Reaction Kinetics of Hydrogen Abstraction Reactions by Hydroperoxyl

Article pubs.acs.org/JPCA

Reaction Kinetics of Hydrogen Abstraction Reactions by Hydroperoxyl Radical from 2‑Methyltetrahydrofuran and 2,5Dimethyltetrahydrofuran Harish Kumar Chakravarty*,† and Ravi X. Fernandes†,‡ †

Physico Chemical Fundamentals of Combustion, RWTH Aachen University, Templergraben 55, D-52056 Aachen, Germany Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, Germany

‡

S Supporting Information *

ABSTRACT: Highly accurate rate parameters for H-abstraction reactions by HO2 radicals are needed for development of predictive chemical kinetic models for ignition. In this article, we report the rate coefficients for reaction of hydroperoxyl radical (HO2) with 2-methyltetrahydrofuran (MTHF) and 2,5-dimethyltetrahydrofuran (DMTHF) computed employing CBS-QB3 and CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ level of theory in the temperature range of 500−2000 K. Conventional transition state theory (CTST) with hindered rotor approximation for low frequency torsional modes and RRHO (rigid-rotor harmonic oscillator) approximation for all other vibrational modes is employed to evaluate the high pressure rate constants as a function of temperature. Rate constant of each individual hydrogen abstraction channel is taken into account to calculate the overall rate constant. Three-parameter Arrhenius expressions have been obtained by fitting to the computed rate constants of all abstraction channels between 500 and 2000 K. Eight transition states have been identified for MTHF and four for slightly more stable trans-DMTHF. Intrinsic reaction coordinates (IRC) calculations were performed to verify the connectivity of all the transition states (TSs) with reactants and products. One dimensional Eckart’s asymmetrical method has been used to calculate quantum mechanical tunneling effect. Results of the theoretically calculated rate coefficients indicate that the hydrogen abstraction by HO2 from the C2 carbon of both MTHF and DMTHF is the most dominant path among all reaction pathways attributed to its lowest barrier height. The total rate coefficients of the MTHF and DMTHF with HO2 at CCSD(T)/cc-pVTZ// B3LYP/cc-pVTZ level of theory are k(T) = 8.60T3.54 exp(−8.92/RT) and k(T)= 3.17T3.63 exp(−6.59/RT) cm3 mol−1 s−1, respectively. At both the level of theories, the predicted total abstraction rate constant for DMTHF is found to be higher as compared to that of MTHF over an entire temperature range of investigation. The overall rate constant calculated at CCSD(T)/ cc-pVTZ//B3LYP/cc-pVTZ level of theory is lower by 1.43 and 3.44 times at 2000 K than the CBS-QB3 level for MTHF and DMTHF, respectively.

1. INTRODUCTION Finding a sustainable efficient renewable energy source in place of the nonrenewable petroleum-derived liquid fuels has been one of the greatest challenges of the 21st century. The Cluster of Excellence “Tailor-Made Fuels from Biomass” at the RWTH Aachen University takes an interdisciplinary research approach toward these new synthetic fuels based on biomass feedstock. The vision of the cluster is to establish innovative and suitable processes for the conversion of whole plants into fuels that are tailor-made for novel low temperature combustion engine processes with high efficiency and low pollutant emissions, paving the way to the next generation of biomass fuels. A combination of tailor-made sustainable fuels derived from renewable raw materials with next generation engines operating at lower temperatures and high pressures in order to reduce air pollution would thereby offer a sustainable alternative for the transportation sector. Tailoring the future biofuels to meet the needs of engines in optimizing their design thus critically relies upon the development of detailed chemical kinetic models that © XXXX American Chemical Society

capture and explain the ignition behavior of these fuels. 2Methyltetrahydrofuran (MTHF) and 2,5-dimethyltetrahydrofuran (DMTHF) are discussed to have a potential to significantly reduce CO2 and pollutant emissions.1 Yang and Shen have explained the feasibility of a one-step catalytic transformation of carbohydrates and cellulosic biomass to tetrahydrofuran derivatives (MTHF and DMTHF) in good yields for liquid fuels. They have shown that the DMTHF, which is a predominant product from hexose, is superior to ethanol.2 The higher boiling point and energy density of 90−92 °C and 35.5 MJ/kg makes the DMTHF a better fuel than ethanol as these properties are currently needed in the typical next generation petroleum-derived transportation fuels.3 Also, cyclic ethers are formed as products experimentally from the reaction of hydroperoxy radicals with molecular oxygen during Received: March 21, 2013 Revised: May 25, 2013

A

dx.doi.org/10.1021/jp402801c | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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combustion of C6−C16 hydrocarbons in the gas phase at lowtemperatures up to 1200 K.4 The consumption of these cyclic ethers by H-abstraction reaction by HO2 radical must be taken into account to improve the accuracy of their kinetic models in autoignition. Also, to the best of our knowledge, there is no literature available on the experimental ignition characteristics from RCM and shock tubes for these potential biofuels (MTHF and DMTHF). In our laboratory, the experimental measurement of ignition time of MTHF and DMTHF using shock tube and RCM is under progress for the temperature range of 500−2000 K. Development of a detailed kinetic model requires the knowledge of kinetic and thermodynamic data of thousands of elementary reactions needed to explain the combustion chemistry of them. These kinetic models include initiation reactions such as H-atom abstraction reactions from hydrocarbons by HO2 radical that are important particularly at temperature above 900 K and below 1200 K resulting in the formation of H2O2. In this intermediate temperature region, H2O2 consecutively decomposes producing two OH, and this is the crucial degenerate chain branching reaction at these temperatures.5 Similar reaction class will be important for biomass generated cyclic oxygenated species like the hydrocarbons even though there are certainly differences in their reactivity. Experimental measurements of rate gives information only in certain temperature range for overall rate constants. However, theoretical investigations can provide the insight to individual temperature-dependent gas phase rate constants of all type of reactions over a wide range of temperature. In the past, theoretical methods have extensively been applied for studying the kinetics of H abstraction reaction by HO2 from hydrocarbons due to experimental difficulty involved in finding a source for HO2.6 Recently, there have been numerous theoretical investigations performed on the abstraction reactions by HO2 from the various molecules including alcohols, esters, aromatic, and aliphatic systems.6−9 Also, thermochemical properties of the series of methyl substituted cyclic alkyl ethers have been reported by Itsaso et al.10 However, both experimental and theoretical rate constants for these sensitive reactions important in the low temperature oxidation mechanisms of the molecules studied here have not yet been reported in literature. The main aim of this work is to provide a comprehensive investigation on the activation energies and temperature-dependent rate coefficient of the hydrogen abstraction reactions by HO2 from different carbons of two compounds, namely, MTHF and DMTHF at CBS-QB3 and CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ levels of theory using conventional transition state theory. In this article, we also report detailed thermochemical parameters, entropies, Gibbs free energies, and enthalpies of reactions calculated at the CBS-QB3 level of theory. These data will certainly provide useful information for the development of an accurate chemical kinetic model of MTHF and DMTHF combustion chemistry, particularly in the intermediate temperature range of 900−1200 K.

