Computational kinetic study on atmospheric oxidation reaction mechanism of 1-fluoro-2-methoxypropane with OH and ClO radicals

2.1 Samples used (HFEs and radicals)

1-fluoro-2-methoxypropane (HFE), OH/ClO radicals were selected from the literature and used for this computational kinetics study (Anderson, 1987; WMO, 2010; Hashemi and Saheb, 2017; Baidya et al., 2017). 2D structures were drawn with ChemDraw ultra V12.0 module and transferred to Spartan 14 v 1.1.4 where the 3D structures were obtained.

2.2 Computational procedures

In this study, Spartan 14 v 114 suite program was used for all the electronic calculations. The geometry optimization of stationary points or all chemical species involved in the reaction were carried out using density functional theory (DFT) based M06-2X method in conjunction with 6–311++G^** basis set since dehydrogenation entails diffuse and polarization functions on Hydrogen (White and Martell, 2015; Hashemi and Saheb, 2017). To improve the results, DFT/M06-2X/6–311++G(2df,2p) single-point calculations were performed on the reacting species involved. This geometry optimization method/basis sets were employed due to the remarkability in their accuracy and the precise stability of the reacting species that were involved (Mishra et al., 2014; Baidya et al., 2017). The minimum energy equilibrium structure obtained at each stationary point has all real frequencies, meanwhile transition state possesses one imaginary frequency. The imaginary frequency in transition state corresponds to the coupling of stretching modes of the breaking C—H/O—C and forming O—C bonds. Transformation from the reactant to product via the transition state (TS) along the minimum energy path was confirmed with the help of intrinsic reaction coordinate (IRC) calculations at the M06-2X level of DF theory (Gour et al., 2016). IRC calculations indicate the formation of pre- and post-reaction complexes of the reactant/product molecule with the OH/ClO radicals (H₂O or HOCl) in both the entry and exit of each reaction route.

The rate constants (k) for dehydrogenation involved in the reactions were derived directly from the general proposed reaction mechanisms in Eqs. (9)–(10).

The rate coefficient of this study was computed as reported by Siaka et al. (2017) as shown in Eq. (11)

The $E_a$ was determined using expression (12).

Where, k_B is Boltzmann’s constant, h is Planck’s constant, ${\mathrm{\Delta }\mathrm{S}}^{\ne }$ is change in entropy’s of transition state, ${\mathrm{\Delta }\mathrm{H}}^{\ne }$ is the change in enthalpy of transition state, T is absolute temperature, R is universal gas constant and k is rate constant.

The total rate coefficient of this investigation is however computed as stated by Galano et al., 2010 as expressed in Eq. (13).

The branching ratios for the dehydrogenation reaction channels, which was reported (Gour et al., 2016) to represent the individual contribution of a reaction channel toward overall reaction rate have also been determined by using an expression in Eq. (14).

The ${{\mathrm{\Delta }}_{\mathbf{r}}{\mathrm{H}}^{\mathrm{o}}}_{\mathrm{r}\mathrm{x}\mathrm{n}}$ , ${{\mathrm{\Delta }}_{\mathbf{r}}{\mathrm{G}}^{\mathrm{o}}}_{\mathrm{r}\mathrm{x}\mathrm{n}}$ as well as ${{\mathrm{\Delta }}_{\mathbf{r}}{\mathrm{E}}^{\mathrm{o}}}_{\mathrm{r}\mathrm{x}\mathrm{n}}$ are computed using Eqs. (15)–(17)

The change in enthalpy, change in entropy as well as Gibb’s free energy of each transition states were estimated using expressions (18)–(20)

3.1 Sample conformers

Fig. 1 shows all the nine (9) possible Conformers of 1-fluoro-2-methoxypropane molecule ranging from the lowest to highest energy conformers.

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Fig. 1a

The optimized structures of reacting species with OH radical.

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Fig. 1b

The optimized structures of reacting species with ClO radical.

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Conformational analysis carried out on H₃CCH(OCH₃)CFH₂ molecule revealed that it has nine (9) possible conformers as illustrated in Figs. 2 and 3. From the analysis, conformer A (88.90 kJmol⁻¹) has the lowest energy predicted. Conformational analysis is however aimed at identifying the possible conformers of molecule H₃CCH(OCH₃)CFH₂ and to select the most stable conformer with lowest energy predicted. Hence, higher energy conformers are not stable and were not considered for this computational study (basic rule of quantum mechanics) (Baidya et al., 2017). The resultant conformers are arranged in Fig. 2 in order of increasing in their energy stabilities, so conformer I (107.67 kJmol⁻¹) has the highest energy predicted and it is the most unstable conformer among all as shown in the Fig. 3.

