Kinetics and Thermochemistry of 2,5-Dimethyltetrahydrofuran and

Article pubs.acs.org/JPCA

Kinetics and Thermochemistry of 2,5-Dimethyltetrahydrofuran and Related Oxolanes: Next Next-Generation Biofuels John M. Simmie* Combustion Chemistry Centre, School of Chemistry, National University of Ireland, Galway, Ireland 091 S Supporting Information *

ABSTRACT: The enthalpies of formation, entropies, specific heats at constant pressure, enthalpy functions, and all carbon− hydrogen and carbon−methyl bond dissociation energies have been computed using high-level methods for the cyclic ethers (oxolanes) tetrahydrofuran, 2-methyltetrahydrofuran, and 2,5dimethyltetrahydrofuran. Barrier heights for hydrogen-abstraction reactions by hydrogen atoms and the methyl radical are also computed and shown to correlate with reaction energy change. The results show a pleasing consistency and considerably expands the available data for these important compounds. Abstraction by Ȯ H is accompanied by formation of both pre- and postreaction weakly bound complexes. The resulting radicals formed after abstraction undergo ring-opening reactions leading to readily recognizable intermediates, while competitive H-elimination reactions result in formation of dihydrofurans. Formation enthalpies of all 2,3- and 2,5-dihydrofurans and associated radicals are also reported. It is probable that the compounds at the center of this study will be relatively cleanburning biofuels, although formation of intermediate aldehydes might be problematic.

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INTRODUCTION One of the most challenging issues in science today is creation of a sustainable refinery to transform inedible biomass into platform chemicals and biofuels.1 In particular, efficient conversion of cellulose by chemical or biological transformations into biofuels but without a negative impact on human or animal food supplies is of increasing importance.2−4 The very recent one-step catalytic transformation of carbohydrates and cellulosic biomass to 2,5-dimethyltetrahydrofuran (DMTHF) and 2-methyl-tetrahydrofuran (MTHF) by Yang and Sen5 shows that chemical methods are being actively developed to provide next-generation biofuels. The authors admit that their process is unlikely to be commercially viable in its current form but is a pointer to development of alternatives to the current market leader ethanol. A cyclic ether, DMTHF, is superior to ethanol with a higher energy density of 35.5 MJ/kg and a higher boiling point of 90−92 °C and is immiscible with water. Not much is known about its blending properties with gasoline in contrast to MTHF whose lower octane rating may limit its application as a blendstock.6,7 Much earlier the potential of 2-methyltetrahydrofuran as an automotive fuel extender had been explored, prompting a study of its atmospheric reactivity by Wallington et al.8 They found that it reacted 40% more rapidly with Ȯ H than the unmethylated tetrahydrofuran (THF). However, there are hardly any reports of the combustion properties of DMTHF or MTHF as a potential liquid transport fuel in shock tubes, flow reactors, flames, internal combustion engines, gas turbines, etc., except for a very recent study of the effects of 2-methylfuran on controlled autoignition.9 In fact, © 2012 American Chemical Society

only for the parent tetrahydrofuran have speciation studies in a jet-stirred reactor and ignition delay times behind reflected shock waves been carried out.11 Very recently, Kasper et al.10 studied premixed low-pressure THF, oxygen, argon flames by VUV-photoionization molecular beam mass spectrometry supplemented by electron ionization MBMS with high mass resolution. They measured the mole fractions of some 60 intermediates ranging from H2 to C4H6O2; their study provides a useful guide to this work because of the special effort that they put into the resolution of the initial fuel-destruction reactions. During the vapor-phase oxidation of C6−C16 hydrocarbons at comparatively low temperatures12−15 substantial amounts of cyclic ethers are formed, chiefly by cyclization of hydroperoxyalkyl radicals. Most detailed chemical kinetic models16 are unclear about the fate of these compounds and simply assume, for example, that tetrahydrofuran is consumed by Habstraction reactions, and the resulting radicals decompose promptly to formaldehyde and allyl radical. In a recent review Battin-Leclerc et al.17 made the point that the kinetic study of the oxidation of cyclic oxygenated compounds is really at its starting point. Since virtually all basic thermochemical and kinetic data are absent for these compounds the objective of this work is to provide a reliable framework as a prerequisite for future experimental, modeling, and simulation studies. Received: February 25, 2012 Revised: April 11, 2012 Published: April 11, 2012 4528

dx.doi.org/10.1021/jp301870w | J. Phys. Chem. A 2012, 116, 4528−4538

The Journal of Physical Chemistry A

Article

Table 1. Isodesmic Reactions for 2,5-Dimethyltetrahydrofuran (Hartrees and kJ mol−1 at 298.15 K) DMTHF CBS-QB3 G3 CBS-APNO ΔfH⊖(298.15 K) ±

−310.481787 −310.794524 −310.903333 −266.50 1.29 DMTHF

CBS-QB3 G3 CBS-APNO Δf H⊖(298.15K) ±

−310.481787 −310.794524 −310.903333 −265.04 2.54 DMTHF

CBS-QB3 G3 CBS-APNO ΔfH⊖(298.15K) ±

−310.481787 −310.794524 −310.903333 −263.98 3.19

+

DME

+

−154.746934 −154.880574 −154.935578 −184.1 0.5 OXTN

+

−192.761645 −192.938442 −193.007660 −80.54 0.63 DEE −233.205870 −233.430134 −233.511488 −184.20 0.8

=

THF

=

−232.017501 −232.239332 −232.322177 −184.20 0.71 THF

=

−232.017501 −232.239332 −232.322177 −184.20 0.71 THF

+

DEE

ΔH(rxn)

