Atmospheric chemistry of ethers, esters, and alcohols on the lifetimes, temperature dependence, and kinetic isotope effect: an example of CF₃CX₂CX₂CX₂OX with OX reactions (X = H, D)

Abstract

The dual-level direct dynamics method is employed to investigate the hydrogen abstraction reaction of CF₃CH₂CH₂CH₂OH (CF₃CD₂CD₂CD₂OD) with OH (OD) radicals. Four possible reaction channels caused by different positions of hydrogen atom attack are found. All the stationary points are studied with the ab initio and density functional theories. Single points computation is further refined by CCSD(T) and QCISD(T) methods combined with the 6-311++G(d,p) basis set in the minimum energy paths (MEP). Rate constants for each reaction channel, obtained by canonical variational transition state (CVT) coupled with the small curvatures tunneling (SCT) correction, are found to coincide with the available data in experiments. Calculations show that the variational effect was small in 200–2000 K, while the tunneling effect is large for every reaction channel in low-temperature regions. It is shown that the H-abstraction from the –CH₂O– group is the primary channel. Standard enthalpies of formation for the species are computed, and the kinetic isotope effects for reactions CF₃CH₂CH₂CH₂OH/CF₃CD₂CD₂CD₂OD + OH and CF₃CH₂CH₂CH₂OH + OH/OD are discussed to provide valuable information for subsequent research. In addition, atmospheric lifetimes of a series of related ethers, esters, and alcohols are estimated. The Arrhenius expression for the title reaction k(T) = 3.43 × 10⁻²¹T^3.22 exp(741.70/T) cm³ per molecule per s is also provided.

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1 Introduction

Rising concern about the potential impact of various industrial chlorofluorocarbons (CFCs) on the Earth's climate has stimulated further search for chemicals that satisfy various industrial needs while having little impact on either stratospheric ozone or climate. Hydrofluorocarbons (HFCs) and hydrofluorochlorocarbons (HCFCs) have found extensive use in replacing CFCs in the past few decades.¹ In general, extensive efforts have been made to search for suitable replacements as a result of HFCs and HCFCs having rather long lifetimes and large greenhouse effect potentials.² Recently, partially fluorinated alcohols (FAs) have been suggested as substitutes for HFCs,³ and the fluorinated ethers (FEs) and FAs are new classes of compounds currently under consideration for use as CFC replacements.^4,5 The FAs are expected to have not the ability to destroy the ozone layer and large reactivity. Because of containing hydrogen atoms, thus, these FAs can be removal by means of reactions with OH radical in the atmosphere.⁶ Hence OH reaction rate constants for such compounds were required to determine their atmospheric lifetimes and possible effects on the Earth's radiation budget. Also, fate of the oxidation products from such reactions were also important in determining environmental acceptability, information on the initial rate of reaction was a necessary first step.

CF₃CH₂CH₂CH₂OH is a primary FAs, which seems to be suitable alternative to HFCs.⁷ Kinetic content of the reaction of CF₃CH₂CH₂CH₂OH with OH radical is crucial to determine the tropospheric lifetimes of CF₃CH₂CH₂CH₂OH and its impact on the environment. In 2010, Albaladejo et al.⁸ have performed a kinetic study of CF₃CH₂CH₂CH₂OH reaction with hydroxyl radical at 298 K. Subsequently, to further investigate temperature effect of reaction of CF₃CH₂CH₂CH₂OH + OH, they have also reported rate constants of the above reaction between 263 to 358 K in experiment.⁷ Hence, theoretical studies on the accurate extrapolation of rate constants in higher temperatures for the title reaction are very necessary. Because no experimental information was available on the branching ratios of the products, it is desirable to give a further understanding of the reaction mechanisms and the dynamics. For the reaction of CF₃CH₂CH₂CH₂OH with OH radical, there are four classes of reaction channels as follows:

CF₃CH₂CH₂CH₂OH + OH → CF₃CH₂CH₂CH₂O + H₂O (R1)

→ CF₃CH₂CH₂CHOH + H₂O (R2)

→ CF₃CH₂CHCH₂OH + H₂O (R3a and R3b)

→ CF₃CHCH₂CH₂OH + H₂O (R4)

No other theoretical or experimental work has reported for above reactions. The mechanisms of reactions of ethers, esters, and alcohols with various free radicals have been comprehensively studied and continue to need paying considerable attention in experiment^7–13 and theory.^14–31 A number of experimental or theoretical investigations were also performed the rate coefficients of the ethers, esters, and alcohols with OH radicals or Cl atoms. However, it is unclear that the lifetime of some ethers, esters, and alcohols in theory or experiment. As is well known, the substituted ethers, esters, or alcohols by fluorine or chlorine will increase the environmental damage and pollution of the atmosphere compared to the un-substituted species. How to explain this issue? The atmospheric lifetimes of these species have a great significance to the understanding of their environmental behaviors and potential impact on human health, which they need to be more accurately estimated. The studies about the atmospheric lifetimes of ethers, esters, and alcohols are discussed detailed in following section. In addition to the atmospheric lifetimes of ethers, esters, and alcohols, we have summarized the recent theoretical researches about the ethers, esters, and alcohols with OH and Cl radicals about the rate constant, calculation methods. For all three systems, the optimized geometries, calculated frequencies are obtained from the density functional theory (DFT) or ab initio method. The rates are computed by using the (improved) canonical variational transition state theory with the small curvatures tunneling correction or canonical transition state theory (CTST). As is known that, the CVT/SCT rate constant is more accurate than the TST rate constant. The CVT/SCT methods not only can investigate the reaction path properties but also analysis the contribution of variational and tunneling effects. Furthermore, the tunneling effects are thought to be significant for H-abstraction reactions with many primary radicals. The canonical transition state theory, based on the assumption that trajectory will not return, is bound to overestimate the rate constant. On basis of the theoretical results, we can also deduce that optimized parameters from B3LYP, MPWB1K, M06-2X, BH&HLYP, BMK, and MP2 can be used to compute the rate constants. For the ethers, if the carbon chain is same, the fluorine or chlorine substitution can decrease the reactivity of C–H bond and the F-substitution results in a greater decrease than Cl-substitution in reactivity trend due to the larger electronegativity. For the rate constant with OH radical as an example, k_CH3OCH3 > k_CH3OCHCl2 > k_CH3OCF3, k_CH3OCH2CH3 > k_CH3OCH2CF3 > k_CH3OCHFCF3, k_CHF2OCH2CF3 > k_CHF2OCHClCF3 > k_CHF2OCHFCF3, k_{CH3OCH2CF2CF3} > k_{CH3OCF2CF2CF3}, k_{(CF3)2CHOCH2F} > k_(CF3)2CHOCH3.^30–39 Comparing the rate constant of OH with CH₃OCH₃ and CH₃OCH₂CH₃, we can find that the k_CH3OCH2CH3 > k_CH3OCH3, which suggest that the rate constant can increase with the carbon chain. Similar conclusions can be also found about the esters and alcohols. For the ethers reactions with Cl atom, esters, and alcohols, the above conclusion is also applicable. We also find that the rate constant of most ethers reaction with hydroxyl radical is larger than that with chlorine atom. However, the esters and alcohols reaction with hydroxyl radical is smaller than that with atomic chlorine. This may be owing to the difference of activation energy.

In this work, the variational transition state theory (VTST) with interpolated single-point energies (ISPE) are adopted to compute rate coefficient product branching ratios. Using the existing rate constants of ethers, esters, and alcohols reaction with OH and Cl radicals in the literatures, the atmospheric lifetime is estimated in this paper. And the literatures, only used for calculating the lifetimes, are presented in the ESI.† The discussion between the experimental and computational results is also listed. The kinetic isotope effects (KIEs) have been verified non-ignorable in studying the nature of some reactions about kinetics in experiment and theory.^40,41 Investigations of KIEs can help elucidate origins of particular deviations from natural abundance and provide detailed insight into dependent isotope reaction mechanisms. The KIEs are likely to be important in the kinetic investigations of the title reaction. As a result, theoretical studies on the KIEs for CF₃CH₂CH₂CH₂OH + OH/OD and CF₃CH₂CH₂CH₂OH/CF₃CD₂CD₂CD₂OD + OH reactions are desirable for laying direction for experiment.

