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Publicly Available Published by De Gruyter November 18, 2021

Reaction of OH with CHCl=CH-CHF2 and its atmospheric implication for future environmental-friendly refrigerant

Olivier Holtomo, Lydia Rhyman, Mama Nsangou, Ponnadurai Ramasami and Ousmanou Motapon

Abstract

In order to understand the atmospheric implication of the chlorinated hydrofluoroolefin (HFO), the geometrical structures and the IR absorption cross sections of the stereoisomers 1-chloro-3,3-difluoropropene were studied using the B3LYP/6-31G(3df) and M06-2X/6-31G(3df) methods in the gas phase. The cis-trans isomerization was assessed using the M06-2X/6-311++G(3df,p)//6-31+G(3df,p) method. The latter method was also employed for thermochemistry and the rate coefficients of the reactions of OH with the cis- and trans-isomers in the temperature ranging from 200 to 400 K. The computational method CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p) was used to benchmark the rate coefficients. It turns out that, the trans-isomer is more stable than cis-isomer and the trans- to cis-isomerization is thermodynamically unfavorable. The rate coefficient follows the Gaussian law with respect to the inverse of temperature. At the global temperature of stratosphere, the calculated rate coefficients served to estimate the atmospheric lifetime along with the photochemical ozone creation potential (POCP). This yielded lifetimes of 4.31 and 7.31 days and POCPs of 3.80 and 2.23 for the cis- and trans-isomer, respectively. The radiative forcing efficiencies gave 0.0082 and 0.0152 W m−2 ppb−1 for the cis- and trans-isomer, respectively. The global warming potential approached zero for both stereoisomers at 20, 100, and 500 years time horizons.

Introduction

In order to find out novel refrigerants, cleaning solvents, carrier of fluids, anaesthetic agents in pharmaceutical industries and compounds with very low global warming potential (GWP), the stereoisomers cis- and trans-1-chloro-3,3-difluoropropene (cis- and trans-CDFP) were considered for the present work. These stereoisomers are the derivatives of cis- and trans-1-chloro-3,3,3-trifluoropropene (cis- and trans-CTFP) [1, 2]. The latter stereoisomers are known to be short-lived compounds. They have global atmospheric lifetimes of 14 and 26 days for cis- and trans-CTFP, respectively [2], [3], [4], [5], [6] obtained at a global temperature of 296 K. In the particular case of trans-CTFP, the lifetime was found to be 46 days at a global temperature of 272 K by Orkin et al. [1] and 30.5 days by Sulbaeck Anderson et al. [6] using the whole atmospheric community climate model. The radiative forcing efficiencies (RFE) were estimated as 0.023 and 0.044 W m−2 ppbv−1 for cis- and trans-CTFP, respectively [2, 3, 5]. The global warming potentials were found to be 48, 14, and 4 at time horizons 20, 100, and 500 years, respectively [1]. These results were obtained under the assumption of atmospheric well-mixed gases, which show the upper limit of RFE. Cis- and trans-CDFP have two fluorine atoms compared to their parents (CTFPs), which include three fluorine atoms. The study of these compounds follows the dynamics of the search of the potential replacement of hydrofluoroethers (HFEs), chlorofluorocarbons (CFCs), hydrochlorofluorocarbons (HCFCs), hydrofluorocarbons (HFCs) and perfluorocarbons (PFCs) in industrial processes [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18].

In the present work, the geometrical structures of the stereoisomers were explored along with their temperature- and pressure-dependent stabilities. The grand canonical ensemble [5] was employed for this purpose over the temperature range 220–370 K at 1 atm, and along the atmospheric altitude ranging from 0 to 60 km [19]. The isomerization from cis- to trans-CDFP and vice versa is presented in order to identify the most abundant compound. The C–H bond dissociation enthalpy (BDE) was calculated at three different sites of the stereoisomers. This thermodynamic parameter is used to determine the selectivity of the preferred site for hydrogen abstraction.

In order to find out the feasibility and the lability of the reactions involving the cis- and trans-CDFP with the OH radical, the enthalpies and free energies of these reactions through the channels R1–R5 were calculated. These reactions were proposed by three different channels for H-abstraction (R1–R3) and two channels for radical adduct (R4 and R5).