+

−233.205870 −233.430134 −233.511488 −252.2 0.8 33DMOXTN

14.05 14.79 13.77 14.20 0.52 ΔH(rxn)

+

−271.221399 −271.488824 −271.583093 −148.2 1.7 DIPE

11.90 12.63 15.03 13.18 1.64 ΔH(rxn)

−311.664864 −311.979982 −312.087310 −318.0 3.0

13.89 14.03 14.00 13.98 0.07

+

MCYCLOP

ΔH(rxn)

+

−235.338424 −235.609445 −235.688812 −106.0 0.9 MOXIRANE

10.46 11.01 11.31 10.92 0.43 ΔH(rxn)

−192.767508 −192.944155 −193.013869 −94.68 0.63

−0.45 −0.27 −0.09 −0.27 0.18

−232.017501 −232.239332 −232.322177 −184.1 0.71

Table 2. Isodesmic Reactions for 2-Methyltetrahydrofuran (Hartrees and kJ mol−1) at 298.15 K MTHF CBS-QB3 G3 CBS-APNO ΔfH⊖ ±

■

CBS-QB3 G3 CBS-APNO Δf H⊖ ±

−271.249642 −271.516909 −271.612981 −224.32 1.47 MTHF −271.249642 −271.516909 −271.612981 −225.98 1.15

+

CYCLOP

+

−196.110268 −196.336060 −196.402314 −76.8 0.81 OXIRANE

=

THF

=

−232.017501 −232.239332 −232.322177 −184.20 0.71 THF

−153.535197 −153.666475 −153.723030 −52.63 0.63

−232.017501 −232.239332 −232.322177 −184.20 0.71

COMPUTATIONAL METHODS Electronic structure calculations were performed with the application Gaussian-0918 employing the model chemistries CBS-QB3, G3, and CBS-APNO.19−23 Although not without disadvantages, this combination of methods tends to give very good results as seen in our earlier work24,25 where both the methodology and the statistical treatment is discussed. Briefly, the enthalpy of formation of the target species, xj, from isodesmic reaction j is calculated algebraically together with an uncertainty uj = (Σui 2 ) 1/2 , where uj encapsulates the uncertainties of the companion species and of the reaction enthalpy. The final reported formation enthalpy is obtained from a weighted grand mean x̅ = ∑(xj/u2j )/∑(1/u2j ) and the final uncertainty from u̅ = 1/[∑(1/u2j )]1/2. In this study the computed reaction enthalpies show very little scatter as seen in Tables 1 and 2, where the reaction enthalpy uncertainty is expressed as ±σ. Computation of thermochemical parameters utilized the THERMO module of the Multiwell package26 and was based on B3LYP/CBSB7 geometries, scaled harmonic frequencies, and relaxed hindered rotor scans. Tetrahydrofuran is ‘conformationally versatile’ with pseudorotation of the puckered ring, resulting in low-frequency modes.27,28 A proper account of its thermochemistry requires a more exact treatment than is done here;29 fortunately the methyl-substituted furans are somewhat less versatile. In DMTHF both methyls can be above the plane, cis conformer,

or one above and one below, trans conformer. The energies of both conformers are virtually identical; the calculations reported here are based on the trans conformer for DMTHF and on the equatorial methyl in MTHF. Barriers to the 3-fold methyl rotations are typically on the order of 12.6−13.4 kJ mol−1. The barrier heights to hydrogen abstraction from all three tetrahydrofurans have been mostly calculated at the CBS-QB3 and G3 levels, but all three model chemistries were employed for the overall reaction energy change; barriers and reaction energies refer to zero-point-corrected electronic energies at 0 K, that is, ΔE‡(0 K) ± σ. Conventional transition state theory calculations were carried out with the same code; 26 contributions to the rate constant from asymmetric Eckart tunnelling were included. ΔfH⊖(298.15 K) of Tetrahydrofurans. The enthalpies of formation and thermodynamic data, in general, are little known for these simple tetrahydrofurans. Pell and Pilcher30 determined the enthalpy of formation of the parent tetrahydrofuran as ΔfH⊖(298.15 K) = −184.2 ± 0.71 kJ mol−1 from measurements of the heat of combustion by flame calorimetry (cf. −184.9 ± 5.2 kJ mol−1 from atomization calculations); their number is therefore adopted and used to determine the values for 2-methyl- and 2,5-dimethyltetrahydrofurans. Isodesmic reactions are employed to calculate the reaction enthalpy via three high-level composite methods, CBS-QB3, G3, and CBS-APNO. Thus, the heat of formation of 2,54529



