Theoretical Studies on the Mechanisms and Dynamics of OH Radicals

J. Phys. Chem. A 2010, 114, 9057–9068

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Theoretical Studies on the Mechanisms and Dynamics of OH Radicals with CH2FCF2OCHF2 and CH2FOCH2F Guicai Song, Xiujuan Jia, Yang Gao, Jie Luo, Yanbo Yu, Rongshun Wang, and Xiumei Pan* Faculty of Chemistry, Institute of Functional Material Chemistry, Northeast Normal UniVersity, 130024 Changchun, People’s Republic of China ReceiVed: March 17, 2010; ReVised Manuscript ReceiVed: July 1, 2010

The mechanisms and dynamics studies of the multichannel reactions of CH2FCF2OCHF2 + OH (R1) and CH2FOCH2F + OH (R2) have been carried out theoretically. Three hydrogen abstraction channels and two displacement processes are found for reaction R1, whereas there are two hydrogen abstraction channels and one displacement process for reaction R2. The minimum energy paths are optimized at the B3LYP/6-311G(d,p) level, and the energy profiles are further refined by interpolated single-point energies (ISPE) method at the BMC-QCISD level of theory. By means of canonical variational transition state theory with small-curvature tunneling correction, the rate constants of reactions R1 and R2 are obtained over the temperature range of 220-2000 K. The rate constants are in good agreement with the experimental data for reaction R1 and estimated data for reaction R2. The Arrhenius expression k1 ) 1.62 × 10-20 T2.75 exp(-1011/T) for reaction R1 and k2 ) 3.40 × 10-21 T3.04 exp(-384/T) for reaction R2 over 220-2000 K are obtained. Furthermore, to further reveal the thermodynamics properties, the enthalpies of formation of reactants CH2FCF2OCHF2, CH2FOCH2F, and the product radicals CHFCF2OCHF2, CH2FCF2OCF2, and CHFOCH2F are calculated by using isodesmic reactions. CH2FCF2OCHF2 + OH f CHFCF2OCHF2 + H2O (R1a,R1a′)

I. Introduction Large quantities of chemicals are emitted into atmosphere, and the resulting issues relating to air quality, particularly to stratospheric ozone depletion, have given rise to international concern. Hydrofluoroethers (HFEs) contain neither chlorine nor bromine and thus have no contribution to ozone depletion. Moreover, the introduction of ether linkage -Omay lead to an even greater reactivity in the troposphere. So they have been suggested as replacement compounds for CFCs and HFCs in industrial applications.1,2 However, they may be evaluated as possible greenhouse gases. The cabon-fluorine bond(s) (C-F) in HFEs are expected to cause absorption in the terrestrial infrared radiation region of 800-1200 cm-1.2 Prior to its large-scale industrial use, assessing its atmospheric chemistry and environmental impact is necessary by determining its atmospheric lifetime. Removal of HFEs from the troposphere will essentially be initiated by reaction with OH radicals, although the reactions with Cl atoms may be of some importance in the marine boundary layer.3,4 The hydroxyl (OH) radical is an important reactive intermediate involved in combustion systems5 and in the oxidation of organic compounds in the atmosphere.6 Reactions of HFEs with OH radicals can contribute to degradation of HFEs, leading to the production of reactive species. In the present work, our attention will focus on the reactions of molecules CH2FCF2OCHF2/CH2FOCH2F with OH rasicals.

The calculations indicate that the dominant pathway in the CH2FCF2OCHF2 + OH reaction is hydrogen abstraction in the CH2F- group, and the displacement procecess are negligible because of the high barrier. For the reaction of CH2FOCH2F with OH, the reaction channels are similar to the system of CH2FCF2OCHF2 with OH. Two H atoms in the CH2F- group in CH2FOCH2F are not equivalent, divided into two types: R2a and R2a′; there is also one displacement process. Three distinct channels are found:

For the reaction of OH with CH2FCF2OCHF2, OH radicals can abstract hydrogen atoms both from CH2F- groups and from -CHF2 groups.

CH2FOCH2F + OH f CHFOCH2F + H2O (R2a,R2a′)

f CH2FCF2OCF2 + H2O (R1b) Since CH2FCF2OCHF2 has C1 symmetry, the two H atoms in the CH2F- group are not equivalent. The hydrogen abstraction in this group can be divided into two types: R1a and R1a′. While, two displacement processes are also considered in this system:

CH2FCF2OCHF2 + OH f CH2FCF2OH + CHF2O (R1c) f CH2FCF2O + CHF2OH (R1d)

* To whom correspondence should be addressed. E-mail: panxm460@ nenu.edu.cn. Phone: +86-431-85099963. Fax: +86-431-85098768.

10.1021/jp102421g  2010 American Chemical Society Published on Web 07/29/2010

f CHFOH + OCH2F

(R2b)

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Similarly to reaction R1, the displacement processe is negligible because of the higher barrier. Chen et al.7 studied experimentally the hydrogen abstraction channel of the reaction CH2FCF2OCHF2 + OH by a relative rate technique over the temperature range of 268-308 K and obtained the total rate constants fitted to be k1 ) 1.62 × 10-20 T2.75 exp(-1011/T). There are no reported experimental data of rate constant, product branching ratios, or dynamics studies for CH2FOCH2F with OH under different temperatures. However, Goto et al.8 evaluated the rate constant by using the empirical estimation method to get a value of 6.0 × 10-14 cm3 molecule-1 s-1 at 298 K for reaction R2; Chandra et al.9 proposed a semiempirical procedure for the estimation of the rate constant, then get the value of 4.7 × 10-14 cm3 molecule-1 s-1 at 298 K for reaction R2. No other theoretical studies have been reported for the two reactions to the best of our knowledge. The aim of the present study is to provide a deep insight into the dynamics nature of the reactions of CH2FCF2OCHF2 and CH2FOCH2F with OH. Moreover, the temperature used in the experiment does not cover the whole temperature range of practical interest. Therefore, theoretical studies on the accurate extrapolation of rate constants to higher temperatures for the title reaction are very desirable. To give an accurate description of the energy profile and the corresponding kinetics, a dual-level (X//Y) direct dynamics method (geometry optimization at a low level and singlepoint energy calculation at a higher level), proposed by Truhlar and co-workers,10-12 is employed in these two reaction systems. The potential energy surface information is obtained directly from electronic structure calculations at the B3LYP/6-311G(d,p) level, and BMC-QCISD theory is used to calulate the single-point energies. The rate constant for each reaction channel is calculated by the variational transition state theory (VTST)13,14 with interpolated singlepoint energies (ISPE).15 The small-curvature tunneling correction is included. Then, the total rate constants over the temperature range of 220-2000 K are obtained as well as the branching ratios. The comparisons between theoretical and experimental results are discussed. II. Computational Method By means of the Gaussian 03 program suite,16 all the electronic structure calculations are carried out. The optimized geometries and harmonic vibrational frequencies of the stationary points involved in reactions R1 and R2, including reactants, complexes, transition states, and products, are calculated using the B3LYP (Becke’s three-parameter nonlocal-exchange functional with the nonlocal correlation functional of Lee-YangParr)17,18 theory with the 6-311G(d,p) basis set. It shows that the B3LYP method is sufficiently accurate for predicting reliable geometries and frequencies of the stationary points through many previous studies.19-22 To quantify the level of trust in the method, the geometries and harmonic vibrational frequencies of all in reactions R1 and R2 are also performed at the BH&HLYP/6-311G(d,p) and MP2(full)/6-311G(d,p) levels. The minimum-energy paths (MEPs) are obtained by intrinsic reaction coordinate (IRC) calculations at the B3LYP/6-311G(d,p) level. To obtain more reliable energy information, further single-point energy calculations for the stationary points and a few extra points along the MEP are carried out at BMC-QCISD23 (a new multicoefficient correlation methods based on quadratic configuration with single and double excitations) by using the B3LYP/6-311G(d,p) and MP2(full)/6-311G(d,p) optimized ge-