level of theory in this compound method.12,13 In the present investigation, the optimization of all transition states using CBS-QB3 model chemistry were carried out using the geometries initially obtained at the B3LYP/6-311++G** level of theory. The vibrational frequencies were scaled by a factor of 0.99 in the calculation of rate coefficient as suggested by Scott and Radom.14 In addition to this, the single-point energy calculations have been performed at CCSD(T)/cc-pVTZ high level using the previously optimized geometry of the stationary points (a minimum or a saddle point) obtained at B3LYP/ccpVTZ level of theory in order to compare with CBS-QB3 energetic. The zero-point energies obtained at B3LYP/ccpVTZ level were added to the CCSD(T)/cc-pVTZ to obtain the total corrected electronic energies.15−26 The scaling factor of 0.9691 was multiplied to the normal-mode vibrational frequencies calculated at the B3LYP/cc-pVTZ level of theory as recommended by Scott and Radom.14 The stationary-point energy results obtained from CCSD(T)/cc-pVTZ calculations have been compared with that of CBS-QB3 calculations and have been described in detail in the results and discussion section. Also, these results certainly provide the insight into the influence of the level of theory on the branching ratio. It has been observed that expectation value of spin operator ⟨Ŝ2⟩, which describes the spin contamination, is about 0.80 before spin annihilation and is close to 0.75 after spin annihilation for all the transition states at the CBS-QB3 level of theory. A similar trend was noticed for all TSs at CCSD(T)/cc-pVTZ level. However, at B3LYP/cc-pVTZ level, values were found to be within the range of 0.756−0.750. All the high-pressure-limit rate constant calculations for the hydrogen abstraction reaction by HO2 from the MTHF and DMTHF have been performed employing the following conventional transition state theory expression27−29 k(T ) = Γl

⎡ −E ⎤ kBT QTS exp⎢ 0 ⎥ ⎣ RT ⎦ h QR

(1)

where Γ is the transmission coefficient used for tunneling correction, l is the reaction path degeneracy, QTS and QR are the total partition function of the transition state and ground state reactants, respectively, barrier height E0 is defined as energy difference between TS and reactant including zero-point energy correction, R is universal gas constant, T is the temperature, kB is Boltzmann constant,and h is Planck’s constant. The reaction path degeneracy used in the rate calculation for the C2 channel in MTHF is 1. It is 1 in the case of C3, C4, and C5 channels due to distinguishable cis- and trans-hydrogens and 3 in the case of H-abstraction from the CH3 group due to three symmetrically identical hydrogen atoms. The reaction path degeneracy used in the rate calculation for the C2 channel in DMTHF is 2 as there are two equivalent hydrogen atoms. It is 2 in the case of C3 channel for both cis and trans pathways and 6 in the case of H-abstraction from the CH3 group due to six identical methyl hydrogen atoms. The RRHO (rigid-rotor harmonic oscillator) approximation has been applied for the calculation of the rotational and vibrational partition function, which is required to compute the total rate constant using TST. All the low frequency torsional modes of the reactant and transition states were treated using one-dimensional hindered rotor approximation. In the case of MTHF, one low frequency vibration corresponding to C−C rotation in the reactant and three low frequency vibrations corresponding to C−C, C−O, and O−H rotations in the transition state are treated as a

2. COMPUTATIONAL METHODS All the electronic structure calculations were performed using the Gaussian09 software package.11 The geometry optimization and frequency calculations were performed with the B3LYP/ CBSB7 level of theory within CBS-QB3 method for all the reactants, transitions states, and products. These calculations are followed by the single-point energy calculations at higher B



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Figure 1. Torsional energy barrier for internal rotations about the C−C, C−O, and O−O bonds in the transition state of H-abstraction by HO2 from C2 of MTHF calculated at the B3LYP/6-311++G** level of theory.

3 using a full rotational potential and a reduced moment of inertia along the rotational axis.

hindered rotor. In the case of DMTHF, two torsional motions corresponding to two C−C rotations in the reactant and four torsional motions corresponding to C−O, O−H, and two C−C rotations in the transition state have been treated as a hindered rotor. A relaxed potential energy scanning has been carried out at the B3LYP/6-311++G** level of theory for all the low frequency vibrational modes corresponding to internal rotations using the optimized geometry of reactants and transition states at the B3LYP/CBSB7 level of theory with 10° increments in torsional angles in order to calculate the rotational barrier height. The rotational barrier height for the internal rotation of H about the O−O bond is between 8.8 and 11.5 kcal/mol in all the transition states of H abstraction by HO2 in both MTHF and DMTHF. The potential barrier height for OH rotation about the C−O bond is in the range of 0.5 to 1.4 kcal/mol in all transition states. The C−C rotation barrier heights are in the range of 3.2−5.5 kcal/mol for the transition state, and for the reactant, it is close to 3.0 kcal/mol. Torsional energy barrier profile for internal rotations about C−C, C−O, and O−O bonds in the transition state of H-abstraction by HO2 from C2 of 2-MTHF calculated at the B3LYP/6-311+ +G** level of theory is given in Figure 1. The C−H and O−H bond lengths involved in the reaction coordinate were fixed in the case of transition states during the scan of torsional angle. The torsional energies for internal rotations along a single bond obtained at the B3LYP/6-311++G** level were fitted to fifth order Fourier series 2 in order to calculate the hindrance potential.

2 h2 ∂ Ψn(Ø) + V (Ø)Ψn(Ø) = En Ψn(Ø) 2Ir ∂Ø2

where Ψ is the wave function, E is the energy, Ø is torsional angle, Ir is reduced moment of inertia assumed to be independent of Ø, V(Ø) is full rotational potential, and h is Plank’s constant. These resulting eigenstate energies were summed to evaluate the partition functions of the torsional modes. These calculations have been performed to provide comparison with the results obtained using Pitzer−Gwinn approximation for the torsional motion and also to benchmark our results. A description of rate constant details provided in this article is based on the Pitzer−Gwinn approximation for torsional motion unless otherwise mentioned. The tunneling effect along the reaction coordinate was taken into account for the abstraction reaction using the unsymmetrical one-dimensional Eckart approximation.31 The rate constants calculated over the temperature range of 500−2000 K using CTST were fitted using least-squares regression to the modified Arrhenius expression, k = ATn exp(−Ea/RT), in order to obtain the kinetic parameters, so that these kinetic parameters obtained in a modified Arrhenius form can directly be used in a detailed chemical kinetic model of these species.

3. RESULTS AND DISCUSSION 3.1. Geometric Parameters and Stationary Point Energies. Optimized geometries of all the transition states for the reaction of MTHF and DMTHF with HO2 at the B3LYP/CBSB7 level are displayed in Figure 2a and b, respectively. The optimized Cartesian coordinates of all reactants and transition states structures have been provided in the Supporting Information. The HO2 radical can abstract hydrogen from the C−H bond of methyl groups and from the C−H bond of MTHF and DMTHF rings. The abstraction of H atom by the HO2 from the methyl group and C2 carbon atom

N

V (Ø) = a0 +

∑ (an cos(nØ) + bn sin(nØ)) n=1

(3)

(2)

The resulting depth of fitted hindrance potential has been used to estimate the partition function using the Pitzer−Gwinn approximation.8,30−32 In addition to this, the rotational eigenvalues for an isolated one-dimensional hindered rotor were solved numerically with one-dimensional Schrödinger eq C



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Figure 2. (a) Geometries of optimized reactants (a) MTHF and (b) DMTHF and the corresponding transition state structures for the hydrogen abstraction reactions by HO2 radical at the B3LYP/CBSB7 level of theory (angles are in degrees and distances are in angstroms). Optimized geometry of both reactants MTHF and DMTHF show the nomenclature used to designate the rate coefficients of the reactions from different types of hydrogen atoms.

of MTHF is denoted via transition states TS1 and TS2, respectively. Each hydrogen atom connected to C3, C4, and C5 is treated differently due to the presence of the methyl group at C2 in MTHF. The cis and trans abstraction reaction pathways from the C3, C4, and C5 carbon atoms of MTHF is represented via transition states TS3a, TS3b, TS4a, TS4b, TS5a, and TS5b, respectively.