(R1) CHF 2 CH = CHCl + O · H CHF 2 CH = C · Cl + H 2 O

(R2) CHF 2 CH = CHCl + O · H CHF 2 C · = CHCl + H 2 O

(R3) CHF 2 CH = CHCl + O · H C · F 2 CH = CHCl + H 2 O

(R4) CHF 2 CH = CHCl + O · H CHF 2 C · H CH ( OH ) Cl

(R5) CHF 2 CH = CHCl + O · H CHF 2 CH ( OH ) C · HCl

The rate coefficients of these reactions were estimated using the variational transition state theory (VTST) taking into account the tunnelling effects [20], [21], [22], [23], [24], [25], [26], [27], [28], [29]. These coefficients served to estimate the atmospheric lifetimes (ALT) of stereoisomers [1], [2], [3], [4, 6], [7], [8], [9], [10], [11], [12] and their photochemical ozone creation potentials (POCP) [8, 30], [31], [32]. The ozone creation can be explained by the fact that, the emitted gases react with the oxidants such OH, NO3 and Cl) in the troposphere and produce the corresponding peroxy/alkoxy radicals. The latter react further with NO to form NO2, which in turn, in the presence of light and oxygen regenerates NO along with the ozone molecule. Further, the RFEs [13], [14], [15], [16], [17], [18] along with the global warming potentials (GWP) [1, 11, 12, 13, 18] were estimated.

Methodology

Computational details

The stereoisomers of cis- and trans-CDFP were fully optimized in the gas phase using the B3LYP/6-31G(3df) and M06-2X/6-31G(3df) methods to obtain their equilibrium geometries. Frequency computations were carried out using the equilibrium geometries to confirm their ground states and to obtain the IR absorption coefficients. It was shown that, these methods are reliable and provide accurate geometry structures and vibrational frequencies [5, 33], [34], [35], [36], [37]. The electronic energies of the species in the isomerization process and thermochemistry parameters were computed using the dual method M06-2X/6-311++G(3df,p)//6-31+G(3df,p). The geometry and energetic features of the species in the reaction channels of the isomers with the OH radical, were investigated using the unrestricted model of the M06-2X/6-311++G(3df,p)//6-31+G(3df,p) method and benchmarked using the unrestricted CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p) method. These two dual methods have produced reliable results on other molecules [7, 8, 11, 38]. The exchange-correlation functional M06-2X was developed for the purposes of thermochemistry and kinetics of chemical reactions [35], [36], [37]. The computational expensive chemical method CCSD [39, 40] was applied to refine the electronic energies in the transition state theory. This is in order to yield accurate results of structures, electronic energies, vibrational frequencies, enthalpies and Gibbs free energies of the species in the reaction processes. The computations were done using the Gaussian 09 [43] and Gaussian 16 suite [44] packages. Gaussian 16 was used by means of resources provided by SEAGrid [45], [46], [47], [48]. The method of direct inversion in the iterative subspace (DIIS) [49] was employed throughout this work for geometry optimizations. The optimizations were carried out without constraints up to the convergence with an accuracy of 10−7 a.u. The equilibrium geometries were validated when all the computed frequencies were positive, except the transition state geometries where an imaginary frequency was observed and further, used in the estimation of rate constant.

The IR harmonic spectra of the stereoisomers in this investigation was produced by the list of frequencies and intensities employing the Gaussian broadening function as depicted in Eq. (1) [5, 41]. Herein, N represents the number of vibrational modes. The superscript k is associated to the kth vibrational peak in the spectrum. A k designates the vibrational intensity expressed in km.mol−1 [42].

(1) ϵ ( ω ) = k = 1 N A k σ k 2 π exp ( ( ω ω k ) 2 2 σ k 2 )

where ω k is the frequency at the origin, ω is any frequency, σ k is the dispersion link to the full width at half maximum (Γ) by the relation Γ = 2 σ 2 ln 2 . A k is the absorption intensity of each band. This absorption coefficient is further converted to absorption cross-section (cm2 mol−1).

Thermochemistry and variational transition state theory

The H-abstraction mechanisms of cis- and trans-CDFP are governed by the bond dissociation enthalpies (BDE) [7, 38, 52], [53], [54] of all the C–H bonds which were calculated at 298 K as per Eq. (2).

(2) BDE 298 = Δ f ( CDFP - C ) + Δ f ( H ) Δ f ( CDFP - CH )

where CDFP-CH designates the stereoisomer at any of the three C–H sites. However, the hydrogen atom transfer (HAT) processes from gaseous CDFP to OH radicals are characterized by the enthalpies and Gibbs free energies of reactions R1–R3 [7, 38, 50], [51], [52]. These were calculated as per Eqs. (3) and (4).

