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Ab initio chemical kinetics of the CH2OO + C2F4 reaction
Accepted Manuscript Research paper Ab Initio Chemical Kinetics of the CH2OO + C2F4 Reaction Tam V.T. Mai, Minh v. Duong, Hieu T. Nguyen, Kuang C. Lin, Lam K. Huynh PII: DOI: Reference:
S0009-2614(18)30493-7 https://doi.org/10.1016/j.cplett.2018.06.013 CPLETT 35712
To appear in:
Chemical Physics Letters
Received Date: Revised Date: Accepted Date:
12 March 2018 2 June 2018 8 June 2018
Please cite this article as: T.V.T. Mai, M.v. Duong, H.T. Nguyen, K.C. Lin, L.K. Huynh, Ab Initio Chemical Kinetics of the CH2OO + C2F4 Reaction, Chemical Physics Letters (2018), doi: https://doi.org/10.1016/j.cplett.2018.06.013
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Ab Initio Chemical Kinetics of the CH2OO + C2F4 Reaction Tam V.-T. Mai,1,2,* Minh v. Duong1, Hieu T. Nguyen1, Kuang C. Lin3 and Lam K. Huynh4,* ` 1
Molecular Science and Nano-Materials Lab, Institute for Computational Science and Technology, SBI Building, Quang Trung Software City, Tan Chanh Hiep Ward, District 12, Ho Chi Minh City, Vietnam. 2 University of Science, Vietnam National University – HCMC, 227 Nguyen Van Cu, Ward 4, District 5, Ho Chi Minh City, Vietnam. 3 Department of Mechanical and Electromechanical Engineering, National Sun Yat-Sen University, Kaohsiung, 80424, Taiwan 4 International University, Vietnam National University – HCMC, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam.
* Corresponding authors. Email address: [email protected] | [email protected] (TVTM); [email protected] | [email protected] (LKH) Tel: (84-8) 2211.4046 (Ext. 3233) Fax: (84-8) 3724.4271
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Contents Abstract ................................................................................................................................................. 3 Introduction ........................................................................................................................................... 4 Computational Details ........................................................................................................................... 5 Results and Discussion .......................................................................................................................... 7 Conclusions .......................................................................................................................................... 15 Acknowledgments ................................................................................................................................ 15 References ............................................................................................................................................ 16
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Abstract The detailed kinetic mechanism of the CH2OO + C2F4 reaction was explored using the accurate composite G4 method and the master equation/Rice–Ramsperger–Kassel–Marcus (ME/RRKM) rate model. Corrections for tunneling, hindered internal rotation and anharmonicity treatments were included. The 1,3-cycloaddition was found to be the rate-determining step with a small barrier ∆V‡(0 K) of 3.5 kcal/mol. The total rate constants were suggested as ktot(T) = 3.69×10-23×T2.91×exp(-1114 K/T) (cm3/molecule/s) for T = 200 – 1000 K & P-independence (P = 76 – 760 torr). Keywords: ozonolysis, Criegee intermediate, Tetrafluoroethene, ab initio kinetics.
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Introduction Ozonolysis of unsaturated hydrocarbons (e.g., those from massive biogenic terpene emissions) is the forming source of Criegee intermediates (CIs) [1] in Earth’s troposphere. It is initiated with a 1,3-cycloaddition of O3 to the C=C double bond of the alkenes to produce the cyclic primary ozonide (POZ). The POZ then decomposes to form the carbonyl oxides (so-called Criegee intermediates) and a carbonyl compound with a large overall exothermicity. The internally excited carbonyl oxides will either decompose via a unimolecular process (~ 37 – 50 %) or become thermalized by collisional energy loss (~ 50 – 63 %) [2, 3]. The thermalized CIs can decay via the unimolecular decomposition or react with other atmospheric species via the bimolecular reactions due to their high reactivity [4-6]. The reported barrier heights at 298 K for the isomerization and dissociation of CH2OO are larger than 17.7 kcal/mol [7]; thus the bimolecular reactions having lower barrier heights (e.g., the calculated value of 3.3 kcal/mol for the title CH2OO+C2F4 reaction in this study) might play a role in the atmosphere. These bimolecular reactions were also recognized to have a crucial effect on the formation of aerosols in the atmosphere [4, 8]. In opposition to the comprehensive experimental and computational studies for the reaction between CIs and alkenes [9-11], the CIs reactions with the perfluoroalkenes, like C2F4, has received no attention although they can contribute to the CI chemistry in the atmosphere. Perfluorocarbons (PFCs) are widely used as solvents and as building blocks in the manufacture of perfluorinated polymers [12]. They are also one of the essential chemicals in human activities and thus in Earth’s atmosphere. Especially, PFCs were considered as an acceptable class of alternative species to replace chlorofluorocarbons (CFCs) over 30 years ago in some applications because their capability of ozone depletion is insignificant when compared to CFC-11 (CCl3F) in
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the stratosphere [13]. The global annual production of perfluoroalkenes is significant and is evaluated to be ~ 50, 20 and 0.01 Tg yr -1 for C2 F4, C3F6 and C4F6, respectively [14], but the amount emitted into the atmosphere remains unclear. Emitted into the troposphere with the largest amount [14], tetrafluoroethene (C2 F4), the simplest perfluoroalkene, is used in the production of such widespread polymers as Teflon and Fluon, and also copolymers such as fluoroelastomers (terpolymers), etc. The most important reactions that can contribute to the removal of C2F4 are bimolecular reactions of C2 F4 with various atmospheric oxidants such as OH, NO3 and O3. In particular, a short atmospheric lifetime of ~ one day is estimated with respect to its reaction with the OH radical [15]. In this work, we carried out accurate ab initio calculations to characterize the temperature-/pressure-dependent kinetic behaviors of the formaldehyde oxide (CH2OO – the smallest CI) with CF2=CF2 (the smallest perfluoroalkene) in the atmospheric conditions, using the state-of-the-art RRKM/ME [16] framework with the corrections from tunneling, hindered rotation and anharmonicity treatments on the accurately constructed potential energy surface (PES). To the best of our knowledge, no study has been reported for the title reaction; thus the present work can provide the helpful information including kinetics or products to the relevant experiments about the reactivity of CIs towards PFCs. Computational Details In this study, all structures of stationary points (reactants, products and transition states) of the title reaction were investigated using B3LYP level of theory [17, 18] and 6-31G(2df,p) basis set. For the broken symmetry issue at the Criegee intermediate, the unrestricted DFT method (UB3LYP) was used with the keyword “guess = (mix, always)” for the initial guess of the HOMO-LUMO mixing. The vibrational frequency analysis of all species was performed at the 5
