Thermochemistry and Kinetics of Angelica and ... - ACS Publications

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Thermochemistry and Kinetics of Angelica and Cognate Lactones Judith Wurmel* and John M. Simmie School of Chemistry, National University of Ireland, Galway, Ireland S Supporting Information *

ABSTRACT: The enthalpies of formation, bond dissociation energies, ionization potentials, and kinetics of reaction with hydrogen atoms and methyl radicals have been systematically calculated for angelica lactone and a number of related furanones. The objective was to provide comprehensive thermodynamic and kinetic data of compounds that are projected to play a role as intermediates in the production of platform chemicals and biofuels.

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INTRODUCTION The production of platform chemicals and fuels from biomass continues to attract much attention.1−3 Most recently Mascal et al. have shown that hydrodeoxygenation of the angelica lactone dimer, a cellulose-based feedstock, can yield branched hydrocarbons in the C7 to C10 range, petrol/gasoline.4 Their dimer, 5,5′-dioxo-2,2′-dimethyl-2,2′,3′,4′,5,5′-hexahydro-2,3′-bifuran, is produced by base-catalyzed conjugate addition in angelica lactone and is not to be confused with the weakly bonded dimers typical of furanones that give rise to anomalous physical properties, vide infra. One known feedstock for making angelica lactones is levuninic acid,5 which features in the top-ten list of chemical opportunities from biorefinery carbohydrates.6 Although these are praiseworthy initiatives, little attention has so far been paid to the properties and reactivities of these species and clearly the consequences of their use should go hand in hand with their biosynthesis, as exemplified by a recent study of 2,5-dimethylfuran.7 Many cyclic esters or lactones have been found as products in the pyrolysis of biomass.8,9 Highly advanced experimental techniques such as tunable synchrotron photoionization mass spectrometry are beginning to be applied to the study of these compounds, which can possess novel chemical features not present in the more traditional hydrocarbons.10,11 Many furanones have been detected in association with PM2.5 aerosols in urban air by thermal desorption and gas chromatography-time-of-flight mass spectrometry.12 Direct experimental or theoretical studies are, however, few and far between. Vasiliu et al.13 have computed some thermodynamic properties of α- and β-angelica lactones (5methyl-2(5H)- and 5-methyl-2(3H)-furanones, respectively); the structures of the parent furanones are shown schematically in Figure 1. Microwave spectroscopy14 has shown that the ring atoms in 2(5H)-furanone or γ-crotonolactone are coplanar, and ́ Rodriguez-Otero and colleagues15 have discussed the thermal © 2014 American Chemical Society

Figure 1. 2(3H)-, 2(5H)-, and 3(2H)-furanones.

cheletropic decarbonylation of 2(3H)-furanone and shown that it is characterized by a high activation energy, a transition structure with the leaving CO group normal to the rest of the molecule and marked aromatization near the transition state, in other words, a classical pericyclic reaction. The physical properties of these species have not been investigated in any detail, with most being estimated; however, many have an extended boiling point range, liquid densities in excess of 1 g cm−3, and large dielectric constants and enthalpies of vaporization. For example, 2(3H)-furanone has an estimated boiling point of 265 °C, an enthalpy of vaporization of 50.3 kJ mol−1 and a density of 1.21 g cm−3 whereas similar acyclic esters, such as the ethenyl ester of acetic acid or the methyl ester of 2-propenic acid, have densities of ∼0.94 g cm−3 and boiling points of ∼78 °C. Given that many of the chemical properties of these compounds are little known, we explore the basic thermochemistry, enthalpies of formation, bond dissociation energies, and adiabatic ionization energies of 12 furanones (Tables 1−4). The majority of these are methyl derivatives of the three basic furanones or oxo-dihydrofurans of which only the first two are true lactones, Figure 1. Our numbering system is shown in Figure 2. In addition, we present data on the reactivity of each Received: March 6, 2014 Revised: May 13, 2014 Published: May 14, 2014 4172

dx.doi.org/10.1021/jp502310v | J. Phys. Chem. A 2014, 118, 4172−4183

The Journal of Physical Chemistry A

Article

species toward H atom abstraction and addition by •H and • CH3 radicals.

stated, are taken from critically evaluated values to be found in the Active Thermochemical Tables and the Third Millennium Database.24 In addition to computations based on isodesmic reactions, in which error cancellation is expected to feature strongly, we also provide numbers derived from atomization reactions25 (using the same two composite methods for consistency) which serve as a check. The atomization calculations are based on computed enthalpy changes at 298.15 K for the reaction:

Figure 2. Numbering system.