The potential energy level diagram describing all eight abstraction reaction pathways of MTHF at the CBS-QB3 level of theory have been summarized in Figure 3. It is clear from Figure 3 that the barrier height of 7.45 kcal/mol for the transition state TS2 is lowest among all reaction channels and is the most favorable reaction pathway. In the case of the TS2 transition state, the breaking C−H bonds are elongated by 19− D



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Figure 3. Potential energy level diagram for the abstraction reactions of MTHF with HO2 calculated at the CBS-QB3 level of theory. All the relative energy values given in brackets corresponds to the CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ level of theory. All the values are given in units of kcal/ mol.

20% as compared to the equilibrium C−H bond length in the MTHF. However, forming O−H bonds are approximately 27.8% longer than the equilibrium O−H bond length in the H2O2 molecule. These structures of TSs are closer to reactant than product implying the early TS for this reaction channel. An almost similar trend for percentage variation in bond length has been noticed for the TS5a and TS5b transition states as well, and their corresponding barrier heights are 9.25 and 9.90 kcal/mol, respectively, which is very close to that of TS2. As shown in the Figure 3, the energy barrier at CBS-QB3 level of theory for TS3a, TS3b, TS4a, and TS4b are 14.74, 14.25, 13.02, and 15.90 kcal/mol, respectively. It shows that the energy barrier for the cis pathway of the C3 channel is 0.5 kcal/mol higher than that of the trans pathway. However, the energy barrier for the cis pathway of the C4 channel is found to be 2.9 kcal/mol lower as compared to that of the trans pathway. These results indicate the kinetic preference for the H-abstraction from the C2 carbon over C3, C4, and C5. The highest energy barrier height of 18.7 kcal/mol needs to be overcome for Habstraction from the methyl group of MTHF through TS1 at the CBS-QB3 level of theory. The C−H bond distances in the TS1, TS3a, TS3b, TS4a, and TS4b are elongated between 25% and 28%, and the forming O−H bonds are varied between 17.8% and 20.8%. These structures of TSs are closer to product than reactant suggesting the late TSs of these reaction channels. The O−O bond is elongated by about 6.4% in all the TSs as

compared to the equilibrium O−O bond length in the HO2 at the CBS-QB3 level of theory. The reaction energies at the CBSQB3 level for H-abstraction by TS1, TS2, TS3a, TS4a, TS5a, TS3b, TS4b, and TS5b are 14.85, 5.17, 10.43, 9.97, 5.78, 10.43, 9.97, and 5.78 kcal/mol, respectively, indicating that all these reactions are endothermic. All these abstraction reactions have been found to be highly endothermic by 5.8−15.5 kcal/mol that can be seen in the potential energy level diagram reported in the Figure 3. The barrier height of all reaction channels of MTHF at the CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ level of theory has been given in the parentheses in potential energy level diagram in the Figure 3. It can be seen from Figure 3 that the barrier height for the transition state TS2 at the CCSD(T)/cc-pVTZ// B3LYP/cc-pVTZ level is 11.16 kcal/mol, which is almost 4 kcal/mol higher as compared to that predicted at the CBS-QB3 level of theory. The highest energy barrier of 20.78 kcal/mol is required for H-abstraction from the methyl group of MTHF by TS2. The energy barrier for TS3a, TS3b, TS4a, TS4b, TS5a, and TS5b transition states are 17.48, 16.81, 15.95, 16.50, 12.12, and 13.54 respectively. The barrier heights predicted for all the reaction channels at the CCSD(T)/cc-pVTZ//B3LYP/ccpVTZ level is 1−4 kcal/mol higher as compared to that predicted by the CBS-QB3 level of theory. The percentage changes in breaking C−H, forming H−O bond lengths of all the TSs of MTHF at the CCSD(T)/cc-pVTZ//B3LYP/ccE



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Figure 4. Potential energy level diagram for the abstraction reactions of trans-DMTHF with HO2 calculated at the CBS-QB3 level of theory. All the relative energy values given in brackets correspond to the CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ level of theory. All the values are given in units of kcal/mol.

dissociation energies (BDEs) at the CBS-QB3 level of theory for the CH2−H, C2−H, C3−H, C4−H, and C5−H bonds of MTHF are 101.4, 91.7, 97.6, 96.5, and 92.3 kcal/mol, respectively. The calculated corresponding values at CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ level of theory are 109.3, 99.3, 105.2, 104.9, and 99.7 kcal/mol, respectively. These trends in BDEs are consistent with their corresponding barrier heights. The bond dissociation energies at the CBS-QB3 level of theory for the CH2−H, C2−H, and C3−H bonds of DMTHF are 101.3, 91.1, and 97.4 kcal/mol, respectively. The calculated corresponding values at the CCSD(T)/cc-pVTZ// B3LYP/cc-pVTZ level of theory are 111.1, 99.9, and 107 kcal/ mol, respectively. These trends in BDEs have also been found to be consistent with their corresponding barrier heights. These calculated values of BDEs at both levels of theory are in good agreement with those reported in the literature.33−35 3.2. Calculations of Kinetic Parameters. The detailed investigation on rate coefficient calculations of MTHF and DMTHF have been performed in order to provide insight into the competition between various reaction channels. The main objective of this work was to estimate the rate parameters through an Arrhenius expression for the hydrogen abstraction reactions by HO2 from MTHF and DMTHF at the CBS-QB3 and CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ levels of theory. The rate constant calculations have been performed in the temperature range of 500−2000 K with an interval of 50 K.

pVTZ level, is approximately similar to that computed at the CBS-QB3 level of theory. The abstraction of H atom by the HO2 from the methyl group and C2 carbon atom of DMTHF is denoted via transition states TS6 and TS7, respectively. The cis and trans abstraction pathways from the C3 carbon atoms of DMTHF is represented via transition states TS8a and TS8b, respectively. All the four abstraction reaction pathways for DMTHF at the CBS-QB3 level of theory has been summarized in the potential energy diagram in Figure 4. It should be mentioned here that the barrier height predicted for all the reaction channels in DMTHF is 0.5−1 kcal/mol lower as compared to those of the MTHF indicating that the alkylation has a slight influence on the barrier height at the CBS-QB3 level of theory. It has been found that the barrier heights in the case of DMTHF follow the similar trend like MTHF at both levels of theory investigated here. All the reactions have been found to be endothermic at both levels of theory that can be seen in the potential energy diagram in Figure 4. The reaction channel C2 is least endothermic by 5.2 kcal/mol, and endothermicity of channels 1 and 3 are 15.4 and 11.5 kcal/mol, respectively. The percentage changes in the breaking C−H; forming H−O bond lengths of all the TSs of DMTHF is approximately similar to that of the MTHF at both levels of theory investigated here. These differences in barrier heights are attributed to the differences in their C−H bond dissociation energies. The bond F