same level, B3LYP/6-31G(2df,p), to identify the nature of optimized stationary points. The zeropoint vibrational energy and wavenumbers were scaled with a factor of 0.9854 [19] prior to their use. The relative energies were then refined by using the G4 [20] composite method whose extrapolation procedure was described in the work of Curtiss et al. [20]. With an absolute energy deviation from the experimental data of 0.83 kcal/mol for 454 test cases [20], the G4 level has shown to be the effective method for characterizing the ozonolysis of the double bond in C2H2/C2H4 [21], C2F4 [22] and α-phellandrene [23] systems. Moreover, it was found to have a similarly good performance for reaction barrier heights [24-26]. Therefore, it could be considered to be a method of choice for the similar title system, CH2OO + C2F4, regarding the accuracy and computational cost (i.e., nine heavy atoms for the title system: three carbon, two oxygen, and four fluorine atoms). The G4 energetic profiles were then compared with less accurate composite methods such as CBS-QB3 [27], CBS-APNO [28], G3 [29] and G3B3 [30] to evaluate their performance for this system. The G4 energies, associated with the B3LYP/631G(2df,p) geometries and frequencies, were used to calculate thermodynamic and kinetic data for the title reaction. All these electronic structure calculations were performed using the Gaussian-09 program package [31]. Thermodynamic and kinetic analyses were carried out using the Multi-Species Multi-Channels (MSMC) code [32] with the assistance of MSMC-GUI [33, 34]. The master equation/Rice–Ramsperger–Kassel–Marcus (ME/RRKM) framework [16], was considered with the inclusion of the quantum tunneling effect using the
[35] model and the hindered
internal rotation (HIR) treatment [36]. For the HIR treatment, the hindrance potential, V ( ) , as a function of torsional angle, θ, along the C-C bond in CHF2–CHO (cf. supplementary Figure S2) was explicitly obtained at the B3LYP/CBSB7 level via relaxed surface scans with the step size
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of 10o for dihedral angles corresponding to the rotation. The anharmonicity treatment was also included using the second-order perturbation theory (PT2) [37] with the vibrational anharmonicity constants xij calculated at B3LYP/6-31G(2df,p) level of theory (cf. supplementary Table S1). For the densities/sums of states of fully coupled anharmonic vibrations, a hybrid method was employed. Direct count algorithm was used for energy levels with sums of states up to 109, and the modified Wang-Landau [38] algorithm by Basire et al. [39] was used for the remaining higher energy levels. The energy-transfer process was computed on the basis of the temperature-dependent exponential-down model with Edown = 250×(298/T)0.8 cm-1 for N2 as the bath gas [40]. The Lennard-Jones (L-J) parameters N2 [41] while
/ kB
/ kB
= 82.0 K and = 3.74 Å were used for
= 445.1 K and = 5.943 Å were taken from the data of 2,5-dimethylfuran
(Mr = 96) [42] assuming to represent the adduct (Mr = 108). Results and Discussion For the title reaction, the energetic reaction profile (0 K) of the CH2OO + C2F4 reaction, calculated at the G4 method, was presented in Figure 1. To facilitate the discussion, the energies relative to that of the separated reactants were presented; otherwise, they would be explicitly stated. The reaction mechanism of CH2OO + C2 F4 , which is similar to the ozonolysis of alkenes, belongs to the class of 1,3-dipolar cycloadditions. The reaction proceeds via a pre-active complex which is located about -2.5 kcal/mol (the relative Gibbs free energy with respect to the reactants’ value at 298 K is +5.7 kcal/mol). The value is found to be comparable to that of the reaction of CH2OO + C2H4 [10] (i.e., -2.2 kcal/mol). The binding energies do not change significantly with different cases of F-atom substitution that was discovered in the of ozonolysis reactions of difluoroethenes [43]. 7
After the formation of the van-der-Waals complex (or the pre-complex), the reaction proceeds through the transition state TS1 to produce the adduct via the 1,3-cycloaddition of CH2OO to the C=C double bond of C2F4. The barrier height of TS1 is located about 3.5 kcal/mol which is 2.9 kcal/mol higher than that of CH2OO + C2H4 [10], obtained at CCSD(T)/aug-ccpVQZ//M06-2X. The cycloaddition step forms a cyclic peroxide (adduct) whose energy is 85.7 kcal/mol below the reactant channel. It is significantly more stable than the POZ formed in the ozonolysis (e.g., -85.7 vs. -80.5 kcal/mol [22] of adducts in the reactions of CH2OO and O3 with C2F4, respectively). The barrier height of TS1, thus, can be expected to be lower according to the Evans-Polanyi principle (e.g., 3.5 vs. 7.0 kcal/mol [22], respectively). The adduct can be rapidly dissociated to the final products, CF2O + CHF2 CHO, by simultaneously breaking O-O, C-C bonds and H-migration in the adduct structure (cf. Figure 1) due to its high exothermicity. The absolute TS2-via barrier height is 32.6 kcal/mol and then leads to the formation of the final products with very large exothermicity overall (i.e., 138.6 kcal/mol below the entrance channel). The adduct formation via TS1 is expected to be the rate-controlling step of oxidation process [43]; thus TS1 was also examined at highly accurate electronic structure method, namely, CCSD(T)/CBS using the Truhlar’s scheme [44] using two points (cc-pVDZ and cc-pVTZ basis sets) based on the B3LYP/aug-cc-pVTZ geometry. The results showed that the binding energy of vdW complex and the ΔV‡(TS1) obtained at G4 (i.e., -2.5 and 3.5 kcal/mol, respectively) are reasonably comparable with those derived from CCSD(T)/CBS//B3LYP/aug-cc-pVTZ (i.e., -3.0 and 3.0 kcal/mol, respectively). The T1 diagnostic [45] values are less than critical values (i.e., ≤ 0.044 [46]), indicating that the single-determinant CCSD wave functions can be appropriately used to estimate the nondynamical correlation; therefore, the CCSD(T), due to the inclusion of the triple excitations, is expected to perform better for the title reaction. It is for these reasons
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that the data obtained from the G4 method are expected to be reliable, especially for the following kinetic analysis.
