Theoretical investigation on the atmospheric fate of the CF₃C(O)OCH(O)CF₃ radical: alpha-ester rearrangement vs. oxidation

Abstract

A detailed quantum chemical study is performed on the unimolecular decomposition reaction of the alkoxy radical, CF₃C(O)OCH(O)CF₃ produced from CF₃C(O)OCH₂CF₃, trifluoroethyl trofluoroacetate (TFETFA) at the MPWB1K and M06-2X level of theories using the 6-31+G(d,p) basis set. Five plausible decomposition pathways including reaction with O₂, α-ester rearrangement and thermal decomposition (C–C, C–H and C–O bonds scission) have been considered in detail. Out of the five prominent decomposition channels, our results reveal that reaction with O₂ is the dominant path for the decomposition of the CF₃C(O)OCH(O)CF₃ radical in the atmosphere involving the lowest energy barrier which is in accordance with recent experimental findings. Our theoretical results also suggest that α-ester rearrangement leading to the formation of trifluoroacetic acid (TFA) has a negligible contribution for decomposition of the title alkoxy radical. The thermal rate constants for the above decomposition pathways are evaluated using Canonical Transition State Theory (CTST) at 298 K.

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Introduction

It is well established that fluorinated esters (FESs) are the primary products of the atmospheric oxidation of hydrofluoroethers (HFEs).^1–6 For example, CF₃C(O)OCH₂CF₃, 2,2,2-trifluoroethyl trifluoroacetate (TFETFA) can be produced from the OH radical and Cl atom initiated oxidation of CF₃CH₂OCH₂CF₃ (HFE-356mf-f) in the atmosphere.⁷ Like HFEs, FESs also undergo photochemical oxidation in the troposphere with atmospheric oxidants, OH radicals or Cl atoms in marine environment. The degradation of FESs produces environmentally burdened product like trifluoroacetic acid (TFA) and COF₂. TFA detected in surface waters has no known sink apart from rainwater and this species may impact on agricultural and aquatic systems.⁸ Thus, it is important to study the kinetics and mechanistic degradation pathways of FESs for complete assessment of atmospheric chemistry as well as to explore the impact of FESs on environment. Considerable attention has been paid in recent years to perform experimental and theoretical studies on the decomposition kinetics of FESs.^9–17 Recently, Bravo et al.⁶ have used density functional theory and the methodology developed by their group to predict infrared spectra and calculate radiative efficiencies (REs) and global warming potentials (GWPs) for a number of FESs.

Blanco et al.^9,10 first experimentally studied the OH radicals and Cl atoms initiated oxidation of TFETFA. A general mechanism of tropospheric degradation of TFETFA is shown in Scheme 1. Stein et al.¹¹ experimentally investigated the thermal decomposition of alkoxy radical CF₃C(O)OC(O)HCF₃ produced by OH and Cl-initiated oxidation of TFETFA in a FTIR smog chamber. Three loss processes were identified at 296 K which include reaction with O₂ to form CF₃C(O)OC(O)CF₃, α-ester rearrangement to produce CF₃CO and harmful CF₃C(O)OH (TFA) and thermal decomposition pathways (C–H, C–C and C–O bonds scission). Among the three reaction pathways, reaction with O₂ is the dominant pathway but at the same time contribution of α-ester rearrangement and thermal decomposition cannot be ignored. In another report, Blanco et al.¹² studied the product distribution of TFETFA with Cl atoms using a 1080 L quartz-glass reaction chamber at (296 ± 2) K and concluded that reaction of O₂ is the major reaction pathways. Interestingly in their report it was also mentioned that α-ester rearrangement pathways is negligible and no TFA was observed. Due to this discrepancy it is important to study the decomposition mechanisms of CF₃C(O)OCH(O)CF₃ especially the α-ester rearrangement as this channel produces environmentally harmful TFA. Thus, there is a need to perform quantum mechanical calculations to determine the energetics involved during the decomposition of CF₃C(O)OCH(O)CF₃ radical. No theoretical study has been performed to elucidate the dissociative pathways of CF₃C(O)OCH(O)CF₃ radical. This motivated us to investigate the decomposition and reactivity mechanism of this radical on a sound theoretical basis. Five plausible decomposition pathways (reaction with O₂, α-ester rearrangement and thermal decompositions including C–H, C–C and C–O bonds scission) of CF₃C(O)OCH(O)CF₃ radical are considered in the present investigation. These are represented as follows:

CF₃C(O)OCH(O)CF₃ + O₂ → CF₃C(O)OC(O)CF₃ + HO₂ (1)

CF₃C(O)OCH(O)CF₃ → CF₃C(O)OH + CF₃C(O) (2)

CF₃C(O)OCH(O)CF₃ → CF₃C(O)OC(O)CF₃ + H (3)

CF₃C(O)OCH(O)CF₃ → CF₃C(O)OC(O)H + CF₃ (4)

CF₃C(O)OCH(O)CF₃ → CF₃C(O)O + CH(O)CF₃ (5)

Scheme 1 Tropospheric degradation of TFETFA.

