The molecular level study of the fate of the CH3CH2C(O)OCH(O)CH3 radical derived from ethyl propionate

ABSTRACT A quantum chemical study has been presented on the decomposition of CH3CH2C(O)OCH(O • )CH3 which is derived from ethyl propionate (CH3CH2C(O)OCH2CH3) using the M06-2X/6-31 + G(d,p) level of theory. The thermal decomposition of CH3CH2C(O)OCH(O • )CH3 is essential to understand the chemistry of combustion of ethyl propionate. Here, the decomposition and oxidative pathways, bond fission and alpha ester rearrangement of CH3CH2C(O)OCH(O • )CH3 have been explored. We have obtained transition states for the different pathways and further verified each transition state by performing intrinsic reaction coordinate (IRC) calculations. The density of state spectra (DOS) was calculated using GaussSum software. The single-point energy calculations are performed at the same function but using larger basis sets such as 6-311++G(d,p) and 6-311++G(3df,2p). We have shown all stationary points and transition states involved in reaction pathways on the potential energy surface (PES) diagram and also discussed the thermochemistry of each reaction pathway. The thermal rate constants of various channels in the decomposition of CH3CH2C(O)OCH(O • )CH3 are determined using the Conventional Transition State Theory (CTST) in the temperature range of 250–450 K and 1atm. From PES, thermochemistry and kinetics analysis, we found that α-ester rearrangement produces propionic acid, which is dominant over the oxidative pathway for the decomposition of CH3CH2C(O)OCH(O • )CH3.


Introduction
During the past decade, it has been globally recognised that biodiesels are a replacement for petroleum-derived diesel fuels as they have similarities in physical properties and concerns about climate change [1][2][3]. These are mainly obtained from vegetable oils or animal fats as a result of the transesterification process. The extensive use of fatty acid alkyl esters in diesel blends will emit into the atmosphere. Ethyl propionate (CH 3 CH 2 C(O)OCH 2 CH 3 ) is a model for studying the fatty acid ethyl esters which are used as the first-generation biodiesel. The tropospheric chemistry of ethyl propionate was explored by Andersen et al. [4] and the fates of alkoxy radicals are discussed. Cl-initiated oxidation of ethyl propionate was investigated by Andersen et al. [4]. The general mechanism of tropospheric degradation of ethyl propionate is given in Scheme 1.
The H-abstraction from the −OCH 2 − group of ethyl propionate generates CH 3 CH 2 C(O)OCHCH 3 alkyl radical which further reacts with molecular oxygen to give peroxy radical CH 3 CH 2 C(O)OCH(OO • )CH 3 . This peroxy radical reacts further with NO in the atmosphere leading to the formation of alkoxy radical CH 3 CH 2 C(O)OCH(O)CH 3 . Three loss processes for the fate of this radical were identified: oxidative pathways (reaction with O 2 ) to form CH 3 CH 2 C(O)OC (O)CH 3 , α-ester rearrangement to produce propionic acid and decomposition to produce propionic formic anhydride and methyl. It is reported that the formation of propionic acid that can be regenerated by α-ester rearrangement but we cannot neglect the contribution of oxidative pathways and thermal decomposition. Thus, the atmospheric insight of CH 3 CH 2 C(O)OCH(O • )CH 3 is needed to understand its role in the atmospheric chemistry of ethyl propionate. To provide a more comprehensive understanding of ethyl propionate chemistry, this study was performed to elucidate the dissociative pathways of CH 3 CH 2 C(O)OCH(O • )CH 3 . In this work, reaction pathways considered for the decomposition of CH 3-CH 2 C(O)OCH(O • )CH 3 include oxidative pathways, direct bond fission and α-ester rearrangement as represented below: Based on previous experimental and theoretical studies [5][6][7][8][9][10][11][12][13][14][15][16][17], it has been established that alkoxy radicals act as intermediates in the atmospheric oxidation of halogenated hydrocarbons. Reisi-Vanani and Hoseinpour [16] reported the five important pathways for the decomposition and reactivity of C 3 F 7 OCH 2 O investigated B3LYP and B3PW91 methods.
