Theoretical Kinetics Studies on the Reaction of CF3CF CF2 with

Article pubs.acs.org/JPCA

Theoretical Kinetics Studies on the Reaction of CF3CFCF2 with Hydroxyl Radical Vahid Saheb* and Navid Yousefi Pourhaghighi Department of Chemistry, Faculty of Sciences, Shahid Bahonar University of Kerman, Kerman, Iran S Supporting Information *

ABSTRACT: The potential energy surface for the reaction of hexafluoropropene with hydroxyl radical is explored by using BB1K density functional method. Single-point energy calculations are performed at CBS-Q level of theory. Semiclassical transition state theory and a modified strong collision/RRKM model are employed to calculate the thermal rate coefficients for the formation of major products as a function of temperature and pressure. It is revealed from the computed rate constants that the major product channels at low temperatures and high pressures are the formation of the primary adducts formed through OH addition to the double bond of CF3CFCF2. At high temperatures and low pressures, however, many products arising from unimolecular decomposition of the chemically activated intermediates become important. P9A (CF3CFCOF + HF) and P7B (CF3COCF2 + HF) are dominant products at elevated temperatures. Semiclassical transition state theory is used to compute the overall high-pressure rate constants over the temperature range of 200−1500 K. The computed rate constants are in accordance with the available experimental data.

■

of CF3CFCF2. They obtained the Arrhenius expression k = 6.0 × 108 L mol−1 s−1 exp(+2.03 kJ mol−1/RT) for the overall rate constant of the reaction. Orkin and co-workers10 measured the rate constant for the CF3CFCF2 + OH reaction by the flash photolysis resonance fluorescence technique over the temperature range 252−370 K and reported the Arrhenius expression k = 3.41 × 108 L mol−1 s−1 exp(+3.38 kJ mol−1/RT) for the reaction. Smog chamber/FTIR techniques were used by Wallington et al. to study the OH radical, the Cl atom, and ozone initiated oxidation of CF3CFCF2 in the presence of air at 296 K.11 They reported the value of 1.45 × 109 L mol−1 s−1 for the rate constant of the title reaction. They found that OH radical and Cl atom-initiated atmospheric oxidation of CF3CFCF2 in 700 Torr of air gives COF2 and CF3C(O)F as major products. The atmospheric lifetime of CF3CFCF2 was estimated to be 9 days with degradation proceeding via reaction with OH radicals to lead finally to trifluoroacetic acid in a molar yield of 100%. Tokuhashi et al.12 carried out kinetic measurements using the flash photolysis and laser photolysis methods combined with the laser-induced fluorescence technique and determined the Arrhenius rate constants as k = 5.26 × 108 L mol−1 s−1 exp(+2.16 kJ mol−1/RT). Jensen and co-workers13 reported the value of k = 3.41 × 109 L mol−1 s−1 at 298 K and 740 Torr using FT-IR detection. In most recent studies, Orkin et al.14 have reported the rate constant expression

INTRODUCTION Since it was discovered that photodissociation of the chlorofluorocarbones (CFCs) in the stratosphere produces significant amounts of chlorine atoms and destroys atmospheric ozone,1,2 an international effort has been made to replace these compounds with environmentally safer alternatives.3 Potential candidates have been unsaturated fluorinated hydrocarbons due to their higher gas-phase reactivity and lack of chlorine atoms.4 However, these fluorinated hydrocarbons are thought to be the source of large amounts of trifluoroacetic acid, CF3COOH, detected in the hydrosphere.5−8 One important member of this class of compounds is hexafluoropropene, CF3CFCF2, which is mainly produced during incineration of municipal waste containing perfluorinated polymers. It is believed that CF3CFCF2 is emitted into the atmosphere and undergoes atmospheric oxidation to give CF3COOH.7 As a consequence, much attention has been paid recently to the kinetics and mechanism of degradation of CF3CFCF2 with important atmospheric oxidizer such as atomic oxygen, atomic chlorine, ozone, and hydroxyl radical.9−14 The reactivity of CF3CFCF2 with OH radicals, known as atmospheric detergents, could be a benchmark of its residence time in the atmosphere. In 1993, McIlroy and Tully studied the CF3CFCF2 + OH reaction by using a laser photolysis/cw, laser-induced fluorescence technique over the temperature range of 244−830 K and at the pressure of 750 Torr.9 On the basis of the accepted mechanism for OH + alkenes reactions, they suggested that the primary reactive step involves OH addition to the double bond © 2014 American Chemical Society