The chemistry of haloalkoxy radicals has been a subject of extensive experimental and theoretical investigations as these species are interesting intermediates in the atmospheric oxidation of halogenated hydrocarbons.^18–26 Due to the significant role played by haloalkoxy radicals formed in the destruction of a variety of organic compounds released into the atmosphere, studying the fate of CF₃C(O)OCH(O)CF₃ radical is needed from the viewpoint of understanding its role in the atmospheric chemistry. Using the power of quantum chemistry methods, our purpose is two-fold: (i) gaining some insight into the fate of the alkoxy radical, to analyzing the mechanism of the assumed “α-ester rearrangement” which leads to the formation of TFA and CF₃C(O) and, (ii) studying the importance of the other pathways that this radical may undergo. To the best of our knowledge, this is the first computational evidence of the occurrence of the α-ester rearrangement for alkoxy radical derived from fluorinated ester leading to the formation of TFA. The thermochemical studies have been performed to analyze the stability of all the species involved in the reactions.

Computational methods

Quantum mechanical calculations were performed with the Gaussian 09 suite of program.²⁷ Geometry optimization of the reactants, products and transition states were made at the MPWB1K²⁸ level of theory using 6-31+G(d,p) basis set. The 6-31+G(d,p) basis set was chosen because the same basis set was used for developing the model functional. In order to see the influence of basis set on the geometrical parameter of the species concerned, calculations have been also performed with Pople's spilt-valence triple-ζ quality 6-311++G(d,p) basis set. This hybrid density functional, MPWB1K has been found to give reliable results for thermo chemistry and kinetics and has been proved to give satisfying results in previous reports.^29–34 In order to determine the nature of different stationary points on the potential energy surface, vibrational frequency calculations were performed using the same level of theory at which the optimization was made. All the stationary points had been identified to correspond to stable minima by ascertaining that all the vibrational frequencies had real positive values. The transition states were characterized by the presence of only one imaginary frequency (NIMAG = 1). To ascertain that the identified transition states connect reactant and products smoothly, intrinsic reaction coordinate (IRC) calculations³⁵ were also performed at the same level. As the reaction energy barriers are very much sensitive to the theoretical levels, the higher-order correlation corrected relative energies along with the density functional energies are necessary to obtain theoretically consistent reaction energies. Therefore, a potentially high-level method such as G2(MP2) has been used for single-point energy calculations. The G2(MP2)³⁶ energy is calculated in the following manner:

E[G2(MP2)] = E_base + ΔE(MP2) + HLC + ZPE

where, E_base = E[QCISD(T)/6-311G(d,p)], ΔE(MP2) = E[MP2/6-311+G(3df, 2p)] − E[MP2/6-311G(d,p)], and HLC (High Level Correction) = −0.00481n_β − 0.00019n_α (n_α and n_β are the number of α and β valence electrons with n_α ≥ n_β) and ZPE = zero-point energy.

In this method the geometry and frequency calculations were performed at MPWB1K/6-31+G(d,p) level. The ZPE thus obtained was corrected with a scale factor of 0.9537 to partly eliminate the systematic errors.²⁸ This dual level calculation G2(MP2)/MPWB1K/6-31+G(d,p) is known to produce reliable thermochemical and kinetic data.^30–34 To ascertain the accuracy of the MPWB1K results, we have also performed single point energy calculation at M06-2X³⁷ method using 6-311++G(d,p) basis set followed by geometry optimization at M06-2X/6-31+G(d,p) level. Finally, in order to make a comparison, transition states are optimized at B3LYP/6-311G(d,p) level of theory.