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Asymmetrical Eckart tunneling corrections in the rate constants have been taken into account for all the reaction channels involved in MTHF and DMTHF. It is calculated to be between 2.9 and 1.2 for all reaction channels for both MTHF and DMTHF at the CBS-QB3 level in the temperature range of 500−1400 K. 3.2.1. MTHF + HO2. The rate coefficients of the reactions involving TS1, TS2, TS3a, TS3b, TS4a, TS4b, TS5a, and TS5b transition states in the reaction of MTHF with HO2 have been represented as k1, k2, k3a, k3b, k4a, k4b, k5a, and k5b, respectively. Table 1 illustrates the comparison of high pressure limit rate Table 1. Summary of Modified Arrhenius Parameters (k = ATn exp(−Ea/RT) Calculated at the CBS-QB3 Level of Theory for the Reaction of MTHF with HO2 Using TST with Pitzer−Gwinn Approximation for Torsional Motions over the Temperature Range of 500−2000 K reaction

A (cm3 mol−1 s−1)

n

Ea (kcal/mol)

MTHF + HO2 → CH2MTHF + H2O2 (k1) MTHF + HO2 → R2MTHF + H2O2 (k2) MTHF + HO2 → R3MTHF + H2O2 (cis pathway) (k3a) MTHF + HO2 → R3MTHF + H2O2 (trans pathway) (k3b) MTHF + HO2 → R4MTHF + H2O2 (cis pathway) (k4a) MTHF + HO2 → R4MTHF + H2O2 (trans pathway) (k4b) MTHF + HO2 → R5MTHF + H2O2 (cis pathway) (k5a) MTHF + HO2 → R5MTHF + H2O2 (trans pathway) (k5b) k3 (k3a + k3b) k4 (k4a + k4b) k5 (k5a + k5b)

3.53 × 1011

0.65

19.04

1.52 × 1010

0.49

8.00

9.78 × 108

0.69

14.80

8.49 × 108

0.70

14.72

7.09 × 108

0.68

12.95

2.05 × 109

0.69

16.03

2.01 × 1010

0.51

9.74

4.34 × 109

0.53

10.28

2.15 × 109 2.11 × 107 2.10 × 1010

0.68 1.26 0.53

14.81 12.91 9.79

Figure 5. Rate coefficients for the eight reaction channels for the abstraction reaction of MTHF with HO2 with Pitzer−Gwinn approximation for torsional motion obtained from the fitting of a modified Arrhenius form at temperatures of 500−2000 K at the CBSQB3 level of theory.

the abstraction reaction from C3 and C4 sites are given by k(T) = 2.15 × 109T0.68 exp(−14.81/RT) and k(T) = 2.11 × 107T1.26 exp(−12.91/RT) cm3 mol−1 s−1, respectively. The rate constant of C3 and C4 channels is much slower as compared to that of C2 and C5. The rate constant values of C3 and C4 channels differ by a factor of 3.81−9.72 in the temperature range of 1200−2000 K from the corresponding values of C2 channel. However, it varies by a factor of 12.0−254.2 in the temperature range of 1200−2000 K. The presence of oxygen atom in the MTHF ring makes the C2−H and C5−H bond much weaker as compared to the C3−H and C4−H bonds as reflected from their BDEs as described before. This leads to the increased rate constant for H-abstraction reaction from C2 and C5 carbon as compared to that from C3 and C4. Also the branching ratio analysis indicates that their contribution to overall rate constant is negligible over the whole temperature window of investigation and its details are given in the branching ratio section. It should be mentioned here that the rate constant presented here for C3, C4, and C5 reaction channels are obtained by summing over their cis and trans reaction pathways. It was in our interest to compare these results with available literature data; however, there are no experimental and theoretical results available for these reactions against which these results can be compared or further discussed. The calculated rate constants for all the abstraction reaction channels at the CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ level of theory is slightly slower than that obtained at the CBS-QB3 level of theory. The calculated rate constant values at the CBSQB3 level for the reaction channel 2 is within a factor of 2.29− 36.7 of the corresponding values at the CCSD(T)/cc-pVTZ// B3LYP/cc-pVTZ level of theory in the temperature range of 500−2000 K. Comparison of high pressure limiting rate constants of all reaction channels, k1−k5b, at the CCSD(T)/ cc-pVTZ//B3LYP/cc-pVTZ level of theory have been summarized in Table S1, and their plots have been provided in Figure S1 of the Supporting Information. Summary of modified Arrhenius parameters calculated at the CBS-QB3 level of theory for the reaction of MTHF with HO2 with 1D-

constants of all reaction channels, k1−k5b, at the CBS-QB3 level of theory for MTHF + HO2 in the temperature range of investigation, and their plots have been provided in the Figure 5. It can be seen from the Figure 5 that the rate constant for C2 and C5 channels is dominant over the methyl channel in the temperature range from the 500 to 1400 K. The barrier height calculated for the reaction channel C2 and C5 is 11.3 and 8.8 kcal/mol lower as compared to that of the methyl channel. However, the higher rate constant values for the methyl channel at temperatures above 1400 K can be attributed to the higher magnitude of the hindered rotor partition functions of the three low frequency vibrational modes in its transition state. Moreover, the rate constant of the C2 channel is slightly faster than that of the C5 over the whole temperature range. This is attributed to the higher barrier height for the reaction channel C5 by 1.5 kcal/mol as compared to that of the C2 channel at the CBS-QB3 level of theory. The rate constant for the abstraction reaction from C2 and C5 channels of MTHF at the CBS-QB3 level of theory are given by k(T) = 1.52 × 1010T0.49 exp(−8.00/RT) and k(T) = 2.10 × 1010T0.53 exp(−9.79/RT) cm3 mol−1 s−1, respectively. The rate constant for the abstraction of methyl hydrogen is expressed by k(T) = 3.53 × 1011T0.65 exp(−19.04/RT) cm3 mol−1 s−1 in the temperature range investigated here. The rates of the C3 and C4 reaction channels are competitive with each other. The rate constant for G



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for DMTHF + HO2 in the temperature range of 500−2000 K, and their plots have been provided in Figure 6. Comparison of

Schrödinger equation for torsional motions over the temperature range of 500−2000 K have also been given in Table 3, Table 2. Summary of Modified Arrhenius Parameters (k = ATn exp(−Ea/RT) Calculated at the CBS-QB3 Level of Theory for the Reaction of Trans Isomer of DMTHF with HO2 Using TST with Pitzer−Gwinn Approximation for Torsional Motions over the Temperature Range of 500− 2000 K reaction trans-DMTHF + HO2 → CH2DMTHF + H2O2 (k6) trans-DMTHF + HO2 → R2DMTHF + H2O2 (k7) trans-DMTHF + HO2 → R3DMTHF + H2O2 (cis pathway) (k8a) trans-DMTHF + HO2 → R3DMTHF + H2O2 (trans pathway) (k8b) k8 (k8a + k8b)


n

Ea (kcal/mol)