2 Methodology and calculations details

Electronic structure calculations are performed with Gaussian 09 program package.⁴² MP2 (ref. 43) level combined with 6-311G(d,p) basis set is adopted to optimize and calculate the equilibrium geometries and frequencies of the reactants, products, complexes, and transition states. The MP2 method has been proven to be an accurate computational model for predicting electronic structure and energies in many articles.^44,45 In addition, M06-2X/6-311G(d,p)⁴⁶ method is also applied to optimize the parameters and calculate the frequencies. Intrinsic reaction coordinate (IRC)^47,48 calculations are done to ensure that the transition states connect to the correct reactants and products at MP2/6-311G(d,p) level. Moreover, single points energies of reactants, products, complexes, and transition states at the MP2/6-311G(d,p) geometries are refined computed by using CCSD(T)⁴⁹ and QCISD(T)⁵⁰ methods coupled with 6-311++G(d,p). The T₁ values of all species in our system are below 0.045, showing that multireference character in CCSD(T) wave function is not an issue.²⁶

By POLYRATE-Version 9.7 program,⁵¹ rate constants are received within 200–2000 K using the canonical variational transition state theory (CVT)^52–54 with the small-curvature tunneling (SCT) correction.^55,56 The relevant expressions are given as [eqn (1) and (2)]:

k^CVT_s(T) = min k^GT(T, s) (1)

In these equations, s is the location of the generalized transition state on the IRC; σ is the symmetry factor; β equals (k_BT)⁻¹ where k_B is Boltzmann's constant; h is Planck's constant; and Q^GT and Q^R are partition functions for the generalized transition state and reactants, respectively. In the calculation of the electronic partition functions, the two electronic states of the OH radicals, with a 140 cm⁻¹ splitting in the ²Π ground state, are included. The total rate constant k is calculated from the sum of the individual rate constants. The severe spin contamination can bring about errors in the barrier height.⁵⁷ The doublet range from 0.754 to 0.779 before annihilation, and after annihilation, the 〈s²〉 is 0.750. This suggests that the wave function is not severely contaminated.

3 Results and discussion

3.1 Stationary points and reaction mechanisms

The structural parameters of stationary points performed at the MP2/6-311G(d,p) and M06-2X/6-311G(d,p) levels are presented in Fig. 1, together with the limited experimental data.²⁸ We can get that the computed values are in accord with the experimental geometries parameters of OH and H₂O (given in the square bracket). Fig. 1 demonstrates that the breaking O–H bond in TS1 is 1.079 Å, which is 12.5% longer than the equilibrium O–H bond in CF₃CH₂CH₂CH₂OH, and the breaking C–H bonds are 6.3%, 9.8%, 8.9%, and 9.6% in TS2, TS3a, TS3b, and TS4 than the equilibrium C–H bonds length in CF₃CH₂CH₂CH₂OH. The forming O–H bonds are elongated by 28.2%, 46.6%, 35.5%, 37.9%, and 35.1% in TS1, TS2, TS3a, TS3b, and TS4 as compared to the O–H equilibrium bond length of H₂O, respectively. The elongation of the breaking bond is smaller than that of the forming bond, indicating that the transition states are reactant-like and the reactions R1–R4 may proceed via early transition states. Consequently, all the transition states can be considered as early barriers. Similar results can be found at the M06-2X/6-311G(d,p) level.

Fig. 1 Optimized geometries of the reactants, products, transition states, and complexes at the MP2 and M06-2X/6-311G(d,p) (in parenthesis) levels and the limited experimental values (in square brackets). Bond lengths are in angstroms and angles in degrees.

The harmonic vibrational frequencies are computed to confirm the stationary nature and to make zero-point energy (ZPE) corrections. The calculated frequencies at the MP2/6-311G(d,p) level are displayed in Table 1, along with the experimental data of OH and H₂O.²⁸ The five transition states are all confirmed by normal-mode analysis to have one and only one imaginary frequency, which corresponds to the stretching modes of coupling between breaking and forming bonds. The values of those imaginary frequencies are 2840i, 1241i, 1860i, 1720i, and 1826i cm⁻¹ for TS1, TS2, TS3a, TS3b, and TS4, respectively. Above large absolute values of the imaginary frequencies indicate that the tunneling effect may be more important in the evaluating of the rate constants.

Table 1 Frequencies (experimental values are in parentheses) (in cm⁻¹) and 〈s²〉 values for the reactants, products, transition states, hydrogen-bonded complexes at the MP2/6-311G(d,p) level^a

Species	Frequencies	〈s^2〉
a Experimental values in parenthesis are taken from ref. 28.
CF3CH2CH2CH2OH	62, 78, 124, 149, 241, 283, 331, 371, 479, 547, 582, 665, 789, 863, 890, 1056, 1071, 1089, 1118, 1190, 1215, 1274, 1275, 1300, 1339, 1353, 1361, 1446, 1495, 1502, 1524, 1554, 3026, 3071, 3102, 3111, 3158, 3177, 3909	0.0
CF3CH2CH2CH2O	70, 76, 124, 149, 277, 326, 371, 383, 491, 547, 586, 665, 782, 863, 936, 1058, 1087, 1094, 1108, 1199, 1254, 1286, 1313, 1325, 1363, 1414, 1429, 1453, 1498, 1518, 3000, 3048, 3100, 3109, 3156, 3175	0.757
CF3CH2CH2CHOH	63, 76, 126, 135, 281, 336, 358, 375, 479, 547, 582, 664, 673, 809, 864, 1018, 1063, 1098, 1143, 1186, 1228, 1261, 1280, 1302, 1353, 1356, 1439, 1490, 1501, 1512, 3049, 3111, 3132, 3159, 3176, 3910	0.760
CF3CH2CHCH2OH	40, 44, 94, 164, 225, 281, 333, 363, 429, 489, 544, 586, 662, 860, 892, 985, 1063, 1106, 1140, 1166, 1188, 1256, 1280, 1298, 1325, 1346, 1442, 1480, 1499, 1531, 2964, 3020, 3053, 3138, 3257, 3914	0.763
CF3CHCH2CH2OH	32, 46, 99, 163, 236, 273, 327, 333, 467, 481, 581, 601, 671, 808, 879, 1037, 1053, 1110, 1153, 1161, 1192, 1236, 1275, 1293, 1329, 1351, 1469, 1494, 1497, 1553, 3035, 3046, 3086, 3148, 3257, 3911	0.762
OH	3855 (3775)	0.754
H2O	1666 (1595), 3908 (3657), 4015 (3756)	0.0
TS1	2480i, 32, 67, 82, 93, 149, 152, 240, 293, 313, 371, 425, 510, 547, 584, 666, 784, 863, 868, 894, 1070, 1073, 1082, 1104, 1198, 1213, 1269, 1289, 1304, 1330, 1341, 1362, 1431, 1458, 1500, 1522, 1550, 1586, 3056, 3104, 3112, 3113, 3161, 3179, 3868	0.779
TS2	1241i, 35, 55, 82, 110, 131, 152, 203, 288, 333, 346, 374, 480, 548, 583, 666, 706, 820, 864, 879, 1046, 1060, 1092, 1115, 1171, 1192, 1261, 1270, 1274, 1304, 1337, 1355, 1364, 1445, 1481, 1507, 1522, 1567, 3066, 3100, 3113, 3158, 3182, 3833, 3900	0.773
TS3a	1860i, 35, 70, 108, 152, 156, 177, 270, 295, 338, 369, 462, 471, 545, 560, 642, 675, 789, 865, 926, 998, 1051, 1087, 1093, 1143, 1197, 1199, 1270, 1283, 1305, 1330, 1350, 1358, 1442, 1478, 1493, 1540, 1569, 3039, 3093, 3094, 3152, 3165, 3793, 3904	0.779
TS3b	1720i, 43, 80, 98, 124, 138, 169, 187, 270, 294, 332, 372, 481, 545, 581, 650, 666, 777, 860, 911, 1006, 1061, 1091, 1102, 1135, 1194, 1202, 1268, 1290, 1301, 1338, 1347, 1393, 1404, 1448, 1491, 1498, 1540, 3016, 3079, 3099, 3151, 3169, 3852, 3915,	0.778
TS4	1826i, 57, 62, 77, 87, 117, 169, 210, 240, 282, 333, 357, 460, 548, 567, 631, 669, 804, 834, 894, 927, 1056, 1082, 1113, 1139, 1186, 1220, 1252, 1276, 1308, 1320, 1337, 1354, 1419, 1479, 1497, 1511, 1555, 3034, 3086, 3094, 3154, 3168	0.778
ER1	19, 50, 75, 96, 125, 151, 209, 282, 306, 331, 371, 478, 502, 547, 583, 666, 683, 792, 864, 891, 1054, 1073, 1081, 1110, 1191, 1215, 1270, 1281, 1302, 1343, 1353, 1369, 1446, 1489, 1502, 1528, 1551, 3048, 3101, 3103, 3115, 3161, 3183, 3706, 3897	0.754
ER2	30, 58, 78, 100, 108, 123, 174, 236, 253, 284, 332, 357, 378, 480, 548, 582, 665, 784, 857, 890, 1058, 1062, 1091, 1117, 1196, 1208, 1267, 1278, 1301, 1340, 1349, 1364, 1445, 1495, 1506, 1518, 1555, 3030, 3085, 3108, 3116, 3164, 3183, 3836, 3911	0.754
ER3	17, 49, 63, 88, 112, 127, 152, 204, 239, 282, 329, 351, 376, 479, 550, 582, 664, 792, 864, 894, 1055, 1079, 1090, 1184, 1164, 1216, 1270, 1276, 1305, 1339, 1355, 1369, 1448, 1496, 1507, 1525, 1555, 3028, 3074, 3104, 3112, 3162, 3181, 3842, 3909	0.755
EP1	13, 50, 72, 80, 107, 126, 149, 173, 245, 288, 343, 371, 488, 495, 547, 585, 615, 665, 793, 863, 964, 1049, 1091, 1094, 1106, 1201, 1253, 1311, 1326, 1363, 1414, 1423, 1456, 1498, 1518, 1686, 3008, 3063, 3101, 3157, 3175, 3857, 3983	0.758
EP2	26, 40, 61, 96, 124, 133, 153, 171, 216, 285, 337, 375, 387, 431, 481, 549, 584, 666, 688, 816, 864, 1023, 1062, 1100, 1147, 1194, 1228, 1259, 1281, 1304, 1354, 1365, 1443, 1489, 1507, 1517, 1674, 6053, 3114, 3130, 3167, 3187, 3838, 3902, 3967	0.760
EP3	34, 35, 78, 89, 144, 196, 200, 245, 286, 316, 372, 392, 411, 424, 542, 554, 563, 666, 706, 848, 898, 938, 1015, 1086, 1164, 1164, 1178, 1205, 1259, 1296, 1303, 1334, 1449, 1488, 1499, 1537, 1704, 3057, 3079, 3119, 3174, 3251, 3787, 3871, 3963	0.763
EP4	18, 35, 67, 86, 102, 116, 184, 211, 235, 240, 268, 311, 332, 338, 474, 489, 579, 609, 660, 806, 868, 1021, 1047, 1103, 1146, 1164, 1184, 1229, 1271, 1298, 1335, 1348, 1475, 1487, 1506, 1562, 1684, 3040, 3062, 3129, 3166, 3260, 3900, 3913, 3996	0.762