Received: June 4, 2014 Revised: September 30, 2014 Published: October 1, 2014 9941

dx.doi.org/10.1021/jp5055099 | J. Phys. Chem. A 2014, 118, 9941−9950

The Journal of Physical Chemistry A

Article

k = 5.87 × 107 × (T/298 K)1.94 L mol−1 s−1 exp(+922/T) for CF3CFCF2 + OH reaction over the temperature range 230−480 K. Recently, Ai et al.15 have performed an ab initio study on the potential energy surface (PES) of the title reaction. The purpose of the present research work is to study the kinetics of the CF3CFF2 + OH reaction and the effect of temperature and pressure on the rate constants for the formation of different possible products. Here, the PES of the reaction is reinvestigated by BB1K and the combination of CBS-Q methods. Statistical rate theories such as transition state and RRKM theories then are used to compute the overall rate constant and the rate constants for many possible reaction products. The computed rate constants are compared to the available experimental data and discussed.

quantum states for reactant, and Q1+ and Q1 are the partition functions for the adiabatic rotations in the transition state and reactant. G(E+vr) and ρ(E) are computed by the Beyer− Swinehart direct count algorithm.24 In this research, the values of k(E), ρ(E), and G(Evr+) are calculated by using the RRKM program from Zhu and Hase.25 Berman and Lin26 have used transition state theory with the application of RRKM theory to the unimolecular decomposition of the chemically activated intermediates to compute the rate constants for a bimolecular reaction proceeding through one chemically activated adduct. a

By applying steady-state approximation to the activated intermediates and using statistical mechanics for equilibrium constant, they obtained the following expression for the rate coefficient of disappearance of the reactants:

COMPUTATIONAL DETAILS Electronic-Structure Calculations. In the present research work, all of the stationary points including minimum energy structures and saddle points are fully optimized by the Hybrid Meta Density Functional Theory (HMDFT), BB1K method, along with the standard basis set 6-31+G(d,p). The BB1K method, developed by Truhlar and co-workers,16 is an abbreviation for “Becke88-Becke95 1-parameter model for kinetics” and is a modified variation of the Becke’s 1988 gradient corrected exchange functional and Becke’s 1995 kinetic-energy-dependent dynamical correlation functional (BB95). The performance of the BB1K method is illustrated for a representative database of very high level calculations of saddle point geometries, barrier heights, and atomization energies. Energies at all of the stationary points are then recalculated with BB1K along with the recommended MG3S17 basis set. To compute accurate energies, the high-level combination method CBS-Q18 is employed to perform single-point energy calculations on the geometries optimized at BB1K/6-31+G(d,p) level. In the original version of CBS-Q theory, the geometries are computed at the B3LYP/CBSB7 or MP2(FC)/631G† levels. However, the use of B3LYP method for geometry optimization of transition states is known to be error prone.19 Chai and Head-Gordon20 have proposed the long-range corrected hybrid density functional, ωB97X-D, which has yielded satisfactory accuracy for thermochemistry, kinetics, and noncovalent interactions. Energies of stationary points are also calculated by this method for the purpose of comparison. All of the quantum chemical calculations were performed with the Gaussian 09 package of programs.21 Dynamical Calculations. As it is discussed in detail in the next section, the reaction proceeds via the addition of OH radical to each carbon of the double bond of CF3CFCF2, leading to two primary chemically activated intermediates called INT1A and INT1B. These intermediates decompose to yield the reactants, other intermediates, and products, or can be deactivated by molecular collisions. In this research, RRKM theory is used to compute the rate constants for decomposition of these vibrationally excited adduct to different products.22,23 According to the RRKM theory, the energy-specific rate constant for unimolecular reaction is given by the following equation: Q 1+ G(Evr+) Q 1 hρ(E)

(2)

b

■

k(E) = σ

c

A + B ⇌ AB* → C + D

+ σBe qtr −Ea / RT k= e h qA qB

∫0

∞

(ω + ke)G(Evr+) −E+ / RT + e dE (ω + ke + ke′) (3)

Here, ke and ke′ are the energy-specific rate constants for unimolecular decomposition of the intermediates to the reactants and products, respectively. The total partition functions for reactants A and B excluding electronic degrees of freedom are given by qA and qB, while qtr⧧ is the product of translational and rotational partition functions for the transition state of entrance channels. σ is the reaction path degeneracy, and Be is the quotient of electronic partition functions of transition state and reactants. In eq 3, ω is the rate constant for de-energization of the activated adducts, which is given by

ω = βcZcoll

(4)

where Zcoll is the collision frequency and βc is the collision efficiency. Troe27 has obtained the following expression for βc: βc = (⟨ΔE⟩down /(⟨ΔE⟩down + FEkBT ))2