(3) Δ H r , 298 ° = Δ f ( CDFP - C ) + Δ f ( H 2 O ) Δ f ( CDFP - CH ) Δ f ( O H )

(4) Δ H r , 298 ° = Δ f ( CDFP - C ) + Δ f ( H 2 O ) Δ f ( CDFP - CH ) Δ f ( O H )

where Δ f H°(Y) and Δ f G°(Y) indicate the standard enthalpy and Gibbs free energy, respectively, of formation of Y. The physical quantity Δ f H°(Y) includes the electronic energy, zero-point vibrational energy (ZPVE), and the thermal correction to enthalpy, while Δ f G°(Y) = Δ f H°(Y) + RT, with R the gas constant. The enthalpies and Gibbs free energies of radical adduct described in reactions R4 and R4 were calculated using Eqs. (5) and (6).

(5) Δ H r , 298 ° = Δ f ( CDFP - CH ( OH ) ) Δ f ( CDFP - CH ) Δ f ( O H )

(6) Δ G r , 298 ° = Δ f ( CDFP - CH ( OH ) ) Δ f ( CDFP - CH ) Δ f ( O H )

The rate constants of the reaction processes R1–R5 were estimated based on the variational transition state theory (VTST) with tunnelling effect incorporated. The conventional TST rate constant at temperature T [53], [54], [55], [56], [57], [58] for a bimolecular reaction is as given in Eq. (7).

(7) k TST ( T ) = σ 2 π β Q TS ( T ) Q React ( T ) exp ( β V 0 )

where β = 1/k B T, k B is the Boltzmann constant, is the reduced Planck's constant. The quantities Q React(T) and Q TS(T) are the partition functions per unit volume of reactants and transition states at temperature T, respectively. σ denotes the number of indistinguishable ways the reactants may approach the activated complex regions. V 0 is the classical barrier height. The quantum tunnelling effects [53], [54], [55], [56], [57], [58] and the corrected rate coefficient are related by Eq. (8).

(8) k ( T ) = k Tunnel ( T ) k TST ( T )

where k Tunnel(T) is the quantum tunnelling factor defined as the ground state transmission coefficient at temperature T [53], [54], [55], [56], [57], [58]. This factor is quantitatively the ratio of the thermally averaged multidimensional semi-classical transmission probability, to the thermally averaged classical transmission probability for scattering by the effective potential. The variational TST with the quantum tunnelling effects was implemented in our homemade FORTRAN 95 program. The program considers only the three states (reactants, transition state, products) on the reaction channel. The potential is interpolated according to the Eckart function [53], [54], [55], [56], [57]. The tunnelling effect are described using Skodje–Truhlar and Wigner expansions. It is worth noting that, Wigner factor is required only if ħv* >> kT, where v* is the imaginary frequency at the transition state. Both expressions are described in details in Ref. [58].

Atmospheric descriptors of gas

Atmospheric lifetime

The rate coefficients of the reactions of OH radical with the stereoisomers were used to estimate the atmospheric lifetime (ALT), τ as given by Eq. (9) [8, 38, 59].

(9) τ OH = 1 k OH [ O H ]

where k OH is the rate coefficient of the reaction of OH radical with the stereoisomers at the average atmospheric temperature of 298 K [38]. The quantity [OH] = 1.0 × 106 mol cm−3 represents the global average atmospheric concentration of the OH radical [30, 31, 59]. In fact, other oxidants as O3, NO3 radicals, and Cl atoms also contribute to the degradation of the gas in the troposphere [30, 31, 59]. However, they are less populated and less reactive compared to OH radical.

Radiative forcing efficiency and global warming potential

The RFE is the rate of energy change per unit area of the globe as measured at the top of the troposphere (tropopause). This rate measures the change in Earth's radiation balance for a 1 ppbv increase in concentration of the given greenhouse gas [5, 13], [14], [15]. Pinnock et al. [14] simplified the procedure of calculating the RFE using the IR spectrum of the given gas without the use of a complex radiative transfer model. In this approach, the RFE was calculated as per Eq. (10).

(10) RFE = i = 1 250 10 σ i ( ω ) F i ( ω )

where σ i (ω) is the absorption cross section (cm2 mol−1) averaged over a 10 cm−1 interval around the frequency ω. The term F i (ω) is the instantaneous cloudy sky radiative forcing per unit cross section (W m−2(cm2 mol−1 cm−1)−1) for a 0–1 ppbv increase in absorber. The detail on this quantity is provided in Ref. [14]. However, for short-lived compounds, the effect of non-atmospherically well-mixed greenhouse gases, needs to be taken into account. Thus, the RFE should be scaled using a correction factor f(τ) =  b /(1+ d ) provided by Hodnebrog et al. [3, 10, 13], where τ (year) is the atmospheric lifetime of the gas ranging from 10−4 to 104 years. The letters a, b, c, and d are real constants with values of 2.962, 0.9312, 2.994, and 0.9302, respectively.

The global warming potential (GWP) of the stereoisomers CDFP at the time horizon t H was calculated using Eq. (11).