Figure 1: ZPE-corrected energetic reaction profile (0 K) of the CH2OO + C2F4 reaction, calculated at G4 level of theory. All values are in kcal/mol. The important optimized parameters for all species were shown in Figure S1 in Supplementary Information. It is found that the geometrical parameters optimized at B3LYP/631G(2df,p) agree well with those of the literature data for the available species (e.g., CH 2OO, 9
C2F4, and CF2O) with the average deviations of less than 0.1 Å and ~ 1 o in bonds and angles, respectively. The optimized geometrical parameters and Vereecken’s data [47], optimized at M06-2X/aug-cc-pVDZ in CH2OO structure, are consistent with each other (cf. Figure S1). As expected, according to the Hammond's postulate, the structures of TS1 and the reactants are very similar; in which the length of O-O bond of TS1 is a slightly larger than its CH2OO value of 1.33 Å (e.g., 1.35 vs. 1.33 Å) and the C2F4 structure is still fairly quite planar. Thus, it can be concluded that the title reaction approaches the TS1 during the early stage of the 1,3cycloaddition, nearly after the formation of the pre-complex becoming consistently with the ozonolysis of C2F4 [22]. The concerted decomposition of the adduct takes place with the concurrent cleavage of both C-C and O-O bonds accompanied with H-migration via TS2, leading to the final products, CF2O + CHF2CHO. The bond lengths of the breaking C-C and O-O bonds are 1.93 and 2.21 Å, respectively (0.36 and 0.75 Å longer than those of the corresponding adduct). The calculated vibrational frequencies, tabulated in Table S1, in general, are slightly higher than those available in the literature with the Mean Absolute Deviations (MADs) of 3.1, 10.2 and 2.0 % for CH2OO, C2F4 and CF2O, respectively. To ensure the validity of the G4 results, Table 1 lists the relative energies of all stationary points in the PES calculated at different composite methods, such as G4, G3B3, G3, CBS-QB3 and CBS-APNO. In general, the energies calculated at G4 are in good agreement with those obtained from other methods (MADs are normally less than 20%) except for the G3 data with the maximum difference of 1.9 kcal/mol for pre-complex. It is noted that the TS2 cannot be located at G3 and CBS-APNO methods that may be attributed to the MP2 and QCISD used in the optimization process, respectively. To give a bigger picture of CIs + C2F4, we extended the data for the larger CIs (e.g., CH3CHOO (syn & anti) and (CH3)2COO); presented in Table 2 and
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compared to the corresponding CIs + C2H4 [10]. It is easily seen in Table 2 that the binding energies in the pre-complex are similar to each other, but the barrier heights of the cycloaddition process of CIs + C2F4 are higher than those of CIs + C2H4. As a result, the reactivity of CIs towards C2F4 can be followed as CH3CHOO (anti) ~ CH2OO > (CH3)2COO > CH3CHOO (syn) that is likely to have the same trend in CIs with ethene [10]. Table 1: Relative energies (in kcal⋅mol-1) of all species involved at different levels of theory at 0 K. The zero-point energy (ZPE) correction was included. Numbers are the energies relative to that of the reactants. Species G4 Pre-complex -2.5 Adduct -85.7 TS1 3.5 TS2 -53.1 CF2O + CHF2CHO -138.6 Mean absolute deviation/G4 (%)
G3B3 -3.3 -86.5 1.8 -54.2 -138.6 15.8
G3 -4.4 -87.1 2.0 N/A -139.1 29.2
CBS-QB3 -3.2 -87.5 2.2 -54.1 -138.5 15.5
CBS-APNO -3.2 -85.7 3.7 N/A -137.8 8.1
Table 2: ZPE-corrected energies relative to the separated reactants of the pre-complex, the cycloaddition of the transition state and the adduct of a set of CIs + C2F4 reactions calculated at G4 method (0 K and in kcal/mol). Values in the parentheses are the estimated values for the CIs + C2H4 reactions [10], calculated at CCSD(T)/aug-cc-pVQZ//M06-2X. Reaction CH2OO CH3CHOO_syn CH3CHOO_anti (CH3)2COO
Pre-complex -2.5 (-2.2) -3.7 (-3.6) -3.5 (-4.0) -4.1 (-4.6)
Cycloaddition TS 3.5 (0.6) 7.7 (4.7) 2.0 (0.5) 6.6 (5.4)
Adduct -85.7 -84.4 -80.3 -79.1
The calculated thermodynamic properties (∆Hf298 K and S298 K) for all species involved in the title reaction were shown in Table S2 and then compared to the literature data to evaluate their reliability. In general, the calculated data agree well with the literature one as discussed in 11
the work [22] for C2F4 and CF2O. It is worth noting that the ∆Hf298 K of CH2OO derived from the W1U method is in excellent agreement with that calculated by the W1 method (e.g., 25.5 vs. 25.3 kcal/mol) [48]. In this part, k(T, P) were characterized by using the PES and quantum information carried out at the G4 method as discussed above. As seen in Figure 1, the stabilization of the pre-reactive complex, formed by the combination of CH2OO and C2F4, can be expected to play an insignificant role due to its energy being ~ 2.5 kcal/mol below the entrance channel. The shadow pre-complex cannot affect the kinetics even at the room temperature as suggested by Vereecken et al. [10, 47]; thus it can be appropriately excluded in kinetic model. Note that the formation of this complex is less favorable at higher temperatures with the positive calculated Gibbs free energies relative to that of the reactants. Figure 2 showed the normalized time-resolved profiles for the title reaction at 298 K and 760 torr using the ME/RRKM model. It is observed that the final products (CF2O & CHF2CHO) are predominant while the stabilization of the adduct does not play any role at the considered conditions.
