Theoretical studies on atmospheric chemistry of (CF3)2C(OH)CH3: Kinetics, mechanism and thermochemistry of gas phase reactions with OH radicals

Journal of Fluorine Chemistry 175 (2015) 185–192

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Theoretical studies on atmospheric chemistry of (CF3)2C(OH)CH3: Kinetics, mechanism and thermochemistry of gas phase reactions with OH radicals Makroni Lily, Asit K. Chandra * Centre for Advanced Studies in Chemistry, North-Eastern Hill University, Shillong 793 022, India

A R T I C L E I N F O

A B S T R A C T

Article history: Received 2 March 2015 Received in revised form 23 April 2015 Accepted 25 April 2015 Available online 11 May 2015

The mechanism, kinetics and thermochemistry of the reaction of (CF3)2C(OH)CH3 with OH radicals are theoretically investigated using DFT based M06-2X functional method. Three important H-abstraction channels have been identified for (CF3)2C(OH)CH3 + OH reaction and one transition state has been located for each reaction channel. Formation of pre-reactive complex at the entry of each reaction channel indicates an indirect mechanism for hydrogen-abstraction reaction. The rate coefficients for (CF3)2C(OH)CH3 are evaluated using canonical transition state theory along with Eckart’s tunneling correction over a wide range of temperature (270–1000 K). At 298 K, our calculated total rate coefficient for (CF3)2C(OH)CH3 + OH reaction is in good agreement with the experimental result. The results show that H-abstraction from the –CH3 group is the predominant channel and has more contribution to the total rate coefficient than that from the –OH group of (CF3)2C(OH)CH3. The standard heats of formation for (CF3)2C(OH)CH3 molecule, (CF3)2C(OH)CH2 and (CF3)2C(O)CH3 radicals are estimated by using groupbalanced isodesmic reactions and the values are 1599.6, 1369.8 and 1335.6 kJ mol1, respectively at 298 K. The atmospheric lifetime of (CF3)2C(OH)CH3 is estimated to be around 5.0 years. The 100-year time horizon global warming potentials of (CF3)2C(OH)CH3 with respect to CO2 is 705. Potential atmospheric degradation routes for the resulting (CF3)2C(OH)CH2 radical is also discussed here. ß 2015 Elsevier B.V. All rights reserved.

Keywords: Fluorinated alcohols M06-2X Potential energy surface Rate coefficient Atmospheric lifetime Global warming potentials

1. Introduction The adverse effect of chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) on the environment is now well known. This has led to an international agreement to completely phase out the use of these compounds and replace them with environmental friendly compounds for industrial and other applications. Partially fluorinated alcohols (HFAs) have been considered as one of the most promising CFC or HCFC substitutes, because they are expected to have higher chemical reactivity due to the presence of the –OH group and therefore shorter atmospheric lifetime [1–4]. As HFAs have been already proposed for broad commercial use as cleaning solvent in various industrial applications [1], it is essential to improve our knowledge of their atmospheric chemistry. The main degradation channel of fluorinated alcohols is the gas-phase reaction with OH radicals and therefore it is a subject of few recent studies [5–8]. An accurate

* Corresponding author. Tel.: +91 3642722622; fax: +91 3642550486. E-mail address: [email protected] (A.K. Chandra). http://dx.doi.org/10.1016/j.jfluchem.2015.04.019 0022-1139/ß 2015 Elsevier B.V. All rights reserved.

knowledge of reaction kinetics is essential for the evaluation of the atmospheric lifetime of any HFA molecule to check whether it can be a suitable replacement for CFCs and HCFCs. Moreover, as HFAs are considered as infrared (IR) radiation absorber due to the presence of the C–O and C–F bonds in these molecules [9,10], it is therefore necessary to determine their climatic impact before large-scale applications. In the present work, we report the results obtained from the detailed theoretical studies of the gas-phase reaction of 1,1,1,3,3,3hexafluoro-2-methyl-propan-2-ol, ((CF3)2C(OH)CH3), molecule with OH radical. To the best of our knowledge, no theoretical study on this reaction has been reported yet. According to our literature survey, the rate coefficients for the gas phase reaction of OH with (CF3)2C(OH)CH3 molecule were experimentally measured by Orkin et al. [11] using a flash photolysis resonance-fluorescence technique over the temperature range 220–370 K and they reported a rate coefficient value of (7.84  0.23)  1015 cm3 mol1 s1 at 298 K. But the experimental study provides primarily the total rate coefficient for the reaction and it is difficult to get mechanism and importance of various reaction channels. Our study focuses on kinetics, mechanism and thermochemistry for the reaction of (CF3)2C(OH)CH3 with OH