(5)

In the above equation, FE is the energy dependence of the density of states and ⟨ΔE⟩down is the average energy transferred in a deactivating collision. The values of ⟨ΔE⟩down for many molecules including the intermediates studied in the present research are not determined experimentally. Pilling and coworkers28 have determined the value of 129 cm−1 for iso-C3H7 radical in N2 bath gas by analysis of the unimolecular rate constants in the falloff region. From both electronic structure and spatial structure standpoints, the iso-C3H7 radical has features similar to those of the activated intermediate radicals studied in the present research work. Therefore, the value of 129 cm−1 is employed here to compute the collision efficiencies. It is found that the calculated rate constants are not affected meaningfully when the values 30 cm−1 higher or lower than 129 cm−1 are used in calculating the rate coefficients. Hou and colleagues29 have studied the reaction of Cl(2P) with ketene, which proceeds through many activated adducts. By using the ideas of Berman and Lin, they have obtained formulas for the total and individual rate constants for various channels. In the present research, by applying steady-state approximation to the activated intermediates and carrying out statistical mechanics manipulations similar to those of Hou et al., expressions for the rate constants of individual channels are derived. Recently, a similar procedure was used by

(1)

where G(E+vr) is the sum of active vibrational and rotational states for the transition state, ρ(E) is the density of active 9942



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Zhang et al.30 in the theoretical study of the kinetics and mechanism of the CF3CHCH2 + OH reaction. These expressions are discussed in the next sections. To calculate the overall high-pressure limiting rate constant for consumption of reactants, more sophisticated semiclassical transition state theory (SCTST) is used.31−34 According to the SCTST, the canonical rate constant, k(T), is given by the following equation:

of freedom, xFF is the (pure real) anharmonicity constant for the reaction path, and ΔV0 is the classical barrier height. The term ε0 is a constant that is included for thermochemistry and kinetics. The power of SCTST is that all of the degrees of freedom including reaction coordinate are assumed to be coupled. In addition, it also accounts naturally for zero-point energy and quantum mechanical tunneling along the curved reaction path in hyperdimensional space. To compute the CRP according to eq 8, the summation should be done over all states of the transition state. In this research, the Nguyen−Barker algorithm35−37 is used for computing the vibrational state densities and CRP for the fully coupled anharmonic vibrations of reactants and transition states, respectively. The Nguyen−Barker algorithm is based on the Wang and Landau38,39 random walk algorithm in energy space for computing densities of states. Basire et al.40 have used the perturbation theory expansion for vibrational energy of fully coupled anharmonic systems to compute quantum densities of states on the basis of the Wang−Landau algorithm. Nguyen and Barker have performed many minor modifications on the Basire et al. algorithm to meet the needs for the density of states and cumulative reaction probabilities in chemical kinetics. They have developed the MULTIWELL Program Suite41 including SCTST and ADENSUM programs for computing the CRPs of transition states and the state densities of the reactants, respectively. The MULTIWELL also contains the program THERMO for computing the thermal rate constants. All three codes are used in the present research work. In this research, all low-frequency torsional vibrational motions are considered as hindered internal rotations. The torsional potential energies are computed at the BB1K/MG3S and fitted to the following general equation:

∞

⧧ 1 ∫−∞ G (E) exp(E /kBT ) dE k(T ) = h Q re(T )

(6)

where h is Planck’s constant, kB is Boltzmann’s constant, T is the temperature, Qre is the total partition function of the reactant(s), and G⧧(E) is the cumulative reaction probability (CRP). The couplings between rotations and vibrations can be neglected at moderate temperatures, leading to the following equation: ∞

⧧ ⧧ ⧧ 1 Q t Q r ∫−∞ Gv (Ev ) exp(E /kBT ) d(Ev ) k(T ) = h Q tQ r Q v (T )

(7)

where the Qt, Qr, and Qv represent the product of translational, rotational, and vibrational partition functions for the reactants ⧧ ⧧ (denominator), and the Q t and Q r represent corresponding values for transition state (numerator). In eq 7, vibrational energy of transition state, Ev, is the variable of integration. The corresponding CRP, which is the sum of tunneling or transmission probabilities of the activated complex, is given by Gv⧧(Ev ) =

∑ ∑ ... ∑ ∑ Pn(Ev ) n1

n2

(8)

nF − 2 nF − 1

where the semiclassical tunneling probability Pn is

N

V (χ ) = V0 +

1 Pn(E) = 1 + exp[2θ(n , E)]

n=1

(9)