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CH2OO + C2F4 → products (T = 298 K & P = 760 torr)
1.0
CF2O + CHF2CHO
Mole fraction
0.8 0.6 0.4 adduct
0.2 0.0 0
5
10 Time (s) 15
20
25
Figure 2: Time-resolved species profiles for the reaction, CH2OO + C2F4 → products at 298 K and 760 torr ([C2F4]0 >> [CH2OO]0 and [C2F4]/[N2] = 10-3; N2 is the bath gas used in the simulation). The eigenpair analysis was shown in Figure S3 to elucidate the reliability of the deterministic model. As easily seen that there is no mixing in eigenvalue spectrum between the fastest chemically significant eigenvalues (CSEs) and the slowest internal energy relaxation eigenvalues (IEREs) in the considered conditions (T = 200 – 1000 K and P = 760 torr); thus, the derived phenomenological rate coefficients using the CSE approach can be used for the considered temperature. The high-pressure rate constants k∞(T) for all elementary reactions were shown in Table S3 for the temperature range of 200 – 1000 K. Figure 3 plotted the total rate constants (CH2OO + C2F4 → products) as a function of temperature at different pressures (e.g., 76 – 760 torr, except for CH2OO + C2F4 → adduct at P = 7600 torr). It was observed that the pressure has no effect on the k(T, P) for the formation of the final products in a range of pressure (P = 76 – 760 torr), 13
which is opposite to the formation of the adduct. The stabilization of the adduct favors at the higher pressure and the pressure-dependence is more noticeable at the high temperature but it still cannot compete with the formation of the product channel at the atmospheric conditions (T = 200 – 400 K & P ≤ 760 torr [4]). Its contribution to the total rate constants can be reasonably neglected at P ≤ 760 torr, leading to the total rate constants, ktot(T) = 3.69×10-23×T2.91×exp(1114.35 K/T) cm3/molecule/s (T = 200 – 1000 K and P-independence in range of 76 – 760 torr).
CH2OO + C2F4 → products logk (cm3/molecule/s)
1.E-14 CF2O + CHF2CHO 1.E-16 Adduct 1.E-18
7600 torr
1.E-20 1.0
1.5
2.0
2.5
3.0 3.5 1000/T (K)
4.0
4.5
5.0
Figure 3: Calculated rate coefficients as a function of temperature at different pressures (P = 76 – 760 torr) for CH2OO + C2F4 → products. It is also mentioned that the anharmonic treatment slightly increases the rate constants for the main channel as depicted in the Figure S4. For example, the rate ratios of the anharmonic to harmonic treatments are ~ 1.10 and 1.03 at T = 298 and 1000 K for the formation of the final products (CH2OO + C2F4 → CF2O + CHFCHO), respectively (cf. Figure S4). The quantum tunneling effect was found to play a minor role for this title system (e.g., the factors of 1.54 ÷ 1.06 and 1.70 ÷ 1.08 from 200 to 1000 K via TS1 and TS2 pathways, respectively); and the HIR
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contribution is almost negligible (e.g., the HIR factor is about unity in the range of 200 – 1000 K for the formation of the final products, CF2O + CHF2CHO). Conclusions In this study, the detailed kinetic mechanism of the CH2OO + C2 F4 → products reaction was firstly investigated by using the accurate electronic calculations accompanied by the stateof-the-art ME/RRKM rate model which includes the corrections for tunneling, hindered internal rotation and anharmonicity treatments. The results showed that the title reaction proceeded with the formation of a shallow van der Waals complex and then formed an adduct, which can immediately decompose to the CF2O (carbonyl fluoride) + CHF2CHO (difluoro acetaldehyde). The study presented that the total rate coefficient (CH2OO + C2F4 → products) is pressureindependent in a range of pressure from 76 to 760 torr and T = 200 – 1000 K. It is found that both the quantum tunneling effect and the anharmonicity treatment slightly increase the rate constants while the HIR treatment has no effect at all. The calculated thermodynamic data and rate coefficients (in NASA and modified Arrhenius formats, respectively) were also explicitly provided at different pressures for further modeling/simulation of related atmospheric systems. Acknowledgments This work was supported by the Institute for Computational Science and Technology (ICST) – Ho Chi Minh City and the Department of Science and Technology – Ho Chi Minh City under the grant no. 208/QĐ-KHCNTT. LKH also acknowledges International University, VNUHCM for providing the computing resources. We are thankful to Tri Pham and Tuyn Phan (ICST) for technical assistance.
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Graphical Abstract
18
Ab Initio Chemical Kinetics of the CH2OO + C2F4 Reaction Tam V.-T. Mai,1,2,* Minh v. Duong1, Hieu T. Nguyen1, Kuang C. Lin3 and Lam K. Huynh4,*
1
Molecular Science and Nano-Materials Lab, Institute for Computational Science and Technology, SBI Building, Quang Trung Software City, Tan Chanh Hiep Ward, District 12, Ho Chi Minh City, Vietnam. 2 University of Science, Vietnam National University – HCMC, 227 Nguyen Van Cu, Ward 4, District 5, Ho Chi Minh City, Vietnam. 3 Department of Mechanical and Electromechanical Engineering, National Sun Yat-Sen University, Kaohsiung, 80424, Taiwan 4 International University, Vietnam National University – HCMC, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam. Highlights
Detailed reaction mechanism of CH2OO + C2 F4 was firstly studied with the accurate composite G4 method.
Time-resolved temperature- and pressure-dependent behaviors of the title reaction were characterized using the master equation/Rice–Ramsperger–Kassel–Marcus (ME/RRKM) rate models.
Corrections for tunneling, hindered internal rotation and anharmonicity treatments were included.