Results and discussion

The fate of fluoroalkoxy radical CF₃C(O)OCH(O)CF₃ during its thermal decomposition in the atmosphere is envisaged to occur via reaction channels (1)–(5). The detailed thermodynamic calculations performed at MPWB1K/6-31+G(d,p) and M06-2X/6-31+G(d,p) levels for reaction enthalpies and free energies associated with reaction channels (1)–(5) are listed in Table 1. Free energy values show that three reactions (1), (2) and (4) are exergonic (ΔG < 0) and thus thermodynamic facile. Results show that reactions (3) and (5) proceeds with high endothermicity of 24.38 (21.17) and 76.05 (72.42) kcal mol⁻¹, respectively at MPWB1K (M06-2X) levels along with a positive free energy change of 16.92 (13.55) and 64.95 (60.95) kcal mol⁻¹, respectively. This envisages that reactions (3) and (5) are unimportant in comparison to reactions (1), (2) and (4) which proceed with negative free energies as listed in Table 1. Optimized geometries of reactant and transition states obtained at the MPWB1K/6-31+G(d,p) and MPWB1K/6-311++G(d,p) levels are shown in Fig. 1. While the same for products are shown in Fig. S1 in ESI.† As shown in Fig. 1 the optimized geometrical parameters obtained at two levels of theory are reasonably in good agreement with each other. This also reveals that the extended basis set has very little effect on the geometry of the titled species involved during the present investigation. The reactants, transition states and products are also optimized at M06-2X/6-31+G(d,p) level of theory and corresponding results are shown in the Fig. S2 in ESI.† Transition states obtained on the potential energy surfaces of reaction channels (1)–(5) are characterized as TS1, TS2, TS3, TS4 and TS5, respectively. The search was made along the minimum energy path on a relaxed potential energy surface. Visualization of the optimized structure of TS1 further reveals the elongation of C–H (C3–H1) bond length from 1.10 to 1.262 Å at MPWB1K and 1.107 to 1.311 Å at the M06-2X level. The structure of transition state TS2 is a five-membered ring as depicted in Fig. 1. It can be observed that, while the hydrogen atom approaches the carbonyl oxygen O1 (O1–H1 = 1.248 Å at MPWB1K and 1.289 Å at M06-2X, C3–H1 = 1.352 Å at MPWB1K and 1.362 Å at M06-2X), the breaking distance C3–O2 increases up to 1.663 Å at MPWB1K and 1.712 Å at M06-2X levels at the transition state location. The two distances C2–O1 and C2–O2 tend to the same value (1.60 Å at MPWB1K and 1.251 Å at M06-2X). The five atoms, O1H1C3O2C2 are almost in a same plane. The analysis of TS3 obtained during the present study for the C–H bond scission reveals the elongation of C–H (C3–H1) bond length from 1.100 to 1.950 Å at MPWB1K and 1.107 to 1.778 Å at M06-2X. At the same time, a shrinkage of the C–O bond (C3–O3) from 1.319 to 1.183 Å at MPWB1K and 1.330 to 1.198 Å at M06-2X and formation of a carbon–oxygen double bond has also been observed. The transition state TS4 which corresponds to the breaking of the C–C bond to give CF₃ + CF₃C(O)OC(O)H reveals the elongation of C–C (C3–C4) bond length from 1.534 to 2.088 Å at MPWB1K and 1.540 to 2.082 Å at M06-2X with a simultaneous shrinkage of the C–O (C3–O3) bond from 1.319 to 1.204 Å at MPWB1K and 1.330 to 1.211 Å at M06-2X. The transition state for reaction channel (5) reveals the elongation of C–O (C3–O2) bond length from 1.415 to 1.880 Å at MPWB1K and 1.428 to 1.922 Å at M06-2X level.

Table 1 Thermochemical data for reaction channels (1)–(5) calculated at MPWB1K/6-31+G(d,p) and M06-2X/6-31+G(d,p) (values in parenthesis) level of theories. All values are in kcal mol⁻¹

Reaction channels	ΔrH°	ΔrG°
Reaction (1) (reaction with O2)	−23.77 (−26.91)	−24.75 (−28.04)
Reaction (2) (α-ester rearrangement)	1.35 (0.47)	−10.72 (−12.50)
Reaction (3) (C–H bond scission)	24. 38 (21.17)	16.92 (13.55)
Reaction (4) (C–C bond scission)	10.47 (9.38)	−2.36 (−3.36)
Reaction (5) (C–O bond scission)	76.05 (72.42)	64.95 (60.95)

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Fig. 1 Optimized geometries of reactant and transition states obtained at MPWB1K/6-31+G(d,p) and MPWB1K/6-311++G(d,p) (italic values) levels of theory. Bond lengths are in angstroms.