πΔE ΩF 1 +

2 1 + 4xFF ΔE /Ω2F

(10)

The quantities in the above equation are computed by the following expressions: F−1

ΔE = ΔV0 + ε0 − E +

∑ ωk⎛⎝nk + ⎜

k=1

F−1 F−1

+

∑ ∑ xkl⎛⎝nk + ⎜

k=1 l=k

F−1

ΩF = ω̅F −

∑ xkF̅ ⎝nk + ⎜

k=1

ω̅F = −iωF

⎛

⎞⎛ 1 ⎟⎜ 1⎞ nl + ⎟ 2 ⎠⎝ 2⎠

and

1 ⎞⎟ 2⎠

xkF ̅ = −ixkF

(14)

The ro-vibrational G matrix-based algorithm described by Harthcock and Laane42,43 is used to compute the effective reduced masses for one-dimensional torsions. The computer program lamm,41 developed by Nguyen and contained in the MULTIWELL Program Suite, is used to compute the effective reduced masses as functions of the dihedral angles χ (radians) and fitted to the following general equation:

The barrier penetration integral, θ(n,T), is given by θ (n , E ) =

∑ V nc cos(nσV (χ + φV ))

N

1 ⎞⎟ 2⎠

I (χ ) = I 0 +

∑ In cos(nσI(χ + φI )) n=1

(15)

The coefficients in eqs 14 and 15 are used by programs ADENSUM and SCTST to solve the Schrödinger equation for the related hindered internal rotations needed to compute densities of states. Two low-lying 2Π electronic levels of OH, with a 140 cm−1 splitting, are used to calculate the electronic contribution to the total partition function of OH radical.

(11)

(12)

■

(13)

RESULTS AND DISCUSSION As aforementioned, Ai et al.15 have also explored the PES of the present reaction at the MCG3//M06-2X/Aug-cc-pVDZ level of theory. Except for two new transition states (TS19A and TS17B), the stationary points located in the present work are the same as their optimized geometries. In the present study, the intermediates, transition states, and products of the reaction are renamed to facilitate the kinetics calculations. On the basis of the stationary points located at the BB1K/6-31+G(d,p) level

In the above expressions, F is the number of internal degrees of freedom of the transition state, ordered so that the reaction coordinate is last; ωk is the harmonic vibrational frequency of the kth vibration, ωF is the imaginary frequency associated with the reaction coordinate, xkl are the vibrational anharmonicity constants for the degrees of freedom orthogonal to the reaction coordinate, xkF are the (pure imaginary) coupling terms between the reaction coordinate and the orthogonal degrees 9943



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Scheme 1

the CBS-Q level, the mechanism of the title reaction can briefly be described as follows. Initially, a van der Waals complex is formed, which is −7.93 kJ mol−1 more stable than the reactants. Next, the reaction proceeds through the transition TS01A (−5.24 kJ mol−1), leading to an initial intermediate that is denoted as INT1A. It should be mentioned that the BB1K method predicts small positive values for the relative energies of TS01A and TS01B. The vibrationally active intermediate INT1A, which is −213.77 kJ mol−1 lower than the reactants, isomerizes to INT2A (−151.73) and INT3A (−193.89) intermediates via TS12A and TS13A, respectively. The isomerization barriers of INT1A to INT2A and INT3A are 163.96 and 157.82 kJ mol−1, respectively. The activated adduct INT2A decomposes to yield COF2 + CF3CHF (P4A), CF3CHFCOF + F (P5A), and CF3 + CHFCOF2 (P6A) through TS24A, TS25A, and TS26A, respectively. The barrier heights for the latter decomposition reactions are 23.83, 121.51, and 177.16 kJ mol−1, respectively. The intermediate INT3A yields CF3CF2COF + H (P7A), CF3 + CF2C(OH)F (P8A), and CF3CFCOF + HF (P9A) by passing through TS37A, TS38A, and TS39A, respectively. The decomposition barriers of INT3A in the latter reactions are 127.77, 175.66, and 118.06 kJ mol−1, respectively. INT1A also passes through the four-membered ring transition state TS19A (−53.18 kJ mol−1) to yield directly CF3CFCOF + HF (P9A). INT1A also passes through the six-membered ring transition state TS1-10A (−27.19 kJ mol−1) to yield CF2CFCOF2 + HF (P10). The relative energies of the stationary points calculated by CBS-Q are illustrated in Figure 2. The