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radical along with its atmospheric implications. Three reaction pathways are feasible for the H-abstraction reaction of (CF3)2C(OH)CH3 + OH; two channels originated from methyl (CH3–) group and another from hydroxyl –C(OH) position. Since hydrogen atoms in the methyl group are in different chemical environment; two reaction pathways are feasible for the H-abstraction from the methyl group; namely channel R1a and R1b. The (CF3)2C(OH)CH3 + OH reaction can be represented as follows,

the heats of formation of (CF3)2C(OH)CH3 molecule, and (CF3)2C(OH)CH2 and (CF3)2C(O)CH3 radicals generated after hydrogen abstraction are computed for the first time. The atmospheric implications such as atmospheric lifetime and its subsequent global warming potential are also reported. Potential atmospheric degradation routes for the resulting (CF3)2C(OH)CH2 radical are also discussed here.

ðCF3 Þ2 CðOHÞCH3 þ OH ! ðCF3 Þ2 CðOHÞCH2 þ H2 O

(R1)

2. Results and discussion

(R2)

2.1. Structure and energetics

ðCF3 Þ2 CðOHÞCH3 þ OH ! ðCF3 Þ2 CðOÞCH3 þ H2 O

k1 k2

In our present study, we employ the DFT based M06-2X/631 + G(d,p) method [12,13] for investigating the potential energy profile for this reaction. The thermochemistry of the reaction and

The ground state structure of (CF3)2C(OH)CH3 was optimized starting from various possible initial geometries and the molecule was found to exist in only one conformation. The optimized

Fig. 1. Optimized structures of (CF3)2C(OH)CH3, transition states, (CF3)2C(OH)CH2 and (CF3)2C(O)CH3 radicals at the M06-2X/6-31 + G(d,p) level. Bond lengths and angles are given in A´˚ and degrees, respectively.

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structure of (CF3)2C(OH)CH3 as obtained from our calculation is shown in Fig. 1. The M06-2X/6-31 + G(d,p) optimized structural parameters for reactants, TS and radicals generated due to hydrogen abstraction are listed in Table 1. As stated before there are three potential hydrogen abstraction sites for (CF3)2C(OH)CH3 conformer, two from the –CH3– site because one H-atom (H7) is non-equivalent from the other two H-atoms (H5 and H6), and one from the –OH site. The C4-H5 bond in (CF3)2C(OH)CH3 molecule is longer by 0.01 A˚ than the C4-H7 bond. Accordingly, one TS each is located for hydrogen abstraction by OH radical from the C4-H5 bond (TS1a), C4-H7 bond (TS1b) and O8-H9 (TS2) of (CF3)2C(OH)CH3. The optimized structures of all these transition states are shown in Fig. 1 along with the structures of the two radicals, (CF3)2C(OH)CH2 and (CF3)2C(O)CH3 generated after hydrogen abstraction. In the process of hydrogen abstraction reaction from a C–H or O–H bond, the C–H or O–H bond breaks and a new O–H bond is formed giving rise to a water molecule. As a result, the breaking C– H or O–H bond length in all TS structures in (CF3)2C(OH)CH3 is found to be longer in a range of 11–18% than the observed C–H or O–H bond length in isolated (CF3)2C(OH)CH3; whereas the forming O  H bond length is elongated by 34–35% than the O–H bond length in H2O molecule. These features indicate the formation of an early transition state. It agrees well to the exothermic nature of this reaction as well as to the Hammond’s postulate [14]. In all the TS structures, the OH  F/O distance is found to be significantly lower than the sum of van der Waals radii of the H and F (O) atom, indicating the presence of hydrogen bonding interaction in TS. For example, the OH  F13 distance in TS1b is 2.389 A˚. It has been observed from many recent studies that the reaction between HFA and OH generally proceeds through the formation of pre- and post-reaction complexes [15–17]. We could also locate such complexes from IRC analysis for each reaction channel of (CF3)2C(OH)CH3 + OH reaction. The optimized structures of the pre-reaction (CR) and post-reaction (CP) complexes are shown in Fig. 2. As shown in the reaction energy profile diagram in Fig. 3, three CR complexes (CR1a, CR1b and CR2) were located at the entry point of three reaction channels (two from the –CH3 site and one from the –C(OH) position) originated from (CF3)2C(OH)CH3 reaction with OH radical. On other hand, three CP complexes (CP1a, CP1b, and CP2) were also found at the exit channels of the reactions.