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The diagrammatic potential energy diagram of the title reaction with ZPE corrections, received at the CCSD(T)/6-311++G(d,p)//MP2/6-311G(d,p) level, is plotted in Fig. 2. At the CCSD(T)/6-311++G(d,p)//MP2/6-311G(d,p) level, the reactant complexes (ER1, ER2, ER3) and product complexes (EP1, EP2, EP3, EP4) lie at the entrances and exits of H-abstraction pathways, respectively. For R1, R2, and R3a, these reactions are found to take place by pre-reaction complex (ER1) with 3.81 kcal mol⁻¹ binding energy. The OH can attack and abstract H of –OH group reaction R1, one of the H of –CH₂O– group reaction R2, or the H of beta carbon reaction R3a. Then, starting from the complex ER1, the transition states (TS1, TS2, and TS3a) are occurred with 8.26, 3.86, and 6.19 kcal mol⁻¹ barriers height, respectively. The geometries and pattern of attack of OH radical ER1 (OH⋯O(H)CH₂CH₂CH₂CF₃) is similar to the pre-complex (OH⋯O(H)CH₂CH₃) of reaction C₂H₅OH with OH radical²⁴ and COM0 (OH⋯O(H)CH₂CH₂CH₂CH₃) of reaction of n-butanol by OH radical,¹⁷ which indicates the ER1 is credible. After crossing these transition states, the product complexes EP1, EP2, and EP3 are respectively formed with energies of 2.21, 2.29, and 5.20 kcal mol⁻¹ below the products.

Fig. 2 Schematic potential energy surface for the reaction of CF₃CH₂CH₂CH₂OH + OH. Relative energies (in kcal mol⁻¹) are calculated at the CCSD(T)/6-311++G(d,p)//MP2/6-311G(d,p) + ZPE level.

For reactions R3b and R4, the reactant compounds ER2 and ER3 are come into being with energies −1.72 and −2.06 kcal mol⁻¹ relative to the reactants. Afterwards, the reactions form EP3 and EP4 in the exit routes by means of TS3b and TS4, respectively, which are about 3.35 and 3.75 kcal mol⁻¹ in energy. The hydrogen-bond attraction interaction between the H atom of –OH and the O atom of CF₃CH₂CH₂CH₂OH in TS3a, the H atom of –OH and the F atom of –CF₃ group in TS3b because of fluorine and oxygen atom have high electronegativities. Both of TS3a and TS3b can proceed via EP3 to form CF₃CH₂CHCH₂OH (P3) and H₂O. By comparing the barrier height of the reaction channels R1–R4 each other, we deduce that R2 is the main contribution channel. Similar results can be shown that the barrier height of OH reaction with CF₃CH₂OH, CF₃CF₂CH₂OH, and CF₃CH₂CH₂OH to abstract the H atom of –CH₂O– is lower than other site.^18–20 Some investigations on Cl atom reaction with FAs have also found that the H atom of –CH₂O– group is the easiest to be abstracted, such as Cl atom with CH_3−nF_nCH₂OH by Wang et al.²² and with CF₃CF₂CH₂OH by Yu²³ and Garzón⁵⁸ et al. For reaction of CF₃CH₂CH₂CH₂OH with Cl atom, only one experimental research performed at 298 K was reported the rate coefficient by Albaladejo et al.⁸ There is no evidence to suggest the most favorable channel in theoretical and experimental analysis. Here, we predict that Cl atom will also attack the –CH₂O– group primarily by the comparison with similar reactions. An in-deep study about the reaction of CF₃CH₂CH₂CH₂OH + Cl and its comparisons with similar reactions will proceed in the future. With respect to reaction trends of some FAs with OH radical, a detailed discussion is shown in the following section of comparison with similar reactions.

3.2 Thermodynamics data prediction

The relative energy (E_r) of species for R1–R4 with ZPE corrections and T₁ diagnostic values at CCSD(T)/6-311++G(d,p) level is organized in Table 2. Reaction enthalpies (ΔH^θ_r,298), reaction Gibbs free energies (ΔG^θ_r,298) for R1–R4, and bonds dissociation energy (D^θ₂₉₈) of C–H in molecule CF₃CH₂CH₂CH₂OH are displayed in Table 3. As listed in Tables 2 and 3, the results acquired by CCSD(T) and QCISD(T) ways show good mutual accord. Note that the following mentioned data is obtained at the CCSD(T)/6-311++G(d,p)//MP2/6-311G(d,p) level. It is easy to see that all of the individual reactions are exothermic From Table 3. The results of ΔG^θ_r,298 indicate that all hydrogen abstraction reactions of CF₃CH₂CH₂CH₂OH by OH radical are spontaneous. Comparing the values of ΔH^θ_r,298 each other of all reactions, it can be seen that heats of exothermic R1 and R2 are the fewest and most, respectively. The value of ΔG^θ_r,298 of reaction R2 is lowest, −21.44 kcal mol⁻¹, which shows that the spontaneous tendency is the largest of all the reactions. The value of D^θ₂₉₈ (99.20 kcal mol⁻¹) of reaction CF₃CH₂CH₂CH₂OH → CF₃CH₂CH₂CHOH + H is lower than that of other reactions, and the D^θ₂₉₈ value of reaction CF₃CH₂CH₂CH₂OH → CF₃CH₂CH₂CH₂O + H (108.64 kcal mol⁻¹) is higher than other reactions. These indicate that owing to the H atom of –CH₂O– is easiest to be dissociated, thus, is easy to be abstracted, and the H atom of –OH is hardest to be dissociated, thus, is difficult to be abstracted. Wang et al. have calculated the D^θ₂₉₈ value of C–H bond of CH_3–xF_xCH₂OH (x = 0–3),^18,22 CF₃CF₂CH₂OH,¹⁹ similar conclusion is obtained in their paper. Comparing the D^θ₂₉₈ values of reaction CF₃CH₂CH₂CH₂OH → CF₃CH₂CHCH₂OH + H and reaction CF₃CH₂CH₂CH₂OH → CF₃CHCH₂CH₂OH + H, we can deduce that the R3 and R4 will be competitive with each other. The above conclusion further supports the cases occurred in the barrier heights for reactions R1–R4 and will be proved again in the section of rate constant computations.