(11) GWP CDFP ( t H ) = RFE CDFP τ OH ( 1 exp ( t H / τ OH ) ) AGWP CO 2 ( t H )

where RFECDFP is the radiative forcing efficiency of the isomers, τ OH is the lifetime of CDFP as expressed in Eq. (9). The term AGWPCO2 is the absolute GWP of carbon dioxide [13].

Photochemical ozone creation potential

The photochemical ozone creation potential (POCP) allows to quantify the ability of a gas to create ozone in the troposphere. A simplified procedure for the POCP calculations has been proposed as given in Eq. (12) [8, 60, 61].

(12) POCP X = α 1 × γ s × γ R × β ( 1 α 2 × n c )

where the subscript X stands for the molecular gases cis- or trans-isomer. The quantities α 1, α 2 and β are real constants with the values of 111, 0.04, and 0.5, respectively [62, 63]. n c indicates the number of carbon atom the gas molecule X. The quantities γ s = 28.05 n B / 6 M X and γ R = 6 k OH X / n B k OH ethene are ozone formation indices obtained from the structure and reactivity of molecule X, respectively. Therein, n B represents the total number of reactive bonds (C–C and C–H) in the molecule, M X is the molecular weight, k OH X is the rate constant for reaction of molecule X with OH radical at 298 K and 1 atm of air, and k OH ethene = 8.64 × 10 12  cm3 mol−1 s−1 is the rate constant for reaction of ethene with OH radicals at 298 K and 1 atm of air [31, 60], [61], [62].

Results and discussions

Structures and stabilities of stereoisomers

Stabilities of stereoisomers

The equilibrium structures of the stereoisomers cis- and trans-CDFP are shown in Fig. 1. Their temperature- and pressure-dependent stabilities over the temperature range 220–370 K at 1 atm, and along atmospheric altitude ranging in 0–60 km are provided in Table 1. The results show that, in the gas phase, the cis-isomer is less populated compared to the trans-isomer. At a pressure level of 1 atm, the population of cis-CDFP decreases with temperature (220–250 K) while that of trans-CDFP increases. The population increases in the temperature range 250–370 K for the cis-isomer and decreases for the trans-isomer. These findings show that, the trans-CDFP is the most abundant and stable stereoisomer.

Fig. 1: 
Equilibrium structures of cis- and trans-CDFP using B3LYP/6-31G(3df) method.

Fig. 1:

Equilibrium structures of cis- and trans-CDFP using B3LYP/6-31G(3df) method.

Table 1:

Boltzmann probability of cis- and trans-CDFP at different temperature and pressure at dual method M06-2X/6-311++G(3df,p)//6-31+G(3df,p).

1 atm Atmospheric altitude
T (K) cis-CDFP trans-CDFP H (km)a T (K)a P (atm)a cis-CDFP trans-CDFP
220 29.65 70.35 0.0 290.2 0.99975 23.15 76.85
230 26.31 73.69 6.0 250.5 0.48941 24.27 75.73
240 22.64 77.36 11.2 215.6 0.23962 25.32 74.68
250 20.42 79.58 15.7 198.0 0.11725 26.27 73.73
260 21.71 78.29 20.3 208.0 0.05742 27.21 72.79
272 22.69 77.31 25.1 216.1 0.02811 28.22 71.78
285 23.32 76.68 30.1 221.5 0.01376 29.25 70.75
298 24.04 75.96 35.2 228.1 0.00674 30.24 69.76
313 25.34 74.66 40.5 240.5 0.00330 31.24 68.76
330 26.47 73.53 46.2 251.9 0.00161 32.29 67.71
350 26.61 73.39 51.9 253.7 0.00079 33.42 66.58
370 26.02 73.98 57.7 247.2 0.00039 34.43 65.57

  1. aVoglozin and Copper.

The behaviour of both stereoisomers over the temperature range 220–370 K and at 1 atm is similar along the atmospheric altitude in the range 0–60 km, where the relative population varies with both temperature and pressure. Besides, the results (Table 1) reveal that, the relative population of cis-CDFP increases with altitude in the troposphere (0–15 km), while that of trans-CTFP decreases. Nevertheless, the short-lived compounds cannot reach the upper troposphere and stratosphere [13]. The two isomers of CDFP are obviously short-lived compounds since they are HFO, and consequently they turn out to be non-uniform along the atmospheric altitude and latitude.