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These CR complexes are formed due to weak interactions between (CF3)2C(OH)CH3 with OH radical through C–H  O and OH  F/O hydrogen bonding as evidenced from the bond lengths shown in Fig. 2, whereas the three CP complexes are resulted from the hydrogen bonding interaction of (CF3)2C(OH)CH2 and (CF3)2C(O)CH3 radicals with H2O molecule. The vibrational frequencies of reactants, all the transition states and two product radicals are listed in Table S.I as supplementary information. The rotational constants for all these structures are also given in Table S.I as these data are necessary for kinetic modeling. The vibrational frequencies for the CR and CP complexes are given as Supplementary Information in Table S.II. These data are not available in the literature and can therefore be useful for further thermochemical and kinetic modeling of reaction involving these species. The relative energies (including ZPE) for all the stationary points involved in reactions (R1) and (R2) and as obtained from both the M06-2X/6-31 + G(d,p) and M06-2X/6-311 + + G(d,p) calculations are given in Table 2. The M06-2X/6-31 + G(d,p) calculated barrier heights for hydrogen abstraction from the C4H5 (TS1a) and C4-H7 bond (TS1b) of (CF3)2C(OH)CH3 amount to 12.68 and 15.98 kJ mol1; whereas the same for hydrogen abstraction from the OH group (TS2) is 17.11 kJ mol1. The M06-2X/6-311 + + G(d,p) calculated barrier heights associated with TS1a and TS1b and TS2 amount to 14.94 and 17.57 and 19.96 kJ mol1, respectively. The barrier heights obtained from the M06-2X/6-311 + + G(d,p) method for hydrogen abstraction are slightly higher than those obtained from the M06-2X/6-31 + G(d,p) method. The values of barrier heights for different channels indicate that H-abstraction from the –CH3 group should be more facile than that from the O–H group. This can be explained from our calculated BDE values for the C4-H5 (426.98 kJ mol1) and hydroxyl (–OH) bond (461.12 kJ mol1) of (CF3)2C(OH)CH3 as listed in Table 2. Since BDE is known to be generally correlated with H-abstraction activation barrier, it is expected that Habstraction from the CH3-position should be the predominant reaction. 0 The heats of reaction ðDr H298 Þ values for reactions (R1) and (R2) are calculated to be 51.00 and 16.82 kJ mol1 at the M06-2X/631 + G(d,p) level and the same amount to be 53.01 and 7.87 kJ mol1, respectively at the M06-2X/6-311 + + G(d,p) level. Therefore, hydrogen abstraction from the CH3-moiety is

Table 1 M06-2X/6-31 + G(d,p) optimized parameters (CF3)2C(OH)CH3, transition states for hydrogen abstraction by OH radical (TS1a, TS1b and TS2) and (CF3)2C(OH)CH2 and (CF3)2C(O)CH3 radicals. Bond lengths and angles are given in A´˚ and degrees, respectively. Parameter

(CF3)2C(OH)CH3

TS1a

TS1b

TS2

(CF3)2C(OH)CH2

(CF3)2C(O)CH3

C1C2/C1C4 C1C3/C4C7 C1C4 C4H5 C4H6 C4H7 C1O8/C1O7 O8H9/O7H8 C3F10/C3F9 C3F11/C3F10 C3F12/C3F11 C2F13/C2F12 C2F14/C2F13 C2F15/C2F14 H  OH C2C1C3 C3C1C4 C2C1C4 C2C1O8/C2C107 C3C1O8/C3C107 C4C1O8/C4C107

1.5422 1.5422 1.5205 1.0904 1.0904 1.0916 1.3993 0.9681 1.3371 1.3444 1.3367 1.3367 1.3444 1.3371 – 110.70 110.24 110.24 108.54 108.54 108.50

1.5425 1.5448 1.5144 1.2222 1.0892 1.0903 1.4037 0.9688 1.3361 1.3429 1.3348 1.3361 1.3440 1.3329 1.2837 110.77 109.77 110.78 108.39 108.33 108.73