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Fig

2. Nine possible Conformers of 1-fluoro-2-methoxypropane molecule.

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Fig. 3

. Plot of conformational analysis results (lowest (A) and highest energy Conformers (I)).

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The Tables 1a and 1b show the results on single-point calculation which was aimed at improving the reacting species energies and enthalpies (kJmol⁻¹) using DFT/M06-2X/6–311++G(2df,2p) level.

The Table 2a shows the thermodynamics calculation results of dehydrogenation reaction routes (R1–R4) that were performed at DFT/M06-2X/6–311++G(2df,2p) with OH radicals. These results indicate that reaction through R1, R2 and R4 routes are endothermic ( $\mathrm{\Delta }{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}>0)$ in nature and thermodynamically unfavorable while reaction across R3 is exothermic. However, route R2 has lowest $\mathrm{\Delta }{\mathrm{E}}_{\mathrm{r}\mathrm{x}\mathrm{n}}$ which accounts for high possibility of dehydrogenation to occurs through route R2 over the others. Also, route R2 has highest ${{\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{S}}^{\mathrm{o}}}_{\mathrm{r}\mathrm{x}\mathrm{n}}$ and lowest ${{\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{G}}^{\mathrm{o}}}_{\mathrm{r}\mathrm{x}\mathrm{n}}$ which implies that, the product of this route is thermodynamically feasible. For this reason, R2 is considered more favored than every other routes and the rate of dehydrogenation reaction along this route is faster. While Table 2b shows the thermodynamics computational results of dehydrogenation reaction routes (R5–R8) that were performed on CH₃CH(OCH₃)CFH₂ at DFT/M06-2X/6–311++G(2df,2p) with ClO radicals. The results indicate that reaction through R6 is endothermic ( $\mathrm{\Delta }{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}>0)$ in nature and thermodynamically unfavorable while dehydrogenation along R5, R7 and R8 are exothermic. The lowest $\mathrm{\Delta }{\mathrm{E}}_{\mathrm{r}\mathrm{x}\mathrm{n}}$ and highest $\mathrm{\Delta }{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}$ nature of R6 accounts for its high possibility of dehydrogenation reaction. R6 with highest ${{\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{S}}^{\mathrm{o}}}_{\mathrm{r}\mathrm{x}\mathrm{n}}$ and lowest ${{\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{G}}^{\mathrm{o}}}_{\mathrm{r}\mathrm{x}\mathrm{n}}$ also explains that, the product from this route is more feasible. Hence, R6 is confirmed more thermodynamically favorable.

There are four possible dehydrogenation carbon sites of H₃CCH(OCH₃)CFH₂ which are —CFH₂, —OCH, —OCH₃, and —CH₃ groups. This resulted to eight transition states (TS1, TS2, TS3, TS4, TS5, TS6, TS7 and TS8) as the system reacted with OH/ClO radicals. For each transition state of the radicals investigated with system, the C—H bond of the dehydrogenation and newly formed bond between H and O atoms in OH/ClO radicals are observed. The intrinsic reaction coordinates (IRC) performed on all transition states at the same level were characterized by the occurrence of one imaginary frequencies identified at (840i, 1125i, 826i and 815i cm⁻¹ for OH radical) and (420i, 350i, 515i and 410i cm⁻¹ for ClO radical). This confirmed the existence of transition states connecting reactants and products for each route. During entrance and exit routes of this reaction study (R1–R8), pre – reactive complexes (RC1, RC2, RC3, RC4, RC5, RC6, RC7 and RC8) and post – reactive complexes (PC1, PC2, PC3, PC4, PC5, PC6, PC7 and PC8) formed have been validated as recommended by White and Martell (2015). Also, hydrogen bond formation was observed in the pre – reactive and post – reactive complexes between Oxygen atom of OH/ClO radicals with H-atom in the H₃CCH(OCH₃)CFH₂ which result from the weak attraction force. Thus, this implies that the reaction routes can proceed through indirect mechanism.