of theory, the mechanism of the CF3CCF2 + OH reaction can be represented by Scheme 1. The geometries of reactants, intermediates, and transition states arising from the reaction of hydroxyl radical with hexafluoropropene are depicted in Figure 1. The CF3CFCF2 + OH reaction proceeds through the addition of OH radical to each carbon atom of the double bond of CF3CFCF2, leading to two primary intermediates INT1A and INT1B; see Figure 1 for the numbering of the carbon atoms. Next, INT1A and INT1B pass through various transition states to yield products or other intermediates. In the following, the results obtained for two general reaction pathways A and B have been presented and discussed. The relative energies of the stationary points located on the potential energy surface of the general reaction path A computed at various levels of theory are listed in Table 1. The molecular structures studied in the present reaction have too many electrons so that the computed energies are sensitive to the level of electron correlation and basis set. It is found that the ωB97X-D method underestimates the relative energies for most of the transition states in comparison with the CBS-Q method. The energies of many species are overestimated by the BB1K method. For example, although the small positive values of 2.91 and 0.90 kJ mol−1 are obtained for the energy of TS01A at BB1K/6-31+G(d,p) and BB1K/MG3S levels, respectively, the more sophisticated CBS-Q method predicts a negative value of −5.24 kJ mol−1. To perform kinetics calculations, the energies computed at the high-level CBS-Q method are employed. On the basis of the relative energies calculated at 9944



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Figure 1. Geometries of reactants, intermediates, and transition states arising from the CF3CFCF2 with OH radicals calculated at the BB1K/631+G(d,p).

harmonic vibrational frequencies and the principal moments of inertia of the reactants, intermediates, and transition states of the general path A, calculated at the BB1K/6-31+G(d,p) level of theory, are provided in Table 1S in the Supporting Information. By applying steady-state approximation to the intermediates INT1A, INT2A, and INT3A, and performing the statistical mechanical manipulations like Hou et al.,29 the following expressions for the rate constants of production of various species are obtained: kINT1A =

kINT2A =

+ σBe qtr

h qA qB + σBe qtr

h qA qB

e−Ea / RT

e−Ea / RT

∫0 ∫0

∞ ωG(E +) vr

B1

e −E

∞ ωA G(E +) 2 vr

B1

+

/ RT

kINT3A =

+ σBe qtr −Ea / RT e h qA qB

∫0

kP4A =


∫0

kP5A =


∫0

dE +

∞

∞

ωA3G(Evr+) −E+ / RT + e dE B1

(18)

k 24A 2 G(Evr+) −E+ / RT + e dE B1

(19)

k 25A 2 G(Evr+) −E+ / RT + e dE B1

(20)

∞

(16)

e −E

+

/ RT

kP6A =

dE + (17)


∫0

∞

k 36A3G(Evr+) −E+ / RT + e dE B1 (21)

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Table 1. Relative Energies of the Stationary Points for the Overall Reaction Channel A Computed at Some Levels of Theory in kJ mol−1a vdW TS01A TS12A TS13A TS24A TS25A TS26A TS37A TS38A TS39A TS19A TS1-10A INT1A INT2A INT3A COF2 + CF3CHF (P4A) CF3CHFCOF + F (P5A) CF3 + CHFCOF2 (P6A) CF3CF2COF + H (P7A) CF3 + CF2C(OH)F (P8A) CF3CFCOF + HF (P9A) CF2CFCOF2 + HF (P10)

BB1Kb

BB1Kc

ωB97X-Dd

CBS-Q

−4.22 2.91 −50.15 −56.82 −118.22 −30.10 36.27 −44.55 −14.59 −76.51 −55.86 −22.21 −214.60 −157.65 −190.67 −187.45 −56.39 −50.73 −93.02 −22.96 −219.18 −45.49

−4.51 0.90 −41.93 −51.71 −116.33 −18.25 36.81 −41.88 −18.25 −69.55 −46.25 −19.26 −205.34 −146.84 −183.52 −168.80 −44.65 −46.44 −89.45 −25.48 −215.59 −43.03

−9.67 −5.39 −55.08 −76.66 −129.93 −40.85 29.38 −76.66 −23.34 −74.17 −74.21 −52.66 −215.47 −150.41 −192.33 −195.49 −53.73 −39.51 −103.96 −24.35 −203.74 −38.95

−7.93 −5.24 −49.81 −55.95 −127.90 −30.22 25.43 −66.12 −18.23 −75.83 −53.18 −27.19 −213.77 −151.73 −193.89 −187.67 −52.25 −36.40 −115.46 −18.81 −228.51 −42.19

a

All values are corrected for zero-point energies. bThe basis set 6-31+G(d,p) is used. cThe basis set MG3S is used. dThe basis set 6-311++G(2d,2p) is used.