Table 2 Relative energies (E_r) (in kcal mol⁻¹) of main species for reactions R1–R4 with the ZPE corrections (in a.u.) and T₁ diagnostic values

Species	ZPE^a	T1^b	Er^a	Er^b	Er^c
a Obtained at the MP2/6-311G(d,p) level.b Obtained at CCSD(T)/6-311++G(d,p)//MP2/6-311G(d,p) level.c Obtained at QCISD(T)/6-311++G(d,p)//MP2/6-311G(d,p) level.
R + OH	0.125401	0.012, 0.010	0.00	0.00	0.00
ER1	0.128756	0.012	−6.09	−3.81	−3.75
TS1	0.123540	0.021	6.40	4.45	4.20
EP1	0.126637	0.014	−14.08	−14.68	−14.80
P1 + H2O	0.122724	0.014, 0.010	−9.70	−12.47	−12.56
TS2	0.123914	0.018	2.34	0.05	−0.25
EP2	0.127140	0.014	−26.50	−22.94	−23.10
P2 + H2O	0.124719	0.014, 0.010	−21.97	−20.65	−20.79
TS3a	0.123836	0.016	3.26	2.38	2.16
ER2	0.127403	0.013	−3.55	−1.73	−1.75
TS3b	0122996	0.016	4.84	3.35	3.13
EP3	0.127929	0.013	−23.26	−20.15	−20.26
P3 + H2O	0.123171	0.013, 0.010	−15.25	−14.95	−15.00
ER3	0.127163	0.012	−3.43	−2.06	−2.07
TS4	0.122411	0.016	5.53	3.75	3.53
EP4	0.126156	0.013	−19.05	−16.75	−16.88
P4 + H2O	0.123683	0.013, 0.010	−14.39	−13.98	−14.08

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Table 3 Reaction enthalpies (ΔH^θ_r,298), reaction Gibbs free energies (ΔG^θ_r,298) for reactions R1–R4 and the calculated bonds dissociation energy (D^θ₂₉₈) of C–H in molecule CF₃CH₂CH₂CH₂OH (in kcal mol⁻¹) with the ZPE or TZPE corrections (thermal corrections to enthalpies or Gibbs free energies)

	MP2	CCSD(T)//MP2	QCISD(T)//MP2
ΔH^θr,298
CF3CH2CH2CH2OH + OH → CF3CH2CH2CH2O + H2O	−9.53	−12.52	−12.62
CF3CH2CH2CH2OH + OH → CF3CH2CH2CHOH + H2O	−21.72	−20.41	−20.54
CF3CH2CH2CH2OH + OH → CF3CH2CHCH2OH + H2O	−14.72	−14.42	−14.48
CF3CH2CH2CH2OH + OH → CF3CHCH2CH2OH + H2O	−13.86	−13.46	−13.56
ΔG^θr,298
CF3CH2CH2CH2OH + OH → CF3CH2CH2CH2O + H2O	−10.38	−13.00	−13.10
CF3CH2CH2CH2OH + OH → CF3CH2CH2CHOH + H2O	−22.75	−21.44	−21.57
CF3CH2CH2CH2OH + OH → CF3CH2CHCH2OH + H2O	−16.78	−16.48	−16.54
CF3CH2CH2CH2OH + OH → CF3CHCH2CH2OH + H2O	−16.02	−15.62	−15.72
D^θ298
CF3CH2CH2CH2OH → CF3CH2CH2CH2O + H	111.47	108.64	108.60
CF3CH2CH2CH2OH → CF3CH2CH2CHOH + H	98.48	99.20	99.12
CF3CH2CH2CH2OH → CF3CH2CHCH2OH + H	106.17	105.88	105.87
CF3CH2CH2CH2OH → CF3CHCH2CH2OH + H	106.71	106.52	106.48

---

The enthalpy of formation (ΔH^θ_f,298) are predicted by means of isodesmic reaction, in which the electron pairs and types of bond are conserved in both sides of the reaction. Herein, the ΔH^θ_f,298 of the reactant CF₃CH₂CH₂CH₂OH and product radicals CF₃CH₂CH₂CH₂O CF₃CH₂CH₂CHOH, CF₃CH₂CHCH₂OH, and CF₃CHCH₂CH₂OH are predicted as follows:

CF₃CH₂CH₂CH₂OH + CH₃ + CH₃ + CH₃ → CH₂OH + CH₃CF₃ + CH₂CH₃ + CH₂CH₃ (R5a)

CF₃CH₂CH₂CH₂OH + CH₃ + CH₃ + CH₄ → CH₃OH + CH₃CF₃ + CH₂CH₃ + CH₂CH₃ (R5b)

CF₃CH₂CH₂CH₂OH + CH₃ + CH₄ + CH₄ → CH₃OH + CH₃CF₃ + CH₂CH₃ + CH₃CH₃ (R5c)

CF₃CH₂CH₂CH₂O + CH₃ + CH₃ + CH₄ → CH₂OH + CH₃CF₃ + CH₂CH₃ + CH₂CH₃ (R6a)

CF₃CH₂CH₂CH₂O + CH₃ + CH₄ + CH₄ → CH₃OH + CH₃CF₃ + CH₂CH₃ + CH₂CH₃ (R6b)

CF₃CH₂CH₂CH₂O + CH₄ + CH₄ + CH₄ → CH₃OH + CH₃CF₃ + CH₂CH₃ + CH₃CH₃ (R6c)

CF₃CH₂CH₂CHOH + CH₃ + CH₃ + CH₄ → CH₂OH + CH₃CF₃ + CH₂CH₃ + CH₂CH₃ (R7a)

CF₃CH₂CH₂CHOH + CH₃ + CH₄ + CH₄ → CH₃OH + CH₃CF₃ + CH₂CH₃ + CH₂CH₃ (R7b)

CF₃CH₂CH₂CHOH + CH₄ + CH₄ + CH₄ → CH₃OH + CH₃CF₃ + CH₂CH₃ + CH₃CH₃ (R7c)

CF₃CH₂CHCH₂OH + CH₃ + CH₃ + CH₄ → CH₂OH + CH₃CF₃ + CH₂CH₃ + CH₂CH₃ (R8a)

CF₃CH₂CHCH₂OH + CH₃ + CH₄ + CH₄ → CH₃OH + CH₃CF₃ + CH₂CH₃ + CH₂CH₃ (R8b)

CF₃CH₂CHCH₂OH + CH₄ + CH₄ + CH₄ → CH₃OH + CH₃CF₃ + CH₂CH₃ + CH₃CH₃ (R8c)

CF₃CHCH₂CH₂OH + CH₃ + CH₃ + CH₄ → CH₂OH + CH₃CF₃ + CH₂CH₃ + CH₂CH₃ (R9a)

CF₃CHCH₂CH₂OH + CH₃ + CH₄ + CH₄ → CH₃OH + CH₃CF₃ + CH₂CH₃ + CH₂CH₃ (R9b)

CF₃CHCH₂CH₂OH + CH₄ + CH₄ + CH₄ → CH₃OH + CH₃CF₃ + CH₂CH₃ + CH₃CH₃ (R9c)

The ΔH^θ_f,298 in experiment for the other species involved in above reactions are (in units of kcal mol⁻¹): CH₃, 34.82; CH₄, −17.8; CH₂OH, −2.2; CH₃OH, −48.1; CH₂CH₃, 28.40; CH₃CH₃, −20.04; CH₃CF₃, −178.94.^18,26 The ΔH^θ_f,298 of the CF₃CH₂CH₂CH₂OH, CF₃CH₂CH₂CH₂O, CF₃CH₂CH₂CHOH, CF₃CH₂CHCH₂OH, and CF₃CHCH₂CH₂OH are calculated at MP2/6-311G(d,p), CCSD(T) and QCISD(T)/6-311++G(d,p)//MP2/6-311G(d,p) levels. As shown in Table 4, the values of ΔH^θ_f,298 for the species obtained at the CCSD(T) and QCISD(T) levels are very close with the greatest difference of 0.13 kcal mol⁻¹. On basis of the computational results, the values of ΔH^θ_f,298 for CF₃CH₂CH₂CH₂OH, CF₃CH₂CH₂CH₂O, CF₃CH₂CH₂CHOH, CF₃CH₂CHCH₂OH, and CF₃CHCH₂CH₂OH are recommended to be (−225.48 ± 0.70), (−173.46 ± 0.73), (−181.36 ± 0.75), (−175.33 ± 0.71), and (−174.40 ± 0.73) kcal mol⁻¹, respectively. These above mentioned results are unavailable in the literature and may be useful for further researching thermodynamics and kinetics of reactions related to these species.