1.5431 1.5441 1.5146 1.0894 1.2223 1.2196 1.4003 0.9688 1.3337 1.3428 1.3395 1.3396 1.3425 1.3340 1.2906 110.79 110.89 110.53 108.45 108.37 107.69

1.5522 1.5413 1.5312 1.0911 1.0897 1.0915 1.3894 1.1325 1.3391 1.3348 1.3407 1.3403 1.3336 1.3396 1.1923 109.99 110.38 109.15 111.12 109.79 106.36

1.5482 1.5482 1.4893 1.0800 1.0810 1.3978 0.9681 1.3349 1.3438 1.3361 1.3361 1.3438 1.3349 – 110.69 109.91 109.91 108.48 108.48 109.32

1.5532 1.5530 1.5256 1.0914 1.0907 1.0913 1.3836 1.3397 1.3281 1.3371 1.3362 1.3290 1.3393 – 109.91 110.72 110.54 105.80 106.21 113.46

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Fig. 2. Optimized structures of pre-reaction (CR) and post-reaction (CP) complexes at the M06-2X/6-31 + G(d,p) level. Bond lengths are given in A´˚ .

thermodynamically more favorable than that from the hydroxyl (–OH) site of (CF3)2C(OH)CH3. However, these results also suggest that the hydrogen abstractions from both the sites of (CF3)2C(OH)CH3 are exoergic in nature. The heats of reaction of isodesmic reactions are known to provide a simple way for calculating accurate heats of formation 0 ðD f H298 Þ from fairly low-level of quantum-chemical calculations. An isodesmic reaction gives accurate heats of formation of unknown organic compound due to the conservation of same type of chemical bonds in reactants and products. In this work, we 0 predict the standard heats of formation D f H298 of (CF3)2C(OH)CH3, (CF3)2C(OH)CH2 and (CF3)2C(O)CH3 by using the following two isodesmic reactions at the M06-2X/6-31 + G(d,p) level. ðCF3 Þ2 CðOHÞCH3 þ 2CH4 ! CH3 CH2 CH3 þ CH3 OH þ CF3 CF3

(R3)

ðCF3 Þ2 CðOHÞCH3 þ 2CHF3 ! 2CF3 CF3 þ CH3 CH2 OH

(R4)

0 ) values of (CF3)2C(OH)CH3 moleHeats of formation (D f H298 cule and (CF3)2C(OH)CH2 and (CF3)2C(O)CH3 radicals as calculated from the isodesmic reactions (R3) and (R4) are listed in Table 3. The 0 literature reported D f H298 values for CH4: 74.6  0.3 kJ mol1; CH3CH2OH: 234.0  2 kJ mol1; CH3CF3: 748.7  3.2 kJ mol1; CHF3: 697.05 kJ mol1; CF3CF3: 1343.9 kJ mol1; CH3OH: 205.0  10 kJ mol1, C3H8: 104.7  0.5 kJ mol1; H2O: 1 241.84 kJ mol and OH: 38.99 kJ mol1 are also used in our 0 calculation [18]. The D f H298 value for (CF3)2C(OH)CH3 molecule is estimated from the average of results obtained for the two isodesmic reactions (R3) and (R4) and it amounts to 1599.6 kJ mol1. Once the 0 0 D f H298 value for (CF3)2C(OH)CH3 is known, the D f H298 values for the two radicals, (CF3)2C(OH)CH2 and (CF3)2C(O)CH3, can easily be

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Fig. 3. Schematic potential energy profile (unscaled) for hydrogen abstraction reaction of (CF3)2C(OH)CH3 + OH. Relative energies (in kJ mol1) of different species are calculated using M06-2X/6-31 + G(d,p) and M06-2X/6-311 + + G(d,p) (within parentheses) methods.

calculated from our calculated heats of reaction values for (R1) and (R2) and the known experimental heats of formation values for OH 0 radical and H2O molecule. The calculated D f H298 values for (CF3)2C(OH)CH2 and (CF3)2C(O)CH3 radicals are 1369.8 and 1335.6 kJ mol1, respectively at the M06-2X/6-31 + G(d,p) level. 2.2. Rate coefficient calculation The rate coefficients for hydrogen abstraction reaction were calculated using the canonical transition state theory [19] kðTÞ ¼ s r G ðTÞ

kB T qTS ðTÞ eDE0 =RT h qHFA ðTÞ:qOH ðTÞ

(1)

Table 2 Relative energies (DErel including ZPE) for all species involved in (CF3)2C(OH)0 CH3 + OH reaction. Reaction enthalpy ðDr H298 Þ and C–H bond dissociation enthalpy (D0298 ) for (CF3)2C(OH)CH3 at 298 K as obtained at the M06-2X/6-31 + G(d,p) and M06-2X/6-311 + + G(d,p) levels. Data are in kJ mol1.