1.38 × 1012

0.64

18.95

8.68 × 1010

0.46

7.84

3.93 × 109

0.70

14.07

5.26 × 109

0.70

15.08

5.29 × 109

0.76

14.38

Table 3. Summary of Recommended Modified Arrhenius Parameters (k = ATn exp(−Ea/RT) Calculated at the CBSQB3 Level of Theory for the Reaction of MTHF with HO2 Using TST with Exact Solution for Torsional Motions Obtained by Solving 1D-Schrödinger Equation over the Temperature Range of 500−2000 K reaction


n

Ea (kcal/mol)

MTHF + HO2 → CH2MTHF + H2O2 (k1) MTHF + HO2 → R2MTHF + H2O2 (k2) MTHF + HO2 → R3MTHF + H2O2 (cis pathway) (k3a) MTHF + HO2 → R3MTHF + H2O2 (trans pathway) (k3b) MTHF + HO2 → R4MTHF + H2O2 (cis pathway) (k4a) MTHF + HO2 → R4MTHF + H2O2 (trans pathway) (k4b) MTHF + HO2 → R5MTHF + H2O2 (cis pathway) (k5a) MTHF + HO2 → R5MTHF + H2O2 (trans pathway) (k5b) k3 (k3a + k3b) k4 (k4a + k4b) k5 (k5a + k5b) total

1.66 × 102

3.47

17.08

6.52 × 101

3.27

6.41

1.12

3.68

12.96

1.66

3.57

11.92

4.25

3.46

11.53

1.54

3.75

13.88

4.37

3.52

7.77

3.93

3.52

8.09

1.18 7.21 × 10−2 7.79 1.95 × 10−3

3.72 4.13 3.53 4.72

12.16 11.46 7.89 4.85

Figure 6. Rate coefficients for the four reaction channels for the hydrogen abstraction reaction by HO2 from the trans conformer of DMTHF obtained from the fitting of a modified Arrhenius expression at temperatures of 500−2000 K at the CBS-QB3 level of theory.

all the rate constants for DMTHF + HO2 reaction calculated at the CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ level of theory have been given in Table S2 of the Supporting Information, and their plots have been provided in Figure S2. The rate coefficients of the reactions involving TS6, TS7, TS8a, and TS8b transition states in the reaction of DMTHF with HO2 are designated as k6, k7, k8a, and k8b, respectively. It was found that the rates for all the reaction channels for the DMTHF follow the same trend like MTHF demonstrating the influence of alkylation. The rate constant calculated for the C2 and C3 channel of DMTHF has been found to be almost an order of magnitude higher than the corresponding channels in MTHF over the entire temperature range of investigation at the CBSQB3 level of theory. It can be seen in Figure 7, which includes the comparison of the rate coefficients for the reaction channels involving 1°, 2°, and 3° hydrogen atom abstraction reactions of MTHF and DMTHF with HO2 at temperatures of 500−2000 K at the CBS-QB3 level of theory. The rate constants calculated at the CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ level of theory show almost similar overall behavior. A similar trend has been observed for the methyl hydrogen abstraction reactions as well. The rate constants evaluated at the CBS-QB3 level of theory for all the abstraction reaction channels of MTHF and DMTHF dominates over the rate constant obtained at the CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ level of theory. Figure 8 illustrates the comparison of global rate constants obtained from the contribution of each hydrogen of MTHF and DMTHF at both levels of theory in the temperature range of 500−2000 K. It can be seen from Figure 8 that at both levels of theory the predicted total abstraction rate constant for DMTHF is higher as compared to that of MTHF over the entire temperature range of investigation. A summary of modified Arrhenius parameters for the global rate constants calculated at both leveld of theory for both the molecules investigated here are tabulated in Table 5. A summary of modified Arrhenius parameters calculated at the CBS-QB3 level

and the corresponding rate constant values at the CCSD(T)/ cc-pVTZ//B3LYP/cc-pVTZ level of theory are reported in Table S3, Supporting Information. It has been noticed that all the rate constant results of MTHF with HO2 obtained by solving the 1D-Schrödinger equation for hindered rotations are almost an order of magnitude faster as compared to those obtained using the Pitzer−Gwinn approximation at both levels of theory in the entire temperature range of investigation. 3.2.2. DMTHF + HO2. The computational calculations on DMTHF have been performed at both levels of theory in order to investigate the effect of alkylation on the rate constants of various reaction channels as compared to that of MTHF. Table 2 explains the comparison of high pressure limit rate constants of all reaction channels, k6−k8b, at the CBS-QB3 level of theory H



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Table 4. Summary of Recommended Modified Arrhenius Parameters (k = ATn exp(−Ea/RT) Calculated at the CBSQB3 Level of Theory for the Reaction of the Trans Isomer of DMTHF with HO2 Using TST with an Exact Solution for Torsional Motions Obtained by Solving the Schrödinger Equation for Torsional Motions over the Temperature Range of 500−2000 K

Figure 7. Comparison of the rate coefficients for the reaction channels involving 1°, 2°, and 3° hydrogen atom abstraction reactions of MTHF and DMTHF with HO2 at temperatures of 500−2000 K at the CBS-QB3 level of theory.

reaction


n

Ea (kcal/mol)

trans-DMTHF + HO2 → CH2MTHF + H2O2 (k6) trans-DMTHF + HO2 → R2MTHF + H2O2 (k7) trans-DMTHF + HO2 → R3MTHF + H2O2 (cis pathway) (k8a) trans-DMTHF + HO2 → R3MTHF + H2O2 (trans pathway) (k8b) k8 (k8a + k8b) total

4.51 × 102

3.59

17.43

1.10 × 10

3.14

6.00

8.08

3.70

12.97

1.22 × 101

3.68

13.80

1.35 × 101 7.75 × 10−3

3.73 4.71

13.26 3.86

3

Table 5. Summary of Modified Arrhenius Parameters for the Total Rate Constants Calculated at the CBS-QB3 and CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ Levels of Theory Using TST with Pitzer−Gwinn Approximation for Torsional Motion for the Reaction of MTHF and DMTHF with HO2 reaction


n

Ea (kcal/mol)

MTHF + HO2 (CBS-QB3) MTHF + HO2 (CCSD(T)/ccpVTZ//B3LYP/cc-pVTZ) DMTHF + HO2 (CBS-QB3) DMTHF + HO2 (CCSD(T)/ccpVTZ//B3LYP/cc-pVTZ)

5.57 8.60

3.50 3.54

4.71 8.92

0.07 3.17

4.18 3.63

3.03 6.59

oscillator and free rotor at the CBS-QB3 level of theory, and the corresponding rate constant values at the CBS-QB3 level of theory have been reported in the Supporting Information in Tables S5−S8. These rate constant calculations have been performed in order to provide comparison with those calculated assuming internal rotors as the hindered rotor employing Pitzer−Gwinn approximation and by solving 1DSchrödinger equation. These results will also be useful to understand the influence of different approximations used for internal rotors on the rate coefficients of the different channels in the temperature range of investigation. The plot presented in the Figure 9 demonstrates the comparison of the rate constants for the reaction channel k6 calculated using four different treatments for internal rotors. It has been noticed that the calculated rate constants obtained using Pitzer−Gwinn approximation and 1D-Schrödinger equation are always faster by almost an order of magnitude as compared to those obtained using RRHO approximation for all reaction channels. However, the rate constant obtained using free rotor approximation for internal rotors is much faster as compared to those obtained using Pitzer−Gwinn approximation and 1DSchrödinger equation. It can also be noticed from Figure 9 that the hindered rotor rate constant approaches the free rotor values at high temperatures, whereas at low temperature, it approaches harmonic oscillator rate constant. It is recommended to use the rate coefficients of both MTHF and DMTHF estimated using the CBS-QB3 method with 1DSchrödinger equation solution for hindered rotors to use in the