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The self-same bond in 2-methyltetrahydrofuran has been reported at 384.1 kJ mol−1 by Denisov et al.41 on the basis of correlations and that in 2,5-dimethyltetrahydrofuran39 at 387.5 kJ mol−1 again based on correlations. These compare with the 388−389 kJ mol−1 of this work. While the agreement is very good for the C2−H bond in these tetrahydrofurans, the similar bond in the unsaturated furan is wildly underestimated by the correlation approach at 408 kJ mol−1 versus values of ∼500 kJ mol−1 obtained through a series of high-level calculations.24 In a theoretical determination of the heats of formation of furan, tetrahydrofuran, and its associated radicals Feller and Franz42 used large basis set coupled cluster calculations with corrections for core/valence, atomic spin−orbit, and relativistic effects to compute atomization energies. Their result for THF of −184.1 ± 2.1 kJ mol−1 is in excellent agreement with the experimental value.30 On the basis of their results, tetrahydrofuran bond energies of 400 ± 5 and 417 ± 5 kJ mol−1 can be extracted for C2−H and C3−H, respectively, which are somewhat higher than those found here, although the BDE dif ferences are in very good agreement. In subsequent work Feller43 recomputed the radical energies at CCSD(T)/ccpVQZ (these could only be estimated in their year 2000 paper) and reports 399 ± 7 and 418 ± 7 kJ mol−1 for C2−H and C3− H, respectively. In a theoretical study of C−H bond dissociation enthalpies in ethers Agapito and co-workers44 report ΔfH⊖(C3−H) = 410 kJ mol−1 for THF from CBS-Q computations versus the 411.6 kJ mol−1 of this study. Breakage of this bond leads to a β-furanyl radical, whereas the formation of the α-furanyl radical arises from breaking the C2−H bond which they put at 392.2 kJ mol−1 versus the 392.4 ± 0.7 kJ mol−1 value of this work. They rationalize these differences between the α- and the β-positions by observing that the higher BDE of the β-C−H bond arises from the lack of stabilization of the β-radical since the O atom is now too far away to be involved in the delocalization of the unpaired electron. The values reported here support their contention that the remoteness from the heterocyclic O atom strengthens the C−H bond; incorporation of one or two methyl groups slightly weakens the C2−H bond while strengthening the more remote C−H bonds. The difference between the α- and the β-radicals is enhanced on methyl substitution by a quite weak hyperconjugative effect. The correlation noted by Przybylak and Cronin45 for the radicals of ethers that stabilization is reflected by the spin distribution with the most stable radicals (that is, those with the weakest C−H bond energies) having spin distributions delocalized over various atoms is true here also. As regards carbon−methyl bonds, values of 361.6 ± 2.4 and 360.8 ± 2.1 kJ mol−1 for MTHF and DMTHF, respectively, can be calculated. It does not appear that previous determinations exist; the closest analogy is with the 358.2 ± 5. kJ mol−1 value for methylcyclopentane.46 The presence of an oxygen atom in the ring thus appears to have very little effect on the C−CH3 bond strength.

dimethyltetrahydrofuran can be calculated from the hypothetical reaction shown schematically in Figure 1 and numerically in Table 1.

Figure 1. Isodesmic reaction for DMTHF.

Once the reaction enthalpy of 13.18 ± 1.64 kJ mol−1 has been calculated the known heats of formation for oxetane,30 THF, and 3,3-dimethyloxetane31 yield ΔfH⊖(298.15K) = −265.04 ± 2.54 kJ mol−1, see Table 1. Together with two other isodesmic reactions involving dimethyl,30 diethyl,32 and di-isopropyl33 ethers as well as THF as companions results in a final enthalpy of formation of −265.95 ± 1.08 kJ mol−1 for DMTFH, Table 1. A value for 2-methyltetrahydrofuran of −225.35 ± 0.91 kJ mol−1 follows by choosing a similar set of isodesmic reactions utilizing oxirane/methyloxirane/THF,30,34 Figure 2, and cyclo-

Figure 2. Isodesmic reaction for MTHF.

pentane/methylcyclopentane/THF35 combinations, Table 2. A value of −228 kJ mol−1 from a CBS-QB3 atomization calculation has been reported by Wijaya et al.13 As a check, a reaction enthalpy of −0.36 ± 0.72 kJ mol−1 can be computed directly for the scrambling reaction: DMTHF + THF = 2MTHF. Thus, this scrambling reaction is essentially thermoneutral within experimental errorunsurprising given its isogeitonic character.36 Finally, if the calculated ΔfH values for MTHF and DMTHF given above are used together with the THF value a reaction enthalpy of −0.55 ± 1.82 kJ mol−1 results, which is in excellent agreement with the directly computed value. This level of agreement shows that a good choice of isodesmic reactions has been made. In conclusion, a consistent set of values has emerged, although these do depend absolutely upon the anchoring number for THF. Bond Dissociation Energies. Bond dissociation energies of each carbon−hydrogen were computed directly from separate calculations of the energies of H atoms, radical, and parent molecule with the results shown in Table 3. Values for the C−H bond adjacent to the O atom in TFH (labeled C2−H in the table) in the literature range37−39 from 384.9 to 391.6 ± 0.4 kJ mol−1 with 385.3 ± 6.7 recommended.40 The computed value of 392.4 ± 0.7 kJ mol−1 lies just within this range. Table 3. Bond Dissociation Energies (kJ mol−1) molecule

