Theoretical Investigation of Intramolecular Hydrogen Shift Reactions in

Article pubs.acs.org/JPCA

Theoretical Investigation of Intramolecular Hydrogen Shift Reactions in 3‑Methyltetrahydrofuran (3-MTHF) Oxidation Prajakta R. Parab,† Naoki Sakade,‡ Yasuyuki Sakai,‡ Ravi Fernandes,§ and K. Alexander Heufer*,† †

Physico Chemical Fundamentals of Combustion, RWTH Aachen University, Schinkelstraße 8, 52062 Aachen, Germany Department of Mechanical Engineering, University of Fukui, Bunkyo 3-9-1, Fukui 9108507, Japan § Physikalisch Technische Bundesanstalt (PTB) Bundesallee 100, 38116 Braunschweig, Germany ‡

S Supporting Information *

ABSTRACT: 3-Methyltetrahydrofuran (3-MTHF) is proposed to be a promising fuel component among the cyclic oxygenated species. To have detailed insight of its combustion kinetics, intramolecular hydrogen shift reactions for the ROO to QOOH reaction class are studied for eight ROO isomers of 3-MTHF. Rate constants of all possible reaction paths that involve formation of cyclic transition states are computed by employing the CBS-QB3 composite method. A Pitzer− Gwinn-like approximation has been applied for the internal rotations in reactants, products, and transition states for the accurate treatment of hindered rotors. Calculated relative barrier heights highlight that the most favorable reaction channel proceeds via a six membered transition state, which is consistent with the computed rate constants. Comparing total rate constants in ROO isomers of 3-MTHF with the corresponding isomers of methylcyclopentane depicts faster kinetics in 3-MTHF than methylcyclopentane reflecting the effect of ring oxygen on the intramolecular hydrogen shift reactions.

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INTRODUCTION Sustainable and promising fuel candidates that can be alternatives or blending components to conventional gasoline or diesel based fuels is the main highlight of today’s world energy resources. Principal reasons are the issues regarding energy security and environmental safety concerning greenhouse emissions.1 In this regard, biofuels are gaining popularity among the other classes of fuels due to advanced synthetic approaches and their compatibility with modern engine technologies.1,2 Since these fuels are novel, more details into their chemical reactivity during combustion is yet to be revealed especially emphasizing the key factors influencing pollutant emissions at engine relevant conditions. Among the cyclic oxygenated species, biosynthetic approaches3−5 are found in the literature for 2-methylfuran (2-MF), 2,5-dimethylfuran (2,5-DMF), 2-methyltetrahydrofuran (2-MTHF), 3-methyltetrahydrofuran (3-MTHF), and 2,5-dimethyltetrahydrofuran (2,5-DMTHF), which have been considered to be favorable additives to gasoline or diesel fuels. Considering tetrahydrofurans, 3-MTHF and 2-MTHF can be synthesized using cellulosic biomass from the biogenic platform chemicals itaconic acid and levulinic acid, respectively.5 Itaconic acid obtained from green biomass6 was selectively converted into lactones and 2-methylbutanediol producing 3-MTHF in remarkable yield of 95% via cyclization of diol. The Cluster of Excellence, Tailor made fuel from Biomass (TMFB) at RWTH Aachen University, Germany, adopts such novel approaches for the biofuel synthesis. The vision of TMFB is to establish innovative © XXXX American Chemical Society

and sustainable 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 advance biofuels. Among furanics, 3-MTHF has been proposed to be one of the promising fuel components by TMFB.7 Understanding combustion phenomena of furans and their derivatives is of growing interest as can be seen from the ongoing research on experimental investigations,8−15 as well as studies dealing with the development of detailed chemical kinetic models.14−17 These detailed chemical kinetics models assist researchers in delineating fuel combustion properties over the wide temperature and pressure regime. However, compared with the broad investigation on hydrocarbon fuels such as alkanes and alcohols, research on cyclic oxygenated compounds, especially furanics, is limited and nearly at its starting point,18 which necessitates further extensive study on their combustion behavior. In this aspect, a review by Zador et al.19 specifically concentrates on the understanding of critical alkylperoxy and hydroperoxyalkyl reactions in relation to the modeling and prediction of low temperature combustion and autoignition. Low temperature combustion in alkanes is initiated by hydrogen atom abstraction from the fuel molecule (RH) to produce alkyl radical (R). In the next step, alkyl radical Received: August 25, 2015 Revised: October 6, 2015

A

DOI: 10.1021/acs.jpca.5b08277 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Table 1. Estimated Hindered Rotor Parameters in Pitzer− Gwinn Approximation bonding atoma C3

Figure 1. Labels of atoms in 3-methyltetrahydrofuran.

hydrogen abstracting C3 in transition states radical centered C3 C2, C5 C4 Cm O in C2−OOH or C5−OOH O in C3−OOH or C4−OOH O in Cm−OOH

type of rotor

V0,b cm−1

σc

CH3 • CH2 CHO CH2OO• CH2OOH OO• OOH CH3 CH3 CH2OOH OO• OOH OO• OOH OO• OOH OH OH OH

1050 400 700 2000 1800 1000 2000 800 150 900 1000 6000 1000 2000 850 1800 2200 1150 1000

3 2 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1

a

Abbreviations, C2, C3, C4, C5, and Cm are defined in Figure 1. The height of the hindrance potential. cThe symmetry number of the internal rotation. b

work, computational calculations are performed to reveal kinetics of important low temperature reaction class in 3-MTHF, which involves internal hydrogen transfer from the peroxy radical (ROO) of the fuel to form the corresponding hydroperoxyalkyl radical (QOOH). Detailed calculations are performed to obtain high-pressure limit rate constants for the titled reactions, and corresponding Arrhenius parameters are presented.