Song et al. ometries. Moreover, the single-point energy calculations with MC-QCISD24 (multicoefficient correlation method based on quadratic configuration interaction with single and double excitations) level are performed for all hydrogen abstraction reaction channels. A group-banlanced isodesmic reaction,25 which has the same number and types of bonds in both the reactants and products, is known to be a relatively accurate working method for calculating enthalpies of reaction. Because of the electronic similarity between reactants and products, isodesmic reactions will cancel the systematic errors in the calculations and lead to accurate results.26 Here, we determine 0 values of CH2FCF2OCHF2, CHFCF2OCHF2, and the ∆Hf,298 CH2FCF2OCF2 in reaction R1 and CH2FOCH2F and CHFOCH2F in reaction R2 using the following isodesmic reactions at the BMC-QCISD level.

CH2FCF2OCHF2 + CH4 + CH4 f CH3OCH3 + CHF2CH3 + CHF3 (R3a) CH2FCF2OCHF2 + CH4 + CH3F f CH3OCH3 + CF3CH3 + CHF3 (R3b) CH2FCF2OCHF2 + CH4 + CH2F2 f CH3OCH3 + CF3CH2F + CHF3 (R3c) CHFCF2OCHF2 + CH4 + CH3F f CH3OCH3 + CHFCF3 + CH2F2

(R4a)

CHFCF2OCHF2 + CH4 + CH2F2 f CH3OCH3 + CHFCF3 + CHF3

(R4b)

CHFCF2OCHF2 + CH3F + CH2O f CH3OCH3 + CF3CF3 + CHO (R4c) CH2FCF2OCF2 + CH4 + CH4 f CH3OCH3 + CHFCF3 + CH3F (R5a) CH2FCF2OCF2 + CH4 + CH4 + CH4 f CH3OCH3 + CH2F2 + CHF3 + CH2CH3 (R5b) CH2FCF2OCF2 + CH4 + CH2F2 f CH3OCH3 + CHFCF3 + CHF3 (R5c) CH2FOCH2F + CH4 f CH3OCH3 + CH2F2

(R6a) CH2FOCH2F + CH4 + CH4 f CH3OCH3 + CH3F + CH3F (R6b)

Investigation of the Reactions of CH2FCF2OCHF2 and CH2FOCH2F

CH2FOCH2F + CH3F f CH3OCH3 + CHF3

(R6c) CHFOCH2F + CH4 + CH4 f CH3OCH3 + CH2F2 + CH3 (R7a) CHFOCH2F + CH4 + CH3F f CH3OCH3 + CHF3 + CH3 (R7b) CHFOCH2F + CH4 + CH2O f CH3OCH3 + CH2F2 + CHO (R7c) The dynamic calculations of the variational transition state theory (VTST)13,14 are performed by means of the Polyrate, version 9.1 program.27 The theoretical rate constants for reactions R1 and R2 over the temperature range of 220-2000 K are calculated using canonical variational transition state theory (CVT)28-30 including small curvature tunneling correction (SCT)31,32 method proposed by Truhlar and co-workers. Canonical variational transition state theory rate constants, kCVT(T), is based on the idea of varying the dividing surface along a reference path to minimize the rate constant. kGT(T,s), with respect to the dividing surface at s is expressed as:

ksCVT(T) ) min kGT(T, s) where, kGT for temperature T and dividing surface at s is that:

kGT(T, s) )

σkBT QGT(T, s) -VMEP(s)/kBT e h ΦR(T)

In this equation, kGT(T,s) is the generalized transition state theory rate constant at the dividing surface s; σ is the symmetry factor accounting for the possibility of more than one symmetry-related reaction path; kB is Boltzmann’s constant; h is Planck’s constant; ΦR(T) is the reactant partition function per unit volume, excluding symmetry numbers for rotation, and QGT(T,s) is the partition function of a generalized transition state at s with a local zero of energy at VMEP(s) and with all rotational symmetry numbers set to unity. To take tunneling effect into account, the CVT rate constant is multiplied by the small-curvature tunneling (SCT) approximation, which is denoted as k(CVT)/(SCT)(T). Most vibrational modes are treated by the quantum-mechanical separable harmonic oscillator approximation. However, the hindered-rotor approximation of Truhlar and Chuang33,34 is used for calculating the partition functions of the lowest modes associated with the torsion. In the calculation of the electronic partition functions, the excited state of the OH radical, with a 140 cm-1 splitting, is included. III. Results and Discussions A. Electronic Structures of Stationary Points. The optimized geometric parameters of all stationary points involved in reactions R1 and R2 calculated at the B3LYP/6-311G(d,p) level are shown in Figure 1, along with the available experimental values of H2O and OH.35 In addition, for the purpose of comparison, all stationary points of hydrogen abstraction reactions of reactions R1 and R2 are also optimized at the BH&H-LYP/6-311G(d,p) and MP2(full)/6-311G(d,p) levels,