Harmonic vibrational frequencies of the stationary points were calculated at MPWB1K/6-31+G(d,p), MPWB1K/6-311++G(d,p) and M06-2X/6-31+G(d,p) levels of theory and the results are given in Tables S1 and S2 in ESI.† These results show that the reactant and products have stable minima on their potential energy surface characterized by the occurrence of only real and positive vibrational frequencies. On the other hand, transition states are characterized by the occurrence of only one imaginary frequency obtained at 1548i, 1131i, 742i, 365i and 632i cm⁻¹ at MPWB1K/6-31+G(d,p) and 1743i, 1059i, 930i, 379i and 723i cm⁻¹ at M06-2X/6-31+G(d,p) for TS1, TS2, TS3, TS4 and TS5, respectively.

Visualization of the imaginary frequency revealed a qualitative confirmation of the existence of transition states connecting reactants and products. Intrinsic reaction coordinate (IRC) calculation³⁵ performed for each transition state at the same level of theory using the Gonzalez–Schlegel steepest descent path in the mass-weighted Cartesian coordinates with a step size of 0.01 (amu^1/2-Bohr) as shown in Fig. 2–4 clearly authenticate a smooth transition from reactants to products along the potential energy surface. The associated energy barriers corresponding to reaction channels (1)–(5) calculated at different levels is recorded in Table 2. This reveals that the energy barrier for H-abstraction reaction of CF₃C(O)OCH(O)CF₃ with O₂ is in the range of 5–10 kcal mol⁻¹ whereas it is in the range of 10–15 kcal mol⁻¹ for α-ester rearrangement. It is obvious from Table 2 the barrier height for reaction with O₂ is considerably lower than that for other decomposition pathways and the dominance of the oxidative pathways of this alkoxy radical in the atmosphere is thus envisioned which is in a good agreement with the experimental findings of Stein et al.¹¹

Fig. 2 IRC plots of transition state (TS1) for reaction channel (1) obtained at MPWB1K/6-31+G(d,p) level of theory.

Fig. 3 IRC plots of transition states (TS2 and TS3) obtained at MPWB1K/6-31+G(d,p) level of theory.

Fig. 4 IRC plots of transition states (TS4 and TS5) obtained at MPWB1K/6-31+G(d,p) level of theory.

Table 2 Calculated energy barriers (ΔE_rel) at different level of theories. All values are in kcal mol⁻¹

Reaction channels	G2(MP2)^a	MPWB1K/6-31+G(d,p)	M06-2X/6-311++G(d,p)	M06-2X/6-31+G(d,p)	B3LYP/6-311G(d,p)	B3LYP/6-31G(d,p)
a MPWB1K/6-31+G(d,p) optimized geometries were used for G2(MP2) calculations.
TS1 (reaction with O2)	10.49	9.59	9.13	9.25	5.47	4.27
TS2 (α-ester rearrangement)	15.92	16.91	15.37	15.51	10.30	9.05
TS3 (C–H bond scission)	29.65	25.26	24.81	25.52	24.64	23.83
TS4 (C–C bond scission)	15.61	15.26	13.97	15.23	12.31	11.73
TS5 (C–O bond scission)	35.27	36.77	32.65	33.96	30.23	27.61

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No experimental or theoretical data are available in the literature to compare the energy barriers associated with the decomposition channels of CF₃C(O)OCH(O)CF₃ considered during the present investigation. However, to ascertain the reliability of the calculated values a comparison is made with the energy values calculated at B3LYP/6-31G(d,p) by Rayez et al.²⁰ for structurally similar species CH₃C(O)OCH(O)CH₃ yielding the energy barrier for α-ester rearrangement and C–C bond scission to be 6.1 and 13.5 kcal mol⁻¹, respectively. Our calculated barrier heights amount to be 5.47 and 10.30 kcal mol⁻¹, respectively at B3LYP/6-311G(d,p) level of theory for α-ester rearrangement and C–C bond scission; whereas the same obtained from the B3LYP/6-31G(d,p) calculations amount to be 4.27 and 9.05 kcal mol⁻¹. The results obtained during the course of the present investigation for α-ester rearrangement and C–C bond scission for CF₃C(O)OCH(O)CF₃ radical show a good agreement with the data obtained by Rayez et al.²⁰ It is seen that the barrier heights for α-ester rearrangement in CF₃C(O)OCH(O)CF₃ are higher than those in CH₃C(O)OCH(O)CH₃. This indicates that the fluorine atoms substitution that withdraws electron density will strengthen the C–H bond which in turn increase the activation energy for the α-ester rearrangement. Thus there is no formation of TFA which is in line with the experimental observation reported by Blanco et al.¹²