Cx HyOz (g) = x 3C(g) + y 2 H(g) + z 3O(g)

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with atomic formation enthalpies of 716.67 ± 0.46, 217.998, and 249.229 ± 0.002 kJ mol−1, respectively, for carbon, hydrogen, and oxygen atoms. The formation enthalpy which results is then labeled as “atomization” in Table 4. We chose 2(5H)-furanone, Figure 1, as the key “anchor” species on which to base all our subsequent results with an enthalpy of formation26 ΔfH°(298.15K) = −260.6 ± 1.0 kJ mol−1, which is in moderate agreement with its atomization value of −260.1 ± 3.0 kJ mol−1 although somewhat lower than a recent determination by combustion calorimetry27 of −257.2 ± 1.6 kJ mol−1. Thus, the enthalpies of formation of the 2(3H)and the 3(2H)-furanones stem directly from this choice. See Table 1.

COMPUTATIONAL METHODOLOGY All the quantum chemistry computations were carried out with the application Gaussian-09.16 The model chemistries CBSQB3,17 CBS-APNO,18 G3,19 G4,20 and W1BD21 were variously employed as appropriate to the specific needs. The composite method CBS-QB3 carries out geometry optimization and frequency calculations at B3LYP/6-311G(2d,d,p) and then a further three single point calculations with extrapolation to the complete basis set limit (CBS). CBS-APNO uses HF/6311G(d,p) to optimize and do frequency calculations and then reoptimizes at QCISD/6-311G(d,p) before four more single point determinations and CBS extrapolation. The G3 chemistry is composed of HF/6-31G(d) energy minimization and frequency computation before a second optimization at MP2(Full)/6-31G(d) together with four single point calculations. The newer G4 method employs a density functional, B3LYP, with a 6-31G(2df,p) basis set to optimize and determine frequencies with another six single point computations. Finally, the W1 theory variant, W1BD, which is computationally the most expensive of the methods used here utilizes the same functional, B3LYP, but with a larger basis set, cc-pVTZ+d, for optimization and frequencies and five single point determinations. For kinetic purposes we have used Truhlar’s M06-2X functional with a 6-311++G(d,p) basis set, which is recommended for the location of transition states and which provides reasonable accuracy but is computationally inexpensive.22 Thermochemistry. Enthalpies of Formation at 298.15 K. The general approach we employ in computing the enthalpy of formation of a target species is to use multiple isodesmic23 reactions, featuring “chaperons” whose own enthalpy of formation has been well established and at least two composite methods to determine the reaction enthalpy. Here, we use the model chemistries CBS-QB3 and G4; these utilize different approaches in the calculation of species electronic energies, enthalpies and free energies. The use of two model chemistries allows a determination of the uncertainties, μ, in our calculations, where μ describes the magnitude of the difference of our calculated numbers. This is rooted in the particular species under investigation and is not a generalized uncertainty transferred from a different set of molecules. The weighted average enthalpy of formation, x,̅ is given by n

x̅ =

Table 1. Species Enthalpies at 298.15 K in hartrees and Reaction and Formation Enthalpies in kJ mol−1 2(3H) −304.802 206 −305.118 145 −250.63 1.10 3(2H)

QB3 G4 ΔfH°(298.15K) u

−304.786 481 −305.101 986 −208.78 1.06

=

2(5H)

ΔHR

=

−304.806 126 −305.121 818 −260.6 1.0 2(5H)