kP7A

+ σBe qtr −Ea / RT = e h qA qB

∫0

∞

k 37A3G(Evr+) −E+ / RT + e dE B1 (22)


kP8A =

∫0

∞

k 38A3G(Evr+) −E+ / RT + e dE B1 (23)


kP9A =

∫0 kP10A =

∞

(k19 + k 39A3)G(Evr+) B1


∫0

∞

e −E

+

/ RT

dE +

(24)

k1 − 10G(Evr+) −E+ / RT + e dE B1

Figure 2. Relative energies of the stationary points located on the doublet ground-state potential energy surface of the reaction path A. The energy values are given in kJ mol−1 and are calculated using CBSQ theory.

(25)

A2, A3, and B1 in the above integrals are obtained from the following expressions: A2 = A3 =

k 21 + k 24

k12 + k 25 + k 26 + ω

(26)

k 31 + k 37

k13 + k 38 + k 39 + ω

(27)

each of the above integrals numerically, the energy-dependent rate constants, k(E), should be computed for many energies. As aforementioned, the OH + CF3CFCF2 can also proceed via the addition of hydroxyl group to the carbon 2 of CF3CFCF2 (reaction path B). The geometries of the intermediates and transition states arising from this reaction path are also shown in Figure 1. The relative energies of the stationary points located on the potential energy surface of the general reaction path B computed at various levels of theory are listed in Table 2. Starting from the initial van der Waals complex, the reaction proceeds through TS01B (−5.92 kJ mol−1), leading to the intermediate denoted as INT1B (−188.42 kJ mol−1). The vibrationally active intermediate INT1B isomerizes to INT2B

B1 = k10 + k12 + k13 + k19 + k1 − 10 + k 21A 2 + k 31A3 +ω

(28)

In the above equations, kij is the energy-specific rate constant for the conversion of the intermediate i to the intermediate or product j. Other quantities are the same as eq 3. To evaluate 9946



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Table 2. Relative Energies of the Stationary Points for the Overall Reaction Channel B Computed at Some Levels of Theory in kJ mol−1a TS01B TS12B TS13B TS17B TS24B TS25B TS36B TS37B INT1B INT2B INT3B CHF2 + CF3COF (P4B) CF3 + CF2HCOF (P5B) CF3COCF3 + H (P6B) CF3COCF2 + HF (P7B)

BB1Kb

BB1Kc

ωB97X-Dd

CBS-Q

3.38 −24.01 −47.48 −33.55 −114.16 −100.29 −39.49 −81.89 −183.00 −156.67 −244.87 −145.95 −142.44 −71.16 −180.38

3.35 −15.20 −41.84 −24.93 −112.75 −99.00 −33.95 −69.58 −173.93 −145.91 −236.58 −143.22 −137.91 −64.92 −172.46

−6.92 −30.51 −67.60 −54.89 −128.58 −109.27 −40.59 −101.77 −212.40 −168.58 −231.61 −154.72 −152.45 −79.15 −186.49

−5.92 −24.54 −47.27 −30.25 −130.37 −116.75 −58.07 −80.74 −188.42 −153.74 −243.57 −150.17 −143.12 −91.15 −191.66

a

All values are corrected for zero-point energies. bThe basis set 6-31+G(d,p) is used. cThe basis set MG3S is used. dThe basis set 6-311++G(2d,2p) is used.

(−153.74 kJ mol−1) and INT3B (−243.57 kJ mol−1) intermediates via TS12B and TS13B, respectively. The isomerization barriers of INT1B to INT2B and INT3B are 163.88 and 141.15 kJ mol−1, respectively. The activated adduct INT2B decomposes to yield CHF2 + CF3COF (P4B) and CF3 + CF2HCOF (P5B) through TS24B and TS25B, respectively. The decomposition barriers of INT2B in the latter reactions are 23.37 and 36.99 kJ mol−1, respectively. The intermediate INT3B yields CF3COCF3 + H (P6B) and CF3COCF2 + HF (P7B) by passing through TS36B and TS37B, respectively. The barrier heights for the latter decomposition reactions are 185.50 and 162.83 kJ mol−1, respectively. INT1B may also produce CF3COCF2 + HF (P7B) directly via passing through the transition state TS17B (−30.25). The relative energies of the stationary points calculated by CBS-Q are illustrated in Figure 3. The harmonic

By applying steady-state approximation to the intermediates INT1B, INT2B, and INT3B, and performing derivations similar to those of the reaction path A, integral expressions for different products are obtained. These expressions are given in the Supporting Information. The RRKM theory (eq 1) is employed to compute the microcanonical rate constants. To compute the integrals in eqs 16−25, a step size ΔE+ = 0.4 kJ mol−1 up to 400 kJ mol−1 was used. The low-frequency vibrations corresponding to torsional motions are regarded as free internal rotations. The calculated rate coefficients for all important product channels at temperatures 298, 500, and 1000 K, as a function of pressure, are demonstrated in Figures 4−6. The corresponding branching

Figure 4. Coefficients for the important product channels computed at temperature 298 K as a function of bath-gas pressure.