The rate constants are calculated using Canonical Transition State Theory (CTST)³⁸ given by the following expression:

where, Γ(T) is the tunneling correction factor at temperature T. Q^‡_TS and Q_R are the total partition function (per unit volume) for the transition states and reactants, respectively. ΔE is the barrier height including zero-point energy correction, k_B is the Boltzmann constant and h is the Plank's constant. R represents the universal gas constant. The partition functions for the respective transition states and reactants at 298 K are obtained from the vibrational frequency calculations made at MPWB1K/6-31+G(d,p) level. Partition functions were computed under rigid rotor and harmonic oscillator (HO) approximations. The tunneling correction factor Γ(T) is defined as the ratio of the quantum mechanical to the classical mechanical barrier crossing rate. The tunneling correction Γ(T) was estimated by using the Eckart's unsymmetric barrier method.^39,40 In this method, the reaction path through TS is fitted first in a model potential functionwhere y = −exp(2πx/L) and A and B are two parameters that depend upon forward and reverse barrier heights. The calculated rate constants at different level of theories for two dominant reaction pathways are recorded in Table 3. The rate constant for oxidation reaction occurring via reaction (1) is calculated to be 7.12 × 10⁻²⁸, 4.47 × 10⁻²⁵ and 2.56 × 10⁻²² cm⁻³ per molecule per s, respectively using G2(MP2)//MPWB1K, M06-2X and B3LYP levels of theory. On the other hand, our modeling calculations performed for the A-factor for reaction (1) comes out to be in range of 2 × 10⁻¹⁸ to 3 × 10⁻²⁰ cm⁻³ per molecule per s. Similar calculations performed to determine the rate constant for α-ester rearrangement via reaction (2) involving TS2 as the transition state yielded a value of 1.10 × 10⁻²² s⁻¹ at 298 K with the associated A-factor of 5.05 × 10⁻¹¹ s⁻¹ at G2(MP2)//MPWB1K level of theory. it can be seen that the calculated rate constants for α-ester rearrangement at G2(MP2)//MPWB1K and M06-2X levels are of same order while at B3LYP level the same is found to be 4.53 × 10⁻¹⁸ s⁻¹. We could not find any experimental or theoretical data available in the literature to make a comparison with the calculated values obtained during the present investigation. We expect that the present study may provide useful information for future laboratory investigations.

Table 3 Calculated pre-exponential factor A and rate constants for two dominant pathways at different level of theories

Reaction channels	G2(MP2)//MPWB1K/6-31+G(d,p)		M06-2X/6-31+G(d,p)		B3LYP/6-311G(d,p)
	A-Factor	Rate constant	A-Factor	Rate constant	A-Factor	Rate constant
a Unit (cm^3 per molecule per s).b Unit (s^−1).
Reaction with O2^a	3.43 × 10^−20	7.12 × 10^−28	2.66 × 10^−18	4.77 × 10^−25	2.59 × 10^−18	2.56 × 10^−22
α-Ester rearrangement^b	5.05 × 10^−11	1.10 × 10^−22	6.23 × 10^−11	2.72 × 10^−22	1.58 × 10^−10	4.53 × 10^−18

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Conclusions

We present here the potential energy profile (including geometries, energies and vibrational frequencies of reactant, transition states and products) and kinetic data for the thermal decomposition and oxidation of CF₃C(O)OCH(O)CF₃ radical investigated at the G2(MP2)//MPWB1K/6-31+G(d,p) level of theory. Energetic calculation reveals that the most dominant decomposition pathway for CF₃C(O)OCH(O)CF₃ is the reaction with O₂ that occurs with the lowest barrier height. The dominance of oxidative pathways established during the present investigation is in accord with the experimental observation made by Stein et al.¹¹ Our results also confirm the negligible importance of α-ester rearrangement to produce TFA as explained by Blanco et al.¹² The thermal rate constant evaluated using canonical transition state theory for the oxidative pathways is found to be 7.12 × 10⁻²⁸ with the corresponding A-factor as 3.43 × 10⁻²⁰ cm⁻³ per molecule per s at 298 K. We hope our theoretical results will help to solve the controversy on the contribution of α-ester rearrangement to produce TFA.

Acknowledgements

Author acknowledges financial support from University Grants Commission, New Delhi in form of UGC-Dr D. S. Kothari Fellowship. Thanks are also due to the reviewers for their valuable comments to improve the quality of the manuscript.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra00881b

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