They concluded that the reaction with atmospheric O 2 is a dominant pathway for OH in the consumption of the C 3 F 7-OCH 2 O radical in the atmosphere. In another study [17], Orlando reported the atmospheric fate of C 2 H 5 -O-CH (O)CH 3 radical derived from the Cl atom-initiated oxidation of diethyl ether and concluded that decomposition via C-C bond cleavage is the major fate of thermalised 1-ethoxyethoxy radical, CH 3 CH 2 OCH(O)CH 3 , throughout the troposphere. Ferenac et al. [18] reported computational studies of the unimolecular pathways for a series of six oxygenated alkoxy radicals and proposed that the reaction with O 2 will be the sole atmospheric fate of CH 3 CH 2 OCH 2 O and CH 3 C(O)CH 2 CH 2 O. By using theoretical methods, Somnitz [19] derived rate coefficients for the unimolecular reaction pathways of 1-butoxyl and 2-pentoxyl radicals, which can undergo 1,5 H-shift isomerisation reactions. Somnitz and Zellner [20] reported the theoretical studies of unimolecular reactions of ethoxy, 1butoxy, 2-butoxy and 2-pentoxy radicals considering C-C bond decomposition and isomerisation reactions. Zhao et al. [21] performed a kinetic study for the chlorine-initiated oxidation of ethyl format using the B3LYP/6-31G(d,p) level. The α-ester rearrangement and reaction with O 2 are the competitive pathways for the decomposition of alkoxy radical HC (O)OCH(O)CH 3 . Rayez et al. [22] reported the energy barrier for α-ester rearrangement and C-C bond scission to be 6.1 and 13.5 kcal mol, respectively for structurally similar species CH 3 C(O)OCH(O)CH 3 at B3LYP/6-31G(d,p) level of theory. In a previous study [23], the potential energy profile and kinetic data for the thermal decomposition and oxidation of CF 3 C (O)OCH(O)CF 3 radical investigated on the G2(MP2)// MPWB1K/6-31 + G(d,p) level of theory.

Computational and kinetic details
All computational investigations involved in this work are performed with the Gaussian 09 suite of the program [24]. DFT investigations are carried out using the M06-2X functional [25] combined with the Pople basis set 6-31 + G(d,p). The M06-2X is a hybrid meta-DFT functional with a high percentage (54%) of Hartree-Fock exchange. This functional gives better thermochemistry and kinetic result and utilised in various previous theoretical studies [26][27][28][29][30][31]. Frequency calculations of all optimised species were further performed at the same level of theory. All the stable species were identified by real and positive frequency values, while the transition state was identified by only one negative frequency. Intrinsic reaction coordinate (IRC) calculations [32] are performed for TS to check the connectivity of TS with reactant and productlike structures. To get more reliable energies for all the species, we performed single-point energy calculations of all the species at the same DFT functional using 6-311++G(d,p), 6-311++G(3df,2p) and aug-ccpVTZ larger basis sets. In addition to this, to validate the accuracy of the structure and energies of the stationary points, calculations are also carried out using the density functional theory method B3LYP [33,34] with the 6-311G(d,p) level.
where Γ(T) is the tunnelling correction factor at temperature T. It is calculated using Eckart's unsymmetric barrier method [36,37]. Q ‡ TS and Q R represent the total partition function (per unit volume) for the transition states and reactants, respectively, which were obtained at the M06-2X/6-31 + G(d,p) level of theory. ΔE is the barrier height including zero-point energy correction. In the present work, the kinetic rate coefficients for reaction pathways (1 − 5) were performed through the Kinetic and Statistical Thermodynamical Package (KiSThelP) programme [38]. The tunnelling correction factor at 298 K is 105.33, 1.81, 1.37, 3.72 and 1.17 for TS1, TS2, TS3, TS4 and TS5, respectively.

Structure, frequency and thermochemistry analysis
First of all, we optimised the alkoxy radical at the M06-2X/6-31 + G(d,p) level of theory and then scanned the molecule with the dihedral angle (C2-O5-C3-C11) to get the most stable conformers. Figure 1(a) depicts the scan plot of the total energy of different conformers with a dihedral angle. Among the various conformers, the most stable conformer of alkoxy radical, as shown in Figure 1(b), having the lowest energy of −421.411 Hartree is considered for a detailed study. The density of state (DOS) spectra of alkoxy radical calculated using Gauss-Sum software [39] is recorded in Figure 1. Electronic structures of all species involved in decomposition and oxidative pathways along with transition states as given in scheme 1 are optimised at the M06-2X/6-31 + G(d,p) level of theory. The optimised geometries of alkoxy radical and transition states are depicted in Figure 2 while those of other products are given in Figure S1 of supporting information. We have also provided bond parameters (in Å) of all optimised species. The optimised geometries in Cartesian Coordinates of alkoxy radicals, transition states and products obtained at the M06-   Table S2 of supporting information. The reactants and transition states are also optimised at the B3LYP/6-311G(d,p) level of theory and corresponding results are shown in Figure S2 of supporting information.