Isomerization of cis- and trans-CDFP in reactions with OH

The schematic of the potential energy surfaces of the addition processes of OH radical to the stereoisomers of CDFP, are shown in Fig. 2 together with the equilibrium structures. The results show that, the ground state electronic energy of cis-isomer is 1.44 kJ.mol−1 higher in energy than that of trans-isomer using the M06-2X/6-311++G(3df,p)//6-31 + G(3df,p) method. When either cis- or trans-CDFP reacts with OH, an energized adduct is formed. The OH radical can add to either sp 2 carbon atom resulting in adducts cis-CDFP-C1-OH and cis-CDFP-C2-OH as shown in Fig. 2. Their respective relative energies are given by −140.33 and −133.56 kJ mol−1. The potential energy surfaces (PES) of the rotations of the chemical groups are set in supporting material (Fig. 1s) for both adducts. The most stable conformers were highlighted along with their enantiomers (Fig. 2s). For each adduct, the enantiomers have almost equal energies. The most stable enantiomers are used in the present investigation.

Fig. 2: 
Potential energy surface for the •OH radical initiated cis–trans isomerization of the compound CDFP using the M06-2X/6-311++G(3df,p)//6-31+G(3df,p) method.

Fig. 2:

Potential energy surface for the OH radical initiated cistrans isomerization of the compound CDFP using the M06-2X/6-311++G(3df,p)//6-31+G(3df,p) method.

The path process of the formation of cis-CDFP-C1-OH is thermodynamically more favourable. Thus, cis-CDFP adds OH to form cis-CDFP-C1-OH which can move to trans-CDFP-C1-OH (−138.47 kJ.mol−1) conformer through the rotation about C1–C2 axis. In fact, the adduct cis-CDFP-C1-OH is formed with enough excess energy which is used to eliminate OH radical in order to form trans-CDFP. The cis-CDFP can also add OH to form cis-CDFP-C2-OH with less energy. A large barrier prohibits internal transfer of OH radical from carbon number C2 to C1. The adduct intermediates can make internal rearrangement and/or thermal decomposition to give the trans-isomer. Similarly, the trans-CDFP also adds OH radical to form cis-CDFP-C1-OH and trans-CDFP-C1-OH in equilibrium with each other or cis-CDFP-C2-OH. However, the process to form cis-CDFP is energetically forbidden. The thermochemistry of the reaction of addition is discussed in Section 3.2. Therefore, the isomerization of trans- to cis-CDFP is thermodynamically forbidden. This finding is similar to that of trans- to cis-CTFP [64].

Infrared absorption cross section

The IR absorption spectra of both stereoisomers cis- and trans-CDFP are presented in Fig. 3. They were simulated using the B3LYP and M06-2X functionals. These spectra were saved over the frequency range 0–2000 cm−1 with the full width at half-maximum of 10 cm−1. Both functionals are in agreement except in the range 1000–1250 cm−1. In this range, two peaks of important intensities are clearly noticeable using the B3LYP functional. It was proved in our previous study [5] and other studies [15], [16], [17] that, this functional is reliable and reproduces well the experiment. The geometrical structures of CDFP and CTFP are closed. The latter has been studied by different authors [1], [2], [3], [4], [5], [6]. Based on these statements, the IR spectra using the B3LYP functional can be used as the benchmark.

Fig. 3: 
IR spectra of cis- and trans-CDFP at different chemical methods. Γ = 10 cm−1 is the full width at half maximum using the B3LYP and M06-2X functionals combined with 6-31G(3df).

Fig. 3:

IR spectra of cis- and trans-CDFP at different chemical methods. Γ = 10 cm−1 is the full width at half maximum using the B3LYP and M06-2X functionals combined with 6-31G(3df).

All the vibrational frequencies of the stereoisomers are summarized in Table S1 as Supplementary material. The intense peaks vibrate at frequencies 1078.18 and 1128.09 cm−1 for cis-CDFP and 1075.43 and 1144.64 cm−1 for trans-CDFP. These two frequencies correspond to the asymmetric and symmetric stretchings of the C–F bonds, respectively. The double bond C=C stretches at 1706.81 and 1701.83 cm−1 for cis- and trans-CDFP, respectively.

The computed IR absorption band strengths (S) over the frequency range 0–2500 cm−1 yielded 1.12 × 10−16 and 1.10 × 10−16 cm2mol−1cm−1 for cis-CDFP using B3LYP/6-31G(3df) and M06-2X/6-31G(3df) methods, respectively. It yielded 1.28 × 10−16 and 1.26 × 10−16 cm2 mol−1 cm−1 for trans-CDFP using B3LYP/6-31G(3df) and M06-2X/6-31G(3df) methods, respectively. It is seen that, the absorption band strength of trans-CDFP is slightly larger than that of cis-CDFP. Thus, trans-CDFP absorbs more energy than cis-CDFP, which reflects the behaviour of radiative forcing efficiency.