Table 4 The standard enthalpy of formation (ΔH^θ_f,298) (in kcal mol⁻¹) for the species CF₃CH₂CH₂CH₂OH, CF₃CH₂CH₂CH₂O, CF₃CH₂CH₂CHOH, CF₃CH₂CHCH₂OH, and CF₃CHCH₂CH₂OH

Species	Isodesmic reaction	MP2		CCSD(T)//MP2		QCISD(T)//MP2
		ΔH^θf,298	Average	ΔH^θf,298	Average	ΔH^θf,298	Average
CF3CH2CH2CH2OH	R5a	−225.45	−226.73	−225.26	−225.40	−225.18	−225.39
	R5b	−228.21		−226.17		−226.17
	R5c	−226.52		−224.78		−224.81
	R6a	−171.18		−173.21		−173.18
CF3CH2CH2CH2O	R6b	−172.94	−171.79	−174.11	−173.35	−174.18	−173.39
	R6c	−171.25		−172.73		−172.81
	R7a	−182.61		−181.09		−181.11
CF3CH2CH2CHOH	R7b	−184.38	−183.22	−182.00	−181.23	−182.10	−181.32
	R7c	−182.68		−180.61		−180.74
	R8a	−175.61		−175.10		−175.04
CF3CH2CHCH2OH	R8b	−177.38	−176.22	−176.00	−175.24	−176.04	−175.25
	R8c	−175.68		−174.62		−174.68
	R9a	−174.75		−174.15		−174.13
CF3CHCH2CH2OH	R9b	−176.52	−175.37	−175.05	−174.29	−175.12	−174.34
	R9c	−174.83		−173.67		−173.76

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3.3 Reaction channel content

A dual-level direct kinetics calculation is adopted to compute the dynamic content at the CCSD(T)/6-311++G(d,p)//MP2/6-311G(d,p) level. Fig. 3a and b depict the classical potential energy curve (V_MEP), ground-state vibrational adiabatic energy curve (V^G_a), and zero-point energy curve (ZPE) as functions of s (amu)^1/2 bohr for the reactions R2 and R3a. From Fig. 3a, it is seen that the plots of the V^G_a and V_MEP are similar, and zenith of V^G_a and V_MEP are same at 0.17 (amu)^1/2 bohr, indicating that the negligible variational effect can be found for the channel R2. Wang and Li have theoretically studied the reactions of some FAs with OH radical or Cl atom, similar results can be found about potential energy curves in their papers.^18,19,22 Fig. 3b shows that the maximum of V^G_a is located as s = −0.34 (amu)^1/2 bohr in the reactant side for R3a. However, the maximum value of V_MEP is located as the saddle point (s = 0). The variational effect may be worthy of consideration in evaluating the rate constant.

Fig. 3 Classical potential energy curve (V_MEP), ground-state vibrational adiabatic energy curve (V^G_a), and zero-point energy curve (ZPE) as functions of s (amu)^1/2 bohr at the CCSD(T)/6-311++G(d,p)//MP2/6-311G(d,p) level (a) for the reaction channel R2 and (b) for the R3a.

Fig. 4a and b exhibit that the variations of the vibrational frequencies along with the MEPs for R2 and R3a, respectively. In the negative of s = −2.0 (amu)^1/2 bohr, the frequencies are connected with those of the pre-complexes, and at about s = 1.5 (amu)^1/2 bohr, the frequencies amount to those of the product complexes. In the process of the reaction, the frequency of mode 1 which is referred to as the “reactive mode” shows an evident drop along with the reaction. This is the characteristic of these reactions which transfer H atoms. Fig. 4b suggests that in the vicinity of the TS, there are 44 frequencies and deep minimum in frequency occurs from 0 to 0.34 (amu)^1/2 bohr.

Fig. 4 Changes of generalized normal-mode vibrational frequencies as functions of s (amu)^1/2 bohr at the CCSD(T)/6-311++G(d,p)//MP2/6-311G(d,p) level for reaction R1 via TS2 (a) and R2 via TS3a (b).

3.4 Rate-constant computations and branching ratios

Seen from Fig. 2, the mechanism of the CF₃CH₂CH₂CH₂OH + OH can be represented as:

R1 + R2 ↔ R1⋯R2 step 1

R1⋯R2 → P1 + P2 step 2

The first reversible step leads to the formation of reactant complex, and the second irreversible step yields the corresponding products. k₁ is the forward rate constant while k₋₁ is the reverse rate constant in the first step. k₂ is equivalent to the second step. According to the steady-state analysis, the total rate constant can be displayed by [eqn (3)]

As first discussed in the paper of Singleton and Cvetanović,⁵⁹ k₋₁ is much larger than k₂, thus k could be rewritten as [eqn (4)]

Using basic statistical thermodynamic theory, the equilibrium constant (K_eq) between the two reactants and the reactant complex can be denoted as [eqn (5)]. Under high-pressure conditions, the k₂ calculated by classical TST method and corresponding rate constant k can be expressed as [eqn (6) and (7)]

In the above equations, the Q_ER, Q_TS, and Q_R are the partition functions of the reactant complex, transition state, and the reactants, respectively. The κ is the tunneling factor; k_B is Boltzmann constant and h is Planck constant. In fact, previous articles for similar mechanisms^60–64 always assumed reactant complex undergoes collisional stabilization in a high-pressure limit. Option “well” can be used for the dynamic calculations in the Polyrate program, so both above steps are considered in the theoretical discussion.

The rate constants of TST, CVT, CVT/SCT for the primary channel R2 and secondary reaction pathway R3a are illustrated in Fig. 5a and b, respectively. The k₁, k₂, k_3a, k_3b, k₄ and k (k= k₁ + k₂ + k_3a + k_3b + k₄) are listed in Table 5 and depicted in Fig. 6 (CVT/SCT rate constants). For reaction R2, Fig. 5a shows that the CVT and TST are overlap each other over the whole temperature range, illustrating that the effect from variational effects may be negligible. Nevertheless, difference between the CVT and CVT/SCT is distinct in 200–800 K and coincide with each other with the temperature increasing, demonstrating that the tunneling effects are momentous at low temperatures and can be ignored when temperatures are above 800 K. The characteristics of the current reactions can be also discovered in other similar systems, as investigated by Wang et al.^18,19,21,22 and other authors.^23,25–31 Moreover, Fig. 5b depicts that the ratios of CVT and TST are 0.75–0.77 in temperature limits from 200 to 2000 K, showing that the we should attach importance to the variational effects in calculations of rate coefficient of R3a. The tunneling effects come under observation to be important for reaction R3a in the temperature of 200–1000 K, while with the temperature increasing, the tunneling effect can be neglectful. For example, the ratios between the CVT/SCT and CVT are 10.92, 3.33, 1.12, and 1.03 at 200, 298, 1000, and 2000 K, respectively. From Table 5, it is pleasing to observe that our rate constants in 200–2000 K are in line with the coefficients in experimental temperatures (263–358 K). So for example, computed values of 3.93 × 10⁻¹², 4.01 × 10⁻¹² and experimental values of 2.62 × 10⁻¹², 3.14 × 10⁻¹² cm³ per molecule per s at 298 and 308 K, respectively. In order to display the calculated and experimental data in point and range style more intuitively, we also depict the CVT/SCT rate constants of k₁, k₂, k_3a, k_3b, and k₄ and the total rate constant k in Fig. 6. As is shown in Fig. 6, positive temperature effect dependence effect can be observed from 230 to 2000 K for the main reaction channel R2. Reaction channels R1, R3a, R3b, and R4 all have positive temperature effect in the whole temperature range.

Fig. 5 Computed TST, CVT, and CVT/SCT rate constants versus 10³/T between 200 and 2000 K (a) for reaction channel R2, (b) for the R3a.

Table 5 Calculated CVT/SCT rate constants (in cm³ per molecule per s) along with the experimental values (italics) for the reaction CF₃CH₂CH₂CH₂OH + OH in the temperature range of 200–2000 K. (The mark of (Y) represents the tunneling effect comes under consideration, and (N) represents the tunneling effects can be neglectful.)

