Introduction

It is well known fact that hydrofluoroethers (HFEs) are designed and widely recommended as a third generation replacement for chlorofluorocarbons (CFCs), hydrofluorocarbon (HFC) and hydrochlorofluorocarbon (HCFC) in industrial applications [1-2]. C₄F₉OCH₃ (HFE-7100), C₄F₉OC₂H₅ (HFE-7200) and C₇F₁₅OC₂H₅ (HFE-7500) are classified as Segregated hydrofluoroethers i.e. ethers with fluorocarbon on one side of the oxygen atom and hydrocarbon on the other. C₄F₉OCH₃ (methoxynonafluorobutane) is commercially available as trade name of HFE-7100 and finds its industrial applications like cleaning electronic equipment, secondary refrigerant and carrier fluids for lubricant. Due to its lower global warming potential HFE-7100 has been proposed to replace FC-72 (C₆F₁₄) [3]. They are also being used as fluorous solvents for the chemical processing of organic electronic materials [4]. By employing relative rate technique Wallington et al. [5] reported a rate constant of 1.2×10^-14 cm³ molecule^-1 s^-1 at 295 K for reaction of HFE-7100 with OH radicals. Subsequently, Cavalli et al.[6] performed another experimental study and reported a significantly lower rate constant value of (7.2 ± 1.6) ×10^-15 cm³ molecule^-1 s^-1 at 295±3 K. Bravo et al.[7] experimentally studied the temperature dependence of n- C₄F₉OCH₃ + OH reaction over the temperature range of 288-368 K and reported the value of (1.49 ± 0.13) 10^-14 cm³ molecule^-1 s^-1. Wallington et al.[5] and Aranda et al.[8] experimentally measured studied Cl-initated hydrogen abstraction of HFE-7100 and reported a rate constant values as k(Cl + n-C₄F₉OCH₃) = (${2.32}_{-0.41}^{+0.46}$9.7±1.4) 10^-13 and k(Cl + n-C₄F₉OCH₃) = (${2.32}_{-0.41}^{+0.46}$1.43 ± 0.28) 10^-13 cm³ molecule^-1 s^-1 at 298 K, respectively. Recently, Mishra et al. [9] reported the rate constant for the atmospheric reaction of n-C₄F₉OCH₃ with OH and Cl radicals and also explored the fate of alkoxy radicals using DFT method.

To the best of our knowledge, the mechanism and kinetics of the reaction between HFE-7100 and HO₂ & NH₂ radicals have not yet been investigated both theoretically and experimentally. Due to the lack of rate constant, the reaction of HFE-7100 with HO₂ & NH₂ radicals should be researched fully and carefully. Therefore, the PES characterizing the HFE-7100 +HO₂/ NH₂ reaction has been theoretically figured out in the present work. In present work, we have studied the mechanism and kinetics of H-abstraction reaction from HFE-7100 with HO₂ and NH₂ radicals using DFT methods. Our calculations suggest that only one reaction channel is feasible for n-C₄F₉OCH₃ + HO₂/NH₂ reactions as given below.

n- C₄F₉OCH₃ + HO₂ n- C₄F₉OCH₂ + H₂O ₂ (1)

n- C₄F₉OCH₃ + NH₂ n- C₄F₉OCH₂ + NH₃ (2)

Computational methods

All electronic structure computations were carried out using the Gaussian 09 software package [10]. Density functional theory (DFT) calculations were performed employing the M06-2X hybrid functional [11] in conjunction with the 6-311++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 [12-17]. 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 [18] 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/6-311++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/6-311++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 (12) 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 reaction channel 2 is more thermodynamically viable. Because Δ_rH^°₂₉₈< 0, the results also show that reaction channel 2 is exothermic in nature.

The reaction channels (1 2) proceed with pre-reactive complexes (RC1 and RC2) in the entrance channel for while for the exit channel product complexes, referred as PC1 and PC2 were also obtained before the formation of final products. The electronic structure of the optimized geometry of the reactants, products, reaction complexes, product complexes and transition states obtained at the M06-2X/6-311++G(d,p) level are shown in Fig. 1. Hydrogen abstraction by HO₂ radical corresponding to reaction channel (1), visualization of the electronic structure of optimized geometry of TS1 revealed that the breaking CH (C2 H14) bond length is elongated from 1.090 to 1.370 Å along with shrinkage of CO bond from 1.437 to 1.395 Å. Similarly, for transition state TS2 corresponding to reaction channel 2, the length of the breaking CH bond (C2 H14) is found to be elongated by 17.79% than the observed CH bond length in isolated HFE-7100 molecule whereas the CO (C2 O3) bond is shortened to 1.416 to 1.437 Å than the CO bond length in isolated HFE-7100 molecule. Table 2 presents the results of the harmonic vibrational frequency calculation at the M06-2X/6-311++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 revealed no imaginary frequency (NIMAG=0). The C2–H14 and O19–H14 stretching modes are represented by the imaginary frequency of TS1 for reaction channel (1), which is 1792 cm¹. This also shows a considerable curvature in the potential energy surface (PES) surrounding the transition state.‬ The imaginary frequency for transition state corresponding to the hydrogen abstraction by NH₂ radical is found to be 1849 cm¹, which corresponds to the stretching modes for hydrogen transfer reaction C2–H14 and N19–H14.