For the oxidative pathway, i.e. CH 3 H6) of the -CHO site was elongated and it was 1.279 Å, while the equilibrium bond distance of the C-H bond distance was 1.102 Å. So the percentage elongation of the C-H bond was 16.06%. In the R2 decomposition pathway, the structure of transition state TS2 for alpha ester rearrangement is a five-membered ring, as depicted in Figure  2. When the H6 atom of the -CHO site approaches the O4 atom of the -CO site in TS2, the bond distance between O4 and H6 was 1.304 Å, while the bond distance of the C-H bond of -CHO was 1.312 Å. Here C-H bond elongation was 19.05%. In TS2, we also observed the breaking distance C3-O5 increases up to 1.757 Å compared to the equilibrium C3-O5 bond distance which was 1.434 Å in CH 3 CH 2 C  The harmonic vibrational frequency calculations of all optimised species (done at the M06-2X/6-31 + G(d,p) level of theory) have been further performed at the same level of theory to obtain various modes of vibration frequency, zero-point energy and thermo-chemical data which are helpful to provide detail information of reaction species and reaction pathways.
The frequency values of all species are displayed in Table S1 of supporting information which reveals that all the stable species have a positive value of frequency, while the transition state has only one negative frequency value. The value of negative frequency is 1695i, 740i, 547i, 1042i and 304i cm −1 for TS1, TS2, TS3, TS4 and TS5, respectively at M06-2X/6-31 + G(d,p) level and 1079i, 312i, 448i, 972i and 252i cm −1 for TS1, TS2, TS3, TS4 and TS5, respectively at B3LYP/6-311G (d,p) level. Visualisation of the normal mode corresponding to the calculated imaginary frequencies shows a well-defined transition state geometry connecting reactants and products during the transition. To further apprehend the presence of the saddle point, Intrinsic Reaction Coordinate (IRC) calculations were carried out at the same level of theory which clearly authenticates a smooth transition from reactants to products along the potential energy surface. The IRC plot obtained from IRC calculations for TS1 (oxidative pathway) is shown in Figure 3 while for other TSs (TS2, TS3, TS4 and TS5), we have shown it in a single IRC plot in Figure 4. These IRC plots clearly showed a smooth transition from reactants to products on the potential energy surface.
Moreover, we have calculated the reaction enthalpies and free energies for reaction channels (R1 − R5) at M06-2X/6-31 + G(d,p) level of theory and results are reported in Table 1. The thermodynamic data reveal that three reactions (R1-R3) are thermodynamically feasible due to their exergonic (ΔG < 0) nature. Moreover, these results also indicate that reaction channels R4 and R5 are thermodynamically not favourable which proceed with high endothermicity along with a positive free energy change.

Energetics and kinetics
Single-point energy calculations for reactants and transition states involved in the decomposition pathways (R1-R5) were also performed using larger basis sets incorporating polarised, diffused and correlation-consistent basis sets using optimised geometries at the M06-2X/6-31 + G(d,p) level. These calculated energies are corrected for zero-point energy with a correction factor of 0.967 [40]. To ascertain the accuracy of the M06-2X results, we have also performed single-point energy calculation for reaction channels (1)(2)(3)(4)(5) at the B3LYP method  Table 2. This reveals that the energy barrier for the H-abstraction reaction of CH 3 CH(O)C (O)OCH 2 CH 3 with O 2 is in the range of 18-19 kcal mol −1 , whereas it is in the range of 11-12 kcal mol −1 for α-ester rearrangement. The results reveal that the M06-2X /6 − 31 + G(d,p) level yields a value of 19.81 and 12.56 kcal mol −1 for hydrogen abstraction by O 2 and α-ester rearrangement pathways, respectively. On the other hand, at M06 − 2X/6 − 311+ +G(3df,2p)//M06-2X /6 − 31 + G(d,p) level yields corresponding values as 18.86 and 11.83 kcal mol −1 , respectively. Zeropoint energy was obtained by the B3LYP/6-311G(d,p) method and corrected with a scale factor of 0.962 [41]. The calculated energy barriers for oxidative pathway (TS1) and α-ester rearrangement (TS2) at B3LYP/6-311G(d,p) level are 17.98 and 10.68 kcal mol −1 , respectively. Also, from Table 2, it is observed that the energy barrier calculated at M06-2X level using different basis sets and B3LYP level significantly alters the energetics of the decomposition of alkoxy radical. While quantitatively comparing the results obtained from the above two methods for various reaction pathways, it is observed that the relative importance of these reaction pathways does not change for exchange-correlation functionals used in DFT calculations, i.e. the favourable reaction path obtained using B3LYP functional is the same in M06-2X functional also. It is obvious from Table 2 that the barrier height for α-ester rearrangement is considerably lower than that for other decomposition pathways. Thus, it may be concluded that the α-ester rearrangement producing propionic acid will be the dominant pathway for this alkoxy radical in the atmosphere which is in good agreement with the experimental findings of Andersen et al. [4].