Figure 8. Comparison of the total rate constants with tunneling correction for the H-abstraction reaction of MTHF and trans-DMTHF with HO2 in the temperature range of investigation at the CBS-QB3 and CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ levels of theory.

of theory for the reaction of DMTHF with HO2 with 1DSchrödinger equation solution for torsional motions over the temperature range of 500−2000 K is also included in the Table 4, and the corresponding rate constant values at the CCSD(T)/ cc-pVTZ//B3LYP/cc-pVTZ level of theory are reported in Table S4, Supporting Information. Similar to MTHF, all rate constant results of DMTHF with HO2 obtained by solving the 1D-Schrödinger equation for hindered rotations are almost an order of magnitude faster as compared to those obtained using Pitzer−Gwinn approximation at both levels of theory in the entire temperature range of investigation. In addition to this, rate constant calculations have also been performed for all the reaction channels of both MTHF and DMTHF assuming internal rotors, namely, C−C, OH, and OOH as harmonic I



Article

constants of MCP with HO2 have been tabulated in Table 6. The rate coefficients of the reactions involving TS9, TS10, and Table 6. Summary of Modified Arrhenius Parameters (k = ATn exp(−Ea/RT) Calculated at the CBS-QB3 Level of Theory for the Reaction of the Trans Isomer of Methyl Cyclopentane (MCP) with HO2 Using TST with an Exact Solution for Torsional Motions Obtained by Solving the 1DSchrödinger Equation for Torsional Motions over the Temperature Range of 500−2000 K

Figure 9. High pressure limit rate constant for DMTHF + HO2 calculated at the CBS-QB3 level of theory for the k6 reaction channel using four different approximations for internal rotors.

reaction


n

Ea (kcal/mol)

MCP + HO2 → CH2MCP + H2O2 (k9) MCP + HO2 → R2MCP + H2O2 (k10) MCP + HO2 → R3MCP + H2O2 (k11)

1.08 × 102

3.51

15.65

5.26

3.48

8.61

2.64

3.66

11.29

TS11 transition states in the reaction of MCP with HO2 are designated as k9, k10, and k11, respectively. Comparison of the rate constant calculated for 1°, 2°, and 3° hydrogen abstraction from MCP, MTHF, and DMTHF with those reported by Carstensen et al.36 and Aguilera-Iparraguirre et al.37 for the corresponding hydrogen abstraction from alkanes have been shown in Figure 11. All the rate coefficient results reported in Figure 11 for MTHF, DMTHF, and MCP with HO2 are calculated at the CBS-QB3 level of theory with the 1DSchrödinger equation solution for torsional motions. These calculations show that the rate constant of the primary methyl hydrogen abstraction reaction from MTHF and MCP is found to be slightly slower as compared to that reported by Carstensen et al. as shown in Figure 11a in the entire temperature range of investigation. The calculated rate of MCP for primary methyl hydrogen abstraction is almost similar to that obtained by Carstensen et al. However, the rate reported by Aguilera-Iparraguirre et al. for alkanes is almost an order of

development of chemical kinetic models. Calculated uncertainties in the rate coefficients at the CBS-QB3 level of theory with 1D-Schrödinger equation solution for hindered rotors is a factor of 2 evolving due to the approximation used in the TST, ab initio calculations, hindered rotor treatment, and tunneling corrections. Rate constant calculations for methyl cyclopentane (MCP) with HO2 have also been performed at the CBS-QB3 level of theory with the 1D-Schrödinger equation solution for torsional motions in order to compare with those of MTHF and DMTHF. Optimized geometries of MCP and the corresponding transition state structures TS9, TS10, and TS11 for the 1°, 3°, and 2° hydrogen atom abstractions by HO2 from MCP at the B3LYP/CBSB7 level of theory are shown in Figure 10. Distances have been reported in the units of angstroms. Rate

Figure 10. Geometries of optimized methylcyclopentane (MCP) and the corresponding transition state structures TS9, TS10, and TS11 for the 1°, 2°, and 3° hydrogen atom abstraction by HO2 from MCP at the B3LYP/CBSB7 level of theory (distances are given in angstroms). J



Article

Figure 11. Comparison of rate coefficients for the reaction channels involving primary (a), tertiary (b), and secondary (c) hydrogen atom abstraction reactions of MTHF, DMTHF, MCP, and alkanes with HO2. Rate coefficients for MTHF, DMTHF, and MCP with HO2 were obtained at the CBS-QB3 level of theory with the 1D-Schrödinger equation solution for torsional motions.

Table 7. Summary of Standard Enthalpy of Formation (kcal/mol), Entropies (cal mol−1 K−1), and Heat Capacities at Specified Temperatures (cal mol−1 K−1) of MTHF Obtained at the CBS-QB3 Level of Theory Cp species

ΔfH0298

S298

300

500

800

1000

1500

MTHF TS1 TS2 TS3a TS3b TS4a TS4b TS5a TS5b

−53.61 −34.37 −45.66 −38.38 −38.87 −40.10 −37.21 −43.87 −43.22

80.81 109.36 102.99 100.53 100.62 100.15 102.00 103.87 101.27

25.45 35.79 35.89 36.30 36.13 35.50 36.21 35.52 35.50

41.41 54.34 53.35 54.09 54.00 53.72 54.41 53.64 53.58

57.67 72.16 71.01 71.60 71.52 71.44 71.84 71.33 71.26

64.82 79.57 78.56 79.10 79.00 78.98 79.27 78.87 78.81

75.67 90.38 89.73 90.22 90.07 90.10 90.30 90.05 90.00

of MCP is intermediate between those reported by Carstensen et al. and Aguilera-Iparraguirre et al. It can be seen from Figure 11c that the rate constant for secondary hydrogen abstraction from MTHF is almost similar to that reported by AguileraIparraguirre et al. for linear alkanes with the HO2 radical. However, the rate constant of MCP lies between MTHF and DMTHF. These differences and similarities of the rate constants in the whole temperature range of investigation

magnitude slower as compared to rates of MCP, MTHF, and DMTHF as shown in Figure 11a. The rate of DMTHF can clearly be seen to be faster as compared to MTHF, MCP, and alkanes in the entire temperature range of investigation. It is clear from Figure 11b that the rate constant for tertiary hydrogen abstraction from both MTHF and DMTHF is faster as compared to both linear and methyl substituted cyclic alkanes. Figure 11b also shows that the calculated rate constant K



Article

Table 8. Summary of Standard Enthalpy of Formation (kcal/mol), Entropies of Formation (cal mol−1 K−1), and Heat Capacities at Specified Temperatures (cal mol−1 K−1) of DMTHF Obtained at the CBS-QB3 Level of Theory Cp species