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COMPUTATIONAL DETAILS Electronic structure calculations involving geometry optimization, vibrational frequencies, and single point energy computation of reactants, transition states (TSs), and products are performed with the CBS-QB3 composite method21,22 implemented in Gaussian 09 package.23 Figure 1 represents the optimized three-dimensional structure of 3-MTHF with the labels used in this study. Considering the oxygen position as 1, ring carbons are numbered from C2 to C5 while Cm represents the methyl side chain carbon. Due to the nonplanar five-membered ring in 3-MTHF, ring hydrogens are distinguished as cis (c) and trans (t) with respect to the methyl side chain, while Hm denotes methyl hydrogen. Vibrational frequencies obtained at B3LYP/ CBSB7 level within CBS-QB3 method are scaled by 0.99 for zero point energy calculations and by 0.97 for the calculation of vibrational partition functions. The high-pressure limit rate constants for the hydrogen shift reactions from ROO radicals of 3-MTHF to form the corresponding QOOH product radicals as a function of temperature are determined with the help of the GPOP program24 employing conventional transition state theory (CTST).25 Asymmetric Eckart tunneling corrections26 are taken into account in CTST rate calculations within the GPOP program. This program suite has been developed for the theoretical interpretation and prediction of the rate constants of elementary reactions from the outputs of the quantum chemical calculation packages. Low frequency torsional modes in

Figure 2. Hindered rotor analysis for the methyl rotor attached to the C3 atom in the tetrahydrofuran ring: (a) definition of torsional angle α, for methyl rotor; (b) potential energy calculated using a CBS-QB3 method (open circle) and fitted curve (line); (c) partition function calculated from eigenstate energies (qexact), in comparison with harmonic oscillator (qHO), free rotor (qFR), and Pitzer−Gwinn (qPG) approximations.

undergoes O2 addition to form alkylperoxy radical (ROO), which is followed by intramolecular hydrogen shift reactions to form hydroperoxy alkyl radicals commonly denoted as QOOH. Kinetics of ROO and QOOH radical species plays an eminent role especially for modeling ignition behavior of the fuel during low temperature combustion. Apart from the importance of this reaction in combustion chemistry, ROO species are also found to be of prime importance in atmospheric chemistry.20 To the best of our knowledge no theoretical kinetic study is found in the literature highlighting low temperature combustion reactions of methyltetrahydrofurans. In the present B


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Figure 4. Species abbreviations used in this study. In ROOx, x is a carbon attaching OO• group. In TSx−y, x is a carbon atttaching OO• group and y is a hydrogen atom abstracted carbon. In QOOHx−y, x is a carbon attaching OOH group and y is a radical centered carbon. In RCHOx, x is a carbon attached to double bonded oxygen.

function (qexact) as seen from Figure 2c. Hence all the partition functions for CH3 internal rotor in ROO, TS, and QOOH are approximated by a Pitzer−Gwinn approximation with hindrance potential height of 1050 cm−1. In the case of TSs wherein hydrogen is abstracted from C3 and in the case of QOOH species involving a radical center on C3, the CH3 rotor is treated with estimated barrier heights of 800 and 150 cm−1 respectively. Similarly all the internal rotors in reactants, transition states, and products are evaluated by representative structure as provided in the Supporting Information (Figure S1−S15) and treated with estimated barrier heights by considering Pitzer−-Gwinn approximation, summarized in Table 1. V0 in Table 1 represents the height of the hindrance potential (cm−1); σ is the symmetry number for all the low frequency torsional modes in reactants, TSs, and products. All partition functions are computed with energy relative to the lowest energy isomer. Figure 3 shows another example of the hindered rotor analysis for a CH2OO• rotor attached to the C3 atom in the tetrahydrofuran ring. As seen in Figure 3a, α is the torsional angle defined between atoms C2−C3−Cm−O1.Figure 3b represents potential energies computed by using a CBS-QB3 method represented by open circles, and the solid curve represents Fourier-series interpolation. The partition functions calculated from eigenstate energies (qexact), in comparison with harmonic oscillator (qHO), free rotor (qFR), and Pitzer−Gwinn (qPG) approximations are highlighted in Figure 3c. Hindered rotor analysis plots evince that the free rotor approximation (qFR) is far off from the exact partition function (qexact), whereas quantitative good agreement can be seen employing Pitzer− Gwinn approximation (qPG) with that of exact partition function (qexact).

Figure 3. Hindered rotor analysis for CH2OO• rotor attached to the C3 atom in the tetrahydrofuran ring: (a) definition of torsional angle, α, for CH2OO• rotor; (b) potential energy calculated using a CBS-QB3 method (open circle) and fitted curve (line); (c) partition function calculated from eigenstate energies (qexact), in comparison with harmonic oscillator (qHO), free rotor (qFR), and Pitzer−Gwinn (qPG) approximations.

reactants, transition states, and products involved in the titled reaction are treated as hindered rotations with the torsional barrier heights computed using Pitzer−Gwinn like approximation.27,28 In order to provide a clear idea about the hindered rotor treatment, the plot of hindered rotor analysis for the methyl rotor attached to the C3 atom in 3-MTHF is shown in Figure 2. As seen from Figure 2a, α is the torsional angle, which is defined as the dihedral angle between atoms C2−C3−Cm−Hm. Open circles in the Figure 2b indicate potential energies calculated for the CH3 rotor in 3-MTHF at CBS-QB3 level, whereas the solid curve represents Fourier-series interpolation. The BEx1D (acronym for Basis-set Expansion solver for 1-Dimensional Schrödinger equation) program29 is used for the calculation of eigenstate energies of the hindered rotation. Partition functions directly derived from the eigenstate energies (qexact) as a function of temperature are shown by the open circles in Figure 2c. Partition functions calculated by assuming harmonic oscillator approximation are represented by qHO, those assuming free rotor approximation by qFR, and those assuming Pitzer−Gwinn approximation by qPG. Pitzer−Gwinn approximation (qPG) with hindrance potential height of V0 = 1050 cm−1 shows excellent agreement with the exact partition C


