Theoretical study on the reactions of C2H5 with CnH2n+1OH (n = 1 - 4): Predicted rate constants and branching ratios

The mechanisms of the reactions of C 2 H 5 with C n H 2n+1 OH (n = 1-4) have been investigated by CCSD(T)//B3LYP/6-311++G(3df,2p) for n = 1 - 3 and CCSD(T)//B3LYP/6-311+G(d,p) for n = 4. Our chemical quantum results show that the C 2 H 5 + CH 3 OH reaction can take place via H-abstraction or substitution channels. The former is the major channel with barrier energies of 13.0 and 14.4 kcal/mol while the latter has to pass over much higher barriers of 42.2 – 52.3 kcal/mol. Similarly, the C 2 H 5 + C n H 2n+1 OH (n = 2 - 4) reactions can mainly occur via H-abstraction channels with barrier energies of 10.4 - 16.4 kcal/mol. The b-H abstraction channel has the lowest barrier energy (11.7 kcal/mol) for t-C 4 H 9 OH while o/a-H abstraction channels have the lowest barrier energies (10.4 - 13.0 kcal/mol) for the others. The rate constants and product branching ratios for individual channels as well as total rate constants have been calculated for the temperature range 300-2500 K by TST theory with Eckart tunneling corrections. The optimized geometries of the related species and predicted heats of reactions agree well with available data.


Introduction
Alcohol fuels (C n H 2n+1 OH, n = 1-4) are recognized as the most promising renewable energy resources [1][2][3][4][5][6][7][8][9]. Methanol (CH 3 OH) can be used in an internal engine via combustion or in a fuel cell. Ethanol (C 2 H 5 OH) is widely used; a large amount of ethanol is used in gasoline engines as an engine fuel such as E10 (i.e., a fuel blend of 10% C 2 H 5 OH and 90% gasoline), E15 (15% C 2 H 5 OH), E85 (85% C 2 H 5 OH), etc. n-Propanol (n-C 3 H 7 OH) and isopropanol (i-C 3 H 7 OH) are potential fuel additives. n-Propanol has a higher heating value than ethanol; isopropanol can readily be used as a fuel for existing engines. Butanols (n/i/s/t-C 4 H 9 OH) may be second-generation biofuel potential biofuels because they do not suffer from the drawbacks as ethanol does. The favorable characteristics of C n H 2n+1 OH (n = 1-4) have led to an increasing number of studies investigating theirs use as a transportation fuel. Speci cally, there are many papers concerned C n H 2n+1 OH (n = 1-4) such as determining the structure of the molecules, vibrational frequencies, and heats of formation [10][11][12]; both experimental and theoretical papers concerning thermal decompositions of C n H 2n+1 OH (n = 1-4) at high-temperatures in the internal engines via combustion [13][14][15][16][17][18][19], or their reactions with various atoms and radicals existed in combustion gas, such as H, OH, CH 3 , etc [20][21][22][23][24][25][26][27][28][29][30][31]. The experimental studies by different techniques report their branching ratio and total rate constants at some speci c conditions while the theoretical studies proposed the mechanisms and kinetics results at wide-range conditions, especially experimental di culty in evaluating the branching fractions mainly arises from the contributions of the secondary reactions. Theoretically, the reactions can occur by various mechanisms including H-abstraction, insertion, and substitution reactions. For example, in the reactions of C 2 H 5 OH with CH 3 radical, Lin et al. [21] proposed that the methyl radical can abstract H atoms in the OH, CH 2 , and CH 3 groups and substitute OH, CH 3 groups in the C n H 2n+1 OH (n = 1-4) molecule. Using the quantum calculations at G2M level of theory, they concluded that the H abstraction channels are more favored than the latter. Based on the predicted potential energy surface, they calculate rate constants and branching ratios for the H-abstraction reactions; their kinetics results are close to the available experiment.
Besides, ethyl radical (C 2 H 5 ) is another important free radical in combustion and atmospheric and environmental chemistry [32][33][34]. Ethyl radical can be formed in the oxidation of natural gas which composes mostly of methane and ethane; for example, ethane can react with O 2 giving C 2 H 5 as [33]: C 2 H 6 + O 2 → C 2 H 5 + HO 2 . It can also be generated when a large hydrocarbon radical decomposes into smaller radicals including ethyl and methyl radicals. C 2 H 5 radical is considered as the simplest alkane radicals which can show oxidation features of big alkane radicals [27]. Therefore, its reactions have been attracted much interest, both experimental and theoretical such as reactions of C 2 H 5 with O 2 , HO 2 , NCO, etc. [34][35][36][37][38].
However, the reactions of C 2 H 5 with C n H 2n+1 OH (n = 1-4) in combustion gas and atmosphere have not been elucidated yet in both mechanisms and kinetics. The present work aims are to elucidate the mechanism for the title reaction through a comprehensive and accurate quantum chemical calculation and to predict the kinetics of individual product channels employing transition state theory with appropriate quantum-mechanical tunneling corrections for combustion applications.