J. Phys. Chem. A, Vol. 114, No. 34, 2010 9059

then their geometric parameters are also shown in Figure 1, as well as the geometric parameters36 obtained from the gas electron diffraction (GED) experiment for the reactant of reaction R2. As shown in Figure 1, the optimized parameters obtained at the three levels are reasonably consistent with each other. The largest discrepancy is 0.10 Å, corresponding to the forming H-O bond in TS2a′ for the calculated bond lengths and 5.9° for the bond angles, corresponding to the forming C-H-O bond angle in TS1b. Although, the theoretical and experimental values35,36 show good agreement with each other when the comparisons are possible. With respect to three hydrogen abstraction channels in reaction R1 at B3LYP/6311G(d,p) level, on the reactant sides, three hydrogen-bonded complexes (CR1a, CR1a′, and CR1b) are stablely located by the hydrogen-bond attractive interaction between O(1) and H(1) and between F(1) and H(2) (Figure 1), due to the high electronegativities to the fluorine and oxygen atoms. On the other hand, the product complexes (CP1a, CP1a′, and CP1b) are found with energies 3.1, 1.3, and 0.7 kcal/mol less than the corresponding products at the exits of the three channels, respectively, at BMC-QCISD//B3LYP/6-311G(d,p) level. The H-O bond distances in CR1a, CR1a′, and CR1b are 2.468, 2.559, and 2.177 Å, whereas the H-C bond distances in CP1a, CP1a′, and CP1b are 3.196, 3.332, and 3.038 Å. Regarding to the transition states TS1a, TS1a′, and TS1b, the breaking C-H bond lengths are 11.4, 11.6, and 12.7% longer than the equilibrium C-H bond lengths in CH2FCF2OCHF2; the forming H-O bond lengths stretch by 35.9, 35.4, and 33.6% over the equilibrium H-O bond lengths in H2O, respectively. The elongation of the forming bond is larger than that of the breaking bond, indicating that TS1a, TS1a′, and TS1b of the title reaction are all reactant-like barriers, that is, all the three reaction channels will proceed via early transition states. This early or late character in the transition states is in keeping with the perspective of Fisher and Radom37 that an endothermic reaction proceeds via a “late” transition state whereas an exothermic reaction corresponds to an “early” transition state.38 The similar results can be obtained for reactions R1a at the BH&H-LYP/ 6-311G(d,p) level. For reaction R2, in fact, two different conformations of the CH2FOCH2F molecule exist, corresponding to C2 and Cs symmetry, separately, and that also were confirmed by previous literatures.36,39 The conformation with C2 symmetry is proved to be the most stable as the starting geometry of the reactant for our calculations. There are two hydrogen abstraction channels in reaction R2. Similarly to reaction R1, it exists as two reactant complexes (CR2a, CR2a′) and two product complexes (CP2a, CP2a′) at the entrance and exit of reaction R2, respectively. So, the two reaction channels in reaction R2 may also proceed via indirect mechanisms. Also, the product complexes CP2a and CP2a′ are stabilized by the hydrogen bond attractive interaction between O and H and between F and H. In the saddle point, TS2a, the lengths of the breaking C-H bond and the newly formed H-O bond are 1.191 and 1.373 Å, respectively, which are 8.2 and 29.9% longer than the corresponding equilibrium bond lengths of C-H in CH2FOCH2F and H-O in H2O. Regarding to TS2a′, the breaking C-H bond is 1.202 Å, stretched by 9.4%, compared to the reactant, and the forming H-O bond is 1.328 Å, 27.6% longer than the equilibrium bond lengths in H2O. On the basis of the above analysis, it is clear that the two hydrogen abstraction reaction channels in reaction R2 also occur via early barriers. The harmonic vibrational frequencies of the stationary points of the reactions calculated at the B3LYP/6-311G(d,p) level are

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Figure 1. Optimized geometries of reactants, products, complexes, and transition states at the B3LYP/6-311G(d,p), BH&HLYP/6-311G(d,p) (in parentheses), MP2(full)/6-311G(d,p) (in square brackets), and experimental values (in braces). Bond lengths are in angstroms, and angles are in degrees.



TABLE 1: Calculated and Experimental Frequencies (in cm-1) for the Reactants, Products, Transition States, and Hydrogen-bonded Complexes for the Title Reactions at the B3LYP/6-311G(d,p) Level species

frequencies (cm-1)