Article

The Journal of Physical Chemistry A Table 2. Thermodynamic Properties ΔfH298 ° , kJ mol−1

a

S298 ° , J mol−1 K−1 a

species

this work

ref

diff

tetrahydrofuran tetrahydrofuran-2-yl tetrahydrofuran-3-yl

−180.0 −7.6 11.1

−184.2 ± 0.71b −2.1 ± 4.2c 15.1 ± 4.2c

4.2 −5.5 −4.0

this work

ref

dif.a

304.1 306.6 310.9

301.7 ± 1.7d

2.4

(Value from this work) − (ref value). bPell et al.30 cFeller et al.32 dClegg et al.31

° ) and Standard Entropies (S298 ° ) at 298.15 K and Heat Capacity at Constant Table 3. Standard Enthalpies of Formation (ΔfH298 Pressure (Cp) for Temperatures between 300 and 1500 K for the Reactants and Products Involved in the Isomerization Reactions Cp (J mol−1 K−1) −1

species

ΔfH298 ° (kJ mol ) calculated

ROO2c ROO2t ROO3 ROO4c ROO4t ROO5c ROO5t ROOm QOOH2c-3 QOOH2c-4 QOOH2c-5 QOOH2c-m QOOH2t-3 QOOH2t-4 QOOH2t-5 QOOH2t-m QOOH3−2 QOOH3−4 QOOH3−5 QOOH3-m QOOH4c-2 QOOH4c-3 QOOH4c-5 QOOH4c-m QOOH4t-2 QOOH4t-3 QOOH4t-5 QOOH4t-m QOOH5c-2 QOOH5c-4 QOOH5c-m QOOH5t-2 QOOH5t-3 QOOH5t-4 QOOHm-2 QOOHm-3 QOOHm-4 QOOHm-5 RCHO2 RCHO4 RCHO5 RCHOm

−190.05 −187.52 −178.71 −161.35 −162.26 −188.02 −191.96 −147.36 −159.64 −145.74 −160.91 −134.03 −159.64 −148.11 −163.29 −135.56 −149.88 −118.60 −139.52 −106.12 −124.72 −120.48 −136.49 −97.03 −139.90 −120.03 −129.88 −96.62 −158.33 −145.68 −138.01 −162.15 −158.72 −144.83 −119.85 −103.82 −96.10 −120.20 −402.25 −320.41 −401.23 −292.70

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S298 ° (J mol

−1

−1

K ) calculated

391.46 397.31 394.72 396.12 391.52 393.32 391.53 404.87 403.94 398.37 393.13 400.36 403.88 402.71 393.73 403.48 401.23 402.54 398.02 410.83 401.70 412.98 401.86 412.67 404.27 414.08 410.44 413.39 400.29 417.93 403.20 398.54 409.67 399.23 415.12 415.54 417.15 415.42 343.05 347.04 343.96 362.86

SPECIES ABBREVIATIONS Species abbreviation adopted for the reactants, TSs, and products are highlighted in Figure 4. All together eight ROO isomers of 3-MTHF has been considered in this study, and

300 K

400 K

500 K

600 K

800 K

1000 K

1500 K

136.95 136.37 138.84 136.69 136.05 136.21 136.70 130.51 139.58 146.06 144.79 143.59 139.58 145.96 145.01 143.54 151.68 150.95 148.81 148.40 147.25 142.48 147.48 144.85 149.75 142.89 148.92 146.60 143.69 145.59 143.57 145.48 139.25 145.36 138.55 142.45 144.95 140.61 114.08 116.64 114.52 110.69

174.72 174.38 176.70 174.40 173.98 174.35 174.62 169.91 177.49 184.29 183.19 181.58 177.49 184.34 183.53 181.62 189.31 188.83 186.99 185.99 184.95 179.67 185.33 182.71 187.19 179.93 186.29 183.80 182.36 184.11 181.69 183.81 177.13 184.16 179.26 179.50 183.57 180.67 147.57 149.74 148.00 144.15

207.21 207.02 208.94 206.95 206.69 207.02 207.19 204.92 210.55 216.75 215.74 214.17 210.55 216.85 216.13 214.25 220.23 220.06 218.50 217.42 216.63 211.81 216.90 214.68 218.44 212.00 217.61 215.44 215.10 216.63 214.30 216.28 210.29 216.79 213.24 211.24 216.40 214.26 176.79 178.64 177.16 173.94

233.76 233.64 235.20 233.59 233.43 233.65 233.78 233.72 237.63 242.94 242.01 240.57 237.63 243.04 242.38 240.67 244.74 244.83 243.51 242.48 241.94 237.91 242.09 240.30 243.34 238.06 242.66 240.86 241.52 242.82 240.70 242.45 237.51 242.98 240.07 237.11 242.61 240.89 200.98 202.58 201.29 198.79

273.54 273.49 274.54 273.53 273.51 273.51 273.60 276.42 277.87 281.53 280.70 279.51 277.87 281.58 280.98 279.63 280.50 280.96 279.95 279.09 278.94 276.43 278.89 277.78 279.69 276.54 279.32 278.11 280.43 281.35 279.62 280.99 277.99 281.41 278.54 275.82 280.47 279.17 237.64 238.91 237.87 236.52

301.67 301.64 302.40 301.75 301.80 301.67 301.75 305.89 305.90 308.41 307.67 306.66 305.90 308.41 307.86 306.79 305.46 306.10 305.29 304.56 304.63 303.18 304.49 303.81 304.99 303.26 304.84 304.00 307.52 308.19 306.75 307.86 306.16 308.17 304.73 303.19 306.34 305.29 263.69 264.74 263.88 263.21