Detailed kinetic sub-mechanism (kinetic and thermodynamic data) was provided for 200– 1000 K and 76–760 torr for further kinetic modeling/simulation.
19
S0009-2614(18)30493-7 https://doi.org/10.1016/j.cplett.2018.06.013 CPLETT 35712
To appear in:
Chemical Physics Letters
Received Date: Revised Date: Accepted Date:
12 March 2018 2 June 2018 8 June 2018
Please cite this article as: T.V.T. Mai, M.v. Duong, H.T. Nguyen, K.C. Lin, L.K. Huynh, Ab Initio Chemical Kinetics of the CH2OO + C2F4 Reaction, Chemical Physics Letters (2018), doi: https://doi.org/10.1016/j.cplett.2018.06.013
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Ab Initio Chemical Kinetics of the CH2OO + C2F4 Reaction Tam V.-T. Mai,1,2,* Minh v. Duong1, Hieu T. Nguyen1, Kuang C. Lin3 and Lam K. Huynh4,* ` 1
Molecular Science and Nano-Materials Lab, Institute for Computational Science and Technology, SBI Building, Quang Trung Software City, Tan Chanh Hiep Ward, District 12, Ho Chi Minh City, Vietnam. 2 University of Science, Vietnam National University – HCMC, 227 Nguyen Van Cu, Ward 4, District 5, Ho Chi Minh City, Vietnam. 3 Department of Mechanical and Electromechanical Engineering, National Sun Yat-Sen University, Kaohsiung, 80424, Taiwan 4 International University, Vietnam National University – HCMC, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam.
* Corresponding authors. Email address: [email protected] | [email protected] (TVTM); [email protected] | [email protected] (LKH) Tel: (84-8) 2211.4046 (Ext. 3233) Fax: (84-8) 3724.4271
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Contents Abstract ................................................................................................................................................. 3 Introduction ........................................................................................................................................... 4 Computational Details ........................................................................................................................... 5 Results and Discussion .......................................................................................................................... 7 Conclusions .......................................................................................................................................... 15 Acknowledgments ................................................................................................................................ 15 References ............................................................................................................................................ 16
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Abstract The detailed kinetic mechanism of the CH2OO + C2F4 reaction was explored using the accurate composite G4 method and the master equation/Rice–Ramsperger–Kassel–Marcus (ME/RRKM) rate model. Corrections for tunneling, hindered internal rotation and anharmonicity treatments were included. The 1,3-cycloaddition was found to be the rate-determining step with a small barrier ∆V‡(0 K) of 3.5 kcal/mol. The total rate constants were suggested as ktot(T) = 3.69×10-23×T2.91×exp(-1114 K/T) (cm3/molecule/s) for T = 200 – 1000 K & P-independence (P = 76 – 760 torr). Keywords: ozonolysis, Criegee intermediate, Tetrafluoroethene, ab initio kinetics.
3
Introduction Ozonolysis of unsaturated hydrocarbons (e.g., those from massive biogenic terpene emissions) is the forming source of Criegee intermediates (CIs) [1] in Earth’s troposphere. It is initiated with a 1,3-cycloaddition of O3 to the C=C double bond of the alkenes to produce the cyclic primary ozonide (POZ). The POZ then decomposes to form the carbonyl oxides (so-called Criegee intermediates) and a carbonyl compound with a large overall exothermicity. The internally excited carbonyl oxides will either decompose via a unimolecular process (~ 37 – 50 %) or become thermalized by collisional energy loss (~ 50 – 63 %) [2, 3]. The thermalized CIs can decay via the unimolecular decomposition or react with other atmospheric species via the bimolecular reactions due to their high reactivity [4-6]. The reported barrier heights at 298 K for the isomerization and dissociation of CH2OO are larger than 17.7 kcal/mol [7]; thus the bimolecular reactions having lower barrier heights (e.g., the calculated value of 3.3 kcal/mol for the title CH2OO+C2F4 reaction in this study) might play a role in the atmosphere. These bimolecular reactions were also recognized to have a crucial effect on the formation of aerosols in the atmosphere [4, 8]. In opposition to the comprehensive experimental and computational studies for the reaction between CIs and alkenes [9-11], the CIs reactions with the perfluoroalkenes, like C2F4, has received no attention although they can contribute to the CI chemistry in the atmosphere. Perfluorocarbons (PFCs) are widely used as solvents and as building blocks in the manufacture of perfluorinated polymers [12]. They are also one of the essential chemicals in human activities and thus in Earth’s atmosphere. Especially, PFCs were considered as an acceptable class of alternative species to replace chlorofluorocarbons (CFCs) over 30 years ago in some applications because their capability of ozone depletion is insignificant when compared to CFC-11 (CCl3F) in
4
the stratosphere [13]. The global annual production of perfluoroalkenes is significant and is evaluated to be ~ 50, 20 and 0.01 Tg yr -1 for C2 F4, C3F6 and C4F6, respectively [14], but the amount emitted into the atmosphere remains unclear. Emitted into the troposphere with the largest amount [14], tetrafluoroethene (C2 F4), the simplest perfluoroalkene, is used in the production of such widespread polymers as Teflon and Fluon, and also copolymers such as fluoroelastomers (terpolymers), etc. The most important reactions that can contribute to the removal of C2F4 are bimolecular reactions of C2 F4 with various atmospheric oxidants such as OH, NO3 and O3. In particular, a short atmospheric lifetime of ~ one day is estimated with respect to its reaction with the OH radical [15]. In this work, we carried out accurate ab initio calculations to characterize the temperature-/pressure-dependent kinetic behaviors of the formaldehyde oxide (CH2OO – the smallest CI) with CF2=CF2 (the smallest perfluoroalkene) in the atmospheric conditions, using the state-of-the-art RRKM/ME [16] framework with the corrections from tunneling, hindered rotation and anharmonicity treatments on the accurately constructed potential energy surface (PES). To the best of our knowledge, no study has been reported for the title reaction; thus the present work can provide the helpful information including kinetics or products to the relevant experiments about the reactivity of CIs towards PFCs. Computational Details In this study, all structures of stationary points (reactants, products and transition states) of the title reaction were investigated using B3LYP level of theory [17, 18] and 6-31G(2df,p) basis set. For the broken symmetry issue at the Criegee intermediate, the unrestricted DFT method (UB3LYP) was used with the keyword “guess = (mix, always)” for the initial guess of the HOMO-LUMO mixing. The vibrational frequency analysis of all species was performed at the 5