CH2FCF2OCHF2

3140, 3132, 3071, 1491, 1446, 1431, 1391, 1314, 1298, 1196, 1157, 1130, 1103, 1100, 1061, 981, 865, 676, 648, 574, 551, 492, 435, 368, 317, 221, 173, 92, 65, 29 3705 (3735)a 3225, 3141, 1439, 1423, 1389, 1271, 1206, 1151, 1146, 1118, 1090, 1049, 876, 708, 659, 588, 564, 527, 448, 434, 370, 313, 220, 166, 69, 57, 29 3133, 3071, 1491, 1444, 1309, 1307, 1243, 1222, 1153, 1126, 1101, 1054, 968, 872, 675, 644, 605, 550, 455, 447, 369, 323, 214, 159, 95, 59, 29 3908 (3756),a 3811 (3657),a 1638 (1595)a 3740, 3139, 3110, 1464, 1428, 1402, 1388, 1288, 1230, 1163, 1146, 1138, 1125, 1118, 1051, 1014, 875, 832, 789, 666, 645, 574, 551, 484, 438, 367, 292, 226, 204, 179, 124, 76, 65, 48, 14, 959i 3736, 3141, 3109, 1464, 1425, 1403, 1388, 1294, 1228, 1161, 1149, 1143, 1129, 1092, 1056, 1029, 901, 820, 772, 662, 642, 600, 545, 457, 451, 371, 296, 248, 226, 185, 118, 90, 62, 54, 29, 1003i 3748, 3133, 3071, 1490, 1461, 1443, 1308, 1301, 1229, 1209, 1189, 1133, 1111, 1102, 1072, 987, 866, 811, 687, 668, 603, 562, 508, 455, 406, 368, 327, 222, 214, 175, 131, 109, 96, 62, 37, 1108i 3693, 3143, 3141, 3076, 1496, 1452, 1432, 1390, 1328, 1292, 1199, 1156, 1134, 1102, 1093, 1057, 982, 846, 674, 647, 577, 550, 488, 438, 375, 369, 329, 223, 210, 185, 123, 87, 74, 59, 19, 12 3895, 3806, 3222, 3144, 1648, 1447, 1427, 1393, 1306, 1202, 1169, 1134, 1127, 1064, 994, 869, 686, 658, 632, 567, 548, 482, 439, 390, 343, 330, 282, 238, 166, 148, 129, 85, 76, 58, 41, 24 3689, 3144, 3142, 3074, 1499, 1450, 1426, 1377, 1307, 1307, 1190, 1172, 1117, 1097, 1088, 1052, 985, 869, 679, 647, 580, 549, 490, 433, 382, 369, 320, 249, 224, 172, 111, 95, 82, 71, 47, 38 3896, 3809, 3223, 3141, 1647, 1439, 1419, 1379, 1277, 1198, 1161, 1114, 1097, 1087, 1042, 873, 740, 663, 622, 573, 547, 494, 431, 369, 352, 328, 244, 226, 180, 136, 110, 86, 64, 62, 48, 44 3728, 3137, 3132, 3070, 1491, 1445, 1443, 1398, 1322, 1293, 1198, 1152, 1141, 1102, 1097, 1049, 978, 854, 672, 642, 583, 548, 476, 448, 369, 325, 319, 222, 188, 170, 109, 92, 65, 63, 33, 14 3905, 3817, 3134, 3072, 1650, 1492, 1444, 1318, 1300, 1246, 1216, 1151, 1104, 1095, 1036, 964, 861, 674, 639, 603, 549, 455, 447, 369, 325, 317, 260, 218, 161, 134, 110, 95, 71, 66, 46, 35 3144, 3141, 3063, 3057, 1527, 1519, 1468, 1436, 1319, 1284, 1214, 1188, 1107, 1023, 995, 990, 586, 552, 302, 162, 74 3164, 3151, 3077, 1522, 1465, 1350, 1306, 1219, 1171, 1093, 1047, 978, 941, 599, 544, 295, 165, 55 3726, 3163, 3117, 3080, 1522, 1485, 1446, 1374, 1323, 1294, 1202, 1185, 1151, 1075, 1053, 1002, 969, 781, 600, 532, 332, 306, 177, 163, 126, 45, 512i 3745, 3149, 3072, 3063, 1528, 1521, 1453, 1366, 1311, 1289, 1203, 1145, 1095, 1065, 1024, 1010, 870, 740, 587, 516, 284, 182, 140, 108, 93, 37, 775i 3650, 3160, 3153, 3074, 3068, 1540, 1521, 1471, 1435, 1327, 1289, 1214, 1189, 1108, 1022, 987, 940, 587, 541, 487, 329, 312, 192, 150, 94, 68, 36 3889, 3802, 3176, 3169, 3097, 1653, 1529, 1457, 1347, 1306, 1230, 1175, 1075, 1019, 959, 942, 601, 548, 416, 345, 288, 251, 192, 134, 129, 94, 47 3628, 3162, 3147, 3071, 3066, 1528, 1522, 1469, 1437, 1325, 1287, 1218, 1180, 1102, 1040, 1010, 971, 591, 564, 546, 328, 304, 167, 148, 90, 74, 25 3887, 3790, 3177, 3139, 3061, 1647, 1512, 1463, 1370, 1307, 1213, 1167, 1119, 1052, 979, 966, 637, 476, 460, 348, 233, 181, 149, 112, 99, 62, 31

OH CHFCF2OCHF2 CH2FCF2OCF2 H 2O TS1a′-OH TS1a-OH TS1b-OH CR1a′ CP1a′ CR1a CP1a CR1b CP1b CH2FOCH2F CHFOCH2F TS2a-OH TS2a′-OH CR2a CP2a CR2a′ CP2a′

a

Reference 40.

listed in Table 1, along with the experimental data of OH and H2O.40 The calculated frequencies are in good agreement with the experimental values, with the largest deviation being 4%. Also, it can be seen that in Table S1 (Supporting Information) the vibrational frequencies of the reactants, products, complexes, and transition state for reaction channel R1a at the B3LYP/6-

311G(d,p) level are in reasonable agreement with those for R1a at the BH&H-LYP/6-311G(d,p) level, as well as those at the MP2(full)/6-311G(d,p) level when a comparison is available. In addition, the vibrational frequencies of C-H (3153, 3150, 3070, 3065) in the molecular CH2FOCH2F obtained from B3LYP/6-311++G(d,p)39 are also consistent with our values

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TABLE 2: Calculated Enthalpies of Formation (kcal/mol) of CH2FCF2OCHF2, CHFCF2OCHF2, CH2FCF2OCF2, CH2FOCH2F, and CHFOCH2F, As Well As Some Available Literature Values B3LYP species

isodesmic reaction

0 ∆Hf,298

CH2FCF2OCHF2

R3a R3b R3c R4a R4b R4c R5a R5b R5c R6a R6b R6c R7a R7b R7c

-308.80 -308.02 -306.87 -258.41 -258.95 -258.64 -258.13 -259.66 -256.24 -148.41 -150.52 -146.80 -99.25 -97.64 -99.78

CHFCF2OCHF2 CH2FCF2OCF2 CH2FOCH2F CHFOCH2F

a

BMC-QCISD//B3LYP

average -307.90 -258.67 -258.01 -148.58 -98.89

0 ∆Hf,298

-309.60 -309.44 -307.52 -259.14 -259.71 -257.78 -257.59 -258.65 -257.06 -147.69 -148.78 -147.17 -95.95 -95.43 -97.98

average -308.85 (-309.81)a (-310.05)a -258.88 -257.77 -147.88 (-148.04 ( 3.1)b (-148.21 ( 3.1)b -96.45 (-101.34 ( 4.2)b (-101.70 ( 4.2)b

BMCQCISD//MP2(full) 0 ∆Hf,298

-310.01 -309.44 -307.56 -259.28 -259.72 -256.45 -258.08 -259.29 -257.31 -147.74 -148.97 -146.96 -98.53 -97.75 -95.07

average -309.00 -258.48 -258.22 -147.89 -97.12

Reference 41. b Reference 42.