DErel

M06-2X/6-31 + G(d,p)

M06-2X/6-311 + + G(d,p)

(CF3)2C(OH)CH3 + OH CR1a CR1b CR2 TS1a TS1b TS2 CP1a CP1b CP2 0 Dr H298 R1 R2 D0298 (CF3)2C(OH)CH2–H (CF3)2C(O–H)CH3

0 17.53 12.38 25.19 12.68 15.98 17.11 68.28 67.11 41.84

0 11.72 11.42 24.60 14.94 17.57 19.96 70.08 69.37 40.88

51.00 16.82 426.98 461.12

where qx (T) represents the partition function for the species x (TS, HFA, OH) at temperature T, kB is the Boltzmann constant, DE0 is the barrier height including ZPE and sr is the degeneracy of each reaction channel. G(T) is a correction factor for taking care of tunneling contribution in H-abstraction reaction and it can be interpreted as the ratio of quantum mechanical rate over classical mechanical rate [20]. The tunneling correction G(T) was estimated by using the Eckart’s unsymmetrical barrier method [20] and following the procedure as discussed in our earlier paper [21]. All vibrational modes, except for the lowest vibrational mode, were treated quantum mechanically as separable harmonic oscillators, whereas for the lowest-frequency mode, the partition function was evaluated by the hindered-rotor approximation by Truhlar and Chuang [22] method. The electronic partition function for OH radical was calculated considering the splitting of 139.7 cm1 of the 2p ground state due to spin-orbit coupling. The existence of pre- and post-reaction complexes at the entry and exit of each reaction channel indicates an indirect hydrogen-abstraction reaction and they can have significant influence on the reaction rate because it changes the shape of potential energy surface for the reaction. To take into account the effect of pre- and post-

Table 3 0 Heats of formation (D f H298 in kJ mol1) values of (CF3)2C(OH)CH3 molecule and (CF3)2C(OH)CH2 and (CF3)2C(O)CH3 radicals calculated from isodesmic reactions (R3) and (R4) using M06-2X/6-31 + G(d,p) method at 298 K. Species

Reaction

0 D f H298

53.01 7.87

(CF3)2C(OH)CH3 (CF3)2C(OH)CH3

427.94 473.09

(CF3)2C(OH)CH2 (CF3)2C(O)CH3

R3 R4 Average R1 R2

1602.6 1596.6 1599.6 1369.8 1335.6

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reaction complex on reaction kinetics, we have followed the procedure proposed by Singleton and Cvetanovic [23] and as mentioned in our earlier papers [21,24]. The rate coefficients for reactions (R1) and (R2) are calculated by using the TST expression (Eq. (1)) and Eckart’s unsymmetrical barrier method for tunneling correction in a wide range of temperature 270–1000 K. As stated before, the H-abstraction reaction between (CF3)2C(OH)CH3 and OH radical has three different channels [two channels for reaction (R1), termed as R1a and R1b, and one channel for reaction (R2)] and they go through TS1a, TS1b and TS2, respectively. The sr value for R1a is two and that for R1b and R2 is one. The G(T) values are 10.8, 10.0 and 72.7 at 298 K for reaction channels R1a, R1b and R2, respectively and the same values are almost one at 1000 K. The contribution from each of these three channels needs to be taken into account while calculating the total rate coefficient (kOH) for the (CF3)2C(OH)CH3 + OH reaction. The total rate coefficient values of (CF3)2C(OH)CH3 reaction with OH radical is therefore obtained from the sum of individual rate coefficients for the reactions (R1a), (R1b) and (R2): kOH = k1a + k1b + k2, where k1a, k1b and k2 are the rate coefficients for the three channels, respectively. Rate coefficient values (in cm3 mol1 s1) for hydrogen abstraction reactions of these three channels and the total rate coefficient (kOH) values as calculated using M06-2X/6-311 + + G(d,p) barrier heights are reported in Table 4. At 298 K, our calculated kOH value for (CF3)2C(OH)CH3 + OH reaction using M06-2X/6-311 + + G(d,p) barrier heights is 7.46  1015 cm3 mol1 s1 which is quite close to the reported rate coefficient value of (7.84  0.12)  1015 cm3 mol1 s1 by Orkin et al. [11]. The kOH values obtained from the M06-2X/631 + G(d,p) results are somewhat higher than those obtained at the M06-2X/6-311 + + G(d,p) level because of lower barrier height for reaction at the former level. Temperature variation of k1a, k1b, k2 and kOH are shown in Fig. 4 along with the available experimental results. It shows that our M06-2X/6-311 + + G(d,p) calculated rate coefficient values agree reasonably well for the entire temperature range for which recent experimental result is available. The contribution of each reaction channel toward the total rate coefficient as given in Table 4 suggests that hydrogen abstraction from the –CH3 group is the major reaction channel throughout the temperature range of our study. However, the contribution of hydrogen abstraction channel