CH2−H

C2−H

C3−H

THF MTHF DMTHF

n/a 430.9 ± 1.5 431.8 ± 1.2

392.4 ± 0.7 388.7 ± 0.4 387.7 ± 0.8

411.6 ± 0.2 415.7 ± 0.3 414.5 ± 0.1 4530

C4−H 411.0 ± 0.5

C5−H

C−CH3

391.9 ± 0.3

n/a 361.6 ± 2.4 360.8 ± 2.1



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preferred. This compares favorably with our computed value of 302.8 J mol−1 K−1 (see Supporting Information document). The constant pressure heat capacity, CP, has been calculated by Dorofeeva29 as 76.6 ± 1.0 J mol−1 K−1 at 298.15 K, 134.4 J mol−1 K−1 at 500 K, and 255.1 J mol−1 K−1 at 1500 K; these are in good agreement with the 80.3, 136.9, and 257.1 J mol−1 K−1 values, respectively, of this work. Hossenlopp51 reported 133.7 ± 2.5 at 500 K. The third Millennium database47 gives data (based on G3B3 calculations and on the heat of formation due to Pell and Pilcher30) in the form of NASA polynomials52 from which one can back calculate S, CP, etc., for THF with application ChemThermo.53 These are in good agreement with the values computed here. Good agreement is obtained with the entropy and specific heats reported by Wijaya et al.13 for 2-methyloxolane, which were obtained from scaled CBS-QB3 frequencies and relaxed B3LYP/6-31G(d) scans of hindered rotorsnot that dissimilar to the procedures used here.

Comparisons with the unsaturated analogues is instructive; the CH2−H bond is much stronger in the tetrahydro species, 431 versus 358 kJ mol−1 in methylfurans, whereas the ringcarbon−H bonds are substantially weaker, 388−416 versus > 500 kJ mol−1. The carbon−methyl bond energies are substantially stronger in the unsaturated furans than in the saturated furans, 480 versus 360 kJ mol−1. ΔfH⊖(298.15 K) of Tetrahydrofuran Radicals. The heats of formation of the various radicals can be extracted from the above-mentioned bond dissociation energies or computed directly. In the case of the tetrahydro-2-furanyl or αtetrahydrofuranyl (abbreviated to THFR2) radical the value obtained from a BDE of 392.4 ± 0.7 kJ mol−1 yields −9.8 ± 1.0 kJ mol−1; this is in good agreement with values of −11.36 ± 1.50 and −11.2 ± 2.1 kJ mol−1 derived from the isodesmic reactions ̇ 2OH THFR2 + CH3OH = THF + CH

■

̇ 2CH 2OH THFR2 + CH3CH 2OH = THF + CH

KINETICS H-Abstraction Reactions. By H Atoms. As a counterpoint to computation of bond dissociation energies the barrier heights faced by H-abstraction reactions by Ḣ have also been computed, see Table 5. Thus, abstraction from methyl faces a higher barrier than abstraction from the ring, abstraction of remote hydrogens face an intermediate barrier of ∼36 kJ mol−1, while abstraction of hydrogens near the heterocyclic O atom have slighter barriers of ∼18 kJ mol−1. The G3 and CBS-QB3 results are reasonably consistent; in the worst-case scenario for abstraction from 2-methyltetrahydrofuran, for example, the average barrier height is 32.4 ± 2.1 kJ mol−1 with the G3 values always consistently higher than the CBS-QB3 viz. 33.9 versus 31.0 kJ mol−1. For reaction energies the position is reversed with G3 being less exothermic at −30.2 kJ mol−1 versus the CBS-QB3 value of −33.2 kJ mol−1. The Evans−Polanyi-type plot shows a pleasing consistency between barrier heights and reaction energies (and bond energies too), Figure 3. Kinetically, therefore, abstraction from the C2 sites dominates over the whole temperature range from 500 to 2000 K with rate constants (in cm3 mol−1 s−1) of

for which the computed reaction enthalpies are 11.76 ± 1.25 and 35.69 ± 1.86 kJ mol−1, respectively. The heats of formation of the companion alcohol and its associated radical are taken from the third Millennium database;47 these probably represent the best known heats of formation of an oxygen-containing carbon-centered radical. The final standard formation enthalpy for α-tetrahydrofuranyl is thus −11.29 ± 1.22 kJ mol−1, while the β-tetrahydrofuranyl radical (THFR3) is less stable by 19.23 ± 0.91 and therefore has a heat of formation of +7.94 ± 1.0 kJ mol−1. The other formation enthalpies can now be computed, see Table 4, via isodesmic reactions of the type Table 4. Radical Formation Enthalpies (kJ mol−1) ΔfH⊖(298.15 K)

radical

−11.3 +7.9 −56.2 −29.2 −33.8 −52.9 −13.9 −98.0 −71.2 −53.9

tetrahydro-2-furanyl tetrahydro-3-furanyl tetrahydro-2-methyl-2-furanyl tetrahydro-2-methyl-3-furanyl tetrahydro-2-methyl-4-furanyl tetrahydro-5-methyl-2-furanyl tetrahydro-2-furanylmethyl tetrahydro-2,5-dimethyl-2-furanyl tetrahydro-2,5-dimethyl-3-furanyl tetrahydro-5-methyl-2-furanylmethyl

± ± ± ± ± ± ± ± ± ±

1.2 1.5 1.8 1.9 2.0 1.8 2.6 1.9 2.0 2.7

C2 k = (3.92 × 105)T 2.354 exp( −321.1/T ) C3 k = (3.38 × 103)T 3.005 exp( −1.967/T ) Me k = (2.14 × 103)T 3.064 exp( −3.309/T )