343.51 343.50 343.90 343.65 343.73 343.53 343.58 348.48 347.05 348.16 347.63 346.96 347.05 348.12 347.72 347.06 342.97 343.62 343.11 342.64 342.85 342.52 342.69 342.47 342.85 342.56 342.90 342.49 347.60 347.95 347.01 347.70 347.37 347.86 343.14 344.06 344.19 343.54 302.37 303.04 302.49 302.45

their abbreviations used are as follows. ROOx indicates alkylperoxy radical with OO positioned on carbon x. As discussed before, cis and trans isomers in ROO, TSs, and QOOH species of 3-MTHF are distinguished by alphabet c and t, respectively. D


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The Journal of Physical Chemistry A ROO2c in Figure 4 indicates alkylperoxy radical with OO group attached to the carbon bearing second position on the tetrahydrofuran ring followed by letter c indicating a cis isomer. TSs are abbreviated as TSx−y, wherein x denotes the carbon with the OO group while the site from which the hydrogen atom is being abstracted is indicated by letter y. TSm−2c denotes a transition state with the OO group centered on the methyl carbon and hydrogen being abstracted from cis carbon at position 2 on the ring. Product species QOOHx−y denotes hydroperoxyalkyl radical with OOH positioned on carbon x with radical center y. In case of 1,3 H-shift reactions, product species RCHOx are formed with x being the carbon bearing doubly bonded oxygen. RCHO2 shown in Figure 4 is formed via 1,3 H-shift reaction in ROO2 isomer of 3-MTHF, which involves hydrogen shift from C2 to form QOOH with radical center C2. This QOOH species is unstable and readily decomposes to give RCHO2 and OH radical.

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Table 5. Reaction Barriers and Energies for Hydrogen Shift Reactions reactanta ROO2c

ROO2t

ROO3

RESULTS AND DISCUSSION

Thermochemistry. Experimental studies on thermodynamic properties of 3-MTHF and its derivatives are not available in literature. However, limited experimental data can be found for tetrahydrofuran and its radical species. Pell and Pilcher30 reported ΔfH°298 for tetrahydrofuran to be −184.2 ± 0.71 kJ mol−1 from measurements of heat of combustion by flame calorimetry, whereas S298 ° as reported by Clegg et al.31 is −1 −1 301.7 ± 1.7 J mol K . In another study, Feller et al.32 theoretically calculated ΔfH°298 for tetrahydrofuran-2-yl and tetrahydrofuran-3-yl radical species. Table 2 lists computed thermodynamic properties of tetrahydrofuran, tetrahydrofuran2-yl, and tetrahydrofuran-3-yl determined in this work by atomization method with the CBS-QB3 method and its comparison with the values from literature.30−32 For tetrahydrofuran-2-yl and tetrahydrofuran-3-yl species, computed ΔfH298 ° are −7.6 kJ mol−1 and 11.1 kJ mol−1, deviating by 5.5 kJ mol−1 and 4.0 kJ mol−1, respectively, from the reported values.32 ΔfH°298 and S°298 values of tetrahydrofuran determined with the CBS-QB3 method differ by 4.2 kJ mol−1 and 2.4 J mol−1 K−1, respectively, from the experimental values,30,31 which are within the uncertainty limit of the CBS-QB3 method. Favorable comparison can be noticed between ΔfH°298 and S°298 determined in this work with that of literature. Hence, thermodynamic properties (standard enthalpies of formation, standard entropies, and heat capacities at constant pressures) for all the reactants and products involved in the isomerization reactions of 3-MTHF are computed employing the CBS-QB3 method and summarized in Table 3. C−H Bond Dissociation Energies. Bond dissociation energies (BDEs) for all C−H bonds in 3-MTHF are computed at CBS-QB3 level of theory and are listed in Table 4. From the

ROO4c

ROO4t

ROO5c

ROO5t

ROOm

Table 4. C−H Bond Dissociation Energies in 3-Methyltetrahydrofuran bonda

D0,b kJ mol−1

C2−H2t or C2−H2c C3−H3 C4−H4t or C4−H4c C5−H5t or C5−H5c Cm−Hm

387 396 406 387 418

H atomb

E0,c kJ mol−1

ΔE,d kJ mol−1

QOOH species

TS ring sizee

H5c Hm H4c H2t

88 97 110 165

28 55 43 −175

6 6 6 4

H3 H5t H4t H3 Hm H2c

207 83 111 112 128 157

29 23 38 26 51 −178

H5c H5t H2t H4t Hm H2c H4c H2c Hm H5c H4t

424 93 107 140 149 201 209 90 96 101 172

23 38 27 58 71 27 58 35 63 24 −122

H5t H3 H2t H5t Hm H3 H4c

192 195 93 106 117 127 171

24 39 20 30 63 40 −122

H5c H2c Hm H4c H5t

190 82 109 126 162

30 29 48 41 −176

H4t H2t H3 H4t H5c

211 87 104 136 168

41 29 32 46 −172

H4c H2c H5c H4c H2t H3 H4t Hm

218 64 67 83 123 126 140 169

46 28 27 49 28 41 49 −109

QOOH2c−5 QOOH2c−m QOOH2c−4 RCHO2 + OH QOOH2c−3 QOOH2t−5 QOOH2t−4 QOOH2t−3 QOOH2t−m RCHO2 + OH QOOH2t−5 QOOH3−5 QOOH3−2 QOOH3−4 QOOH3−m QOOH3−2 QOOH3−4 QOOH4c−2 QOOH4c−m QOOH4c−5 RCHO4 + OH QOOH4c−5 QOOH4c−3 QOOH4t−2 QOOH4t−5 QOOH4t−m QOOH4t−3 RCHO4 + OH QOOH4t−5 QOOH5c−2 QOOH5c−m QOOH5c−4 RCHO5 + OH QOOH5c−4 QOOH5t−2 QOOH5t−3 QOOH5t−4 RCHO5 + OH QOOH5t−4 QOOHm−2 QOOHm−5 QOOHm−4 QOOHm−2 QOOHm−3 QOOHm−4 RCHOm + OH