Table 4 Rate coefficient values (in cm3 mol1 s1) for three reaction channels R1a (k1a), R1b (k1b) and R2 (k2) for hydrogen abstraction reactions of (CF3)2C(OH)CH3 with OH radical and total rate coefficient (kOH) values as calculated using M06-2X/6311 + + G(d,p) barrier heights. Temperature range

M06-2X/6-311 + + G(d,p)

T (K)

k1a  1015

k1b  1015

k2  1015

kOH  1015

270 298 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

4.49 4.94 6.57 9.12 12.75 17.61 23.92 31.90 41.79 53.85 68.33 85.50 105.6 129.0 155.8 186.4

0.54 0.70 1.11 1.76 2.74 4.12 6.01 8.52 11.74 15.80 20.83 26.95 34.28 42.97 53.15 64.95

2.26 1.82 1.68 2.00 2.62 3.55 4.81 6.47 8.58 11.20 14.41 18.26 22.83 28.19 34.41 41.55

7.29 7.46 9.36 12.88 18.11 25.28 34.74 46.89 62.11 80.86 103.6 130.7 162.7 200.1 243.4 292.9

Fig. 4. Rate coefficients for hydrogen abstraction reactions of three reaction channels (k1a,k1b and k2) and total rate coefficient (kOH) for (CF3)2C(OH)CH3 + OH reaction and comparison with experimental results (Ref. [11]).

from the –OH group cannot be neglected, especially at lower temperature. For example, the contribution of this channel is almost 31% at 270 K and only 7% at 1000 K. Similar observations were also made from the study of CF3CH2OH + OH reactions [15]. The Arrhenius plot of the total rate coefficient values shows significant non-linear behavior, especially at lower temperature, because of contribution from different reaction channels as well as important tunneling contribution. The rate coefficient in the temperature range of 270–1000 K can be best described by the following model equation: k ¼ AT n eDEoK =RT

(2)

From above Eq. (2), the activation energy, Ea, can be expressed as: Ea ¼ DE0k þ nRT

(3)

The M06-2X/6-311 + + G(d,p) calculated rate coefficient values for the reaction between (CF3)2C(OH)CH3 with OH radical in the temperature range of 270–1000 K are fitted in the model Eq. (2) and found to be well described by the following equation:   622 kOH ¼ 1:92  1026  T 4:24 exp T

(4)

The value of activation energy, Ea, for (CF3)2C(OH)CH3 + OH reaction calculated from Eq. (3) is 5.31 kJ mol1 at 298 K. 3. Atmospheric implications 3.1. Atmospheric lifetime The value of kOH measured in the present work can be used to provide an estimate of the atmospheric lifetime of (CF3)2C(OH)CH3 with respect to reaction with OH radicals. While calculating OHbased lifetime, the use of 272 K as an average tropospheric temperature and methyl chloroform (CH3CCl3) as a chemical of well known source and sink [25] have been suggested to minimize the errors resulting from neglecting the specific temperature dependences. Thus, lifetime estimations for HFAs are generally calculated on the basis of gas-phase removal by OH only and with