same level, B3LYP/6-31G(2df,p), to identify the nature of optimized stationary points. The zeropoint vibrational energy and wavenumbers were scaled with a factor of 0.9854 [19] prior to their use. The relative energies were then refined by using the G4 [20] composite method whose extrapolation procedure was described in the work of Curtiss et al. [20]. With an absolute energy deviation from the experimental data of 0.83 kcal/mol for 454 test cases [20], the G4 level has shown to be the effective method for characterizing the ozonolysis of the double bond in C2H2/C2H4 [21], C2F4 [22] and α-phellandrene [23] systems. Moreover, it was found to have a similarly good performance for reaction barrier heights [24-26]. Therefore, it could be considered to be a method of choice for the similar title system, CH2OO + C2F4, regarding the accuracy and computational cost (i.e., nine heavy atoms for the title system: three carbon, two oxygen, and four fluorine atoms). The G4 energetic profiles were then compared with less accurate composite methods such as CBS-QB3 [27], CBS-APNO [28], G3 [29] and G3B3 [30] to evaluate their performance for this system. The G4 energies, associated with the B3LYP/631G(2df,p) geometries and frequencies, were used to calculate thermodynamic and kinetic data for the title reaction. All these electronic structure calculations were performed using the Gaussian-09 program package [31]. Thermodynamic and kinetic analyses were carried out using the Multi-Species Multi-Channels (MSMC) code [32] with the assistance of MSMC-GUI [33, 34]. The master equation/Rice–Ramsperger–Kassel–Marcus (ME/RRKM) framework [16], was considered with the inclusion of the quantum tunneling effect using the
[35] model and the hindered
internal rotation (HIR) treatment [36]. For the HIR treatment, the hindrance potential, V ( ) , as a function of torsional angle, θ, along the C-C bond in CHF2–CHO (cf. supplementary Figure S2) was explicitly obtained at the B3LYP/CBSB7 level via relaxed surface scans with the step size
6
of 10o for dihedral angles corresponding to the rotation. The anharmonicity treatment was also included using the second-order perturbation theory (PT2) [37] with the vibrational anharmonicity constants xij calculated at B3LYP/6-31G(2df,p) level of theory (cf. supplementary Table S1). For the densities/sums of states of fully coupled anharmonic vibrations, a hybrid method was employed. Direct count algorithm was used for energy levels with sums of states up to 109, and the modified Wang-Landau [38] algorithm by Basire et al. [39] was used for the remaining higher energy levels. The energy-transfer process was computed on the basis of the temperature-dependent exponential-down model with Edown = 250×(298/T)0.8 cm-1 for N2 as the bath gas [40]. The Lennard-Jones (L-J) parameters N2 [41] while
/ kB
/ kB
= 82.0 K and = 3.74 Å were used for
= 445.1 K and = 5.943 Å were taken from the data of 2,5-dimethylfuran
(Mr = 96) [42] assuming to represent the adduct (Mr = 108). Results and Discussion For the title reaction, the energetic reaction profile (0 K) of the CH2OO + C2F4 reaction, calculated at the G4 method, was presented in Figure 1. To facilitate the discussion, the energies relative to that of the separated reactants were presented; otherwise, they would be explicitly stated. The reaction mechanism of CH2OO + C2 F4 , which is similar to the ozonolysis of alkenes, belongs to the class of 1,3-dipolar cycloadditions. The reaction proceeds via a pre-active complex which is located about -2.5 kcal/mol (the relative Gibbs free energy with respect to the reactants’ value at 298 K is +5.7 kcal/mol). The value is found to be comparable to that of the reaction of CH2OO + C2H4 [10] (i.e., -2.2 kcal/mol). The binding energies do not change significantly with different cases of F-atom substitution that was discovered in the of ozonolysis reactions of difluoroethenes [43]. 7
After the formation of the van-der-Waals complex (or the pre-complex), the reaction proceeds through the transition state TS1 to produce the adduct via the 1,3-cycloaddition of CH2OO to the C=C double bond of C2F4. The barrier height of TS1 is located about 3.5 kcal/mol which is 2.9 kcal/mol higher than that of CH2OO + C2H4 [10], obtained at CCSD(T)/aug-ccpVQZ//M06-2X. The cycloaddition step forms a cyclic peroxide (adduct) whose energy is 85.7 kcal/mol below the reactant channel. It is significantly more stable than the POZ formed in the ozonolysis (e.g., -85.7 vs. -80.5 kcal/mol [22] of adducts in the reactions of CH2OO and O3 with C2F4, respectively). The barrier height of TS1, thus, can be expected to be lower according to the Evans-Polanyi principle (e.g., 3.5 vs. 7.0 kcal/mol [22], respectively). The adduct can be rapidly dissociated to the final products, CF2O + CHF2 CHO, by simultaneously breaking O-O, C-C bonds and H-migration in the adduct structure (cf. Figure 1) due to its high exothermicity. The absolute TS2-via barrier height is 32.6 kcal/mol and then leads to the formation of the final products with very large exothermicity overall (i.e., 138.6 kcal/mol below the entrance channel). The adduct formation via TS1 is expected to be the rate-controlling step of oxidation process [43]; thus TS1 was also examined at highly accurate electronic structure method, namely, CCSD(T)/CBS using the Truhlar’s scheme [44] using two points (cc-pVDZ and cc-pVTZ basis sets) based on the B3LYP/aug-cc-pVTZ geometry. The results showed that the binding energy of vdW complex and the ΔV‡(TS1) obtained at G4 (i.e., -2.5 and 3.5 kcal/mol, respectively) are reasonably comparable with those derived from CCSD(T)/CBS//B3LYP/aug-cc-pVTZ (i.e., -3.0 and 3.0 kcal/mol, respectively). The T1 diagnostic [45] values are less than critical values (i.e., ≤ 0.044 [46]), indicating that the single-determinant CCSD wave functions can be appropriately used to estimate the nondynamical correlation; therefore, the CCSD(T), due to the inclusion of the triple excitations, is expected to perform better for the title reaction. It is for these reasons
8
that the data obtained from the G4 method are expected to be reliable, especially for the following kinetic analysis.