MTHFRy + THF = MTHF + THFRz

The tunnelling contributions range from 60% at 1000 K diminishing to 20% at 1500 K for the methyl and C3 abstractions; those for the C2 site are some 50% lower. By Methyl Radical. H abstraction by Ċ H3 follows a similar pattern with the highest barrier faced by removal of a side-chain H atom and the least for the near H atom, Table 6.

where y = 2−5 and z = 2, 3, etc., all of these anchored by the result for α-tetrahydrofuranyl. Entropies and Heat Capacities. For tetrahydrofuran reported values48−50 of the entropy at 298.15 K range from 288 to 299.1 to 301.7 ± 1.7 J mol−1 K−1 with the latter

Table 5. G3 Barriers and Reaction Enthalpies for H Abstraction by Ḣ (kJ mol−1) at 0 K CH2−H molecule THF MTHF DMTHF

E† 48.5 50.2

C2−H

C3−H

C4−H

C5−H

ΔrH

E†

ΔrH

E†

ΔrH

E†

ΔrH

E†

ΔrH

−12.1 −10.2

21.6 14.0 16.2

−47.5 −51.5 −52.4

35.2 36.1 38.0

−29.3 −25.3 −26.5

33.9

−30.2

20.3

−48.1

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hydrocarbon oxidation. However, the barrier for these reactions is ∼200 kJ mol−1 and thus unlikely. The increased reactivity noted by Wallington et al.8 must arise from the additional channel open to MTHF but not to THF, that is, abstraction from the methyl groupcounterbalanced by the loss of one abstractable hydrogen from a C2 site. The other channels are of comparable reactivity for both species. Bond Scission. The weakest bond in the molecule is the methyl−ring bond, C−CH3; an estimate of the rate constant for C−C scission kcc can be gleaned from the calculated equilibrium constant for DMTHF = MTHFR5 + Ċ H3 and on the assumption that the rate constant55 for methyl + ethyl recombination of k = (2.04 × 10−9)T−0.562 exp(−10.3/T) cm3 molecule−1 s−1 is transferable. Under this assumption, kcc = (4.214 × 1024)T−2.329 exp(−44 356/T) s−1. Ring-Opening Reactions. β-Radical. Existing detailed chemical kinetic models assume that radical attack on THF results in H-atom abstraction to form an unspecified radical, which then ring opens with an activation energy of 146 kJ mol−1 to yield formaldehyde and allyl radical.11 This is the case in reality for the β-furanyl radical (THFR3), which ring opens to form a carbon-centered ethenyloxymethyl radical Ċ H2OCH2CHCH2 with a barrier height of 137.3 ± 1.3 kJ mol−1this then presumably bond scissions to the requisite products, Figure 4.

Figure 3. Evans−Polanyi plot for H abstractions by Ḣ (BDE): triangles, THF; squares, MTHF; circles, DMTHF.

As previously discussed, abstraction from the C2 sites dominates over the whole temperature range from 500 to 2000 K with rate constants (in cm3 mol−1 s−1) of Figure 4. Ring opening of tetrahydrofuran β-radical via C−C bond scission.

C2 k = (2.43 × 103)T 2.818 exp( −4392/T ) C3 k = (1.08 × 103)T 2.887 exp( −6251/T )

However, formation of an oxygen-centered radical intermediate is equally possible and in fact faces a slightly lower barrier of 129.4 ± 1.8 kJ mol−1 for THFR3, Figure 5; the final products are however the same.

Me k = (9.74 × 102)T 2.886 exp( −7521/T )

By OH Radical. H-abstraction barriers encountered by the OH radical are much lower than those above; for example, abstraction from the side chain slumps from 70 (Ċ H3) to 50 (Ḣ ) to 13 (Ȯ H) kJ mol−1. Abstraction from the other sites is less straightforward involving formation of both pre- and postreaction complexes as evidenced by the negative barriers found. In their overview of these types of weakly bound complexes Galano and Alvarez-Idaboy54 tabulate binding energies ranging from −13 to −31 kJ mol−1 for a series of Ȯ H-radical complexes with oxygenated volatile organic compoundsthe values encountered here of −26.3 and −20.1 kJ mol−1 for DMTHF pre- and postreaction complexes during H abstraction from the C3 site are therefore typical. Another channel from these prereaction complexes is through ‘addition’ to the O atom by OH leading to formation of an alkyl hydroperoxide radical, that is, the reverse of the way in which cyclic ethers are typically formed during low-temperature

Figure 5. Ring-opening of tetrahydrofuran β-radical via C−O bond scission.

A similar pattern holds for the β-radicals of 2-methyltetrahydrofuran and 2,5-dimethyltetrahydrofuran, namely, two distinct channels with roughly identical barriers, Figure 6. The initially formed products P5a−P5d via TS5 then undergo further β-scission to give products P7 via transition states TS7a−TS7d, Figure 7, and the P6 intermediates yield

Table 6. G3 Barriers and Reaction Enthalpies for H Abstraction by Ċ H3 (kJ mol−1) at 0 K CH2−H molecule THF MTHF DMTHF

E† 68.3 70.0

C2−H

C3−H

C4−H

C5−H

ΔrH

E†

ΔrH

E†

ΔrH

E†

ΔrH

E†

ΔrH

−6.8 −4.9

47.7 40.7 42.8

−42.2 −46.2 −47.1

56.2 60.4 59.0

−23.9 −20.0 −21.1

54.9

−24.8

46.3

−42.8

4532



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Figure 6. Fate of β-radical: CBS-QB3 barrier heights and energy changes at 0 K (kJ mol−1).