A schematic potential energy profile of the unimolecular decomposition and reactivity of alkoxy radical obtained at the M06 − 2X/6 − 311++G(3df,2p)//M06-2X /6 − 31 + G(d,p) level with zero-point energy (ZPE) corrections is plotted in Figure 5. In the construction of the energy diagram, zeropoint energy corrected total energy has been utilised. These energies are plotted with respect to the ground state energy of CH 3 [23].
The calculated rate constants in the temperature range of 250-450 K for reaction pathways (R1-R5) are recorded in Table 3. The rate constant for oxidation reaction occurring via reaction (R1) is 5.49 × 10 −21 at 298 K, while the rate constant for α-ester rearrangement via reaction 2 involving TS2 as the transition state yielded a value of 9.88 × 10 3 s −1 at M06-2X/6-311++G(3df,2p)//M06-2X//6-31 + G(d,p) level. The rate constant for thermal decomposition via C − C bond cleavage (pathway R3) involving TS3 as the transition state yielded a value of 1.94 × 10 2 s −1 at 298 K and 1 atm. A similar calculation was performed for C − H bond cleavage that occurred via TS4 yielding the rate constant 3.08 × 10 −3 s −1 at 298 K and 1 atm. The obtained rate constant for the decomposition channel involving C -O bond cleavage (TS5) at 298 K and 1 atm was 1.62 × 10 −6 s −1 . Our results for rate constant calculation reveal that the oxidative pathways are poorly kinetic driven. The rate constant calculated in the temperature range of 250-450 K shows that the decomposition and reactivity of CH 3 CH 2 C(O)OCH(O • )CH 3 radical increase with temperature and the α-ester rearrangement is the dominant pathway for the degradation of CH 3 CH 2 C(O)OCH(O • )CH 3 radical in the atmosphere. In the atmosphere, the alkoxy studied here is produced from the tropospheric degradation of ethyl propionate initiated by OH radical. In the lower troposphere, the fate of CH 3 CH 2 C(O)OCH(O • )CH 3 radical may decompose via α-ester rearrangement leading to the production of propanoic acid CH 3 CH 2 C(O)OH and CH 3 C(O) radical. CH 3 C(O) radical may react with O 2 to form CH 3 C (O)OO, which may further react with NO 2 to form CH 3 C (O)OONO 2 . The second possibility of this CH 3 C(O)OO peroxy radical is that the reaction with NO produces CH 3 and CO 2 . We could not find any experimental or theoretical data available in the literature to make a comparison with the calculated values obtained during the present investigation. We expect that the present study may provide useful information for future laboratory investigations.

Conclusions
Oxidation and decomposition reaction pathways, thermochemistry and kinetics for CH 3 CH 2 C(O)OCH(O • )CH 3 radical (which is produced from ethyl propionate) have been investigated using the DFT method at M06-2X functional along with 6-31 + G(d,p) basis set. We further refined the energy of all optimised species using 6-311++G(d,p) and 6-311++G (3df,2p) large basis sets. At M06-2X/6-311++G(3df,2p)//M06-2X/6-31 + G(d,p) level of theory, the energy barriers for the channels R1-R5 are 18.86, 11.83, 12.80, 20.79 and 24.52 kcal mol −1 , respectively. The thermal rate constant (at 298 K.) for the dominant pathways via reaction channel (R2) is 9.88 × 10 3 at M06-2X/6-311++G(3df,2p)//M06-2X/6-31 + G(d,p) level. Our results reveal that the most dominant decomposition pathway for CH 3 CH 2 C(O)OCH(O • )CH 3 radical is α-ester rearrangement producing propionic acid that occurs with the lowest barrier height. The rate constants in the range of 250-450 K were also obtained. The results showed that decomposition and reactivity rate increase with increasing temperature. This conclusion is in line with the experimental and theoretical studies for other structurally similar alkoxy radicals.  Note: The unit of the rate constant is s −1 except for TS1 which is in cm 3 molecule −1 s −1 .