5 6 6 5 6 4 6 6 5 5 5 5 5 6 6 5 4 5 5 6 5 6 5 4 5 6 7 5 4 5 6 6 5 4 5 6 7 6 6 5 6 4

a

Reactant abbreviations and their chemical structures are given in Figure 4. bThe position of hydrogen atom being abstracted is given in Figure 1. cReaction barriers. dReaction energies. eRing size of the transition state.

computed values, it is observed that the C−H BDEs values for the secondary hydrogen atoms, α positions to the ring oxygen (H2t, H2c, H5t, and H5c in Figure 1) is 387 kJ mol−1

a

Atom labels are given in the Figure 1. bC−H bond dissociation energies calculated using CBS-QB3 method. E


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Figure 5. High pressure limit rate constants of the intramolecular hydrogen shift reactions in (a) ROOm, (b) ROO3, (c) ROO2c, (d) ROO2t, (e) ROO4c, (f) ROO4t, (g) ROO5c, and (h) ROO5t.

for 1,3 H-shift reactions were noticed to be highly negative ranging from −109 kJ mol−1 for ROOm reactant to −178 kJ mol−1 for ROO2t isomer highlighting the highly exothermic nature of these reactions. In the ROO3 isomer, 1,3 H-shift products are not observed due to the unavailability of hydrogen at this site. However, significantly high relative barrier heights for 1,3 H-shift makes these reaction channels least dominant among others. ΔE for all other reaction paths excluding the reactions proceeding via four-membered TSs are endothermic in nature. One of the factors affecting the energy barriers of these reactions is found to be the cis/trans position of the abstracted hydrogen to the OO radical center in 3-MTHF. For H5t hydrogen shift in ROO2t isomer, computed E0 is 83 kJ mol−1, which is 341 kJ mol−1 lower than the H5c shift in the same isomer. In ROO4c, E0 for H5c abstraction is 101 kJ mol−1, which is about 90 kJ mol−1 lower than the energy barrier involved for the abstraction of H5t. These results illustrate that H-shift cis to the peroxy group is accompanied by lower E0 than trans. Proximity of the ring oxygen in 3-MTHF to the abstracted hydrogen also influences E0 due to the higher electronegativity of the oxygen atom compared with the carbon resulting in weakening of C−H bond strengths on adjacent carbon sites. This effect is discussed in detail under BDEs section. Of all 3-MTHF isomers under study, significantly, the lowest E0 is noticed for H-shift reactions in the ROOm isomer (with OO radical on the methyl side chain). E0 for H-shift in this isomer from C2 and C5 are 64 and 67 kJ mol−1, respectively, which is about 15−20 kJ mol−1 lower than C5 H-shift in ROO2t and ROO2c. The ⟨S2⟩ eigenvalues calculated at MP2/CBSB3 level within CBS-QB3 composite method are given in Table S1 in the Supporting Information. Among all the transition states, reaction of ROO2t isomer forming TS2t−5c to give QOOH2t−5 showed large ⟨S2⟩ eigenvalue. Considering the spin-contamination correction in the CBS-QB3 method, which is −5.2 kJ mol−1 for ⟨S2⟩ = 0.96, the possible errors in

corresponding to the weakest C−H bond in 3-MTHF. The lower BDE of these secondary C−H bonds compared with C4−H4 bonds (also a secondary C−H) is due to the presence of the oxygen heteroatom adjacent to C2 and C5. Since the oxygen atom is comparatively more electronegative than carbon, this results in the weakening of C−H bond strengths at positions adjacent to the ring oxygen. The observed trend for C−H BDEs in 3-MTHF is C2, C5 (secondary) < C3 (tertiary) < C4 (secondary) < Cm (primary). As noticed, C2−H and C5−H bonds are weaker than C3−H3 (tertiary) by nearly 9 kJ mol−1, whereas the observed difference in BDEs between C2 and C5 and C4 (both secondary) is found to be around 19 kJ mol−1. A primary C−H bond, as expected, is the strongest among all the C−H bonds in 3-MTHF, with C−H BDE value of 418 kJ mol−1. Reaction Barriers and Energies. Reaction barriers involved for the intramolecular hydrogen shift reactions in ROO isomers of 3-MTHF are computed by considering the difference in energies (at CBS-QB3 method) between the TSs and reactants, represented by E0. The CBS-QB3 energy differences between products and reactants are used to compute reaction energies, ΔE, for the title reactions. Table 5 summarizes calculated E0 and ΔE for the intramolecular hydrogen shift reactions in all ROO isomers of 3-MTHF considered in this study. As seen from the values of reaction barriers, the lowest E0 is obtained for the 1,5 H-shift reactions making it the most favorable reaction channel among others. Relative energy barriers for reactions involving six membered TSs (1,5 H-shift reactions) in all ROO isomers are found to lie within 64− 96 kJ mol−1, with the lowest energy barrier (64 kJ mol−1) corresponding to ROOm isomer for the reaction involving H-shift from C2. Reactions involving H-shift from the same carbon site as that of the OO radical center proceed via a fourmembered TS giving RCHOx (x = 2, 4, 5, and m) and OH radical instead of hydroperoxyalkyl radical. Reaction energies F