Figure 8. β-Scission of P6 intermediates P6 → TS8 → P7 at CBSQB3.

Figure 7. β-Scission of P5 intermediates P5 → TS7 → P7.

Figure 9. Fate of α-radical: CBS-QB3 barrier heights and energy changes at 0 K.

exactly the same final products but via TS8a−TS8d, Figure 8. In the case of THF the allyl radical will give rise to propene and but-1-ene via Ḣ and Ċ H3 termination reactions, both of which were among the intermediates detected in the flame studies,10 while for DMTHF the methylallyl (2-buten-1-yl or 1-methyl-2propenyl) radical would give rise to but-1-ene and 3-methylbut-1-ene. α-Radical. For the α-radicals a not dissimilar situation pertains: two channels occur, one involving cleavage of a C−O bond (TS1) and the other cleavage of a C−C bond (TS2), Figure 9, but these two routes now have markedly different barrier heights. Once this initial β-scission has taken place it is followed by further β-scission reactions to complete the ring-opening process. In the case of the carbon-centered radicals (TS3), P1a−P1d, this is shown in Figure 10 and in the case of the Ocentered radicals (TS4), P2a−P2d, in Figure 11. In both cases products P3a−P3d result, and the potential energy diagram illustrates this point for the case of the α-

tetrahydrofuranyl radical, Figure 12. The presence of 2oxomethyl or formylmethyl radical in the products P3a provides a ready explanation for the large amounts of propanal and ethanal found in both the flame and the jet-stirred reactor studies.10,11 Note that these were the only oxygenated intermediates identified in the latter work. In addition to the β-scission reaction P1a → TS3 → P3a isomerization reactions involving 1,3- and 1,4-hydrogen shifts to form products are possible, Figure 13. Formation of a 1-oxobutyl radical, P16a, via a 1,4-shift is favored by a CBS-QB3 barrier of 71.0 kJ mol−1 as opposed to formation of 1formylpropyl, P17a, which faces a barrier of 139.0 kJ mol−1. Kinetically, therefore, below 1000 K the 1,4-H-shift prevails and above 1000 K the β-scission reaction, k(3a); the 1,3-shift, k(17a), does not compete 4533



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Figure 12. Potential energy diagram at CBS-QB3.

Figure 10. β-Scission of C-centered radicals P1 → TS3 → P3 at CBSQB3.

Figure 13. 1,3-H-shifts and 1,4-H-shifts; CBS-QB3 barriers and energy changes at 0 K.

ments at 30−80 °C. The computed high-pressure limit rate constant obtained here is (5.78 × 1014)exp(−8476/T) s−1; Méreau et al.58 report A∞’s of 1.8−7.5 × 1014 s−1 and Ea’s of 65.3−68.6 kJ mol−1 for propionyl decomposition from G2(MP2), B3LYP, and BH&HYLP calculations. The 1-oxobutyl radical P16a has a calculated mean adiabatic ionization energy of 6.66 eV and is slightly more stable by 7.5 ± 1.5 kJ mol−1 at 0 K than the P17a isomer, which was tentatively identified by Kasper et al.10 as the source of signals at m/z = 71 and with an ionization energy of ∼9.8 eV. The ready elimination of CO probably accounts for the consequent formation of n-butane, which was a feature of the flame studies; 10 times as much but-1-ene is formed presumably from the products P7a. Of course, ‘blocking’ the position at the doubly bonded carbon with a methyl group, P1b and P1d in Figure 9, prevents facile 1,4-H-atom transfer; P1c is not hampered, and the barrier for a 1,4-H-shift at 77.1 kJ mol−1 is almost identical to the previous case. Side-Chain Radicals. In the case of radicals formed by abstraction of a hydrogen atom from the methyl side chain a similar choice presents itself. One channel proceeds via a oxygen-centered radical (TS9) and the other via an carboncentered radical (TS10), Figure 14. The intermediate products P9 then undergo further reaction via TS11 to yield products P11, Figure 15, while intermediates P10 proceed to products P12 via TS12, Figure 16.

Figure 11. β-Scission of O-centered radicals P2 → TS4 → P3 at CBSQB3.

k(3a) = (2.63 × 1013)exp( −11 230/T ) k(16a) = (7.73 × 1011)exp( −7782/T ) k(17a) = (1.00 × 1012)exp( −15 685/T )

The 1-oxo-butyl radical P16a can easily eliminate CO and form an n-propyl radical ̇ ̇ OCCH 2CH 2CH3 → OC + CH 2CH 2CH3

The computed barrier of 61.9 kJ mol−1 is in good agreement with reported activation energies of 61−63 kJ mol−1 for RCH2Ċ O → RĊ H2 + CO, where R = CH3 and C2H5 by Pokidova et al.,56 and 61.1 kJ mol−1 of Kerr and Lloyd57 for 1oxo-propyl (propionyl) radical decomposition from measure-

Figure 14. Ring-opening choices for side-chain radicals at CBS-QB3. 4534



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Figure 15. β-Scission of O-centered radicals P9 → TS11 → P11 at CBS-QB3.