Figure 3. Relative energies of the stationary points located on the doublet ground-state potential energy surface of the reaction path B. The energy values are given in kJ mol−1 and are calculated using CBSQ theory.

ratios for the most important product channels are plotted in Figures 1S−3S in the Supporting Information (the product channels with branching ratios less than 0.01 are neglected). As can be seen from the computed rate coefficients and branching ratios at 298 K (Figure 4 and Supporting Information Figure 2S), especially at high pressures, the dominant channels are the formation of the initial intermediates INT1A and INT1B. After

vibrational frequencies and the principle moments of inertia of the intermediates and transition states of the general path B, calculated at the BB1K/6-31+G(d,p) level of theory, are provided in Table 2S in the Supporting Information. 9947



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Figure 7. Thermal rate coefficients for the several product channel of the CF3CFCF2 + OH computed at temperatures in the range of 200−1500 K and at the pressure 760 Torr. The rate constants for each reaction channel are presented in different colors for clarity.



Figure 8. Branching ratios for the major product channels of the CF3CFCF2 + OH computed at temperatures in the range of 200− 1500 K and at the pressure 760 Torr. The rate constants for each reaction channel are presented in different colors for clarity. The reaction channels with branching ratios less than 0.01 are neglected.

stabilization processes of INT1A and INT1B, the most important processes are the formation of INT3B and P7B. It should be mentioned that at low pressures, which the rate constants for stabilization of INT1A and INT1B reduce, the rate coefficients for the formation of other products increase. It is revealed that the rate coefficients for the formation of INT2A, P5A, P6A, P8A, and INT2B have minor contributions to the overall rate constant. The computed rate coefficients and branching ratios at 500 K show that as temperature increases the products originated from the decomposition of chemically activated intermediates (P4A, P7A, P9A, P4B, P6B, and P7B) become comparable with the formation of INT1A and INT1B (Figure 5 and Supporting Information Figure 3S). The computed rate constants and branching ratios at 1000 K (Figure 6 and Supporting Information Figure 4S) reveal that the rate coefficients for the formation of the chemically activated adducts significantly decrease and other product channels become dominant. Except for INT1A, the computed branching ratios for all of the activated intermediates are below 0.01 and neglected in Supporting Information Figure 4S. The calculated rate coefficients for all important product channels at pressure 760 Torr, as a function of temperature, are demonstrated in

Figure 7. The corresponding branching ratios are also plotted in Figure 8. As can be seen, at low temperatures, the main products are INT1A and INT1B. However, at higher temperatures, the rate coefficients for the formation of the products P4A, P7A, P8A, P9A, P4B, P6B, and P7B increase, and those for the formation of INT1A and INT1B decrease. In addition, P9A and P7B become dominant products as temperature is elevated. It is noteworthy to mention that both P9A and P7B are originated via two chemically activated intermediates; see Scheme 1. The detailed analysis of the present computed rate constants reveals that most of P9A and P7B are directly formed from INT1A and INT1B via TS19A and TS17B, respectively. To calculate the overall high-pressure limiting rate constant for consumption of reactants, SCTST (eqs 6−13) is used. Vibrational anharmonicity coefficients, xij, needed for semiclassical transition state theory, are calculated at the ωB97X-D/ cc-pVTZ level of theory. Table 3S in the Supporting Information provides the anharmonicity constants matrix for the transition state TS01A. Here, the low vibrational frequencies, corresponding to torsional vibrational motions, 9948



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The fitted parameters A, n, E, and T0 are obtained to be 3.38 × 1014, −1.336, 12 760, and 2297, respectively.