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 [18] 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 Fig. 2. Table 3 summarizes the energy of each optimized geometry obtained during present study, at M06-2X/6-311++G(d,p), level of theory. In order to compute zero-point energy (ZPE) for stationary points, we have performed frequency calculation at the M06-2X/6-311++G(d,p) level of theory. Zero-point energy (ZPE) thus obtained were corrected with a scale factor of 0.967 [19] and the total energies of each species were calculated on potential energy surface. Fig. 3 shows a schematic potential energy profile of HFE-7100 reactivity with the HO₂ and NH₂ radicals using zero-point energy (ZPE) corrections. The ground state energy of HFE-7100 + HO₂/NH₂, 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 19.41 and 9.18 kcal mol¹, respectively. From these results, it can be emphasize that the hydrogen abstraction by NH₂ radical is more facile than the hydrogen abstraction by HO₂ radical.

Kinetics calculation

The conventional transition state theory (CTST) [20] and Eckart's tunneling correction [21] were used to calculate the rate coefficient values for various reaction channels spanning the 250–450 K temperature range using the following formula.

The represents symmetry factor whereas tunneling correction factor at temperature T is represented by the symbol (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 E for the barrier height incorporating zero point energy correction. The value of symmetry factor for reaction channels (12) has been taken as 3. 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 constant for TS1 and TS2 were found to be 4.09×10²⁹ and 1.79×10¹⁸ cm³ molecule¹ s¹ respectively at M06-2X/6-311++G(d,p) level of theory. The results in this study are very important to understand the mechanism and kinetics of the atmospheric reactions of HFE-7100 with other species such as NH₂, CH₃, etc. They will help researchers in working with various experiments related to this species in the future.

Conclusions

The mechanism and kinetics, as well as thermodynamics of the atmospheric reaction of HFE-7100 with HO₂ & NH₂ radicals have been investigated based on the quantum chemical theory. The DFT method in conjunction with the basic set 6-311++G(d,p) has been employed to optimize for the species related in this reaction, such as reactants, intermediate states, transition states, and products. Single-point energies for all species on the potential energy surface has been calculated using M06-2X/6-311++G(d,p) level. The reaction channel follows an indirect path through the formation of pre- and post- reaction complexes on the potential energy surface. The thermal rate constant for the H atom abstraction of HFE-7100 by HO₂ and NH₂ radical is found to be 4.09×10²⁹ and 1.79×10¹⁸ cm³ molecule¹ s¹ at 298 K. Our results suggest that hydrogen abstraction by NH₂ radical is likely the dominant route for the atmospheric oxidation of HFE-7100 under reaction conditions.

Acknowledgments: BKM acknowledges financial support from the Department of Science and Technology, New Delhi in the form of project under DST-SERB CRG scheme (CRG/2023/002561).

Conflict of Interest- The Authors declare no conflict of interest.

Data Availability- Data sharing is not applicable to this article.

Funding Declaration- The research presented in the article does not receive external funding from grants, agencies, or organizations.

AI Usage Declaration- No generative AI tools were used in the preparation of this manuscript.

Author's Contribution- Conceptualization: NP & NKG; Methodology, BKM and DD;

Writing, review & editing, all authors. All authors have read and agreed to the published version of the manuscript.

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Table1 Thermochemical data for reaction channels (12) calculated at M06-2X/6-311++G(d,p) level of theory. All values are in kcal mol^-1.

Table 2 Harmonic vibrational frequencies of reactants, transition states and products at M06-2X/6-311++G(d,p) level of theory.

Table 3 Relative energies (in kcal mol¹) with zero-point energy correction for the reactants, reaction complexes, transition states, product complexes and products at M06-2X/6-311++G(d,p) level of theory.

Table 4: Rate constants of different reaction channels and overall rate constant (in cm³ molecule¹ s¹) within the temperature range of 250450 K at M06-2X/6-311++G(d,p) level of theory.

Fig. 1: Optimized geometry of reactants, reaction complexes, transition states, product complexes and products obtained at M06-2X/6-311++G(d,p) level of theory. Bond lengths are in angstroms.

Fig. 2: IRC plots performed for transition states TS1 and TS2 obtained at M06-2X/6-31!++G(d,p) level of theory.

Fig. 3: Potential energy diagram for the reaction of HFE-7100 with HO₂ and NH₂ radicals at M06-2X/6-311++G(d,p) level of theory.