Computation Methods
All structures involved the C 2 H 5 + C n H 2n+1 OH (n = 1 -4) reactions have been fully optimized by the DFT-B3LYP method [39,40] excluding the transition state TS39 (see later) along with 6-311++G(3df,2p) and 6-311+G(d,p) basis sets for n = 1 -3 and n = 4, respectively. Vibrational frequencies predicted at the same level of theory as the optimizations have been used for the rate constant calculations as well as zeropoint energy (ZPE) corrections. They have also been employed for the determination of the optimized structures, in which the reactants (C 2 H 5 and C n H 2n+1 OH (n = 1 -4)) and products possessed all positive vibrational frequencies, whereas each transition state (TS1-TS39) has only one imaginary frequency. To get more reliable energies for all the species, we performed higher-level single-point energy calculations with the CCSD(T) method [41,42] and the same basis sets based on the B3LYP optimized geometries.
The total energy of a species is the sum of the corresponding single-point energy by the CCSD(T) method with the ZPE corrections. All the ab initio calculations have been performed using the Gaussian 09 collection of programs [43].
The rate constants for individual channels of the title reactions have been calculated using the transition state theory (TST) [44] including Eckart tunneling effects [45] in the temperature range of 300 -2500 K. In the TST calculations, the k TST for each channel has been estimated as follows: Where E TS and E A+B are potential energies of the TS (transition state) and A+B (reactants); Q A , Q B , and Q TS are partition functions of the A, B, and TS; σ, k B , T, h, and N A are symmetry number, Boltzmann's constant, the temperature, the Planck's constant, and Avogadro's number, respectively. All the kinetics calculations have been performed with the Multiwell code [46]; the rate constants for individual channels as well as total reactions have been used to t a modi ed Arrhenius equation for and presented in Tables 2 and S1 in the electronic supporting information (ESI). Table 2 Arrhenius parameters [k(T)= AT n e -E/RT ] for the C 2 H 5 + C n H 2n+1 OH (n = 1, 2) reactions.
The reaction of C 2 H 5 + n/i-C 3 H 7 OH: For the C 2 H 5 + n-C 3 H 7 OH system, there are four reaction channels as clearly shown in Figure S2a: the  Figure S2b). It is noticed that the energy barrier for the α-H abstraction (TS21) is only 10.4 kcal/mol which is the lowest energy barrier among the C 2 H 5 + C n H 2n+1 OH (n = 1 -4) reactions because of the effect of the two CH 3 groups and OH group in i-C 3 H 7 OH molecule.
This barrier is also lower ~ 2 -6 kcal/mol than the others at TS22 (12.7 kcal/mol) and TS23 (16.4 kcal/mol) suggesting that the α-H abstraction channel should be the major channel in the C 2 H 5 + i- The reaction of C 2 H 5 + n/i/s/t-C 4 H 9 OH: For the C 2 H 5 + n/i/s/t-C 4 H 9 OH systems, we calculate with a smaller basic set at the CCSD(T)//B3LYP/6-311+G(d,p) level of theory because of their large systems. For the C 2 H 5 + t-C 4 H 9 OH reaction, Figure S2 shows kcal/mol) also agrees well with those for n/i/s-C 4 H 9 OH with the values of 15.6-16.0 kcal/mol (see Fig. 3S in the ESI). It is noticed that TS39 is the unique species in the title reactions optimized at the BHandHLYP/6-311+G(d,p) level because we cannot nd it at the B3LYP/6-311+G(d,p) level of theory. Its relative energy, therefore, is calculated from energies of TS39, t-C 4 H 9 OH, and C 2 H 5 species at the CCSD(T)//BHandHLYP/6-311+G(d,p) level. The C 2 H 5 + i-C 4 H 9 OH reaction has four channels including o-H, α-H, β-H, and γ-H abstractions in which the lowest energy barrier is the β-H abstraction (TS31, 11.7 kcal/mol) because of the effect of the two CH 3 groups in the i-C 4 H 9 OH molecule. Energy barriers for the o-H, α-H, and γ-H abstraction channels in the C 2 H 5 + i-C 4 H 9 OH reaction, 12.6, 12.3, and 15.6 kcal/mol at TS29, TS30, and TS32, respectively, also agree well with the corresponding values at 12.9, 12.1, and 15.8 kcal/mol for n-C 3 H 7 OH + C 2 H 5 reaction as discussed above. For the reactions of the C 2 H 5 radical with n/s-C 4 H 9 OH, Figure S2 shows that there are ve channels in which the o-H and α-H abstraction channels have lowest the barrier energies. The o-H abstractions occur via TS24 and TS33 lying 12.6 above the reactants for both n-C 4 H 9 OH and s-C 4 H 9 OH, respectively. The α-H abstractions are slightly lower than those for o-H abstractions with relative energies of 11.9 and 11.0 kcal/mol for n-C 4 H 9 OH and s-C 4 H 9 OH, respectively while the values for the other channels are 13.8 -16.0 kcal/mol. It is clear that the difference between the barrier energies is small suggesting that all of the channels can contribute at high temperatures.