(3144, 3141, 3063, 3057) in this work. Their good agreements confirm the accuracy and reliability of the calculated rate constants. The number of imaginary frequencies (0 or 1) indicates whether a minimum or a transition state has been located. All transition states are verified by normal-mode analysis with one and only one imaginary frequency, corresponding to the stretching modes of the coupling breaking and forming bonds; the reactants, products, and the complexes in reactions correspond to “zero” imaginary frequencies, which meaning local minimums. The values of those imaginary frequencies calculated at the B3LYP/6-311G(d,p) level are 959i, 1003i, 1108i, 511i, and 775i cm-1 for reactions R1a, R1a′, R1b, R2a, and R2a′, respectively. B. Energetics. To thoroughly understand the kinetics and mechanism of these reactions, particularly in atmospheric modeling, accurate thermodynamic values are important. We predict the enthalpies of formation (∆H0f,298) of CH2FCF2OCHF2, CHFCF2OCHF2, CH2FCF2OCF2, CH2FOCH2F, and CHFOCH2F using the isodesmic reactions R3-R7. The experimental ∆H0f,298 of the other species involved in the reactions are: CH4, -17.89 kcal/mol; CH3OCH3, -43.99 ( 0.12 kcal/mol; CHF2CH3, -118.78 ( 0.95 kcal/mol; CHF3, -166.60 kcal/mol; CH3F, -56.8 ( 2 kcal/mol; CF3CH3, -178.94 kcal/mol; CH2FCF3, -214.1 ( 2 kcal/mol; CHFCF3, -166.5 kcal/mol; CH2F2, -107.71 kcal/mol; CF3CF3, -321.2 kcal/mol; CH2O, -25.98 ( 0.01 kcal/mol; HCO, 10.55 ( 0.1 kcal/mol; CH2CH3, 28.4 ( 0.5 kcal/mol; CH3, 34.82 kcal/mol. The enthalpies of formation obtained at BMC-QCISD//B3LYP/6-311G(d,p) and BMC-QCISD//MP2(full)/6-311G(d,p) (in brackets) levels are shown in Table 2. To ensure accuracy, the average values of the enthalpies of formation are also calculated, which are -309.78 (-309.00), -259.43 (-258.48), -258.12 (-258.22), -147.74 (-147.89), and -95.69 (-97.12) kcal/ mol for CH2FCF2OCHF2, CHFCF2OCHF2, CH2FCF2OCF2, CH2FOCH2F, and CHFOCH2F, respectively. In addition, in Table 2 we can see that the enthalpies of formation of CH2FCF2OCHF2 obtained at BAC-MP2/6-31G(d,p) and AACMP2/6-31G(d,p) levels (-309.81 and -310.05 kcal/mol, respectively),41 consistent with our values and the enthalpies of formation of CH2FOCH2F and CHFOCH2F, 148.04 ( 3.1 (148.21 ( 3.1) and 101.34 ( 4.2 (101.70 ( 4.2) kcal/mol at MP2/6-31++g(2d,2p) and MP2/6-311++g(2d,2p)42 levels, respectively, also show good agreement with this work, if the error taken into account.

The relative energies (Er) of main species for reactions R1 and R2 with zero-point correction to energy (ZPE) are listed in Table 3, and the reaction enthalpies (∆H0r,298) and reaction gibbs 0 for reactions R1 and R2 with thermal free energies ∆Gr,298 correction to enthalpy (TZPE), and thermal correction to gibbs free energy at the low level are listed in Table 4, calculated at B3LYP/6-311G(d,p), BMC-QCISD//B3LYP/6-311G(d,p), MCQCISD//B3LYP/6-311G(d,p), and BMC-QCISD//MP2(full)/6311G(d,p) (only in Table 3) levels. As shown in Tables 3 and 0 0 , ∆Gr,298 , and Er values obtained at the BMC4, the ∆Hr,298 QCISD//B3LYP and MC-QCISD//B3LYP show good mutual agreement. Table 4 also lists the calculated bond dissociation 0 ) of the C-H bond in CH2FCF2OCHF2 and energies (D298 CH2FOCH2F at the B3LYP/6-311G(d,p), BMC-QCISD//B3LYP/ 6-311G(d,p), and MC-QCISD//B3LYP/6-311G(d,p) along with other theoretical results.42,43 As shown in Table 4, the results obtained at the BMC-QCISD//B3LYP/6-311G(d,p) and MCQCISD//B3LYP/6-311G(d,p) levels are in good agreement with the largest deviation about 0.40 kcal/mol. Due to the lack of 0 ) of the C-H in CH2FCF2OCHF2 the experimental values (D298 and CH2FOCH2F, so no comparison between theory and experiment can be made. However, the calculated values (D0298) for CHF2OCHF-H, CH2FCF2OCF2-H, and CH2FOCHF-H (101.75, 104.54, and 100.42 kcal/mol, respectively) at BMCQCISD//B3LYP/6-311G(d,p) in this work show good consistency with the previous literature results (102.66 (103.47), 105.07 (104.76), and 100.38 (101.34) kcal/mol, respectively)43 obtained at the B3P86/6-311++G(3df,2p) and B3P86/6-31G(d′) levels of theory (B3P86/6-31G(d′) values in parentheses). In addition, the calculated values (D0298) for CH2FOCHF-H (101.91 ( 3.3, 98.85 ( 2.9, and 98.66 ( 2.9 kcal/mol)42 at MP2/321++g(2d,2p), MP2/6-31++g(2d,2p), and MP2/6-311++ g(2d,2p) levels, respectively, also demonstrate consistency with our work. The schematic potential energy diagrams for the reactions of CH2FCF2OCHF2/CH2FOCH2F with OH radical obtained at the B3LYP/6-311G(d,p) and BMC-QCISD//B3LYP/6-311G(d,p) levels are plotted in Figures 2a and 2b. Figure 2a shows that five hydrogen-bond complexes, CR1a (-3.39 kcal/mol), CR1a′ (-2.26 kcal/mol), CR1b (-1.67 kcal/mol), CR1c (-0.69 kcal/ mol), and CR1d (-1.36 kcal/mol) are located at the reactant side of channels R1a, R1a′, R1b, R1c, and R1d, respectively; and there are five complexes, CP1a, CP1a′, CP1b, CP1c, and CP1d, located at the product sides of the five reaction channels,



TABLE 3: Relative Energies (Er) of Main Species for Reactions R1 and R2 at the B3LYP/6-311G(d,p), BMC-QCISD//B3LYP/ 6-311G(d,p), MC-QCISD//B3LYP/6-311G(d,p), and BMC-QCISD//MP2(full)/6-311G(d,p) Levels (kcal/mol) with ZPE Corrections at the Low Level Er (R1)

Er (R2)

species

ZPE

B3LYP

BMC-QCISD//B3LYP

MC-QCISD//B3LYP

BMC-QCISD//MP2(full)

R1 CR1a TS1a CP1a CR1a′ TS1a′ CP1a′ P1a(a′) CR1b TS1b CP1b P1b R2 CR2a TS2a CP2a CR2a′ TS2a′ CP2a′ P2a(a′)

0.078947 0.080925 0.076261 0.080015 0.080766 0.076082 0.080119 0.077531 0.080577 0.075842 0.080602 0.078537 0.074851 0.077330 0.073427 0.077164 0.077456 0.071981 0.076500 0.074033

0.00 -4.44 -1.79 -19.22 -3.46 -1.37 -18.76 -13.99 -4.22 -1.16 -14.33 -11.46 0.00 -5.03 -4.45 -20.39 -4.29 -2.24 -18.92 -15.45