−10.29 −9.64 −9.97 0.46 ΔHR

−304.806 126 −305.121 818 −260.6 1.0

−51.58 −52.07 −51.82 0.35

Both of these are in good agreement with the atomization values of −250.1 ± 2.6 and −208.2 ± 3.4 kJ mol−1, respectively. The methyl derivatives can now be derived from our primary anchor value and from six chaperons from the series of three working reactions for α-angelica lactone, shown in Table 2. The largest uncertainty in the reaction enthalpies is less than 6% in relative terms, but less than 0.5 kJ mol−1 in absolute terms for the working reaction #1. The final weighted average is therefore −302.04 ± 0.63 kJ mol−1, Table 3. Now all the subsequent methylated furanones can be directly derived from this second anchor value, using the same head-to-head comparison as in Table 3, with the condensed results shown in Table 4. The advantage of the methodology employed here in this work is that all the heats of formation are directly related to the anchor value; a ±1% change in that value, amounting to ±2.6 kJ mol−1, directly impacts on all of the other 11 species in a highly predictable manner. Our formation enthalpies for α-angelicalactone, 5-methyl2(3H), and β-angelicalactone, 5-methyl-2(5H), are in excellent agreement with high level Gaussian 09 calculations by Vasiliu et al.13 who optimized geometries using DFT, calculated harmonic vibrational frequencies using B3LYP/DZVP2 and

n 2

∑ (xi/ui )/∑ (1/ui 2) 1

method QB3 G4 ΔfH°(298.15K) u method

1

and the final uncertainty μ̅ by μ̅ = {√∑(1/μi2)}−1. The enthalpies of formation of the chaperon or companion species that appear in each isodesmic reaction, unless otherwise 4173



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Table 2. Species Enthalpies at 298.15 K in hartrees and Reaction and Formation Enthalpies in kJ mol−1 #1

5-methyl-2(3H)-furanone

QB3 G4 x1 u1 #2

−344.038 294 −344.406 361 −301.51 1.19 5-methyl-2(3H)-furanone

QB3 G4 x2 u2 #3

−344.038 294 −344.406 361 −302.10 1.06 5-methyl-2(3H)-furanone

QB3 G4 x3 u3

−344.038 294 −344.406 361 −302.38 1.06

+

C6H6

+

−231.784 285 −232.088 577 83.20 0.30 C2H6

+

−79.626 126 −79.733 666 −83.77 0.16 C2H4

=

−78.412 646 −78.517 879 52.55 0.14

QB3 G4 Mean u

−344.033 012 −344.401 268 −288.42 0.72

=

5-methyl-2(3H)furanone

ΔHR

−344.038 294 −344.406 361 −302.04 0.63

−13.87 −13.37 −13.62 0.35

=

−304.806 126 −305.121 818 −260.60 1.00 2(5H)-furanone

=

−304.806 126 −305.121 818 −260.60 1.00 2(5H)-furanone −304.806 126 −305.121 818 −260.60 1.00

+

+

+

C6H5CH3

ΔHR

−271.013 239 −271.370 153 50.40 0.35 C3H8

8.44 7.79 8.11 0.46 ΔHR

−118.850 349 −119.010 253 −104.4 0.3 C3H6 −117.641 177 −117.798 824 20.265 0.32

20.86 20.89 20.87 0.02 ΔHR 9.55 9.45 9.50 0.07

predicted heats of formation starting with the optimized B3LYP/DZVP2 lowest energy conformers. Bond Dissociation Energies. The bond dissociation energies are computed directly from the reaction enthalpy for the dissociation reaction X−Y → X• + Y•, with the use of two composite methods; the G4 method employed above for closed shell species is less reliable in determining the electronic energies of organic radicals28 and so here we employ the combination CBS-QB3 and G3. Note that for isodesmic and atomization energy calculations, used previously, one only determines the enthalpy of neutral molecular species, and that of atoms; so the combination of CBS-QB3 and G4 was sufficient. Here, the enthalpy of radical species must be calculated and now G4 is no longer the optimum choice. The G3 method does energy minimization and frequency calculation at the HF/6-31G(d) level, followed by a reoptimization at MP2(full)/6-31G(d) and then four single point energy corrections. Although the reoptimization methodology employed in G3 can be problematic, the fact that G3 uses a different procedure to CBS-QB3 is advantageous as it ensures that the results are effectively geometry independent. In general, the agreement between the two composite methods, exemplified by the uncertainty of one standard deviation, is very good, Table 5. The results are shown in Table 5 and are broadly in line with previous values found for alkylfurans29 and alkyltetrahydrofurans.30 For example, all C(sp2)−H bonds are very strong, approaching 500 kJ mol−1 (see the C4 and C5−H bonds in the 2(3H)- and 3(2H)-furanones and the C3 and C4−H bonds in the 2(5H)-furanones), whereas the C(sp3)−H bonds are much weaker at 320−360 kJ mol−1, as exemplified by the C3−H bonds in all the 2(3H)-furanones, the C5−H bonds in the 2(5H)-furanones, and the C2−H bonds in the 3(2H)furanones. The ring carbon to methyl bonds range from 456−472 for C(sp2)−CH3 bonds and 279−301 kJ mol−1 for the much weaker C(sp3)−CH3 bonds. The CH bonds in the methyl groups similarly fall into two distinct groups ∼370 kJ mol−1 for those methyls bonded to an sp2 carbon (allyl stabilization) and 430 kJ mol−1 for those bonded to an sp3 carbon. Comparison of our C3−H BDE values for 2(3H) and 5methyl-2(3H) with those by Pratt and Porter31 shows that although the absolute BDE values differ considerably, the relative differences of the basic furanone and its alkyl substituted derivative agree quite well. Thus, Pratt and Porter