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C2 site, which is at α position to the ring oxygen. The proximity of the ring oxygen to the abstracted hydrogens (H2c and H2t) results in lower C2−H2c and C2−H2t BDE values as seen in Table 4. C2−H2 and C5−H5 bonds in 3-MTHF exhibit BDE values of 387 kJ mol−1; however, their rates differ by 4−6 times in the temperature range 500 to 1250 K as observed from the Arrhenius plot in Figure 5a. QOOHm−2 formation is observed to proceed via a six membered TS ring, while a conjugated/bicyclic TS involving five and eight membered ring formation is seen in the case of QOOHm−5 production. The BDE for the C4−H bond is found to be 406 kJ mol−1, which is about 19 kJ mol−1 higher than C2−H (387 kJ mol−1) bonds in 3-MTHF, reflecting slower kinetics for QOOHm−4 formation compared with QOOHm−2 and QOOHm−5. 1,3 H-shift leading to RCHOm is a minor channel among all other H-shift reactions owing to its very high energy barrier of 169 kJ mol−1. This channel proceeds via a four membered TS ring, which further readily forms RCHOm and OH radical. H-Shift Reactions in ROO3. QOOH3−5 and QOOH3−2 formation (Figure 5b) are the most favorable paths in the ROO3 isomer proceeding via six and five membered TS rings, respectively, rate constants of which tend to approach values of 4.4 × 107 s−1 and 3.2 × 107 s−1 at 1250 K, while a difference of about an order of magnitude can be seen in the low temperature regime around 500 K. Although both transition states involves hydrogen shift from the site α to the ring oxygen, variation in rate constant arises due to the difference in the ring size of the TSs as discussed in the case of the ROOm isomer. Kinetics of QOOH3−4 and QOOH3−m are much slower than QOOH3−5 and QOOH3−2. QOOH3−4 is produced via a five membered ring TS like QOOH3−2; however, significant difference in rate constant between the two channels arises due to weaker C2−H bond strength assisting easy H-shift to produce QOOH3−2. H-shift from Cm, the primary carbon center in 3-MTHF, is least feasible accompanied with high energy barrier of 149 kJ mol−1 due to a strong Cm−Hm bond (418 kJ mol−1 BDE). Due to the instability of the formed primary radical, the rate constant for this channel is lowest among others as expected. H-Shift Reactions in ROO2c, ROO2t, ROO5c, and ROO5t (Neighboring Ring O). C−H BDEs at C2 and C5 sites are observed to be lowest among all C−H bonds in 3-MTHF, making these sites most favorable for hydrogen abstraction and further O2 addition to form the corresponding alkylperoxy radical (ROO) during low temperature combustion. ROO2c, ROO2t, ROO5c, and ROO5t represents alkylperoxy radicals formed after the first O2 addition on C2 and C5, neighboring the ring oxygen. The most favorable reaction channels in ROO2c and ROO2t involve H-shift from C5 to form QOOH2c−5 and QOOH2t−5, respectively, as shown in Figure 5c,d. Considerable difference can be seen in the kinetics of QOOH2c−3 and QOOH2t−3 toward lower temperature formation from ROO2c and ROO2t isomers, respectively, which may be due to the formation of hydrogen bonding between the oxygen atom of the peroxy group and the ring hydrogen H2t in the TS of former isomer. The second possible reason could be that in the ROO2c, the C3 hydrogen is trans to the peroxy radical while it is cis in the latter isomer making H-shift in ROO2t facile. Comparing the rate constant for the H-shift from Cm in ROO2c and ROO2t (Figures 5c,d) shows that a difference of around 2 orders of magnitude is determined in the high temperature regime. In ROO5c and ROO5t

the potential energy barrier may be as large as the magnitude of the correction, −5.2 kJ mol−1. High Pressure Limit Rate Constants. Arrhenius plots for the high pressure limit rate constants of the intramolecular hydrogen shift reactions for eight ROO isomers of 3-MTHF are highlighted in Figure 5. Rate constants for all possible hydrogen shift reaction channels are determined by fitting the calculated rate to the modified Arrhenius expression given as k = ATn exp(−Ea/(RT)) in the temperature range of 500 to 2000 K. Arrhenius rate parameters for each isomerization channel are listed in Table 6. Reactant and product abbreviations implemented in Table 6 are highlighted in Figure 4. Table 6. High-Pressure Limit Rate Constants for the Hydrogen Shift Reactions in 3-MTHF rate constantb reactant

a

ROO2c

ROO2t

ROO3

ROO4c

ROO4t

ROO5c

ROO5t

ROOm

product

a

RCHO2 + OH QOOH2c−3 QOOH2c−4 QOOH2c−5 QOOH2c−m RCHO2 + OH QOOH2t−3 QOOH2t−4 QOOH2t−5 QOOH2t−m QOOH3−2 QOOH3−4 QOOH3−5 QOOH3−m QOOH4c−2 QOOH4c−3 RCHO4 + OH QOOH4c−5 QOOH4c−m QOOH4t−2 QOOH4t−3 RCHO4 + OH QOOH4t−5 QOOH4t−m QOOH5c−2 QOOH5c−4 RCHO5 + OH QOOH5c−m QOOH5t−2 QOOH5t−3 QOOH5t−4 RCHO5 + OH QOOHm−2 QOOHm−3 QOOHm−4 QOOHm−5 RCHOm + OH

A 6.94 6.70 5.84 7.04 2.91 2.85 3.48 1.51 3.59 8.04 7.38 1.26 2.14 1.33 2.67 1.63 3.20 2.21 1.76 1.90 1.54 9.00 8.12 6.41 5.62 6.58 5.00 1.93 8.62 1.77 2.18 8.36 9.20 1.00 3.24 1.21 2.88

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

106 101 104 105 105 106 104 104 105 103 104 102 105 102 105 101 105 105 105 105 103 105 104 104 105 103 106 104 105 105 103 106 106 104 106 106 106

n

E/R

1.774 2.939 2.040 1.663 1.902 1.764 2.154 2.121 1.709 2.218 2.035 2.909 1.780 2.983 1.757 3.044 2.136 1.870 1.848 1.877 2.692 2.104 2.095 2.072 1.684 2.428 1.775 2.103 1.693 1.927 2.631 1.803 1.234 2.265 1.368 1.315 1.883

18241 21369 11036 8723 9853 17371 11098 11139 8127 13023 10586 13503 9252 14555 8898 19638 18618 10005 9762 9231 12166 18675 10380 11936 8066 12539 17946 11034 8577 10421 13418 18680 6256 12426 8532 6389 18483

a

Reactant and product abbreviations and their chemical structures are given in Figure 4. bRate constants are given by the Arrhenius expression, k (s−1) = ATn exp(−E/(RT)).