Rate constant calculations
Based on the PES and molecular parameters of all the related species in the C 2 H 5 + C n H 2n+1 OH (n = 1 -4) reactions calculated by both the CCSD(T) and B3LYP methods as discussed above, we calculated the individual and total rate constants with TST considering Eckart tunneling effect in the temperature range of 300 -2500 K; the results are presented in Fig. 4 for the C 2 H 5 + C n H 2n+1 OH (n = 1, 2) reactions and in Fig. S4 in the ESI for the C 2 H 5 + C n H 2n+1 OH (n = 3, 4) reactions. The branching ratios calculated from the individual and total rate constants for each channel are presented in Figs. 5 and S5 for the reactions of C 2 H 5 with C n H 2n+1 OH (n = 1, 2) and C n H 2n+1 OH (n = 3, 4), respectively.
It can be seen in Fig. 4 and S4 that all the rate constants have positive temperature dependence re ecting the fact that each channel has prominent and distinct barrier energy. For the C 2 H 5 + CH 3 OH reaction, the rate constants for the substitution reactions via TS3 -TS6 is very much smaller than those for Habstraction via TS1 and TS2 for all the considered temperatures (see Figure 5a). For example, the values for the channels via TS1 and TS3 are 4.06 ⋅ 10 −16 and 1.70 ⋅ 10 −24 (cm 3 molecule −1 s −1 ) at 1000 K, respectively. Therefore, the branching ratios for the channels via TS3 -TS6 are very small with the highest value is only ~4 ⋅ 10 −3 for the channel via TS4 at 2500 K. This is because the barrier energies for these channels are much higher (> 27 kcal/mol) than those for the H-abstraction channels as discussed above. As a result, the H-abstraction channels giving PR1 (CH 3  For convenient modeling applications, the temperature dependence of the individual reaction rate constants for the title reactions given in terms of three parameters ts the form AT n exp(-E/T) expressions in the temperature range of 300 -1000 K are summarized in Table II.

Conclusions
Mechanism and kinetics for the reactions of C 2 H 5 + C n H 2n+1 OH (n = 1 -4) have been investigated for the rst time by both quantum-chemical and TST calculations. The quantum-chemical results show that the tile reactions can mainly undergo H-abstraction with barrier energies of 10.4 -16.4 kcal/mol. The rate constants and product branching ratios have been calculated for the temperature range of 300-2500 K. The predicted rate constants and branching ratios for the H-abstraction reactions have been calculated using the transition state theory with quantum-mechanical tunneling corrections for the temperature range. The kinetics results show that all the rate constants increase when temperature increases. For the C 2 H 5 + i-C 4 H 9 OH reaction, the β-H abstraction channels via barrier energy of 11.7 kcal/mol giving (CH 3 ) 2 CCH 2 OH + C 2 H 6 are dominated at all the considered temperatures. For the C 2 H 5 + t-C 4 H 9 OH reaction, there are two channels including o-H and β-H abstractions via barrier energy of 12.8 and 15.4 kcal/mol, respectively, in which the latter is more favor at high temperatures (> 1500K). For others, the α-H abstraction channels are dominated at temperatures below 500K but all of the products via H abstraction channels can contribute at a high-temperature range of 2000-2500K. The temperature dependence of the individual reaction rate constants for the title reactions is provided for further modeling applications. Our geometries and heats of reaction are in good agreement with available experimental data. Figure 1 Geometries of the reactants and products related to the C 2 H 5 + C n H 2n+1 OH (n = 1, 2) reactions. a-j The values in the parenthesis are from the literature. [10,36,[47][48][49][50][51][52][53]

Figure 2
Geometries of the transition states related to the C 2 H 5 + C n H 2n+1 OH (n = 1, 2) reactions.

Supplementary Files
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