0.00 -3.39 2.65 -21.41 -2.26 3.36 -19.56 -18.31 -1.67 4.17 -16.20 -15.52 0.00 -2.41 1.10 -21.47 -2.71 2.89 -21.26 -19.64

0.00 -2.19 3.78 -20.57 -1.22 4.47 -18.82 -17.85 -1.51 5.45 -15.18 -14.96 0.00 -1.45 2.34 -20.34 -2.39 3.92 -20.36 -19.04

0.00 -2.55 2.65 -21.39 -1.81 3.37 -19.23 -18.03 -1.16 3.98 -16.48 -15.54 0.00 -2.14 0.36 -21.67 -2.88 2.75 -21.53 -19.65

0 0 TABLE 4: Reaction Enthalpies ∆Hr,298 and Reaction Gibbs Free Energies ∆Gr,298 for Reactions R1 and R2, and Dissociation 0 Energies D298 of C-H Bonds in CH2FCF2OCHF2 and CH2FOCH2F at the B3LYP/6-311G(d,p), BMC-QCISD//B3LYP/ 6-311G(d,p) and MC-QCISD//B3LYP/6-311G(d,p) Levels (kcal/mol) with ZPE or TZPE Corrections at the Low Level, As Well As Some Available Literature Values

0 ∆Hr,298

0 ∆Gr,298

D0298

a

R1a (R1a′) R1b R2 (R2a′) R1a (R1a′) R1b R2 (R2a′) CH2FCF2OCHF2 f CHFCF2OCHF2 + H CH2FCF2OCHF2 f CH2FCF2OCF2 + H CH2FOCH2F f CHFOCH2F + H

B3LYP

BMC-QCISD//B3LYP

MC-QCISD//B3LYP

-13.55 -11.15 -15.13 -15.11 -12.37 -16.84 97.63

-17.86 -15.22 -19.32 -19.43 -14.36 -21.03 101.75

-17.41 -14.65 -18.72 -18.97 -15.87 -20.42 102.01

100.17

104.54

104.91

96.18

100.42

100.83

literature values

102.66a 103.47a 105.07a 104.76a 100.38a 101.34a 101.91 ( 3.3b 98.85 ( 2.9b 98.66 ( 2.9b

Reference 43. b Reference 42.

being 3.10, 1.25, 0.68, 1.71, and 2.59 kcal/mol lower than the products, respectively. The reaction R1 proceeds via five transition states (TS1a, TS1a′, TS1b, TS1c, and TS1d), with the energies being 2.65, 3.36, 4.17, 72.36, and 49.77 kcal/mol. The potential barrier height of reaction channel R1a is only about 0.71 kcal/mol lower than that of channel R1a′, and both path ways lead to the same product (P1a). Thus, hydrogen abstractions from CH2F- groups may be kinetically and thermodynamically competitive channels. The value of TS1b is about 1.52 and 0.81 kcal/mol higher than that of TS1a and TS1a′. Furthermore, three hydrogen abstraction channels are all 0 obtained at the exothermic. The reaction enthalpies ∆Hr,298 BMC-QCISD level of theory are -17.86 and -15.22 kcal/mol for reaction channels R1a (R1a′) and R1b, respectively, and the reaction gibbs free energies ∆G0r,298 are -19.43 and -14.36 kcal/ mol. So, hydrogen abstractions from CH2F- may be main channels. For the displacement reaction channel R1c (R1d), the barrier height is about 69.71 (47.12), 69.00 (46.41), and 68.19 (45.60) kcal/mol higher than those of reaction channels R1a, R1a′, and R1b, respectively. Thus, the hydrogen abstraction reaction channels are the objects worthy of consideration, and

the displacement process should be negligible. From Figure 2b, three hydrogen-bond complexes exist at the entrances of reaction channels R2a, R2a′, and R2b with energies about 2.41, 2.71, and 1.97 kcal/mol lower than the reactants. Also, three complexes (CP2a, CP2a′, and CP2b) are found at the exits, which are about 1.83, 1.62, and 2.98 kcal/mol lower than the products. The values of TS2a and TS2a′ (1.10 and 2.89 kcal/ mol) for channels R2a and R2a′ are much lower than the value of TS2b (44.53 kcal/mol) for displacement reaction channel R2b. In addition, the ∆H0r,298 is -19.32 kcal/mol for reaction channels 0 is -21.03 kcal/mol. Similarly to R2a (R2a′), and the ∆Gr,298 reaction R1, reaction channels R2a and R2a′ may be competitive channels, and the hydrogen abstraction reactions in CH2FOCH2F with OH reaction are more favorable while the displacement process negligible. The reaction mechanisms get from the calculation of relative free energies is consistent with our former analysis from relative energies. C. Reaction Path Properties. Dual-level (X//Y) direct dynamics calculations are carried out at the BMC-QCISD// B3LYP level with the VTST-ISPE approach for the hydrogen abstraction in reactions R1 and R2. The reactant and product

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Figure 2. (a) Schematic potential energy surface for reaction CH2FCF2OCHF2 + OH. Relative energies (in kcal/mol) are calculated at the B3LYP/ 6-311G(d,p) + ZPE (in parentheses) and BMC-QCISD//B3LYP/6-311G(d,p) + ZPE levels. (b) Same as (a) except for reaction CH2FOCH2F + OH.

complexes for the reaction channels are taken into account in the dynamic calculations performed by the Polyrate program. The calculation results note that reaction channels R1a, R1a′, and R1b in R1 have similar characters. Also, channels R2a and R2a′ in reaction R2 are similar. So we give an example of reaction channels R1a and R2a to illuminate the reaction-path properties of the title reaction in this section. The classical potential energy curve (VMEP), ground-state vibrationally adiabatic energy curve (VGa ), and zero-point energy curve (ZPE) as a function of the intrinsic reaction coordinate s, (amu)1/2 bohr by BMC-QCISD//B3LYP method are depicted in Figures 3a and 3b. The ZPE curves are all practically constant as s varies, sometimes, with only a drop near the saddle point. From Figure 3a, we can see that the ZPE curve is almost no drop near the saddle point. The VMEP and VGa curves are similar in shape, and the maxima are also located at the same position, that indicating

a rather small and negligible variational effect. The corresponding plots for reaction channels R1a′ and R1b are similar to that of channel R1a, depicted in Figure S1. In Figure 3b, because VMEP has a low classical barrier height, the locations of the maximum on the VGa curve for reaction channel R2a slightly shift to s ) -0.18 (amu)1/2 bohr, implying that the variational effect will have some influence on the calculation of the rate constants. Samely, the corresponding plot for channel R2a′ is also shown in Figure S1 because of similarity. The following study of the rate constants will further testify this view. Figures 4a and 4b show the variation of the generalized normal-mode vibrational frequencies along the MEP for reaction channels R1a and R2a. From Figure 4a, the frequencies start from s ) -2.0 (amu)1/2 bohr in the reactant region, associated with the reactant complex (CR1) to product region about s ) 2.0 (amu)1/2 bohr associated with the product complex (CP1).