H-Shift Reactions in ROOm. Figure 5a highlights high pressure limit rate constant comparison of all possible hydrogen shift reaction channels in the ROOm isomer. Higher rate is obtained for QOOHm−2 formation involving H-shift from the G


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Figure 6. Product branching ratio of the intramolecular hydrogen shift reactions in (a) ROO2c, (b) ROO2t, (c) ROO3, (d) ROO4c, (e) ROO4t, (f) ROO5c, (g) ROO5t, and (h) ROOm.

H


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of 3-MTHFyl radicals on O2, isomerization, HO2 eliminations, and the subsequent reactions of QOOH radicals (second addition or unimolecular decompositions). 3-MTHF H-Shift Reaction Comparison with Methylcyclopentane. In order to understand the effect of ring oxygen on the kinetics of intramolecular hydrogen shift reactions in 3-MTHF, we carried out its comparison with similar reactions in methylcyclopentane (mcyc5), which is also a five membered ring compound with methyl substituent but without ring oxygen. Figure 7 represents mcyc5 structure with atom labels adopted in this study.

isomers, the most dominant channel involves 1,5 H-shift from C2, whereas formation of RCHO5 via 1,3 H-shift is least favorable, as indicated by the slowest rates for this channel in Figure 5g,h. H-Shift Reactions in ROO4c and ROO4t. Arrhenius plots e and f in Figure 5 summarize H-shift reactions in ROO4c and ROO4t isomers, respectively. Reactions involving H-shift from C2 and C5 are most favorable, associated with lowest energy barriers in both isomers. In ROO4c, 1,5 and 1,4 H-shift reactions forming QOOH4c−m and QOOH4c−5 follow similar kinetics in the entire temperature regime as depicted in Figure 5e, although these channels proceed via different TS rings. In ROO4t, H-shift from C3 and Cm to form QOOH4t−3 and QOOH4t−m, respectively, demonstrate similar kinetics as shown in Figure 5f Product Branching Ratio. Branching ratio for the intramolecular hydrogen shift reactions in ROO isomers of 3-MTHF from all possible abstraction sites are computed to provide an overall idea about the favorability of a particular reaction channel over 500 to 1250 K. For the hydrogen shift reactions in ROOm, branching ratio is depicted by Figure 6h, wherein at 500 K almost 99% contribution is seen from the C2 and C5 sites, which are α positions on the 3-MTHF ring, neighboring the ring oxygen atom. The percentage from these sites at 1250 K is around 88%, which is slightly lowered compared with 99% in the lower temperature regime. The remaining 11% at 1250 K arises from the C4 site to form QOOHm−4 radical. In the higher temperature regime, all isomers of 3-MTHF as summarized in Figure 6 show a higher percentage of product branching ratio from the α sites (C2 and C5), which varies from 84% in ROO2c to almost 100% in ROO3 isomer. Higher contribution from these sites arises because C−H bonds neighboring the ring O atom are weakest as observed from the computed C−H BDEs values ensuring faster H shift. ROO2c and ROO2t isomers depict comparatively different percentages for H shift from the methyl side chain. The former isomer with OO substituent at cis position to the methyl group contributes around 16% at low temperature, whereas around 43% is seen at high temperature as represented in Figure 6a, while almost no contribution is observed in latter isomer as summarized in Figure 6b. The major contribution of ROO2c for QOOH2c−m formation is due to the cis position of the peroxy radical to the abstracted H resulting in a highly favorable six membered ring transition state. However, in ROO2t, due to the trans position of the peroxy radical to the methyl hydrogen, this channel is not favored. The same reason holds for no QOOH2c-3 formation in the ROO2c isomer, while 17% is contributed for QOOH2t-3 due to cis H at the C3 site in ROO2t. Figure 6d,e displays branching ratios of ROO4c and ROO4t isomers, respectively. Analyzing percentages from C2 and C5 sites, we observed major contribution from C2 in both. Computed product branching percentages for QOOH4c−m production from ROO4c are 15% and 26% at 500 and 1250 K, respectively. In ROO5c and ROO5t as highlighted in Figure 6f,g, considerable branching fraction arises from C2 sites on the ring approaching almost 100% at lower temperature, whereas they are 89% and 77%, respectively at 1250 K. Figure 6c shows branching percentages of ROO3 depicting major contribution from C2 and C5 sites. Analyzing individual contribution from C2 and C5 sites, QOOH3−5 is observed in higher fraction over the entire temperature range than QOOH3−2. Isomerization may or may not be a kinetic limiting step regarding the whole complex mechanism that includes addition

Figure 7. Labels of atoms in methylcyclopentane.