Table 3. Calculation of Species Enthalpy Using Anchor Value and Reaction and Formation Enthalpies in kJ mol−1 4-methyl-2(3H)furanone

2(5H)-furanone

Table 4. Formation Enthalpies of Methyl Furanones in kJ mol−1

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Table 5. Bond Dissociation Energies in kJ mol−1

Figure 3. C−H Bond dissociation energies, kJ mol−1.

Table 6. Ionization Energies in eV furanone 2(3H) 5-methyl-2(3H) 4-methyl-2(3H) 3-methyl-2(3H) 2(5H) 5-methyl-2(5H) 4-methyl-2(5H) 3-methyl-2(5H) 3(2H) 5-methyl-3(2H) 4-methyl-3(2H) 2-methyl-3(2H) a

CBS-QB3

G3

G4

mean

±

lit.

9.33 8.94 8.90 9.20 10.26 10.11 10.04 10.11 9.56 9.14 9.02 9.37

9.32 8.93 8.91 9.19 10.78 10.08 10.42 10.17 9.59 9.18 9.11 9.41

9.27 8.86 8.83 9.13 10.16 9.99 9.90 10.18 9.54 9.13 8.99 9.34

9.31 8.91 8.88 9.17 10.22a 10.06 10.01a 10.15 9.57 9.15 9.04 9.37

0.03 0.05 0.05 0.04 0.05 0.06 0.13 0.04 0.03 0.03 0.06 0.04

10.70,39 9.28,40 9.67,41 9.7642 8.97 ± 0.05,11 9.62 ± 0.0543

10.65,41 10.5742

9.5440

Mean of CBS-QB3, G4, CBS-APNO, and W1BD values.

in our systems for comparable sites the range is 460−471 kJ mol−1. Comparable bonds in cyclopropane are much stronger than those in the furanones studied here. Castelhano and Griller33 reported BDEs for sp3 C−H bonds of 400 ± 4.2 kJ mol−1 for cyclopentane which are high in comparison to our values of 323, 333, and 361 kJ mol−1 for 2(3H), 2(5H), and 3(2H), respectively. Similar sp3 C−H bond strengths of 358 ± 7 kJ mol−1 are, however, reported for 1,3-cyclopentadiene,34 which is more directly comparable to our systems. A reported bond dissociation energy for the sp3 C−H of a methyl substituted cyclopentane carbon35 is 392.3 kJ mol−1, which we compare to the BDE (C−H) of 3-methyl-2(3H), 5methyl-2(5H), and 2-methyl-3(2H) where the carbon in question is also bonded to a methyl group. Our values are considerably lower for 3-methyl-2(3H), 309.1 kJ mol−1, and 5-

reported a weaker BDE for the alkyl substituted ring structure by 0.84 kJ mol−1, whereas our corresponding value is 1.3 kJ mol−1. In their study of stabilities of carbon centered radicals, Wright et al.32 quoted 321.8 kJ mol−1 for the BDE(C3−H) in 2(3H), a BDE(C5−H) of 333.9 kJ mol−1 for 2(5H) and a BDE(C2−H) of 376.6 kJ mol−1 for 3(2H), which agree well with our respective values of 323.2, 333.2, and 361.3 kJ mol−1, with the exception of the last one which differs by about 15 kJ mol−1. A previous study by Simmie and Curran reported BDEs of C−H from sp2 carbons in furan29 of approximately 500 kJ mol−1, which agree well with values calculated in this study, ranging from 477−505 kJ mol−1. Equally, C−CH3 bond energies in the furans range between 469−480 kJ mol−1 depending on the location and degree of alkylation, whereas 4175



