 10−4 Torr. An unsymmetrical Eckart potential was used to calculate the tunneling factor κ. For the addition/elimination mechanism, the κ was always in the range 1.2−1.0 from 200 to 3000 K at the bath gas of Ar. The calculated results indicated that the tunneling effect is not significant at the whole temperature region (200− 3000 K) for the addition/elimination mechanism. For the main direct abstraction step, the κ is relatively large at the low temperatures. The values of κ at 200, 300, and 500 K are 3.9 × 104, 254, and 12.4 at the bath gas of Ar, respectively. However, this significant tunneling effect cannot influence our kinetic calculations significantly. For example, at 200 K, even if the tunneling correction is included, the dominant channel is still the addition with a rate of 1.43 × 10−12 cm3 molecule−1 s−1 because this value is about 4 orders of magnitude higher than that for the abstraction pathway (about 2.87 × 10−16 cm3 molecule−1 s−1). From 1000 to 3000 K, κ is in the range 1.7−1.1 for direct hydrogen abstraction. It is indicated that the tunneling effect is not significant at higher temperatures. Similar conclusions take place at the bath gas of N2. 3.4. Comparison with Similar Reactions. To give a deeper understanding of the reaction mechanism of CF3CH CH2 + OH, it is worthwhile to compare the title reaction with the analogous reaction CH3CHCH2 + OH,44,45 which has been extensively studied both experimentally and theoretically. All have addition and hydrogen abstraction mechanisms. By comparing the theoretical results, we find that both reactions involve the same initial association, that is, the O atom in OH group attacking on the CC double bond to form weakly bound complex with no barrier, and the association process leading to the stable intermediates. However, because the CF3 radical with higher electronegativity strongly attracts electrons located at the CC double bond, the electron density on the CC double bond is reduced, which leads to a decrease of the
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ASSOCIATED CONTENT
S Supporting Information *
Tables of moments of inertia and rotation symmetry numbers, Cartesian coordinates, harmonic vibrational frequencies, and calculated rate constants. Figures of the calculated minimum energy path, high-pressure limit rate constants, and the pressure dependence of the rate constants. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel: 0431-85099511. Fax: 0431-85099511. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work supported by the Science Foundation for Young Teachers of Northeast Normal University. We also appreciate the invaluable comments and good suggestions from the reviewers.
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REFERENCES
(1) Wallington, T. J.; Schneider, W. F.; Worsnop, D. R.; Nielsen, O. J.; Sehested, J.; DeBruyn, W.; Shorter, J. A. Environ. Sci. Technol. 1994, 28, 320A−326A. (2) Houghton, J. T.;et al., Eds. Climate Change 2001: The Scientific Basis; Cambridge University Press: Oxford, U.K., 2000. (3) Sekiya, A.; Misaki, S. CHEMTECH 1996, 26, 44−48.
3180