T (K)	k1	k2	k3a	k3b	k4	k
a Obtained from ref. 7.b Obtained from ref. 8.
200	2.02 × 10^−15 (Y)	3.73 × 10^−12 (Y)	3.09 × 10^−14 (Y)	3.25 × 10^−15 (Y)	8.86 × 10^−16 (Y)	3.77 × 10^−12 (Y)
230	2.78 × 10^−15 (Y)	3.64 × 10^−12 (Y)	3.78 × 10^−14 (Y)	6.62 × 10^−15 (Y)	2.58 × 10^−15 (Y)	3.69 × 10^−12 (Y)
263	3.84 × 10^−15 (Y)	3.69 × 10^−12 (Y)	4.72 × 10^−14 (Y)	1.31 × 10^−14 (Y)	6.61 × 10^−15 (Y)	3.76 × 10^−12 (Y)
						(2.41 ± 0.25) × 10^−12 ^a
270	4.11 × 10^−15 (Y)	3.71 × 10^−12 (Y)	4.95 × 10^−14 (Y)	1.49 × 10^−14 (Y)	7.89 × 10^−15 (Y)	3.79 × 10^−12 (Y)
						(2.63 ± 0.27) × 10^−12 ^a
278	4.43 × 10^−15 (Y)	3.74 × 10^−12 (Y)	5.22 × 10^−14 (Y)	1.72 × 10^−14 (Y)	9.57 × 10^−15 (Y)	3.82 × 10^−12 (Y)
						(2.48 ± 0.30) × 10^−12 ^a
287	4.81 × 10^−15 (Y)	3.78 × 10^−12 (Y)	5.53 × 10^−14 (Y)	2.02 × 10^−14 (Y)	1.18 × 10^−14 (Y)	3.87 × 10^−12 (Y)
						(2.42 ± 0.26) × 10^−12 ^a
298	5.33 × 10^−15 (Y)	3.83 × 10^−12 (Y)	5.94 × 10^−14 (Y)	2.43 × 10^−14 (Y)	1.49 × 10^−14 (Y)	3.93 × 10^−12 (Y)
						(2.62 ± 0.32) × 10^−12 ^b
308	5.83 × 10^−15 (Y)	3.89 × 10^−12 (Y)	6.33 × 10^−14 (Y)	2.85 × 10^−14 (Y)	1.84 × 10^−14 (Y)	4.01 × 10^−12 (Y)
						(3.14 ± 0.32) × 10^−12 ^a
323	6.67 × 10^−15 (Y)	3.99 × 10^−12 (Y)	6.96 × 10^−14 (Y)	3.59 × 10^−14 (Y)	2.46 × 10^−14 (Y)	4.13 × 10^−12 (Y)
						(3.53 ± 0.37) × 10^−12 ^a
338	7.61 × 10^−15 (Y)	4.10 × 10^−12 (Y)	7.63 × 10^−14 (Y)	4.46 × 10^−14 (Y)	3.22 × 10^−14 (Y)	4.26 × 10^−12 (Y)
						(3.34 ± 0.34) × 10^−12 ^a
358	9.05 × 10^−15 (Y)	4.27 × 10^−12 (Y)	8.61 × 10^−14 (Y)	5.85 × 10^−14 (Y)	4.51 × 10^−14 (Y)	4.47 × 10^−12 (Y)
						(3.54 ± 0.37) × 10^−12 ^a
400	1.29 × 10^−14 (Y)	4.69 × 10^−12 (Y)	1.10 × 10^−13 (Y)	9.75 × 10^−14 (Y)	8.38 × 10^−14 (Y)	4.99 × 10^−12 (Y)
500	2.86 × 10^−14 (Y)	6.06 × 10^−12 (Y)	1.84 × 10^−13 (Y)	2.61 × 10^−13 (N)	2.67 × 10^−13 (Y)	6.80 × 10^−12 (Y)
600	5.82 × 10^−14 (Y)	7.89 × 10^−12 (Y)	2.89 × 10^−13 (Y)	5.60 × 10^−13 (N)	6.42 × 10^−13 (Y)	9.44 × 10^−12 (Y)
800	1.91 × 10^−13 (Y)	1.30 × 10^−11 (Y)	6.11 × 10^−13 (Y)	1.75 × 10^−12 (N)	2.29 × 10^−12 (N)	1.78 × 10^−11 (Y)
1000	4.91 × 10^−13 (Y)	2.03 × 10^−11 (N)	1.11 × 10^−13 (Y)	4.02 × 10^−12 (N)	5.71 × 10^−12 (N)	3.16 × 10^−11 (N)
1200	1.06 × 10^−12 (Y)	2.95 × 10^−11 (N)	1.82 × 10^−13 (N)	7.67 × 10^−12 (N)	1.15 × 10^−11 (N)	5.16 × 10^−11 (N)
1500	2.69 × 10^−12 (Y)	4.58 × 10^−11 (N)	3.31 × 10^−13 (N)	1.62 × 10^−11 (N)	2.56 × 10^−11 (N)	9.36 × 10^−11 (N)
1800	5.69 × 10^−12 (N)	6.79 × 10^−11 (N)	5.33 × 10^−13 (N)	2.88 × 10^−11 (N)	4.70 × 10^−11 (N)	1.55 × 10^−10 (N)
2000	8.70 × 10^−12 (N)	8.57 × 10^−11 (N)	6.95 × 10^−13 (N)	3.95 × 10^−11 (N)	6.57 × 10^−11 (N)	2.07 × 10^−10 (N)

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Fig. 6 Computed rate constants for the reaction pathways of CF₃CH₂CH₂CH₂OH + OH (k₁, k₂, k_3a, k_3b, and k₄), and the total rate constant k (k = k₁ + k₂ + k_3a + k_3b + k₄) at the CCSD(T)/6-311++G(d,p)//MP2/6-311G(d,p) level together with the experiment data as functions of 10³/T.

Fig. 7 shows branching ratios of each pathways. It can be found that channel R2 plays a fundamental role within 200–2000 K. However, the contribution of channel R1 is fewest in the whole temperature range. Competitive channels R3 contributes more than R4 to the total reaction coefficient when the temperature is below 800 K, but with the temperature increasing, channel R4 should be considered. When the temperature is above 800 K, contributions of the reaction pathways are in this order, k₂ > k₄ > k₃ > k₁. Thus, for the multi-channel reaction, the dominant channel is the H-abstraction from the –CH₂O– group leading to the product CF₃CH₂CH₂CHOH.

Fig. 7 Computed branching ratios versus 10³/T between 200 and 2000 K for the reaction of CF₃CH₂CH₂CH₂OH + OH.

3.5 Kinetic isotope effects (KIEs)

KIEs for the systems CF₃CH₂CH₂CH₂OH + OD (R′) and CF₃CD₂CD₂CD₂OD + OH (R*) have been investigated over the whole temperature scope of 200–2000 K, in which the KIEs are defined as the specific values of the between k^H and k^D. The calculated KIEs for reactions R1′ (R1*), R2′ (R2*), R3a′ (R3a*), R3b′ (R3b*), and R4′ (R4*) are displayed in the Fig. 8a and b, respectively. It can be seen that the KIEs of the total rate coefficients k/k′ and k/k* are normal, that is, larger than 1 (k^H/k^D > 1) at the whole temperature range. In general, the KIEs of the k/k′ and k/k* mostly increase with the decreasing of temperature. For the main pathway R2, the KIEs of k₂/k′₂ and k₂/k^*₂ also get a similar circumstance with the total reaction rate constant. For reaction channel R3a, the KIEs for R3a′ are within 0.40–0.70, suggesting that a noticeable inverse (k^H/k^D < 1) exists. The KIEs for R3a* are within 1.1–1.2 (around 1.0), indicating that the KIE is of less importance for this channel. The KIEs for R4′ are within 0.86–1.00, 1.00–1.24 at the temperature range of 200–287 K and 287–2000 K, respectively. This implies a noticeable inverse can be found in the 200–287 K for R4′ and a slight normal KIE between 287 and 2000 K. Similar results exist in the 200–500 K for R4*. Comparing the KIEs of R′ with R*, we find that the results of KIEs result from the CF₃CH₂CH₂CH₂OH + OD (R′) and CF₃CD₂CD₂CD₂OD + OH (R*) are different and the KIEs of main pathway R2* is larger than R2′. For example, the KIEs are 2.06 at 298 K, 1.95 at 500 K, 1.73 at 1000 K, and 1.45 at 2000 K for R*, and 1.27 at 298 K, 1.11 at 500 K, 1.05 at 1000 K, and 1.04 at 2000 K for R′. Taking a comparison between the reactions R1′–R4′, it is seen that the R3a′ affected by the KIE is significant. However, we find that the KIE for R1* is 6.99, 6.10, 4.02, and 3.07 at 298, 500, 1000, and 2000 K, respectively, which suggests that the KIE of R1* is the most important of for reactions R1*–R4*. Above isotope effects have also been found in many reactions.^{39–41,65,66} Although there can be not provide a comparison between corresponding experiment and theory, our results can add unprecedented information for using in further experimental study.

Fig. 8 Plot of the calculated ratios k₁/k′₁ (k₁/k^*₁), k₂/k′₂ (k₂/k^*₂), k_3a/k′_3a (k_3a/k^*_3a), k_3b/k′_3b (k_3b/k^*_3b), and k₄/k′₄ (k₄/k^*₄) versus 10³/T in the temperature range of 200–2000 K.