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methyl chloroform (MCF) as reference

t HFA OH ¼

kMCF ð272 KÞ MCF t kHFA ð272 KÞ OH

(5)

where t HFA OH is the lifetime for HFA, kHFA and kMCF are the rate coefficients for the reactions of OH radicals with (CF3)2C(OH)CH3 and methyl chloroform (MCF), respectively at T = 272 K and t MCF OH = 5.99 years [25]. Taking the values of rate coefficients for 15 kMCF = 6.14  10 [25] and calculated rate coefficient value of kHFA = 7.40  1015 cm3 mol1 s1 for (CF3)2C(OH)CH3 at 272 K, the estimated atmospheric lifetime is found to be 5.0 years which is in good agreement with the value reported (6.27 years) by Orkin et al. [11]. 3.2. Global warming potential (GWP)

Scheme 1. Atmospheric degradation of (CF3)2C(OH)CH3 initiated by OH radical.

Global Warming Potential of a compound is a relative measure of how much heat it traps in the atmosphere [26]. The GWP can be estimated for any chosen timescale by combining radiative forcing efficiency with atmospheric lifetime as described by Pinnock et al. [27]. Radiative forcing efficiency can be measured by combining the IR absorption cross section and the instantaneous radiative forcing per unit cross section per wave number [26,27]. Our previous papers [24,28] describe the methodology for calculating GWP of a species using quantum chemical methods, and therefore the same is not repeated here. The DFT based B3LYP method combined with the 6–31G** basis set were used for the theoretical calculation of radiative efficiency, the infrared intensities and the wavenumbers of harmonic vibrational frequencies as prescribed by others [29,30]. Frequencies were corrected by a scaling factor v¯ scal ¼ 0:977v¯ calc þ 11:664 cm1 as suggested by Bravo et al. [30], where v¯ calc is the calculated vibrational wave number and v¯ scal is the empirically corrected one. Table 5 provides the tropospheric lifetime, radiative efficiency and GWP value of 100 year time horizon for (CF3)2C(OH)CH3 along with the available reported results. Our computed GWP value of 705 is in good agreement with the reported value of 710 by Orkin et al. [11]. The radiative efficiency of (CF3)2C(OH)CH3 is calculated to be 0.39 W m2 ppb1. There is no experimental reported value available to compare with our theoretically calculated radiative efficiency value for (CF3)2C(OH)CH3 molecule (Scheme 1). 3.3. Atmospheric fate of (CF3)2C(OH)CH2 radical We have carried out a theoretical investigation of atmospheric degradation mechanism of (CF3)2C(OH)CH2 alkoxy radical via decomposition reactions that involve oxidation reactions and C–C bond scission using quantum chemical methods. The geometries, frequencies and energies of the radicals and the transition states leading to their decomposition have been optimized using M062X/6-31 + G(d,p) method. The loss mechanism of (CF3)2C(OH)CH2 and the formation of products are estimated by taking the following plausible decomposition channels including oxidation with atmospheric O2 and NO using quantum chemical method: ðCF3 Þ2 CðOHÞCH3 þ OH ! ðCF3 Þ2 CðOHÞCH2 þ H2 O

(R5)

Table 5 Atmospheric Lifetimes of (CF3)2C(OH)CH3 at 272 K and GWP for 100 year horizon estimated using the results from B3LYP/6-311G(d,p) level. Atmospheric lifetime (years)

Radiative efficiencies (W m2 ppb1)

Global warming potentials w.r.t. CO2 for 100 year time horizon

Reference

6.27 5.0

n/a 0.39

710 705

Ref. [11] This work

ðCF3 Þ2 CðOHÞCH2 þ O2 ! OOCH2 CðCF3 Þ2 OH þ M

(R6)

OOCH2 ðCF3 Þ2 OH þ NO ! OCH2 CðCF3 Þ2 OH þ NO2

(R7)

OCH2 CðCF3 Þ2 OH ! OCH2 þ CðCF3 Þ2 OH

(R8)