Figs. 4a and 4b show potential energy surfaces (OH/ClO) of the reaction at DFT/M06-2X/6–311++G(2df,2p) with arbitrary ground energies of the reactants taken as zero. Route R2/R6 in Figs. 4a and 4b is the most favorable route of dehydrogenation since they are characterized by lowest energies.

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Fig. 4a

Potential energy surface of dehydrogenation reaction routes performed at DFT/M06-2X/6–311++G(2df,2p) for 1-fluoro-2-methoxypropane with OH radical.

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Fig. 4b

Potential energy surface of dehydrogenation reaction routes performed at DFT/M06-2X/6–311++G(2df,2p) for 1-fluoro-2-methoxypropane with ClO radical.

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The Tables 3a and 3b show that reaction of OH/ClO radicals with the sample proceeded in two steps: (1) transition state formation and (2) product formation. According to the Gibb’s free energies of the two steps computed in each radical cases, the rate determining step (RDS) of each reaction channel was identified on the basis of ${\mathrm{\Delta }\mathrm{G}}^{\#}$  >  ${\mathrm{\Delta }\mathrm{G}}_1$ . Thus, first steps i.e. transition states formation across all reaction channels in the two Tables (3a and 3b) were the RDS. The rate determining steps are the slowest steps in the reaction between the HFE and the radical species that were investigated.

Table 4 shows the branching ratios for dehydrogenation reaction across the routes in the two radical cases which represent the individual contribution of a reaction channel toward overall reaction rate. For route one in OH radical case, the branching ratio is higher which can be attributed to Fluorine atom attach to carbon one. The total k_ClO value (1.23 * 10⁶ s⁻¹) is higher than total k_OH value (9.13 * 10³ s⁻¹). Thus, the difference between k_ClO and k_OH is 1.22 * 10⁶ s⁻¹. This implies that in an ideal atmospheric condition, OH radicals are expected to be higher than ClO radicals since they (OH) are the major atmospheric scavenger through which atmospheric pollutants are removed (primary degradation). However, whenever ClO radicals over shadow OH radicals at the atmosphere the possibility of ozone depletion cannot be quantified.

Furthermore, Tables 5 (a and b) and 6 (a and b) illustrate some significant transformation and comparisons in bond lengths variation of the reactant complexes (RC1_, RC2, RC3, RC4, RC5, RC6, RC7 and RC8), transition states (TS1_, TS2, TS3, TS4, TS5, TS6, TS7 and TS8), product complexes (PC1_, PC2, PC3, PC4, PC5, PC6, PC7 and PC8) and products (P1_, P2, P3, P4, P5, P6, P7 and P8) that were involved in the eight routes of dehydrogenation from CH₃CH(OCH₃)CFH₂ with OH and ClO radicals.

In addition, Tables 7 (a and b) and 8 (a and b) also illustrate some significant chemical transformation and comparisons in the bond angles variation of the reactant complexes (RC1_, RC2, RC3, RC4, RC5, RC6, RC7 and RC8), transition states (TS1_, TS2, TS3, TS4, TS5, TS6, TS7 and TS8), product complexes (PC1_, PC2, PC3, PC4, PC5, PC6, PC7 and PC8) and products (P1_, P2, P3, P4, P5, P6, P7 and P8) that were involved in the eight routes of dehydrogenation from CH₃CH(OCH₃)CFH₂ with OH and ClO radicals.

3.2 Reaction mechanism and rate of reaction

The two overall reaction mechanism proposed entail two basic steps as $$\text{A}+\text{B}\underset{{\text{k}}_{-1}}{\stackrel{{\text{k}}_1}{\rightleftharpoons }}{\text{TS}}_1$$ $${\text{TS}}_1\stackrel{{\text{k}}_2}{\to }\text{P}$$

By applying the steady state approximation to be above equations, we got Eq. (21)

Substitutes Eq. (21) into Eq. (22) to gives Eq. (23)

If [A] and [B] concentration is 1 M, then Eq. (23) becomes Eq. (24)

There are two chemical conditions of which one may be applicable. First is when ${\mathrm{k}}_{-1}\gg {\mathrm{k}}_1$ and second is when ${\mathrm{k}}_{-1}\ll {\mathrm{k}}_1$ . The first condition transforms Eqs. (24)–(26)

3.3 Atmospheric implications

The atmospheric lifetime of 1-fluoro-2-methoxypropane is estimated by assumption that its primary removal from atmosphere occurs through its reaction with oxidants (atmospheric radicals). In that case, it can be estimated using Eq. (27).