Figure 17. Formation of 2,3- and 2,5-dihydrofurans from β-radicals; G3 barriers and ΔH at 0 K.

Figure 16. β-Scission of C-centered radicals P10 → TS12 → P12 at CBS-QB3.

This, however, is not the end of the story as further βscission reactions can take place, resulting, for example, in formation of ethanal (acetaldehyde), ethene, and vinyl radical from both P11b and P12b. Kinetics of β-Scission Reactions. For the α-radical of 2,5dimethyltetrahydrofuran (DMTHFR2) ring opening, Figure 9, proceeds with a barrier of 91.7 kJ mol−1 to yield the 1-methyl-4oxopentyl radical; this and other calculated rate constants are shown in Table 7. Both MTHFR2 and THFR2 have very Table 7. Rate Constants for Ring-Opening Reactions radical DMTHFR2 P1d P2d DMTHFR3 P5d P6d

C5⇝O1 TS1d C3⇝C4 TS2d TS3d TS4d C2⇝O1 TS5d C5⇝C4 TS6d TS7d TS8d

Figure 18. Formation of 2,3-dihydrofurans from α-radicals; CBSAPNO barriers and energy change at 0 K.

ki/ s−1

bond broken (4.88 (7.41 (2.76 (6.88 (2.22 (3.90 (1.24 (3.79

× × × × × × × ×

13

10 )exp(−11 505/T) 1013)exp(−17 581/T) 1012 T0.399)exp(−10 493/T) 1011)exp(−4850/T) 1013)exp(−15 318/T) 1013)exp(−16 350/T) 1013 T0.424)exp(−8174/T) 1013)exp(−16 294/T)

Table 8. Dihydrofuran Formation Enthalpies (298.15 K; kJ mol−1) species 2,3-dihydrofuran 2,5-dihydrofuran 2,3-dihydro-5-methylfuran 2,3-dihydro-2-methylfuran 2,5-dihydro-2-methylfuran 2,3-dihydro-2,5-dimethylfuran 2,5-dihydro-2,5-dimethylfuran

similar barriers and ring-opening rate constants yielding 4oxopentyl and 4-oxobutyl radicals respectively. Elimination of H Atom. Elimination of a hydrogen atom from the β-radicals can lead to formation of 2,3- or 2,5dihydrofuran, Figure 17. The α radicals in contrast can only lead to 2,3-dihydrofurans, Figure 18. Both of these species were found by Kasper et al.10 in their premixed THF flames with the 2,3-dihydrofuran isomer being 2−3 times more abundant. This is a reflection of the greater number of formation routes and probably to the greater thermodynamic stability of the 2,3- over the 2,5-dihydrofuran. This latter observation holds for the methyl-substituted species as well, Table 8, with an additional

ΔfH⊖ −76.6 −63.2 −126.2 −119.7 −104.7 −172.3 −149.3

± ± ± ± ± ± ±

1.6 1.9 1.7 1.8 1.5 2.7 2.3

enhancement in stability seen for 2,3-dihydro-5-methylfuran with a methyl group located at the double bond; see below for a more detailed analysis. Even in the case of the β-radicals, where both 2,3- and 2,5dihydrofurans can be formed, there is a slight kinetic preference for formation of 2,3-dihydrofurans as evidenced by the lower barriers faced by TS13s, which are ∼15% lower in comparison 4535



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to TS14s. The results obtained for the reverse of reactions αradical → TS15 → P15 is somewhat problematic because the computed G3 barriers are very low and sometimes negative. There is no evidence for formation of prereaction complexes the IRC is clear on this point; the indications are that the compound method employed is incapable of a correct description. However CBS-APNO calculations do indicate small but positive reverse barriers. A somewhat similar situation was encountered in addition of an H atom to ethenol, CH2 CH(OH); addition to the methylene carbon is accompanied by a much smaller barrier59 than similar addition to the OH end of the double bond. Kinetics of H-Atom Eliminations. These processes are competitive with the β-scissions which lead to ring opening as discussed earlier. For example, in the case of the β-radical of 2,5-dimethyltetrahydrofuran the rate constants are

value for the vinyl radical. The resulting numbers are shown in Table 9; the bond dissociation energies of hydrogens attached Table 9. Formation Enthalpies of Dihydrofuran Radicals (298.15 K; kJ mol−1) radical 2,3-dihydro-5-furanyl 2,3-dihydro-4-furanyl 2,5-dihydro-3-furanyl 2,3-dihydro-2-methyl-5-furanyl 2,3-dihydro-2-methyl-4-furanyl 2,5-dihydro-2-methyl-3-furanyl 2,5-dihydro-2-methyl-4-furanyl 2,3-dihydro-2,5-dimethyl-4-furanyl 2,5-dihydro-2,5-dimethyl-3-furanyl