Figure 1: ZPE-corrected energetic reaction profile (0 K) of the CH2OO + C2F4 reaction, calculated at G4 level of theory. All values are in kcal/mol. The important optimized parameters for all species were shown in Figure S1 in Supplementary Information. It is found that the geometrical parameters optimized at B3LYP/631G(2df,p) agree well with those of the literature data for the available species (e.g., CH 2OO, 9
C2F4, and CF2O) with the average deviations of less than 0.1 Å and ~ 1 o in bonds and angles, respectively. The optimized geometrical parameters and Vereecken’s data [47], optimized at M06-2X/aug-cc-pVDZ in CH2OO structure, are consistent with each other (cf. Figure S1). As expected, according to the Hammond's postulate, the structures of TS1 and the reactants are very similar; in which the length of O-O bond of TS1 is a slightly larger than its CH2OO value of 1.33 Å (e.g., 1.35 vs. 1.33 Å) and the C2F4 structure is still fairly quite planar. Thus, it can be concluded that the title reaction approaches the TS1 during the early stage of the 1,3cycloaddition, nearly after the formation of the pre-complex becoming consistently with the ozonolysis of C2F4 [22]. The concerted decomposition of the adduct takes place with the concurrent cleavage of both C-C and O-O bonds accompanied with H-migration via TS2, leading to the final products, CF2O + CHF2CHO. The bond lengths of the breaking C-C and O-O bonds are 1.93 and 2.21 Å, respectively (0.36 and 0.75 Å longer than those of the corresponding adduct). The calculated vibrational frequencies, tabulated in Table S1, in general, are slightly higher than those available in the literature with the Mean Absolute Deviations (MADs) of 3.1, 10.2 and 2.0 % for CH2OO, C2F4 and CF2O, respectively. To ensure the validity of the G4 results, Table 1 lists the relative energies of all stationary points in the PES calculated at different composite methods, such as G4, G3B3, G3, CBS-QB3 and CBS-APNO. In general, the energies calculated at G4 are in good agreement with those obtained from other methods (MADs are normally less than 20%) except for the G3 data with the maximum difference of 1.9 kcal/mol for pre-complex. It is noted that the TS2 cannot be located at G3 and CBS-APNO methods that may be attributed to the MP2 and QCISD used in the optimization process, respectively. To give a bigger picture of CIs + C2F4, we extended the data for the larger CIs (e.g., CH3CHOO (syn & anti) and (CH3)2COO); presented in Table 2 and
10
compared to the corresponding CIs + C2H4 [10]. It is easily seen in Table 2 that the binding energies in the pre-complex are similar to each other, but the barrier heights of the cycloaddition process of CIs + C2F4 are higher than those of CIs + C2H4. As a result, the reactivity of CIs towards C2F4 can be followed as CH3CHOO (anti) ~ CH2OO > (CH3)2COO > CH3CHOO (syn) that is likely to have the same trend in CIs with ethene [10]. Table 1: Relative energies (in kcal⋅mol-1) of all species involved at different levels of theory at 0 K. The zero-point energy (ZPE) correction was included. Numbers are the energies relative to that of the reactants. Species G4 Pre-complex -2.5 Adduct -85.7 TS1 3.5 TS2 -53.1 CF2O + CHF2CHO -138.6 Mean absolute deviation/G4 (%)
G3B3 -3.3 -86.5 1.8 -54.2 -138.6 15.8
G3 -4.4 -87.1 2.0 N/A -139.1 29.2
CBS-QB3 -3.2 -87.5 2.2 -54.1 -138.5 15.5
CBS-APNO -3.2 -85.7 3.7 N/A -137.8 8.1
Table 2: ZPE-corrected energies relative to the separated reactants of the pre-complex, the cycloaddition of the transition state and the adduct of a set of CIs + C2F4 reactions calculated at G4 method (0 K and in kcal/mol). Values in the parentheses are the estimated values for the CIs + C2H4 reactions [10], calculated at CCSD(T)/aug-cc-pVQZ//M06-2X. Reaction CH2OO CH3CHOO_syn CH3CHOO_anti (CH3)2COO
Pre-complex -2.5 (-2.2) -3.7 (-3.6) -3.5 (-4.0) -4.1 (-4.6)
Cycloaddition TS 3.5 (0.6) 7.7 (4.7) 2.0 (0.5) 6.6 (5.4)
Adduct -85.7 -84.4 -80.3 -79.1
The calculated thermodynamic properties (∆Hf298 K and S298 K) for all species involved in the title reaction were shown in Table S2 and then compared to the literature data to evaluate their reliability. In general, the calculated data agree well with the literature one as discussed in 11
the work [22] for C2F4 and CF2O. It is worth noting that the ∆Hf298 K of CH2OO derived from the W1U method is in excellent agreement with that calculated by the W1 method (e.g., 25.5 vs. 25.3 kcal/mol) [48]. In this part, k(T, P) were characterized by using the PES and quantum information carried out at the G4 method as discussed above. As seen in Figure 1, the stabilization of the pre-reactive complex, formed by the combination of CH2OO and C2F4, can be expected to play an insignificant role due to its energy being ~ 2.5 kcal/mol below the entrance channel. The shadow pre-complex cannot affect the kinetics even at the room temperature as suggested by Vereecken et al. [10, 47]; thus it can be appropriately excluded in kinetic model. Note that the formation of this complex is less favorable at higher temperatures with the positive calculated Gibbs free energies relative to that of the reactants. Figure 2 showed the normalized time-resolved profiles for the title reaction at 298 K and 760 torr using the ME/RRKM model. It is observed that the final products (CF2O & CHF2CHO) are predominant while the stabilization of the adduct does not play any role at the considered conditions.