Figure 3. (a) Classical potential energy curve (VMEP), ground-state vibrationally adiabatic energy curve (VGa ), and zero-point energy curve (ZPE) as functions of s (amu)1/2 bohr at the BMC-QCISD//B3LYP/6311G(d,p) level for reaction channel R1a. (b) Same as in (a) except for reaction R2a.

Figure 4. Changes of the generalized normal-mode vibrational frequencies as function of s (amu)1/2 bohr at the B3LYP/6-311G(d,p) level. (a) for reaction R1a; (b) for reaction R2a.

In the process of the reaction, we can see that 35 vibrational frequencies exist in the vicinity of the transition state. Most of them do not change significantly on going from the reactants to products. However, only mode 1 (the bold line in Figure 4a) named the “reactive mode” has obvious change near the saddle point. The “reactive mode”, which is the typical behavior of hydrogen-transfer reaction connects the stretching vibrational mode of the breaking and forming bonds. The deep minimum in frequency occurs in the range from s ) -0.09 to 0.43 (amu)1/2 bohr for reaction channel R1a. Similar to Figure 4a, there are 26 vibrational frequencies in Figure 4b and the main regions of s for reaction channel R2a are from -0.09 to 0.52 (amu)1/2 bohr in the“reaction mode”. The related plots of the generalized normal-mode vibrational frequencies for reaction channels R1a′, R1b, and R2a′ are located in Figure S2. D. Rate Constant Calculations. The PES information on the basis of the BMC-QCISD//B3LYP/6-311G(d,p), is put into the Polyrate program. The rate constants for the reactions CH2FCF2OCHF2/CH2FOCH2F + OH are calculated by using TST, CVT, and CVT with small-curvature tunneling (SCT) correction over the temperature range 220-2000 K. Taking reaction channels R1a and R2a as examples, the TST, CVT, and CVT/SCT rate constants of channels R1a and R2a are presented in Figures 5a and 5b; the contributions of variational

and tunneling to rate-constant calculations are then analyzed in this paper. The corresponding plots of R1a′, R1b and R2a′ are shown in Figure S3. In Figure 5a, we can find that the rate constants of the TST and CVT for reaction channel R1a are almost superposed on each other over the whole temperature range (220-2000 K), suggesting that the variational effect on the rate constants is very small or almost negligible for reaction R1a. The variational effect is defined as the ratio between the CVT and TST rate coefficients. However, in Figure 5b, the variational effect for reaction channel R2a is somewhat large over the temperature range of 220-600 K. These results accord with the analysis above to variational effect by comparing the plots of VGa and VMEP. Moreover, by contrasting the CVT and CVT/SCT rate constants in Figures 5a and 5b, we can find that SCT correction (that is the ratio between CVT/SCT and CVT rate constant) plays an important role in the calculation of rate constants at low temperatures for reaction channel R1a and R2a, and CVT/ SCT rate constants are asymptotic to the CVT ones at higher temperatures; For example, the ratios of k(CVT/SCT)/k(CVT) are 6.0, 2.5, 1.6, 1.1, 1.0, and 0.9 at 220, 298, 400, 600, 1000, and 2000 K for reaction channel R1a and are 2.2, 1.5, 1.2, 1.0, 1.0, and 1.0 for channel R2a, respectively. Figures 6a and 6b show the dependence on the temperature of CVT/SCT rate constants for reactions R1 and R2 (R1a, R1a′,

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Figure 5. (a) Computed TST, CVT, and CVT/SCT rate constants as a function of 103/T between 220-2000 K for the reaction channel R1a. (b) Same as (a) except for reaction channel R2a.

R1b, R2a, and R2a) with the corresponding experimental data7 for reaction R1 and the empirical value speculated from the experimental data about CH2FOCH2F with CI,8 as well as other theoretical value9 for reaction R2. The total rate constant is the sum of individual rate constants: k1 ) k1a + k1a′ + k1b, k2 ) k2a + k2a′. The calculated CVT/SCT rate constants are in excellent agreement with the available literature values7-9 if the experimental uncertainties are taken into account. For reaction R1, the calculated total rate constant (4.23 × 10-15, 4.96 × 10-15, 5.80 × 10-15, 6.74 × 10-15, and 7.81 × 10-15 cm3 molecule-1 s-1) at 268, 278, 288, 298, and 308 K, respectively, is good agreement with two groups of available experiment values (3.10 × 10-15/3.00 × 10-15, 3.90 × 10-15/4.20 × 10-15, 4.70 × 10-15/ 4.40 × 10-15, 5.80 × 10-15/6.00 × 10-15, and 7.30 × 10-15/ 6.50 × 10-15 cm3 molecule-1 s-1) at every corresponding temperature.7 The largest deviation between the theoretical and experimental values remains within a factor of approximately 0.12. For reaction R2, our calculated rate constant at 298 K (6.06 × 10-14 cm3 molecule-1 s-1) is consistent with available literature value (6.0 × 10-14 cm3 molecule-1 s-1) very well, estimated by using the empirical estimation method,8 and slightly higher than the semiempirical value 4.7 × 10-14 cm3 molecule-1 s-1.9 Thus, the present calculations may provide reliable prediction of the rate constants for the title reaction over a wide temperature range. From Figure 6, we can see that the calculated rate constants for the reactions CH2FCF2OCHF2/CH2FOCH2F with OH at lower temperature are smaller than that obtained at

Song et al.