ΔfH⊖ 191.4 200.7 217.7 147.6 157.3 161.4 160.4 126.7 138.2

± ± ± ± ± ± ± ± ±

6.1 6.0 6.1 6.0 5.9 6.0 6.0 6.1 6.0

k(13d) = (3.37 × 1014)exp( −16 911/T ) k(14d) = (1.94 × 1014)exp( −18 939/T )

to double-bonded carbons are, not unexpectedly, all ∼500 kJ mol−1, very similar to the very high BDEs found for furans themselves.24 Interestingly, the C5−H bond dissociation energies are some 10 kJ mol−1 weaker than the C4−H bonds in the 2,3-dihydrofurans; this is in contrast with the furans where all ring-carbon−hydrogen bonds are equally strong.

that is, formation of the 2,3-isomer via TS13d is always favored by a factor of 100 at 500 K diminishing to a factor of 5 at 2000 K. In the case of the α-radical only one channel is possible and leads to 2,3-dihydrofuran; the rate constant in the case of the 2,5-dimethyl derivative is

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CONCLUSION Formation enthalpies ΔfH⊖(298.15 K) for 2-methyltetrahydrofuran and 2,5-dimethyltetrahydrofuran have been calculated and shown to be self-consistent with the known formation enthalpy of tetrahydrofuran. These were then used to determine heats of formation of a number of 2,3- and 2,5dihydrofurans. Harmonic oscillator, rigid rotor, and 1D-hindered rotor approximations have been used to compute entropy, specific heat at constant pressure, and enthalpy function for all three furans. There is reasonable agreement with previous data for tetrahydrofuran, but the values for MTHF and DMTHF are novel. The bond dissociation energies for carbon−hydrogen and carbon−methyl bonds have been determined and agree with some previous results in the literature, but this work rationalizes and provides a comprehensive data set of all possible C−H and C−CH3 bond energies in these systems. The radical formation enthalpies of many tetrahydro- and dihydrofurans have been determined. The barrier heights and reaction enthalpies for all possible hydrogen-atom abstraction reactions by H atoms and methyl radicals have been computed and shown to be internally consistent and also to correlate nicely with both reaction enthalpies and bond dissociation energies. Analysis of β-scission reactions from the initial α-, β-, and side-chain radicals, from each tetrahydrofuran parent molecule, show that irrespective of the paths followed the final products are the same, although kinetically the actual path traced is important. Formation of partially unsaturated dihydrofurans is shown to be competitive with ring opening. It is anticipated that pyrolysis and/or oxidation of dimethyltetrahydrofuran and less alkylated tetrahydrofurans can be readily simulated with a detailed chemical kinetic model given the familiar nature of the intermediates formed as shown here, although more work may be required to deal with the dihydrofuran compounds.

k(15d) = (2.84 × 1014)exp( −19 027/T )

ΔfH⊖(298.15 K) of Dihydrofurans. There is considerable disagreement in the heat of formation of even the simplest dihydrofuran. For example, values of −77.1 ± 2.8 kJ mol−1 derived from hydrogenation data of Allinger et al.60 by Slayden and Liebman,62 −72.25 ± 0.41 kJ mol−1 by Steele et al.,61 and most recently −98.4 kJ mol−1 by the Bozzelli group65 for 2,3dihydrofuran. Thus, in this case there is no ‘anchor’ that can be trusted to deliver on all the other formation enthalpies; consequently, both the atomization method and an isodesmic reaction (involving 2,3-dihydrofuran, tetrahydrofuran, and furan) were employed to determine this critical number. The values obtained are −76.5 ± 4.4 and −76.6 ± 1.6 kJ mol−1, respectively, which bisect the previous literature results. Consequently, the latter is adopted to anchor all subsequent dihydrofuran species, Table 8. This is in good agreement with the −76.7 kJ mol−1 value from atomization and isodesmic (involving THF, ethane, and ethene and, THF, cyclohexane, and cyclohexene chaperons) calculations at G3(MP2)//B3LYP by Taskinen,63 who concluded that the experimental value for the 2,3-isomer of −72.3 ± 0.4 kJ mol−1 was slightly too high. The extra stability of the 2,3-isomer over that of the 2,5-isomer of 13.4 ± 3.5 kJ mol−1 found here has been previously noted by Taskinen et al.,64 who reported 12.6 ± 0.5 kJ mol−1 in solution of dimethylsulfoxide, and in the theoretical calculations of Lay et al.65 The only other literature values are for 2,3-dihydro-5methylfuran (4,5-dihydro-2-methylfuran) of −122.6 kJ mol−1 from equilibrium measurements by Cocks and Egger66 and −130.2 ± 3.5 kJ mol−1 from bomb calorimetry by Pihlaja and Heikkila.67 The value reported here of −126.2 ± 1.7 kJ mol−1 is neatly bracketed by these earlier results. ΔfH⊖(298.15 K) of Dihydrofuranyl Radicals. The formation enthalpies of dihydrofuranyl radicals can be computed based on a series of isodesmic reactions, all of these anchored by previous work on 2- and 3-furyl radicals, which in turn were based on a 4536



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ASSOCIATED CONTENT

S Supporting Information *

Geometries and energies of reactants, intermediates, and transition states as well as entropies, specific heats, and enthalpy functions for all three oxolanes. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Computational resources were provided by the e-Irish National Infra Structure, e-INIS, programme, and, the Irish Centre for High-End Computing, ICHEC.

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Kinetics and Thermochemistry of 2,5-Dimethyltetrahydrofuran and

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