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(4) Atkinson, R. In Air Pollution, the Automobile, and Public Health; Watson, A. I., Bates, R. R., Kennedy, D., Eds.; National Academic Press: Washington, DC, 1988; pp 99−132. (5) Finlayson-Pitts, B. J.; Pitts-Jr, J. N.; Chemistry of the Upper and Lower Atmosphere; Academic Press: London, 2000. (6) Tokuhashi, K.; Takahashi, A.; Kaise, M.; Kondo, S.; Sekiya, A.; Fujimoto, E. Chem. Phys. Lett. 2000, 325, 189−195. (7) Hurley, M. D.; Ball, J. C.; Wallington, T. J. J. Phys. Chem. A 2007, 111, 9789−9795. (8) Du, B. N.; Feng, C. J.; Zhang, W. C. Chem. Phys. Lett. 2009, 479, 37−42. (9) Papadimitriou, V. C.; Talukdar, R. K.; Portmann, R. W.; Ravishankara, A. R.; Burkholder, J. B. Phys. Chem. Chem. Phys. 2008, 10, 808−820. (10) Acerboni, G.; Beukes, J. A.; Jensen, N. R.; Hjorth, J.; Myhre, G.; Nielsen, C. J.; Sundet, J. K. Atmos. Environ. 2001, 35, 4113−4123. (11) Perry, R. A.; Atkinson, R.; Pitts, J. N. J. Chem. Phys. 1977, 67, 458−462. (12) Mashino, M.; Ninomiya, Y.; Kawasaki, M.; Wallington, T. J.; Hurley, M. D. J. Phys. Chem. A 2000, 104, 7255−7260. (13) Zhang, Y. J.; et al. Comput. Theor. Chem. 2011, 965, 68−83. (14) Hurley, M. D.; Wallington, T. J.; Javadi, M. S.; Nielsen, O. J. Chem. Phys. Lett. 2008, 450, 263−267. (15) Orkin, V. L.; Huie, R. E.; Kurylo, M. J. J. Phys. Chem. A 1997, 101, 9118−9124. (16) Sulbaek-Andersen, M. P.; et al. J. Photochem. Photobiol. A Chem. 2005, 176, 129−135. (17) Thomsen, D. L.; Jørgensen, S. Chem. Phys. Lett. 2009, 481, 29− 33. (18) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; J r-Vreven, T.; Kudin, K. N.; Burant, J. C.; et al.; Gaussian 03, revision B.03; Gaussian, Inc.: Wallingford, CT, 2004. (19) Moller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618−622. (20) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154− 2161. (21) Gonzalez, C.; Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523− 5527. (22) Lynch, B. J.; Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2005, 109, 1643−1649. (23) Baboul, A. G.; Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. J. Chem. Phys. 1999, 110, 7650−7657. (24) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479−483. (25) Sun, J. Y.; Tang, Y. Z.; Sun, H.; Jia, X. J.; Pan, X. M.; Wang, R. S. J. Comput. Chem. 2010, 31, 1126−1134. (26) Sun, J. Y.; Tang, Y. Z.; Jia, X. J.; Wang, F.; Sun, H; Wang, R. S. J. Chem. Phys. 2010, 132, 064301−1. (27) Sun, J. Y.; Wang, R. S.; Wang, B. S. Phys. Chem. Chem. Phys. 2011, 13, 16585−16595. (28) Lee, T. J.; Taylor, P. R. Int. J. Quantum Chem. 1989, S23, 199− 207. (29) Rienstra-Kiracofe, J. C.; Allen, W. D.; Schaefer, H. F. III. J. Phys.Chem. A 2000, 104, 9823−9840. (30) Peiró-García, J.; Nebot-Gil, I. Chem. Phys. Chem. 2003, 4, 843− 847. (31) Peiró-García, J.; Nebot-Gil, I. J. Comput. Chem. 2003, 24, 1657− 1663. (32) Schlegel, H. B.; Sosa, C. Chem. Phys. Lett. 1988, 145, 329−333. (33) Ignatyev, I. S.; Xie, Y.; Allen, W. D.; Schaefer, H. F. J. Chem. Phys. 1997, 107, 141−155. (34) Holbrook, K. A.; Pilling, M. J.; Robertson, S. H.; Unimolecular Reactions; J. Wiley: Chichester, U.K, 1996. (35) Hou, H.; Wang, B. S.; Gu, Y. S. J. Phys. Chem. A 2000, 104, 320−328. (36) Hou, H.; Wang, B. S. J. Chem. Phys. 2007, 127, 054306−1. (37) Tang, Y. Z.; Wang, R. S.; Wang, B. S. J. Phys. Chem. A 2008, 112, 5295−5299. (38) Berman, M. R.; Lin, M. C. J. Phys. Chem. 1983, 87, 3933−3942.
(39) Stein, S. E.; Rabinovitch, B. S. J. Chem. Phys. 1973, 58, 2438− 2445. (40) Astholz, D. C.; Troe, J.; Wieters, W. J. Chem. Phys. 1979, 70, 5107−5116. (41) Klopman, G.; Joiner, C. M. J. Am. Chem. Soc. 1975, 97, 5287− 5288. (42) Troe, J. J. Chem. Phys. 1977, 66, 4745−4757. (43) Troe, J. J. Phys. Chem. 1979, 83, 114−126. (44) Zhou, C. W.; Li, Z. R.; Li, X. Y. J. Phys. Chem. A 2009, 113, 2372−2382. (45) Vega-Rodriguez, A.; Alvarez-Idaboy, J. R. Phys. Chem. Chem. Phys. 2009, 11, 7649−7658. (46) NIST Computational Chemistry Comparison and Benchmark Database. http://srdata.nist.gov/cccbdb/.
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