Thermodynamics of reactions

The reaction processes of the OH radical with the stereoisomers cis- and trans-CDFP happen from five different channels as presented in reactions R1–R5. The enthalpies of these reactions (BDE) at 298 K and 1 atm are reported in Table 2. It comes out that, the BDE increases in the following order: BDE (C3–H3) < BDE (C1–H1) < BDE (C2–H2). Therefore, the most thermodynamically favourable site for radical attacks by H-abstraction is at atom C3 for both stereoisomers.

Table 2:

BDE (kJ.mol−1) of bond lengths C–H in CDFP isomers, and the enthalpy ΔH° (kJ.mol−1) and Gibbs free energy ΔG° (kJ.mol−1) of H-atom transfer (HAT) processes to OH at 298 K.

H-abstraction Adduct
C1–H1 C2–H2 C3–H3 Site C1 Site C2
BDE
cis-CDFP 417.80 432.09 331.74
trans-CDFP 417.94 438.29 330.28
ΔH° ,298 /HAT
cis-CDFP −34.00 −19.70 −120.05 −136.00 −120.66
trans-CDFP −33.85 −13.50 −121.51 −136.58 −128.98
ΔG° ,298 /HAT
cis-CDFP −38.30 −25.23 −122.94 −95.84 −78.57
trans-CDFP −38.21 −19.51 −125.33 −95.46 −88.24

The enthalpy changes Δ H r , 298 and Gibbs free energy changes Δ G r , 298 of reactions involving the isomers and OH radical were calculated at 298 K and 1 atm (Table 2) in order to predict the feasibility and spontaneity of the reaction channels. It turns out that, the reaction channels including H-abstractions and radical adducts are exothermic. The enthalpies of the reactions of addition are lower than that of H-abstraction. Thus it follows that, the radical adduct pathways are thermodynamically more preferable. The pathway R4 is more competitive than R5. On considering Δ G r , 298 results, it comes out that, the reaction channels R1–R5 are spontaneous as Δ G r , 298 is negative. Therefore, from the thermodynamic point of view, all the reaction channels are feasible.

Kinetics of reactions

The temperature dependent rate coefficients for the reaction channels from R1 to R5 were calculated in the temperature range 200–400 K using the M06-2X/6-311++G(3df,p)//6-31 + G(3df,p) and CCSD/cc-pVTZ//M06-2X/6-31 + G(3df,p) methods. The equilibrium structures of reactants, transition states (TSs), and products are presented in Fig. 4 for the cis-isomer and in Fig. 5 for the trans-isomer. For the comprehension of chemical reactions, the relative electronic energy of each of the three states along the minimum energy path (MEP) is essential and presented in Fig. 6. These energies are given relative to the electronic energies at the reactants of each pathway. The classical barrier height of each path is directly read as the relative energy of TS, accordingly. The values of the different classical barrier heights are shown in Fig. 6. The MEPs were interpolated using the Eckart unsymmetrical function on the energies of the three states (reactants-TS-products). The classical barrier heights of the reactions of addition are lower than those of H-abstraction. This means that, the reactions of addition are faster than those of H-abstraction. The results of rate coefficients are tabulated in Table 2s–5s (Supplementary material) for each stereoisomer along with the branching ratio of each reaction channel. Only those obtained at ambient temperature 298 K are reported in Table 3. The total rate coefficient was calculated as the sum over all the rate coefficients of the different reaction paths. It comes out that, the rate coefficients along the reaction channels of adducts are smaller than those of H-abstractions. The branching ratio of adduct paths tends to zero. The greatest contribution to the total rate coefficient comes from the H-abstraction of site C1–H1 followed by those of site C2–H2 and C3–H3, respectively. Therefore, the reaction paths of H-abstraction are kinetically more labile.

Fig. 4: 
Reactants, transition states, and products for the reactions of •OH radicals with cis-CDFP at different channels. The electronic energy using CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p) of each step of the process are presented in kJ/mol relative to reactants. The other amounts are the interatomic distance (Å) along the MEP.

Fig. 4:

Reactants, transition states, and products for the reactions of OH radicals with cis-CDFP at different channels. The electronic energy using CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p) of each step of the process are presented in kJ/mol relative to reactants. The other amounts are the interatomic distance (Å) along the MEP.

Fig. 5: 
Reactants, transition states, and products for the reactions of •OH radicals with trans-CDFP at different channels. The electronic energy using CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p) of each step of the process are presented in kJ/mol relative to reactants. The other amounts are the interatomic distance (Å) along the MEP.