The decomposition reaction via b–C–C bond scission and the atmospheric oxidation reaction with oxygen and NO have been considered. Atmospheric degradation of (CF3)2C(OH)CH3 compound is initiated by OH radical attack which abstracts an alkyl hydrogen, and the alkyl radical formed will then rapidly add oxygen to give peroxy radical OOCH2C(CF3)2OH [31]. This reaction surmounts a relatively high energy barrier of 146.77 kJ mol1, but it is exothermic by 120.99 kJ mol1. Then peroxy radicals instantaneously react with NO to give the corresponding alkoxy radicals RO (OCH2C(CF3)2OH) [32,33] and this reaction has a barrier height of 96.86 kJ mol1 and exothermic by 50.93 kJ mol1. These two successive reactions produce the simplest a-alkoxy radical (OCH2C(CF3)2OH). Further, the OCH2C(CF3)2OH radical undergoes decomposition reaction by C–C bond scission leading to CH2O and C(CF3)2OH products and having much lower energy barrier of 72.98 kJ mol1, but endothermic by 46.68 kJ mol1. Thus, our quantum chemical calculations for the possible degradation pathways of the alkoxy radical predict that reaction (R8) via C–C bond scission leading to CH2O and C(CF3)2OH is kinetically more favorable due to lower barrier height and C(CF3)2OH molecule to be the major product. This C(CF3)2OH radical can further undergo atmospheric oxidation reactions. As far as our knowledge is concerned, there is no experimental evidence to compare with our calculated results for the possible degradation pathways of (CF3)2C(OH)CH3 molecule in the atmosphere. The results obtained from our theoretical calculation suggest that decomposition reaction with O2 and C–C bond scission are possible loss processes of (CF3)2C(OH)CH2 alkoxy radical in the atmosphere. 4. Conclusions The potential energy profile and reaction kinetics for the reaction of (CF3)2C(OH)CH3 with OH radical are investigated at the M06-2X level of theory. The hydrogen abstraction reactions of (CF3)2C(OH)CH3 with OH radicals proceed via indirect mechanism involving the formation of weakly-bound hydrogen bonded complexes at the entry and exit of each reaction channel. Our calculations suggest that the H-abstraction from the methyl group is thermodynamically and kinetically more favorable than the –OH group of (CF3)2C(OH)CH3. However, contribution for H-abstraction from the –OH cannot be neglected, especially at lower temperature region. The barrier height for the dominant H-abstraction pathway for (CF3)2C(OH)CH3 is calculated to be 14.94 kJ mol1 at the M06-

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2X/6-311 + + G(d,p) level. The thermal rate coefficient for the Habstraction reaction of (CF3)2C(OH)CH3 with OH radicals is calculated to be 7.46  1015 cm3 mol1 s1 at 298 K, which is in good agreement with the available recent experimental result. 0 The calculated gas-phase D f H298 values for (CF3)2C(OH)CH3 molecule and the radicals generated due to H-abstraction, (CF3)2C(OH)CH2 and (CF3)2C(O)CH3, are 1599.6, 1369.8 and 1335.6 kJ mol1, respectively. The atmospheric lifetime and GWP at 100 year horizon of (CF3)2C(OH)CH3 are estimated to be 5.0 years and 705, respectively. 5. Computational details In the present study, all the electronic structure calculations were carried out using Gaussian 09 suite of program [34]. The geometries of all the stationary points including reactants, complexes, transition states (TS) and products were optimized using M06-2X/6-31 + G(d,p) method [12,13]. This newly developed hybrid meta DFT method M06-2X [12] is shown to be an efficient DFT method for kinetic modeling and thermochemical analysis. Frequency calculations were performed for each stationary point to ensure that the minimum energy structure has all real frequency, whereas transition state possesses one and only one imaginary frequency. The imaginary frequency in TS was found to correspond to the coupling of stretching modes of the breaking C– H/O–H and forming O–H bonds via normal mode analysis. Single point calculations were also performed at the M06-2X/6311 + + G(d,p) level for further refining the energetics of the reaction path. The M06-2X/6-31 + G(d,p) functional was used to perform the intrinsic reaction coordinate (IRC) [35,36] calculations to confirm that the TSs found were related to hydrogen abstraction reactions and associated with desired reactants and products. The IRC calculations reveal the formation of H-bonded complex in both the entry and exit site of each reaction channel indicating the existence of pre- and post-reaction complexes of HFA molecule and product radicals with OH radical and H2O molecule. Acknowledgement A.K.C. thanks Computer Centre, NEHU for computing facilities and M.L. thanks UGC for a senior research fellowship. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jfluchem.2015. 04.019. References [1] Fluorocarbon Manufacturers Association (Ed.), Tokutei Furon Siyousakugen Manyuaru, Tokyo, 1990.

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