Computational Study on Cl- Driven Oxidation of CF?C(O)CH?COCH?: A Thermochemical and Kinetic Study

Abstract

A detailed quantum chemical study was carried out to unravel the reaction mechanism, kinetics, and thermochemistry governing the gas-phase oxidation of 1,1,1-trifluoro-pentane-2,4-dione (CF?C(O)CH?C(O)CH?, TFP) by Cl radical, employing the M06-2X density functional. The most thermodynamically stable conformer of TFP was identified under ambient conditions. Two predominant hydrogen-abstraction channels were characterized, both involving the formation of pre-reactive complexes, thereby indicating an indirect abstraction mechanism. Temperature-dependent rate coefficients for these pathways were computed for the first time over the 250–450 K temperature range using Canonical Transition State Theory (CTST). Our result Based on the calculated kinetic parameters, the atmospheric lifetime of TFP was estimated to be approximately 161.42 days.

Keywords

Introduction

Scheme 1: Oxidation of TFP initiated by Cl radical

In the present study, density functional theory (DFT) calculations were carried out to evaluate the energetic profiles, optimized geometries, and harmonic vibrational frequencies of the reactants, products, and transition states associated with the hydrogen-abstraction reactions of keto form of TFP.

COMPUTATIONAL METHODS

All electronic structure computations were carried out using the Gaussian 09 software package [7].  Density functional theory (DFT) calculations were performed employing the M06-2X hybrid functional [8] in conjunction with the 6-31+G(d,p) basis set. The M06-2X functional is well recognized for its reliable performance in predicting thermochemical properties and reaction kinetics and has demonstrated good agreement with experimental and theoretical results in numerous prior studies [9-14]. Harmonic vibrational frequency analyses were conducted at the same level of theory to characterize the nature of the optimized stationary points and to obtain zero-point energy corrections. These calculations confirmed that stable species correspond to true minima with no imaginary frequencies, whereas each transition state exhibits a single imaginary frequency associated with the reaction coordinate. Intrinsic reaction coordinate (IRC) calculations [15] were further performed to ensure that each transition state properly connects the relevant reactant and product minima. Using the optimized geometries obtained at the M06-2X/6-31+G(d,p) level, more accurate single-point energy calculations were subsequently carried out and the resulting energies were used to evaluate the relative energy differences (ΔE) among all stationary points.

RESULTS AND DISCUSSION

At the M06-2X/6-31+G(d,p) level, the calculated thermodynamic data for the species has been recorded in Table 1. The reaction enthalpies (Δ_rH^°) and free energies (Δ_rG^°) at 298 K for loss processes (1-2) are documented in Table 1. These thermodynamic functions were determined with thermal corrections to the energy at 298 K. The calculated Δ_rH° and Δ_rG° values at 298 K indicate that the decomposition pathways taken into consideration in this investigation are feasible and spontaneous. It is evident from Table 1 that the reaction channel 2 is more thermodynamically viable. Because Δ_rH^°₂₉₈< 0, the results also show that reaction channels (1-2) are exothermic in nature. In order to identify, the most stable conformer of TFP scan calculation has been performed by rotating dihedral angle (C6-C5-C1-C12) and the most stable conformer of TFP has taken in consideration for further study. The result obtained during scan calculation has been depicted in Figure 1. For the hydrogen abstraction reactions, we have considered two reaction routes (1-2), mainly hydrogen abstraction from the -CH₃ group and -CH₂ group.  Pre-reactive complexes (RC1 and RC2) have been found in the entrance channel for reactions (1-2) in the current investigation. The exit channel also contains product complexes, referred to as PC1 and PC2, before the final product is distributed.  The C-H bond of the departing hydrogen and the newly generated bond between the H and Cl atom are crucial structural characteristics that must be monitored throughout the development of transition states. Figure 2 shows the electronic structure of the optimized geometry of the reactant, products, reaction complexes, product complexes, and transition states that were produced at the M06-2X/6-31+G(d,p) level. Visualization of the electronic structure of optimized geometry of TS1 corresponding to reaction channel (1) it has been observed that the breaking C-H (C12- H13) bond length is 25.31% greater than the observed C-H bond length in the isolated TFP molecule, while the forming H...Cl bond length is 15.54% longer than the H-Cl bond length in isolated HCl molecule, This implies that the barrier of the reaction 1 is closer to the product. It is emphasized that the reactions with Cl atom proceed via late transition state which is in consonance with Hammond’s postulate [16]. Similarly, for transition state TS2 for reaction channel 2, the length of the breaking C-H bond (C5 -H3) is found to be elongated  by 17.21% than the observed C -H bond length in isolated TFP molecule whereas the forming H...Cl bond length is longer by 21.09% than the H-Cl bond length in isolated HCl molecule. This implies that the barrier of the reaction 2 is closer to the reactant, and that the reactions with Cl atoms proceed via early transition state. Table 2 presents the results of the harmonic vibrational frequency calculation at the M06-2X/6-31+G(d,p) level. Each transition state has one imaginary frequency due to its first order saddle point character, while the analysis of the harmonic vibrational frequency of minima including reactants, reactant complexes (RCs), product complexes (PCs), and products (P1 and P2) revealed no imaginary frequency (NIMAG = 0). The Cl16–H13 and C12–H13 stretching modes are represented by the imaginary frequency of TS1 for reaction channel (1), which is 1132 cm^-1. This also shows a considerable curvature in the potential energy surface (PES) surrounding the transition state. The imaginary frequency for the hydrogen abstraction from the -CH₂ group involving TS2 is determined to be 1031 cm^-1, which corresponds to the stretching modes for hydrogen transfer reactions Cl16–H3 and C5–H3.  The representation of the normal-mode corresponding to the calculated imaginary frequencies shows a clear transition state geometry connecting reactants and products during transition. To further ascertain whether a transition state exists on the potential energy surface, the intrinsic reaction coordinate (IRC) calculation [15] is performed at the same theoretical level using the Gonzalez-Schlegel steepest descent path in the mass-weighted Cartesian coordinates with a step size of 0.01(amu^1/2- bohr). Additional proof that the transition state truly connects the intended reactant and product along the corresponding potential energy surface is given by the results of IRC calculations, which are shown in Figure 3. Table 3 summarizes the energy of each optimized geometry obtained during present study, at M06-2X/6-31+G(d,p), level of method. In order to compute zero-point energy (ZPE) for stationary points, we have performed frequency calculation at the M06-2X/6-31+G(d,p) level of theory,. Zero-point energy (ZPE) thus obtained were corrected with a scale factor of 0.967 [17] and the total energies of each species were calculated on potential energy surface. Figure 4 shows a schematic potential energy profile of TFP reactivity with the Cl radical using zero-point energy (ZPE) corrections. The ground state energy of TFP + Cl, which includes ZPE, is plotted against these energies, with zero being used randomly. For TS1 and TS2, the energy barrier determined at the M06-2X/6-311+G(d,p) level is 1.12 and 0.26 kcal mol^-1, respectively. From these results, it can be emphasize that the hydrogen abstraction from the -CH₂ group is more facile than the hydrogen abstraction from –CH₃ group. It ia in line with the experimental finding of Lugo et al. [6].