Figure 6. Calculated rate constants for the reaction channels R1 and R2, respectively, and the total rate constants k1 (k1 ) k1a + k1a′ + k1b) and k2 (k2 ) k2a + k2a′) are obtained at the BMC-QCISD//B3LYP/6311G(d,p) level along with the experimental values as a function of 103/T. (a) for reaction R1; (b) for reaction R2.

higher temperature. Therefore, the degradation reactions R1 and R2 may have the positive-temperature effect in the atmosphere. In addition, the temperature dependence of the k1a/k1, k1a′/k1, k1b/k1, k2a/k2, and k2a′/k2 branching ratios are plotted in Figures 7a and 7b. For reaction R1, hydrogen abstractions from the CH2F- groups (R1a, R1a′) are more competitive than that from the CHF2- groups (R1b) over the whole temperature range, whereas the contribution of channel R1b should be considered at the higher temperature range of 800-2000 K; that is to say, the fluorine substitution decreases the reactivity of the C-H bond because F is strongly electron-withdrawing. The channels R1a and R1a′ are competitive, leading to the same main product CHFCF2OCHF2. In the low-temperature range, channel R1a shows significant preponderance, but the preponderance is gradually disappear as the temperature increases. For example, k1a/k1 branching ratio is 0.46 corresponding the value of k1a′/k1 branching ratio being 0.50 at 500 K. With the temperature increasing, channel R1a′ makes a greater contribution to the total rate constant, so it would be the main reaction pathway at higher temperatures. Regarding to reaction R2, channel R2a is the dominant reaction pathway at the lower temperatures. However, channel R2a′ plays a more important role to the total rate constant when the temperature gradually increases, leading that it would be the main reaction route at higher temperatures.



to be -308.85, -258.88, -257.12, -147.88, and -96.45 kcal/ mol, respectively, by using the isodesmic reaction models. The rate constants for hydrogen abstraction reaction channels of reactions R1 and R2 calculated by the CVT incorporating SCT correction are in good agreement with the corresponding experimental and estimated values. The variational effect is very small or almost negligible over the whole temperature region for reaction R1, although it is somewhat important in lowertemperature region for reaction R2. The SCT correction plays an important role for reactions R1 and R2 in the rate constant calculation within the lower-temperature region. For reaction R1, the contribution of channel R1a is main below 500 K. However, channel R1a′ become important and channel R1b must be taken into account at higher temperatures. For reaction R2, channel R2a is dominant below 600 K, but reaction channel R2a′ is more competitive as the temperature increases. The three parameter expressions for the title reaction within 220-2000 K are k1 ) 1.62 × 10-20 T2.75 exp(-1011/T) for reaction R1 and k2 ) 3.40 × 10-21 T3.04 exp(-384/T) for reaction R2. We hope the theoretical results may be useful for further experimental studies on the dynamical properties of the title reactions. Acknowledgment. The authors thank Professor Donald G. Truhlar for providing the Polyrate, Version 9.1 program. This work is supported by the Training Fund of NENU’s Scientific Innovation Project (NENU-STC07016). We are greatly thankful for the referees’ helpful comments.

Figure 7. Calculated branching ratios for reactions CH2CF2OCHF2 + OH (R1) and CH2FOCH2F + OH (R2) as a function of 103/T between 220 and 2000 K. (a) for reaction R1; (b) for reaction R2.

For example, the k2a/k2 branching ratios are 0.87, 0.78, 0.46, and 0.21 at 220, 298, 600, and 1600 K, respectively. The experimental data at other temperatures are lacking since the measurements in the experiment7 were performed in a narrow temperature range (268-308 K) for reaction R1. Also, there is little experimental data for reaction R2. For convenience of future experimental measurement, the three-parameter fits based on the CVT/SCT rate constants at the BMC-QCISD// B3LYP/6-311G(d,p) level within 220-2000 K give the expression as follow (in units of cm3 molecule-1 s-1):

k1 ) 1.62 × 10-20T2.75exp(-1011/T) k2 ) 3.40 × 10-21T3.04exp(-384/T) IV. Conclusions In the present work, the reactions of CH2FCF2OCHF2 + OH (R1) and CH2FOCH2F + OH (R2) are investigated theoretically by the dual-level direct dynamics method at the BMC-QCISD//B3LYP/6-311G(d,p) level. For reactions R1 and R2, hydrogen abstractions in CH2F- group are the main reaction channel and displacement processes are negligible. Each reaction proceeds via indirect mechanism. The standard enthalpies of formation of CH2FCF2OCHF2, CHFCF2OCHF2, CH2FCF2OCF2, CH2FOCH2F, and CHFOCH2F are calculated

Supporting Information Available: In Supporting Information, we provide calculated frequencies (in cm-1) for the reactants, products, complexes, and transition states for the reaction R1a at the B3LYP/6-311G(d,p), BH&H-LYP/6311G(d,p) (in parenthese), MP2(full)/6-311G(d,p) (in square brackets), and experimental values (in braces) listed in TABLE 1. The classical potential energy curve (VMEP), ground-state vibrationally adiabatic energy curve ( ), and zero-point energy curve (ZPE) as a function of the intrinsic reaction coordinate s, (amu)1/2 bohr by BMC-QCISD//B3LYP method are depicted in Figures 1a, 1b, and 1c, corresponding to reaction channels R1a′, R1b, and R2a′, respectively. We also show the variation of the generalized normal-mode vibrational frequencies along the MEP for reaction channels R1a′, R1b, and R2a′ in Figure 2, as well as the TST, CVT, and CVT/SCT rate constants of channels R1a′, R1b, and R2a′ are presented in Figures 3a, 3b, and 3c, respectively. This information is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Sekiya, A.; Misaki, S. J. Fluorine Chem. 2000, 101, 215. (2) Sekiya, A.; Misaki, S. Chemtech. 1996, 26, 44. (3) Nathan, O.; Sellevag, S. R.; Nielsen, C. J. EnViron. Sci. Technol. 2004, 38, 5567. (4) Jia, X. J.; Liu, Y. J.; Sun, J. Y.; Sun, H.; Su, Z. M.; Pan, X. M.; Wang, R. S. J. Phys. Chem. A 2010, 114, 417. (5) Warnatz, J. In Combustion Chemistry; Gardiner, W. C.; Jr., Ed.; Springer-Verlag: New York, 1984. (6) Finlayson-Pitts, B. J.; Jr.; Pitts, J. N. Atmospheric Chemistry; Wiley: New York, 1986. (7) Chen, L.; Kutsuna, S.; Tokuhashi, K.; Sekiya, A.; Takeuchi, K.; Ibusuki, T. Int. J. Chem. Kinet. 2003, 35, 239. (8) Goto, M.; Kawasaki, M.; Wallington, T. J.; Hurley, M. D.; Sharratt, A. P. Int. J. Chem. Kinet. 2002, 34, 139. (9) Chandra, A. K.; Uchimaru, T.; Urata, S.; Sugie, M.; Sekiya, A. Int. J. Chem. Kinet. 2003, 35, 130. (10) Truhlar, D. G. In The Reaction Path in Chemistry: Current Approaches and PerspectiVes; Heidrich, D., Ed.; Kluwer Dordrecht: The Netherlands, 1995; p 229. (11) Hu, W. P.; Truhlar, D. G. J. Am. Chem. Soc. 1996, 118, 860.

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