Fig. 5:

Reactants, transition states, and products for the reactions of OH radicals with trans-CDFP at different channels. The electronic energy using CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p) of each step of the process are presented in kJ/mol relative to reactants. The other amounts are the interatomic distance (Å) along the MEP.

Fig. 6: 
Potential energy surfaces of the reactions of •OH radicals with cis- and trans-CDFP using CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p). TSC1, TSC2, TSH1, TSH2, and TSH3 as well as PC1, PC2, PH1, PH2, and PH3, are the transition states and product complexes at sites C1 and C2 for radical adducts and sites C1–H1, C2–H2, and C3–H3 for H-abstraction, respectively. The classical barrier heights of the potentials are reported in parenthesis.

Fig. 6:

Potential energy surfaces of the reactions of OH radicals with cis- and trans-CDFP using CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p). TSC1, TSC2, TSH1, TSH2, and TSH3 as well as PC1, PC2, PH1, PH2, and PH3, are the transition states and product complexes at sites C1 and C2 for radical adducts and sites C1–H1, C2–H2, and C3–H3 for H-abstraction, respectively. The classical barrier heights of the potentials are reported in parenthesis.

Fig. 7: 
Total rate coefficients of the reactions of •OH radicals with cis- and trans-CDFP using CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p).

Fig. 7:

Total rate coefficients of the reactions of OH radicals with cis- and trans-CDFP using CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p).

Table 3:

Rate constant k OH n (10−13 cm3 mol−1 s−1) and branching ratio of the reaction of OH radicals with of cis- and trans-CDFP at different channels (n = 1–5) at 298 K. Channels 1, 2, and 3 are H-abstractions from sites C1–H, C2–H, and C3–H respectively. Channels 4 and 5 are radical adducts from sites C1 and C2 respectively.

cis-CDFP trans-CDFP
H-abstraction Radical adduct Total H-abstraction Radical adduct Total
k OH 1 k OH 2 k OH 3 k OH 4 k OH 5 k OH k OH 1 k OH 2 k OH 3 k OH 4 k OH 5 k OH
Rate constant
M06-2X 55.2 19.2 0.3170 6.04 × 10−3 1.06 × 10−2 74.7 43.5 221.0 0.107 6.98 × 10−3 0.220 264.4
CCSD 20.5 6.31 0.0111 2.88 × 10−3 2.19 × 10−3 26.9 13.6 2.04 0.171 3.88 × 10−3 6.06 × 10−2 15.8
Branching ratio
M06-2X 73.84 25.71 0.42 0.01 0.01 16.47 83.41 0.04 0.00 0.08
CCSD 76.45 23.49 0.04 0.01 0.01 85.61 12.91 1.08 0.02 0.38

The fit of the total rate coefficients of the cis- and trans-isomers over the temperature range 200–400 K are shown in Fig 7. Thisyielded the Arrhenius temperature-dependent rate coefficients as per Eqs. (13) and (14).

(13) k OH c i s ( T ) = 1.006 × 10 5 exp ( 4517.80 T )

(14) k OH t r a n s ( T ) = 8.467 × 10 6 exp ( 4641.57 T )

with coefficient of determination r 2 = 0.999. These equations are stated in cm3 mol−1 s−1 unit. With the lack of experimental results, Eqs. (13) and (14) may help for future experimental research. Elsewhere in Table 3, it can be observed that, the results from the M06-2X/6-311++G(3df,p)//6-31+G(3df,p) method are greater than those from the CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p) method. This is more pronounced for the trans-isomer. The greatest discrepancies of rate coefficients between both methods comes from the H-abstractions at carbon (sp 2) sites C1 and C2. In fact, the classical barrier heights at both carbon sites are higher for the M06-2X/6-311++G(3df,p)//6-31+G(3df,p) compared with CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p) methods.

Atmospheric implication

The results of atmospheric lifetime (ALT) of the stereoisomers are reported in Table 4. They were estimated to be 4.31 and 7.31 days for the cis- and trans-CDFP, respectively using the rate coefficients obtained by the CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p) method. Since the ALTs are of the order of few days, the stereoisomers tends to degrade near the emission zone, which have negligible impact towards global warming. A significant increase of ALTs is observed when comparing with the cis- and trans-CTFP (14 and 26 days, respectively) [1], [2], [3], [4], [5]. This is the effect of the substitution of –CF3 by –CHF2 as presented in the Introduction section.

Table 4:

Atmospheric lifetime ALT (day), radiative forcing efficiency RFE (W m−2 ppbv−1) over the frequency range 0–2500 cm−1, and global warming potential GWP at time horizon 20, 100, and 500 years of cis- and trans-CDFP. The corrected values of RFEs are the NG, where UG and NG stand for uniform gas and non-uniform gases, respectively.