All together six ROO isomers of mcyc5 are considered in this work. Structures of all six isomers with species abbreviation are represented in Figure 8. Like 3-MTHF, isomers of mcyc5 are

Figure 8. ROO isomers of methylcyclopentane.

distinguished as cis (c) and trans (t) with respect to methyl substituent on the five membered ring. Alkylperoxy radicals of mcyc5 are abbreviated as ROOx, with x being the position of the peroxy group. BDEs of all the C−H bonds in mcyc5 (Figure 9b) are computed with the CBS-QB3 composite method and compared with 3-MTHF values as shown in Figure 9a. At C2 and C5 sites in 3-MTHF, BDEs are found to be around 10 kJ mol−1, lower than those for the corresponding positions in mcyc5. The ring oxygen in 3-MTHF is found to have a I


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ring oxygen effect is observed on Cm−Hm bonds (Figure 9). As expected and discussed before, the lowest energy barriers in all ROO isomer of 3-MTHF are observed for the hydrogen transfer from C2 and C5 positions due to the weakest C−H BDE at these sites. For ROO2t isomers of both species, the energy barrier for H-shift from C5 (83 kJ mol−1) is found to be 22 kJ mol−1 lower than that in mcyc5 (105 kJ mol−1). Similar to 3-MTHF, the lowest energy barrier in mcyc5 is observed for the ROOm isomer involving H-shift from the C2 site; however, the reaction barrier in 3-MTHF is around 14 kJ mol−1 lower compared with that in mcyc5. Figure 10a−h compares total rate constant of 3-MTHF with mcyc5. Total rate constants for 3-MTHF and mcyc5 isomers are obtained by summing individual rate constants from all possible H-shift channels in a specific isomer. Solid and dashed lines in Figure 10a−h denote total rate constants computed for 3-MTHF and mcyc5, respectively. The ROOm isomer of 3-MTHF is found to have the highest rate constant over the entire temperature range as seen from Figure 10a, approaching

significant effect on BDE values at carbon sites adjacent to the ring oxygen atom, and this effect is observed to become less pronounced at sites away from this heteroatom. Value of the BDE at the C3 position in 3-MTHF is around 6 kJ mol−1 higher than that of the corresponding site in mcyc5, while no

Figure 9. C−H BDE comparison of (a) 3-MTHF with (b) methlcyclopentane in kJ mol−1 computed at CBS-QB3 method.

Figure 10. Comparison of total rate constants for (a) ROOm, (b) ROO3, (c) ROO2c, (d) ROO2t, (e) ROO4c, (f) ROO4t, (g) ROO5c, and (h) ROO5t with methlcyclopentane. Solid and dashed lines denote 3-methyltetrahydrofuran and methylcyclopentane, respectively.

Figure 11. Comparison of rate constants ROO2c with methlcyclopentane: (a) hydrogen shift from C2 or C5, (b) hydrogen shift from C3 or C4, and (c) hydrogen shift from Cm. Solid and dashed lines denote 3-methyltetrahydrofuran and methylcyclopentane, respectively. J



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a value 5.7 × 108 s−1 at 1250 K. Reaction kinetics of 3-MTHF isomers are observed to be faster than those of the corresponding isomers of mcyc5. Comparison of rate constants for individual sites in the ROO2c isomer of 3-MTHF with ROO2c isomer of mcyc5 is summarized in Figure 11. At lower temperature, a difference of about 2 orders of magnitude is seen between 3-MTHF and mcyc5 rate constants at the C5 site, which tends to differ by an order of magnitude at higher temperature as shown in Figure 11a. Reaction kinetics for C5 and Cm hydrogen transfer in ROO2c of 3-MTHF (Figure 11a,c, respectively) are faster than the corresponding isomer of mcyc5 over the temperature range 500 to 1250 K; however, observed kinetics for the hydrogen shift from C3 and C4 sites as shown in Figure 11b are faster in mcyc5 than in 3-MTHF. Comparison of rate constants for the titled reaction in the remaining seven ROO isomers of 3-MTHF with mcyc5 are summarized in Figures S16−S22 in the Supporting Information. From these comparisons, the effect of the ring oxygen can be clearly seen at C2 and C5 sites due to comparatively faster kinetics determined at these sites in 3-MTHF than in mcyc5. This is attributed to the lower BDEs at C2 and C5 sites in 3-MTHF due to the neighboring electronegative oxygen atom. These results indicate that the ring oxygen has a significant effect on the reaction kinetics of the intramolecular hydrogen shift reactions in all 3-MTHF isomers under this study.

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CONCLUSION

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +49 241 80-95370. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the 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 3-MTHF, 3-methyltetrahydrofuran; mcyc5, methylcyclopentane; TS, transition state; BDE, bond dissociation energy REFERENCES

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In this work, we performed theoretical study for computing high pressure limiting rate constants for the intramolecular H-shift reactions in alkylperoxy radicals (ROO) of 3-MTHF to form the corresponding hydroperoxyalkyl radicals (QOOH). All possible H-shift reaction channels from eight ROO isomers of 3-MTHF were studied, and the corresponding relative reaction barriers are reported. The most dominant H-shift channel is the one proceeding via a six membered transition state, whereas 1,3 H-shift are least favorable due to very high energy barriers for this channel. C−H bond dissociation energies at C2 and C5 sites in 3-MTHF are lowest (387 kJ mol−1) as a result of the neighboring electronegative oxygen atom. Weaker C−H bonds strengths at these sites assist easier H-shift compared with the C3, C4, and Cm. Effect of ring oxygen on the kinetics of the titled reaction is analyzed by comparing rate constant of 3-MTHF with ROO isomers of mcyc5. Total rate constant (obtained by summing individual rate constants) for 3-MTHF is found to be faster than that of mcyc5 in all isomers under study.

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b08277. Spin contamination for the transition state calculations of 3-MTHF, plots of hindered rotor treatment for the internal rotors in reactants, TSs and products in 3-MTHF, comparison of rate constants for the intramolecular H-shift reactions in ROO2t, ROO3, ROO4c, ROO4t, ROO5c, ROO5t and ROOm isomers of 3-MTHF with mcyc5, external symmetry and chirality number of 3-MTHF species, and reaction barriers and energies for the isomerization reactions in mcyc5 (PDF) K


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