3.6 Comparison with similar reactions

It is desirable to make a comparison between the title reaction and the similar alcohols (OH radical with the CH₃CH₂CH₂CH₂OH, CH₃CH₂CH₂OH, CF₃CF₂CH₂OH, CF₃CH₂CH₂OH, CF₃CH₂OH, CH₃CH₂OH, CF₃OH, and CH₃OH) in dynamics.^{14–16,18–20,24} The comparisons will give some worthy similarities and differences. Comparing the overall rate constants of OH + CF₃(CH₂)_mOH (m = 0−3) each other, we can find the following relationship at 298 K: k_{CF3CH2CH2CH2OH} > k_CF3CH2CH2OH > k_CF3CH2OH > k_CF3OH. This trend could be attributed to the electron donating group effect. The rate constants will increase with the increasing of carbon chain when CF₃(CH₂)_mOH reaction with electron withdrawing group, like OH radical. To compare the overall reaction constants of OH with CH₃(CH₂)_mOH (m = 0–3),^15–17,24 similar conclusion can be found, in which should be as: k_{CH3CH2CH2CH2OH} > k_CH3CH2CH2OH > k_CH3CH2OH > k_CH3OH. It should be noted that for the reactions of OH with R(CH₂)_nOH (R = –CF₃ or –CH₃; n = 1–3), the attack takes place at the –CH₂O– group for the most part, which was discussed in the preceding part of the text. In fact, the fluorine substitution can decrease the reactivity, it is a matter of concern that OH radical reaction with a series of alcohols about rate coefficient at 298 K are in the sequence: k_CF3CH2CH2OH > k_CF3CF2CH2OH, k_CH3CH2CH2OH > k_CF3CH2CH2OH, _kCH3CH2OH > k_CF3CH2OH, k_CH3OH > k_CF3OH.

3.7 Atmospheric lifetime of ethers, esters, and alcohols

The atmospheric lifetime can be estimated by the expression can be shown as [eqn (8)–(10)]:

Using the average atmospheric OH and Cl concentrations⁶⁷ of 1 × 10⁶ and 1 × 10⁴ molecule per cm³, the atmospheric lifetime is estimated based on the existing data to add atmospheric content of the ethers, esters, and alcohols. Using the total rate constant 3.82 × 10⁻¹² cm³ per molecule per s at 278 K and the OH concentrations of 1.0 × 10⁶ molecule per cm³, the computed atmospheric lifetime of CF₃CH₂CH₂CH₂OH is being of 3.03 days, which coincides with the values of 3.70 days and 4.5 days in experiment.^7,8 The lifetime of CF₃CH₂CH₂CH₂OH is relatively short, suggesting its inconsiderable impact to the global warming of Earth. In addition, theoretical researches about the ethers, esters, and alcohols with OH radicals and Cl atoms about the rate constant, calculation methods, and lifetimes are summarized in Tables S1a–S1c.† For the ethers, esters, and alcohols, because of the atmospheric lifetime is going conversely with the rate constant when the concentration of OH and Cl radicals is set to be constant. For example, the atmospheric lifetime of CF₃OCH₂CF₃ is 0.521 years, which is smaller than that of CF₃OCHFCF₃ (24.38 years). For typical esters and alcohols, the atmospheric lifetimes are in this order, τ_CF3COOCH3>τ_CF2HCOOCH3, τ_CF3CH2OH>τ_CH3CH2OH. Therefore, the fluorine or chlorine substitution can increase lifetime of ethers, esters, and alcohols, that is, more and more fluorine or chlorine substitution can add its contribution to the global warming of Earth and ability to destroy the ozone layer. In terms of atmospheric lifetimes, the disadvantage of fluorine or chlorine substitution can be explained thoroughly.

Due to experimental data is lacking in higher temperatures, the fitted three-parameter on basis of the calculated rate constants within 200–2000 K give expressions as follows (in units of cm³ per molecule per s):

k₁(T) = 3.27 × 10⁻²⁴T^3.79 exp(–483.24/T)

k₂(T) = 3.43 × 10⁻¹⁹T^2.50 exp(579.78/T)

k_3a(T) = 1.53 × 10⁻²⁰T^2.62 exp(8.69/T)

k_3b(T) = 1.60 × 10⁻¹⁸T^2.33 exp(−1333.72/T)

k₄(T) = 3.90 × 10⁻¹⁸T^2.30 exp(−1689.15/T)

k(T) = 3.43 × 10⁻²¹T^3.22 exp(741.70/T).

4 Conclusions

In this article, reaction of CF₃CH₂CH₂CHOH with OH radical is investigated in kinetics by the dual-level direct method. The PES information is obtained at the CCSD(T) and QCISD(T)/6-311++G(d,p)//MP2/6-311G(d,p) levels. By means of the group-balanced isodesmic reaction R5a–R9c, the standard enthalpy of formation obtained by combining the results at the CCSD(T) and QCISD(T) levels based on the MP2 geometries are: (−225.48 ± 0.70) kcal mol⁻¹ for CF₃CH₂CH₂CH₂OH, (−173.46 ± 0.73) kcal mol⁻¹ for CF₃CH₂CH₂CH₂O, (−181.36 ± 0.75) kcal mol⁻¹ for CF₃CH₂CH₂CHOH, (−175.33 ± 0.71) kcal mol⁻¹ for CF₃CH₂CHCH₂OH, and (−174.40 ± 0.73) kcal mol⁻¹ for CF₃CHCH₂CH₂OH.

The rate constants of all the reactions are calculated by CVT incorporating SCT correction. The agreement between theoretical and experiment result is very excellent. For the dominant channel R2, the variational effect is almost not existing or negligible in the temperature range of 200–2000 K. The KIEs for the main channel and total reaction are normal and decrease with the temperature increasing. Atmospheric lifetimes of a series of relevant ethers, esters, and alcohols are estimated. The estimated atmospheric life time of CF₃CH₂CH₂CH₂OH is expected to be around 3.03 days. The relatively short atmospheric lifetime of CF₃CH₂CH₂CH₂OH make its negligible contribution towards ozone depletion. The three-parameter Arrhenius expression for the title reaction is k(T) = 3.43 × 10⁻²¹T^3.22 exp(741.70/T) cm³ per molecule per s. We hope the present theoretical studies are helpful for further understanding the title reaction.

Acknowledgements

The authors thank Professor Donald G. Truhlar for providing the Polyrate, Version 9.7 program. We are grateful to financial support from National Natural Science Foundation of China (No. 21377021).