H298

S298

300

500

800

1000

1500

trans-DMTHF TS6 TS7 TS8a TS8b

−63.68 −44.45 −55.95 −49.13 −48.03

85.83 117.13 111.04 108.49 109.37

31.57 42.00 42.03 42.21 41.53

50.13 63.04 62.09 62.93 62.50

68.88 83.25 82.23 82.97 82.74

77.19 91.80 90.95 91.59 91.43

89.90 104.49 103.96 104.46 104.41

4. CONCLUSIONS The major objective of this work was to provide the detailed comprehensive kinetic results for reaction of HO2 with MTHF and DMTHF using high level computational calculations in the high pressure limit. In this article, we provide the individual and total rate constants of all the reactions channels of hydrogen abstraction reactions of MTHF and MDTHF with HO2 computed using CTST employing the CBS-QB3 and CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ levels of theory. All the low frequency torsional motions in the reactants and transition states have been treated using the Pitzer−Gwinn approximation. Quantum mechanical tunneling correction has been taken into account using the unsymmetrical Eckart’s method. The rate constants calculated were fitted using the modified Arrhenius expression, k = ATn exp(−Ea/RT), in order to obtain the kinetic parameters in the combustion temperature range of 500−2000 K. A present computational calculation result indicates that the reaction at the C2 site is the most dominant pathway for both MTHF and MDTHF because of its lower barrier height. However, barrier height for the methyl hydrogen abstraction reaction pathway for both MTHF and DMTHF is found to be highest. The computed C−H bond dissociation energies of both MTHF and DMTHF are consistent with their corresponding barrier heights and found to be in good agreement with the literature values. All the reaction channels investigated herein for reaction of MTHF and DMTHF with HO2 are endothermic. At both levels of theory, the predicted global abstraction rate constant for DMTHF is found to be higher as compared to that of MTHF over the whole temperature range of investigation. This is attributed to the reduction in the barrier height due to methyl substitution for all the abstraction reaction channels. The rate constants evaluated at the CBS-QB3 level of theory for all the abstraction reactions channels of MTHF and DMTHF dominate over the rate constant obtained at the CCSD(T)/ cc-pVTZ//B3LYP/cc-pVTZ level of theory. These results provide valuable rate coefficient data, which will be useful for the development of accurate chemical kinetic models for combustion of MTHF and DMTHF in order to determine the profiles of combustion products in the NTC region that has a significant concentration of HO2. We recommend the use of rate coefficients estimated using the CBS-QB3 method with 1D-Schrödinger equation solution for hindered rotors in the development of chemical kinetic models.

between linear alkanes, cyclic alkanes, and oxygenated cyclic alkanes are attributed to their differences in the energy barriers. 3.3. Entropy and heat capacities. Summary of standard enthalpy of formation (kcal/mol), entropies (cal mol−1 K−1), and heat capacities at specified temperatures (cal mol−1 K−1) of reactants MTHF and DMTHF and their transition states for reaction with HO2 have been obtained at the CBS-QB3 level of theory and is tabulated in Tables 7 and 8. The contribution of hindered rotation to the entropy and heat capacity is taken into account usingthe Pitzer−Gwinn approximation for both reactant and transition state. The standard entropies of formation at 298 K for MTHF and DMTHF are 80.8 and 85.8 cal mol−1 K−1, respectively. 3.4. Branching Ratio. Another objective of this work was to calculate the product branching ratio and to determine the influence of the level of theory on the branching ratio. Figures S3 and S4 given in the Supporting Information exhibit the branching ratio for abstraction reactions as a function of temperature for the different carbon sites and methyl group for MTHF at the CBS-QB3 and CCSD(T)/cc-pVTZ//B3LYP/ccpVTZ levels of theory, respectively. The calculated branching ratio for the C2 channel of MTHF was found to be 76.9, 48.1, and 13.2% at 500, 1000, and 2000 K at the CBS-QB3 level of theory, respectively. It was found to be 0.07, 13.7, and 67.4%, respectively, at similar temperatures for methyl hydrogen abstraction. For the C3 and C4 channels, it is found to be less than 2% over the entire temperature range of investigation. The branching ratio of C5 channel was significantly lower as compared to that of the C2 channel, and it is 22.2% at 500, 36.2% at 1000, and 16.1% at 2000 K. The branching ratio described here for the C5 channel is obtained by summing over its cis and trans reaction pathways. The C2 and C5 channels are found to be dominant at temperatures below 1200 K, and the methyl hydrogen abstraction dominates at temperatures above this. In the case of the methyl hydrogen of DMTHF, it is 0.07, 17.2, and 77.8% at 500, 1000, and 2000 K, respectively. For the C2 channel, it was found to be 99.9, 81.4, and 20.0% at 500, 1000, and 2000 K temperatures, respectively. It indicates the increasing abstraction probability of the methyl H-abstraction channel with increasing temperature and decreasing probability of C2 channel with increasing temperature. The branching ratio for C3 channel is almost negligible over the whole temperature range of investigation. These results indicate that the overall trend observed for the DMTHF at the CBS-QB3 level of theory is similar to that of MTHF. Almost similar overall behavior has been observed for both molecules at the CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ level of theory as well. The product branching ratio for DMTHF at both levels of theory has been displayed in Figures S5 and S6 in the Supporting Information.

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ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates of reactants and all the transition states as well as rate constants, branching ratios, thermodynamic parameters, fitted potential energy profiles of internal rotors, and IRC calculation results for the reaction of MTHF and L