are treated as hindered internal rotations. First, molecular geometries and energies are computed at discrete values of torsional angles, χ, at the BB1K/6-31+G(d,p) level of theory. Next, the effective reduced masses for one-dimensional torsions are computed by using the ro-vibrational G matrix-based algorithm of Harthcock et al.42,43 The computed potential energies and reduced moments of inertia are fitted to eqs 14 and 15, respectively. It is found that the fitted values of parameters for torsional motions of the CF3 group in CF3CFCF2 and transition states TS01A and TS01B, corresponding to the CF3 torsional motions, are similar. Therefore, their corresponding partition functions must be the same, and their values are canceled from the numerator and denominator of eq 7. The computed and fitted potential energies for the OH torsional motion of TS01A are given in the Supporting Information. On the basis of the information obtained from Table 1 and Supporting Information Tables 1S and 3S, SCTST is used to calculate the overall thermal rate coefficients of the C3F6 + OH reaction over the temperature range of 200−1500 K. In all of the experimental studies performed on the kinetics of the C3F6 + OH reaction, the overall rate constants are measured, and no data are reported on the reaction products. In some research works, the products of the reaction are determined in the presence of O2 and NO molecules, which could be attributed to the subsequent reaction of O2 and NO molecules with the intermediates or products of the C3F6 + OH reaction. Figure 9

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CONCLUSION In this research, electronic structure theories are employed to compute the energies and other molecular properties of the stationary points on the potential energy surface of the reaction of hydroxyl radical with hexafluoropropene. Semiclassical transition state theory and a modified strong collision/RRKM model are employed to calculate the thermal rate coefficients for many product channels as a function of temperature and pressure. The calculated overall rate constants for the reaction OH + C3F6 are in good agreement with the available experimental data at moderate temperatures. The present calculations show that the dominant product channels at low temperatures and high pressures are the formation of the primary activated adducts formed from OH addition to the double bond of CF3CFCF2 (INT1A and INT1B). At moderate temperatures, the products originated from the unimolecular reactions of the INT1A and INT1B become important. The formation of many products including P4A (COF2 + CF3CHF), P7A (CF3CF2COF + H), P8A (CF3 + CF2C(OH)F), P9A (CF3CFCOF + HF), P4B (CHF2 + CF3COF), P6B (CF3COCF3 + H), and P7B (CF3COCF2+HF) formed from unimolecular degradation of the chemically activated intermediates become important as temperature increases. P9A and P7B are dominant channels at elevated temperatures.

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ASSOCIATED CONTENT

S Supporting Information *

Vibrational wave numbers and moments of inertia of all of the optimized geometries, and anharmonicity matrix for TS01A. Expressions for the rate constants of channel B products. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel./fax: +98-34-33222033. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Professor John R. Barker for providing the MultiWell-2011.2b programs. We are grateful to Shahid Bahonar University of Kerman Research Council for the financial support of this research.

Figure 9. Thermal overall rate coefficients for the CF3CFCF2 + OH reaction computed at temperatures in the range of 200−1500 K. “Solid line” is calculated using CBS-Q barrier height, “dashed line” using BB1K/MG3S barrier height. Experimental data are given for the purpose of comparison. (●) from ref 9, (■) from ref 10, (×) from ref 11, (▲) from ref 12, and (◆) from ref 13.

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(1) Molina, M. J.; Rowland, F. S. Stratospheric Sink for Chlorofluoromethanes: Chlorine Atom-Catalysed Destruction of Ozone. Nature 1974, 249, 810−812. (2) Rowland, F. S.; Molina, M. J. Estimated Future Atmospheric Concentrations of Trichlorofluoromethane (Fluorocarbon-11) for Various Hypothetical Tropospheric Removal Rates. J. Phys. Chem. 1976, 80, 2049−2056. (3) Finlayson-Pitts, B. J.; Pitts-Jr, J. N. Chemistry of the Upper and Lower Atmosphere; Academic Press: London, 2000. (4) Wallington, T. J.; Schneider, W. F.; Worsnop, D. R.; Nielsen, O. J.; Sehested, J.; DeBruyn, W.; Shorter, J. A. Environmental Impact of CFC Replacements- HFCs and HCFCs. Environ. Sci. Technol. 1994, 28, 320A−623A.

shows the computed rate coefficients for consumption of the reactants in comparison with the literature data. As can be seen, the computed rate constants using CBS-Q barrier height are in accordance with the experimental data. The rate constants are slightly underestimated by BB1K/MG3S method. As the final production of the present research, the computed rate constants by using CBS-Q barrier heights are fitted to Zheng and Truhlar’s rate constant expression:44 ⎡ − E (T + T ) ⎤ 0 ⎥ k(T ) = AT n exp⎢ 2 2 ⎣ T + T0 ⎦

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Theoretical Kinetics Studies on the Reaction of CF3CF CF2 with

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