Stereoisomer ALT RFE GWP POCP
UG NG 20 100 500
cis-CDFP 4.31 0.18 0.0082 0.50 0.14 0.05 3.80
trans-CDFP 7.31 0.21 0.0152 1.48 0.45 0.14 2.24

The radiative forcing efficiencies (RFEs) were estimated based on the narrow band model [14]. The results are compiled in Table 4. It turns out that, the RFEs of the cis- and trans-CDFP were found to be 0.18 and 0.21 W.m−2.ppbv−1, respectively using the IR absorption cross section obtained using the B3LYP/6-31G(3df) method. These results were estimated based on the fact that, the gases are uniformly well-mixed in the atmosphere (Pinnock et al. [14]). However, the ALTs above are short enough, which lead to the atmospherically not well-mixed stereoisomers. Therefore, the results were corrected with the mean of the scaling factor provided in Section 2.3.3 [3, 10, 13]. These scaling factors were calculated to be 0.0453 and 0.0722 for the cis- and trans-CDFP, respectively. Accordingly, the corrected RFEs were 0.0082 and 0.0152 W.m−2.ppbv−1 for the cis- and trans-CDFP, respectively. These values are smaller than their parent molecules cis- and trans-CTFP, given by 0.024 and 0.044 W.m−2.ppbv−1, respectively [2], [3], [4], [5].

The global warming potentials (GWPs) of the cis- and trans-CDFP were estimated as presented in Eq. (11) for 20, 100, and 500 years time horizons (Table 4). It turns out that, the GWP values are much lower for both stereoisomers. Despite this negligible impact towards global warming, the GWPs of cis-CDFP are lower than those of trans-CDFP. The results for the cis- and trans-CTFP reveal a GWP at 100 years time horizon to be approximately 3 and 10, respectively [1]. These are greater than those of cis- and trans-CDFP which are given by 0.14 and 0.45, respectively. Therefore, substituting a fluorine of the –CF3 group by a hydrogen atom lowers the GWPs.

The estimated photochemical ozone creation potentials (POCPs) of both stereoisomers are compiled in Table 4. It comes out that, the POCP values are 3.80 and 2.23 for the cis- and trans-CDFP, respectively. These values are within the POCP ranging between those of methane (0.6) and ethane (12.3), which are excluded from air quality regulations [30, 61, 65]. Based on this, both stereoisomers are inefficient ozone producer. The discrepancy between the POCPs of both stereoisomers comes from the difference of rate coefficients of the reactions of the stereoisomers with hydroxyl radical.

Conclusions

The equilibrium structures and IR absorption cross section were obtained using the B3LYP/6-31G(3df) method, which served to estimate the radiative forcing efficiencies (RFEs) using the Narrow Band model. As the gases are non-homogeneous in the atmosphere, the obtained results were refined by the atmospheric lifetimes assessed using the CCSD/cc-pVTZ//M06-2X/6-31+G(3df,p) method. This method was used to determine the temperature-dependent rate coefficients of the reactions of OH radical with the cis- and trans-CDFP over the range 200–400 K at pressure level of 1 atm. It was found that, the different reaction channels are exothermic. The H- abstraction from carbon sp 2 (C1 and C2) are thermodynamically more feasible than carbon sp 3 (C3). The radical adduct at both sites of carbon sp 2 (C1 and C2) are the most thermodynamically feasible pathway. However, the branching ratios of rate coefficients show that, the H-abstraction at the carbon site C1 have a large contribution followed by the carbon sites C2 and C3, respectively. The branching ratio are low enough for the reactions of addition, meaning that they are kinetically inert. The atmospheric lifetimes of both stereoisomers were found to be low and, show a negligible impact towards global warming. The lower values of RFEs impacted significantly in reducing the global warming potential values which are less compared to those of CO2. The POCP values suggest that, both stereoisomers have insignificant contribution in the production of tropospheric ozone. This work may lay the foundation for future experimental research.


Corresponding author: Olivier Holtomo, Department of Physics, Faculty of Science, University of Bamenda, Bambili P.O. Box 39, Cameroon; and Department of Physics, Faculty of Science, University of Maroua, Maroua P.O. Box 814, Cameroon, e-mail:

Article note: A collection of invited papers based on presentations at the Virtual Conference on Chemistry and its Applications (VCCA-2020) held on-line, 1–31 August 2020.


Funding source: Abdus Salam International Centre for Theoretical Physics

Award Identifier / Grant number: OEA-NET 05

  1. Research funding: The authors are grateful to the Abdus Salam ICTP for their financial support to this work through the OEA-NET 05 project.

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Published Online: 2021-11-18
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