Article

(13) Montgomery, J. A.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VI. Use of Density Functional Geometries and Frequencies. J. Chem. Phys. 1999, 110, 2822−2827. (14) Scott, A. P.; Radom, L. Harmonic Vibrational Frequencies: An Evaluation of Hartre-Fock, Moller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors. J. Phys. Chem. 1996, 100, 16502−16513. (15) Becke, A. J. Density Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (16) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle− Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (17) Dunning, T. H. Gaussian-Basis Sets for Use in Correlated Molecular Calculations 0.1. the Atoms Boron Through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007−1023. (18) Kendall, R. A.; Dunning, T. H.; Harrison, R. J. ElectronAffinities of the 1st-Row Atoms Revisited: Systematic Basis-Sets and Wave-Functions. J. Chem. Phys. 1992, 96, 6796−6806. (19) Woon, D. E.; Dunning, T. H. Gaussian-Basis Sets for Use in Correlated Molecular Calculations 0.3. the Atoms Aluminum Through Argon. J. Chem. Phys. 1993, 98, 1358−1371. (20) Peterson, K. A.; Woon, D. E.; Dunning, T. H. Benchmark Calculations with Correlated Molecular Wave-Functions 0.4. the Classical Barrier Height of the H + H2 → H2 + H Reaction. J. Chem. Phys. 1994, 100, 7410−7415. (21) Wilson, A. K.; van Mourik, T.; Dunning, J. Gaussian Basis Sets for Use in Correlated Molecular Calculations. VI. Sextuple Zeta Correlation Consistent Basis Sets for Boron through Neon. J Mol. Struct. 1996, 388, 339−349. (22) Cizek, J. On the Use of the Cluster Expansion and the Technique of Diagrams in Calculations of Correlation Effects in Atoms and Molecules. In Advances in Chemical Physics; John Wiley & Sons, Inc.: New York, 1969; pp 35−89. (23) Purvis, G. D.; Bartlett, R. J. A Full Coupled-Cluster Singles and Doubles Model: the Inclusion of Disconnected Triples. J. Chem. Phys. 1982, 76, 1910−1918. (24) Scuseria, G. E.; Schaefer, H. F. Is Coupled Cluster Singles and Doubles (CCSD) More Computationally Intensive Than Quadratic Configuration-Interaction (QCISD). J. Chem. Phys. 1989, 90, 3700− 3703. (25) Scuseria, G. E.; Janssen, C. L.; Schaefer, H. F. An Efficient Reformulation of the Closed-Shell Coupled Cluster Single and Double Excitation (CCSD) Equations. J. Chem. Phys. 1988, 89, 7382−7387. (26) Pople, J. A.; Headgordon, M.; Raghavachari, K. Quadratic Configuration-Interaction: A General Technique for Determining Electron Correlation Energies. J. Chem. Phys. 1987, 87, 5968−5975. (27) Petersson, G. A. Perspective on ″The Activated Complex in Chemical Reactions″ Eyring H (1935) J Chem Phys 3: 107. Theor. Chem. Acc. 2000, 103, 190−195. (28) Truhlar, D. G.; Garrett, B. C.; Klippenstein, S. J. Current Status of Transition-State Theory. J. Phys. Chem. 1996, 100, 12771−12800. (29) Laidler, K. J.; King, M. C. Development of Transition-State Theory. J. Phys. Chem. 1983, 87, 2657−2664. (30) Zhou, C. W.; Simmie, J. M.; Curran, H. J. Rate Constants for Hydrogen Abstraction by HO•2 from n-Butanol. Int. J. Chem. Kinet. 2012, 44, 155−164. (31) Johnston, H. S.; Heicklen, J. Tunneling Corrections for Unsymmetrical Eckart Potential Energy Barriers. J. Phys. Chem. 1962, 66, 532−533. (32) Pitzer, K.; Gwinn, W. Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation. I. Rigid Frame with Attached Tops. J. Chem. Phys 1942, 10, 428−440. (33) Simmie, J. M. Kinetics and Thermochemistry of 2,5Dimethyltetrahydrofuran and Related Oxolanes: Next Next-Generation Biofuels. J. Phys. Chem. A 2012, 116, 4528−4538. (34) Tumanov, V. E.; Kromkin, E. A.; Denisov, E. T. Estimation of Dissociation Energies of C−H Bonds in Oxygen-Containing

DMTHF with HO2. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(H.K.C.) E-mail: [email protected]. Tel: 49/(0)241/ 80-26409. Fax: 49/(0)241/80-22175. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Cluster of Excellence “Tailor Made Fuels from Biomass,” which is funded by the Excellence Initiative by the German federal and state governments to promote science and research at German universities.

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ABBREVIATIONS MTHF, 2-methyltetrahydrofuran; DMTHF, 2,5-dimethyltetrahydrofuran; CTST, conventional transition state theory; RRHO, rigid-rotor harmonic oscillator; IRC, intrinsic reaction coordinates; TSs, transition states

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REFERENCES

(1) Janssen, A. J.; Kremer, F. W.; Baron, J. H.; Muether, M.; Pischinger, S.; Klankermayer, J. Tailor-Made Fuels from Biomass for Homogeneous Low-Temperature Diesel Combustion. Energy Fuels 2011, 25, 4734−4744. (2) Yang, W.; Sen, A. One-Step Catalytic Transformation of Carbohydrates and Cellulosic Biomass to 2,5-Dimethyltetrahydrofuran for Liquid Fuels. ChemSusChem 2010, 3, 597−603. (3) Christensen, E.; Yanowitz, J.; Ratcliff, M.; McCormick, R. L. Renewable Oxygenate Blending Effects on Gasoline Properties. Energy Fuels 2011, 25, 4723−4733. (4) Jones, J.; Fenske, M. Chemicals from Hydrocarbons by Vapor Phase Oxidation. Ind. Eng. Chem. 1959, 51, 262−266. (5) Westbrook, C. K. Chemical Kinetics of Hydrocarbon Ignition in Practical Combustion Systems. Proc. Combust. Inst. 2000, 28, 1563− 1577. (6) Altarawneh, M.; Al-Muhtaseb, A. H.; Dlugogorski, B. Z.; Kennedy, E. M.; Mackie, J. C. Rate Constants for Hydrogen Abstraction Reactions by the Hydroperoxyl Radical from Methanol, Ethenol, Acetaldehyde, Toluene, and Phenol. J. Comput. Chem. 2011, 32, 1725−1733. (7) Altarawneh, M. K.; Dlugogorski, B. Z.; Kennedy, E. M.; Mackie, J. C. Rate Constants for Reactions of Ethylbenzene with Hydroperoxyl Radical. Combust. Flame 2013, 160, 9−16. (8) Tan, T.; Pavone, M.; Krisiloff, D. B.; Carter, E. A. Ab Initio Reaction Kinetics of Hydrogen Abstraction from Methyl Formate by Hydrogen, Methyl, Oxygen, Hydroxyl, and Hydroperoxy Radicals. J. Phys. Chem. A 2012, 116, 8431−8443. (9) Altarawneh, M.; Dlugogorski, B. Z.; Kennedy, E. M.; Mackie, J. C. Theoretical Study of Reactions of HO2 in Low-Temperature Oxidation of Benzene. Combust. Flame 2010, 157, 1325−1330. (10) Auzmendi-Murua, I.; Charaya, S.; Bozzelli, J. W. Thermochemical Properties of Methyl-Substituted Cyclic Alkyl Ethers and Radicals for Oxiranes, Oxetanes, and Oxolanes: C−H Bond Dissociation Enthalpy Trends with Ring Size and Ether Site. J. Phys. Chem. A 2012, 117, 378−392. (11) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision B.01; Gaussian, Inc.: Wallingford, CT, 2009. (12) Montgomery, J. A.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VII. Use of the Minimum Population Localization Method. J. Chem. Phys. 2000, 112, 6532− 6542. M



Article

Compounds from Kinetic Data for Radical Abstraction Reactions. Russ. Chem. Bull. 2002, 51, 1641−1650. (35) Denisov, E. T.; Tumanov, E. V. Estimation of the Bond Dissociation Energy from the Kinetic Characteristics of Radical LiquidPhase Reactions. Russ. Chem. Rev. 2005, 74, 905−938. (36) Carstensen, H. H.; Dean, A. M.; Deutschmann, O. Rate Constants for the H Abstraction from Alkanes (R−H) by R′O•2 Radicals: A Systematic Study on the Impact of R and R′. Proc. Combust. Inst. 2007, 31, 149−157. (37) Aguilera-Iparraguirre, J.; Curran, H. J.; Klopper, W.; Simmie, J. M. Accurate Benchmark Calculation of the Reaction Barrier Height for Hydrogen Abstraction by the Hydroperoxyl Radical from Methane. Implications for CnH2n+2 where n = 2 −4. J. Phys. Chem. A 2008, 112, 7047−7054.

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Reaction Kinetics of Hydrogen Abstraction Reactions by Hydroperoxyl

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