Notes and references

1. T. J. Wallington, W. F. Schneider, D. R. Worsnop, O. J. Nielsen, J. Sehested, W. J. Debruyn and J. A. Shorter, Environ. Sci. Technol., 1994, 28, 320–326.
2. T. Kelly, V. Bossoutrot, I. Magneron, K. Wirtz, J. Treacy, A. Mellouki, H. Sidebottom and G. Le Bras, J. Phys. Chem. A, 2005, 109, 347–355.
3. Environmental Protection Agency, EPA, http://www.epa.gov.
4. M. D. Hurley, T. J. Wallington, M. P. Sulbaek Andersen, D. A. Ellis, J. W. Martin and S. A. Mabury, J. Phys. Chem. A, 2004, 108, 1973–1979.
5. E. Moreno, A. Aranda, Y. Díaz-de-Mera, A. Notario, D. Rodríguez and I. Bravo, Atmos. Environ., 2012, 60, 76–81.
6. D. R. Salahub and C. Sandorfy, Chem. Phys. Lett., 1971, 8, 71–74.
7. M. Antinolo, E. Jimenez and J. Albaladejo, Environ. Sci. Technol., 2011, 45, 4323–4330.
8. E. Jimenez, M. Antinolo, B. Ballesteros, E. Martinez and J. Albaladejo, ChemPhysChem, 2010, 11, 4079–4087.
9. Y. Diaz-de-Mera, A. Aranda, I. Bravo, D. Rodriguez, A. Rodriguez and E. Moreno, Environ. Sci. Pollut. Res., 2008, 15, 584–591.
10. M. Antinolo, S. Gonzalez, B. Ballesteros, J. Albaladejo and E. Jimenez, J. Phys. Chem. A, 2012, 116, 6041–6050.
11. Y. N. Indulkar, S. SenGupta, S. B. Waghmode, A. Kumar, S. Dhanya and P. D. Naik, Atmos. Environ., 2011, 45, 6973–6979.
12. I. Bravo, Y. Diaz-de-Mera, A. Aranda, K. Smith, K. P. Shine and G. Marston, Phys. Chem. Chem. Phys., 2010, 12, 5115–5125.
13. M. D. Hurley, J. A. Misner, J. C. Ball, T. J. Wallington, D. A. Ellis, J. W. Martin, S. A. Mabury and M. P. Sulbaek Andersen, J. Phys. Chem. A, 2005, 109, 9816–9826.
14. K. Brudnik, J. T. Jodkowski, E. Ratajczak, R. Venkatraman, A. Nowek and R. H. Sullivan, Chem. Phys. Lett., 2001, 345, 435–444.
15. A. Galano, J. R. l. Alvarez-Idaboy, G. Bravo-Perez and M. E. Ruiz-Santoyo, Phys. Chem. Chem. Phys., 2002, 4, 4648–4662.
16. P. Seal, G. Oyedepo and D. G. Truhlar, J. Phys. Chem. A, 2013, 117, 275–282.
17. J. Moc and J. M. Simmie, J. Phys. Chem. A, 2010, 114, 5558–5564.
18. Y. Wang, J. Y. Liu, Z. S. Li, L. Wang and C. C. Sun, J. Comput. Chem., 2007, 28, 802–810.
19. Y. Wang, J. Y. Liu, Z. S. Li, L. Wang, J. Y. Wu and C. C. Sun, J. Phys. Chem. A, 2006, 110, 5853–5859.
20. T. Y. Jin, C. G. Ci, Y. Wu and J. Y. Liu, Comput. Theor. Chem., 2013, 1007, 63–75.
21. Y. Wang, J. Y. Liu and Z. S. Li, Chem. Phys., 2007, 335, 28–36.
22. Y. Wang, J. Y. Liu and Z. S. Li, J. Comput. Chem., 2007, 28, 2517–2530.
23. A. Y. Yu and H. X. Zhang, J. Mol. Model., 2013, 19, 4503–4510.
24. S. Xu and M. C. Lin, Proc. Combust. Inst., 2007, 31, 159–166.
25. F. Y. Bai, Y. Q. Sun, X. Wang, Z. M. Jia, R. S. Wang and X. M. Pan, J. Mol. Model., 2014, 20, 2419.
26. F. Y. Bai, X. L. Zhu, Z. M. Jia, X. Wang, Y. Q. Sun, R. S. Wang and X. M. Pan, ChemPhysChem, 2015, 16, 1768–1776.
27. G. C. Song, X. J. Jia, Y. Gao, J. Luo, Y. B. Yu, R. S. Wang and X. M. Pan, J. Phys. Chem. A, 2010, 114, 9057–9068.
28. X. J. Jia, Y. J. Liu, J. Y. Sun, H. Sun, Z. M. Su, X. M. Pan and R. S. Wan, J. Phys. Chem. A, 2010, 114, 417–424.
29. F. Y. Bai, G. Sun, X. Wang, Y. Q. Sun, R. S. Wang and X. M. Pan, J. Phys. Chem. A, 2015, 119, 1256–1266.
30. H. Sun, H. W. Gong, X. M. Pan, L. Z. Hao, C. C. Sun, R. S. Wang and X. R. Huang, J. Phys. Chem. A, 2009, 113, 5951–5957.
31. J. Y. Wu, J. Y. Liu, Z. S. Li and C. C. Sun, J. Chem. Phys., 2003, 118, 10986–10995.
32. B. K. Mishra, M. Lily, R. C. Deka and A. K. Chandra, J. Mol. Graphics Modell., 2014, 50, 90–99.
33. B. K. Mishra, M. Lily, A. K. Chandra and R. C. Deka, J. Phys. Org. Chem., 2014, 27, 811–817.
34. D. Bhattacharjee, B. K. Mishra and R. C. Deka, J. Mol. Model., 2015, 21, 1–8.
35. B. K. Mishra, M. Lily, A. K. Chakrabartty, D. Bhattacharjee, R. C. Deka and A. K. Chandra, New J. Chem., 2014, 38, 2813–2822.
36. K. Jogeshwari Devi and A. K. Chandra, Chem. Phys. Lett., 2011, 502, 23–28.
37. B. K. Mishra, A. K. Chakrabartty and R. C. Deka, Mol. Phys., 2014, 112, 1512–1519.
38. L. Yang, J. Y. Liu, L. Wang, H. Q. He, Y. Wang and Z. S. Li, J. Comput. Chem., 2008, 29, 550–561.
39. L. Yang, J. Y. Liu, S. Q. Wan and Z. S. Li, J. Comput. Chem., 2009, 30, 565–580.
40. L. Yang, J. Y. Liu and Z. S. Li, J. Chem. Theory Comput., 2008, 4, 1073–1082.
41. V. I. Jaramillo and M. A. Smith, J. Phys. Chem. A, 2001, 105, 5854–5859.
42. M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. W. M. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. A. Keith, G. A. Petersson and J. A. Pople, et al., Gaussian 09, Gaussian Inc., Wallingford, CT, 2009.
43. C. Møller and M. S. Plesset, Phys. Rev., 1934, 46, 618–622.
44. H. Zhang, L. Yang, J. Y. Liu and Z. S. Li, J. Comput. Chem., 2012, 33, 203–210.
45. X. J. Jia, Y. J. Liu, J. Y. Sun, H. Sun, F. Wang, Z. M. Su, X. M. Pan and R. S. Wang, J. Comput. Chem., 2010, 31, 2263–2272.
46. Y. Zhao and D. G. Truhlar, Acc. Chem. Res., 2008, 41, 157–167.
47. C. Gonzalez and H. B. Schlegel, J. Chem. Phys., 1989, 90, 2154–2161.
48. C. Gonzalez and H. B. Schlegel, J. Phys. Chem., 1990, 94, 5523–5527.
49. K. Raghavachari, G. W. Trucks, J. A. Pople and M. Head-Gordon, Chem. Phys. Lett., 1989, 157, 479–483.
50. J. A. Pople, M. Head-Gordon and K. Raghavachari, J. Chem. Phys., 1987, 87, 5968–5975.
51. J. C. Corchado, Y. Y. Chuang, P. L. Fast, W. P. Hu, Y. P. Liu, G. C. Lynch, K. A. Nguyen, C. F. Jackels, A. Fernandez-Ramos and B. A. Ellingson, et al., POLYRATE, version 9.7, University of Minnesota, Minneapolis, MN, 2007.
52. B. C. Garrett and D. G. Truhlar, J. Chem. Phys., 1979, 70, 1593–1598.
53. B. C. Garrett and D. G. Truhlar, J. Am. Chem. Soc., 1979, 101, 4534–4548.
54. B. C. Garrett, D. G. Truhlar, R. S. Grev and A. W. Magnuson, J. Phys. Chem., 1980, 84, 1730–1748.
55. D. H. Lu, T. N. Truong, V. S. Melissas, G. C. Lynch, Y. P. Liu, B. C. Garrett, R. Steckler, A. D. Isaacson, S. N. Rai, G. C. Hancock, J. G. Lauderdale, T. Joseph and D. G. Truhlar, Comput. Phys. Commun., 1992, 71, 235–262.
56. Y. P. Liu, G. C. Lynch, T. N. Truong, D. H. Lu, D. G. Truhlar and B. C. Garrett, J. Am. Chem. Soc., 1993, 115, 2408–2415.
57. H. B. Schlegel and C. Sosa, Chem. Phys. Lett., 1988, 145, 329–333.
58. A. Garzón, M. Antiñolo, M. Moral, A. Notario, E. Jiménez, M. Fernández-Gómez and J. Albaladejo, Mol. Phys., 2013, 111, 753–763.
59. D. L. Singleton and R. J. Cvetanović, J. Am. Chem. Soc., 1976, 98, 6812–6819.
60. V. H. Uc, J. R. Alvarez-Idaboy, A. Galano, I. Garcia-Cruz and A. Vivier-Bunge, J. Phys. Chem. A, 2006, 110, 10155–10162.
61. J. R. Alvarez-Idaboy, L. Reyes and N. Mora-Diez, Org. Biomol. Chem., 2007, 5, 3682–3689.
62. J. R. Alvarez-Idaboy, N. Mora-Diez and A. Vivier-Bunge, J. Am. Chem. Soc., 2000, 122, 3715–3720.
63. J. R. Alvarez-Idaboy, N. Mora-Diez, R. J. Boyd and A. Vivier-Bunge, J. Am. Chem. Soc., 2001, 123, 2018–2024.
64. A. Cruz-Torres and A. Galano, J. Phys. Chem. A, 2007, 111, 1523–1529.
65. M. T. Baeza-Romero, D. R. Glowacki, M. A. Blitz, D. E. Heard, M. J. Pilling, A. R. Rickard and P. W. Seakins, Phys. Chem. Chem. Phys., 2007, 9, 4114–4128.
66. L. Wang, Y. Zhao, J. Wen and J. Zhang, Theor. Chem. Acc., 2013, 132, 1–14.
67. O. W. Wingenter, M. K. Kubo, N. J. Blake, T. W. Smith Jr, D. R. Blake and F. S. Rowland, J. Geophys. Res., 1996, 101, 4331–4340.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra04902h

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