12
CH2OO + C2F4 → products (T = 298 K & P = 760 torr)
1.0
CF2O + CHF2CHO
Mole fraction
0.8 0.6 0.4 adduct
0.2 0.0 0
5
10 Time (s) 15
20
25
Figure 2: Time-resolved species profiles for the reaction, CH2OO + C2F4 → products at 298 K and 760 torr ([C2F4]0 >> [CH2OO]0 and [C2F4]/[N2] = 10-3; N2 is the bath gas used in the simulation). The eigenpair analysis was shown in Figure S3 to elucidate the reliability of the deterministic model. As easily seen that there is no mixing in eigenvalue spectrum between the fastest chemically significant eigenvalues (CSEs) and the slowest internal energy relaxation eigenvalues (IEREs) in the considered conditions (T = 200 – 1000 K and P = 760 torr); thus, the derived phenomenological rate coefficients using the CSE approach can be used for the considered temperature. The high-pressure rate constants k∞(T) for all elementary reactions were shown in Table S3 for the temperature range of 200 – 1000 K. Figure 3 plotted the total rate constants (CH2OO + C2F4 → products) as a function of temperature at different pressures (e.g., 76 – 760 torr, except for CH2OO + C2F4 → adduct at P = 7600 torr). It was observed that the pressure has no effect on the k(T, P) for the formation of the final products in a range of pressure (P = 76 – 760 torr), 13
which is opposite to the formation of the adduct. The stabilization of the adduct favors at the higher pressure and the pressure-dependence is more noticeable at the high temperature but it still cannot compete with the formation of the product channel at the atmospheric conditions (T = 200 – 400 K & P ≤ 760 torr [4]). Its contribution to the total rate constants can be reasonably neglected at P ≤ 760 torr, leading to the total rate constants, ktot(T) = 3.69×10-23×T2.91×exp(1114.35 K/T) cm3/molecule/s (T = 200 – 1000 K and P-independence in range of 76 – 760 torr).
CH2OO + C2F4 → products logk (cm3/molecule/s)
1.E-14 CF2O + CHF2CHO 1.E-16 Adduct 1.E-18
7600 torr
1.E-20 1.0
1.5
2.0
2.5
3.0 3.5 1000/T (K)
4.0
4.5
5.0
Figure 3: Calculated rate coefficients as a function of temperature at different pressures (P = 76 – 760 torr) for CH2OO + C2F4 → products. It is also mentioned that the anharmonic treatment slightly increases the rate constants for the main channel as depicted in the Figure S4. For example, the rate ratios of the anharmonic to harmonic treatments are ~ 1.10 and 1.03 at T = 298 and 1000 K for the formation of the final products (CH2OO + C2F4 → CF2O + CHFCHO), respectively (cf. Figure S4). The quantum tunneling effect was found to play a minor role for this title system (e.g., the factors of 1.54 ÷ 1.06 and 1.70 ÷ 1.08 from 200 to 1000 K via TS1 and TS2 pathways, respectively); and the HIR
14
contribution is almost negligible (e.g., the HIR factor is about unity in the range of 200 – 1000 K for the formation of the final products, CF2O + CHF2CHO). Conclusions In this study, the detailed kinetic mechanism of the CH2OO + C2 F4 → products reaction was firstly investigated by using the accurate electronic calculations accompanied by the stateof-the-art ME/RRKM rate model which includes the corrections for tunneling, hindered internal rotation and anharmonicity treatments. The results showed that the title reaction proceeded with the formation of a shallow van der Waals complex and then formed an adduct, which can immediately decompose to the CF2O (carbonyl fluoride) + CHF2CHO (difluoro acetaldehyde). The study presented that the total rate coefficient (CH2OO + C2F4 → products) is pressureindependent in a range of pressure from 76 to 760 torr and T = 200 – 1000 K. It is found that both the quantum tunneling effect and the anharmonicity treatment slightly increase the rate constants while the HIR treatment has no effect at all. The calculated thermodynamic data and rate coefficients (in NASA and modified Arrhenius formats, respectively) were also explicitly provided at different pressures for further modeling/simulation of related atmospheric systems. Acknowledgments This work was supported by the Institute for Computational Science and Technology (ICST) – Ho Chi Minh City and the Department of Science and Technology – Ho Chi Minh City under the grant no. 208/QĐ-KHCNTT. LKH also acknowledges International University, VNUHCM for providing the computing resources. We are thankful to Tri Pham and Tuyn Phan (ICST) for technical assistance.
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The authors also would like to thank the editor(s) and anonymous reviewers for useful comments that significantly improved the quality of this work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]
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Graphical Abstract
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Ab Initio Chemical Kinetics of the CH2OO + C2F4 Reaction Tam V.-T. Mai,1,2,* Minh v. Duong1, Hieu T. Nguyen1, Kuang C. Lin3 and Lam K. Huynh4,*
1
Molecular Science and Nano-Materials Lab, Institute for Computational Science and Technology, SBI Building, Quang Trung Software City, Tan Chanh Hiep Ward, District 12, Ho Chi Minh City, Vietnam. 2 University of Science, Vietnam National University – HCMC, 227 Nguyen Van Cu, Ward 4, District 5, Ho Chi Minh City, Vietnam. 3 Department of Mechanical and Electromechanical Engineering, National Sun Yat-Sen University, Kaohsiung, 80424, Taiwan 4 International University, Vietnam National University – HCMC, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam. Highlights
Detailed reaction mechanism of CH2OO + C2 F4 was firstly studied with the accurate composite G4 method.
Time-resolved temperature- and pressure-dependent behaviors of the title reaction were characterized using the master equation/Rice–Ramsperger–Kassel–Marcus (ME/RRKM) rate models.
Corrections for tunneling, hindered internal rotation and anharmonicity treatments were included.
Detailed kinetic sub-mechanism (kinetic and thermodynamic data) was provided for 200– 1000 K and 76–760 torr for further kinetic modeling/simulation.
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