Kinetics calculation

The conventional transition state theory (CTST) [18] and Eckart's tunneling correction [19] were used to calculate the rate coefficient values for various reaction channels spanning the 250–450 K temperature range using the following formula. 

k= sGTkBTh Q‡TSQR exp-ΔERT                              (3)

The s represents symmetry factor whereas tunneling correction factor at temperature T is represented by the symbol G(T). The total partition functions (per unit volume) for the reactants and transition states are denoted by Q_R and

,, respectively. R stands for the universal gas constant, k_B for the Boltzmann constant, h for Planck's constant, and DE for the barrier height incorporating zero point energy correction. The value of symmetry factor for reaction channels (1-2) has been taken as 3 and 2, respectively. The tunneling correction factor for two reaction channels at 298 K is found to be 2.54 and 2.89, respectively. The obtained rate coefficients in the temperature range of 250 – 450 K for reaction pathways (1–2) are recorded in Table 4. At 298 K, our calculated rate constants for TS1 and TS2 were found to be 6.96×10^-13 and 6.47×10^-12 cm³ molecule^-1 s^-1 respectively at M06-2X/6-31+G(d,p) level of theory. The computed overall k_Cl value at 298 K is found to be 7.17´10^-12 cm³ molecule^-1 s^-1 for TFP with Cl reaction. Our calculated rate constant for the reaction of TFP with Cl radical is in good agreement with the reported value of 7.4 ´10^-12 cm³ molecule^-1 s^-1 at (298 ± 2) K by Lugo et al. [6] The percentage branching ratios for each of the reaction channels determined at 298 K are found to be 9.72 and 90.28 %, respectively. From these results, it can be emphasize that the hydrogen abstraction from the -CH₂ group is kinetically more advantageous than the other reaction pathway i.e. abstraction from –CH₃ group.

Atmospheric lifetime

In general, tropospheric lifetime (τ_eff) of TFP can be estimated by assuming that its removal from troposphere occurs only through the reactions with Cl atoms.  Then (τ_eff) can be expressed as [20],

τ_eff = τ_Cl

where, τ_Cl = (k_Cl × [Cl])^-1. Using the 298 K value of k_Cl = 7.17×10^-12 cm³ molecule⁻¹ s⁻¹ and the global average atmospheric Cl concentrations of 1.0 ×10⁴ molecule cm^-3 [21], the estimated atmospheric lifetime of  TFP is found to be 161.68 days.

CONCLUSIONS

In summary, the present study provides a comprehensive potential energy surface and rate constant data for the atmospheric and environmental consequence of TFP molecule initiated by Cl radical by employing M06-2X/6-31+G(d,p) level of theory. We have done various inquires involving the optimization of structural parameters, energy profiles, thermochemistry, and kinetics of the TFP with Cl radical. For that, we have identified two reaction channels which follow an indirect path through the formation of pre- and post- reaction complexes on the potential energy surface. All rate constants, computed by canonical transition state theory are in reasonable agreement with the limited experimental data. The thermal rate constant for the H atom abstraction of TFP by Cl radical is found to be 7.17×10^-12 cm³ molecule^-1 s^-1 at 298 K. The calculated branching ratios for two reaction channels are found to be 9.72 % and 90.28 % respectively at 298 K. Our results suggest that hydrogen abstraction from the -CH₂ group is likely the dominant route for Cl-initiated oxidation of TFP under reaction conditions. The atmospheric lifetime for TFP molecule is estimated to be 161.68 days.

CONFLICTS OF INTEREST

The authors declare no conflicts of interest.

ACKNOWLEDGMENTS

The authors acknowledge financial support from the Department of Science and Technology, New Delhi in the form of project under DST-SERB CRG scheme (CRG/2023/002561).

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