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Table 7. H-Abstraction by •H; Barriers and Reaction Enthalpies and Arrhenius Parametersa species 2(3H)-furanone

3-methyl-

4-methyl-

5-methyl-

2(5H)-furanone

3-methyl-

4-methyl-

5-methyl-

3(2H)-furanone

2-methyl-

4-methyl-

5-methyl-

a

site

E‡

ΔRH

C3 C4 C5 C3 C4 C5 Me C3 C5 Me C3 C4 Me C3 C4 C5 C4 C5 Me C3 C5 Me C3 C4 C5 Me C2 C4 C5 C2 C4 C5 Me C2 C5 Me C2 C4 Me

29.3 87.0 85.3 21.4 84.8 84.3 50.3 27.6 84.9 32.3 28.6 86.6 39.0 88.5 79.3 30.6 78.2 30.6 42.6 88.0 28.9 36.5 88.5 78.5 24.7 51.8 35.2 92.2 75.7 26.6 91.3 74.7 51.1 34.3 75.0 35.4 34.8 90.6 39.3

−109.8 +60.2 +54.0 −126.3 +58.3 +53.0 −6.7 −109.6 +55.8 −68.8 −112.8 +59.8 −58.3 +62.4 +48.7 −102.6 +49.0 −101.8 −57.5 +62.3 −93.8 −59.2 +60.7 +47.8 −117.6 −4.3 −72.8 +68.7 +41.2 −90.7 +66.7 +38.5 −1.3 −75.4 +41.0 −54.6 −69.2 +67.2 −49.7

A 2.67 5.65 9.31 2.09 1.53 2.09 4.79 4.34 4.45 4.00 2.84 1.89 5.10 1.03 2.31 1.11 6.59 1.08 2.16 4.91 9.26 6.91 4.77 6.44 6.65 1.85 1.10 2.06 5.63 6.36 7.12 1.90 2.43 8.71 4.98 2.35 3.90 2.92 8.98

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

105 107 106 105 107 106 105 105 107 103 105 107 103 108 107 105 107 105 103 107 10−1 102 107 106 105 105 107 108 106 105 107 106 105 104 106 106 103 104 103

n

Ea

2.519 1.970 2.137 2.483 2.235 2.330 2.393 2.503 2.018 2.953 2.460 2.025 2.660 1.941 2.059 2.629 2.075 2.599 3.125 1.978 4.079 3.239 1.932 2.163 2.363 2.540 2.270 1.893 2.270 2.387 1.940 2.310 2.433 2.628 2.290 2.142 3.073 2.918 2.106

14.70 81.92 77.69 8.89 78.44 76.12 38.07 13.84 79.28 14.06 14.33 79.45 22.03 84.19 72.92 14.72 71.84 14.95 21.67 83.08 7.34 20.94 83.31 70.00 12.69 38.44 26.71 88.51 67.24 13.95 86.43 64.86 38.41 18.27 65.83 23.89 17.52 80.92 15.94

Units: ATn/s−1; E‡, ΔRH, and Ea/kJ mol−1.

methyl-2(5H) 321.1 kJ mol−1, as a result of stabilization of the radical through delocalization. Our value for 2-methyl-3(2H) is 346.4 kJ mol−1, suggesting an expected higher stability of our radical compared to cyclopentane. Bond dissociation energies for C−CH3 from an sp3 carbon in cyclopentane36 and cyclopentene37 have been reported as 358.2 ± 5.0 kJ mol−1 and 299.2 ± 8.4 kJ mol−1, respectively. Naturally, our values agree better with values reported for the unsaturated cyclopentene, which is more like our systems. The best agreement is noted with our value for 5-methyl-2(5H) of 301.2 kJ mol−1, with less satisfactory agreement for 3-methyl2(3H) of 279.2 kJ mol−1 and 2-methyl-3(2H) of 331.4 kJ mol−1. We find excellent agreement with Stein’s BDEs38 for CH2−H bonded to an sp2 carbon in 1,3 cyclopentadiene of 361.9 ± 8.4 kJ mol−1 and our values, which range from 362 to 380 kJ mol−1. Overall, our calculated BDEs are consistent with previously reported values for comparable systems such as cyclic alkenes, dienes, furans and alkyl furans.

Influence of Methyl Group. The presence of a methyl group reduces the C−H bond energy at the same site, Figure 3, for all three furanones. The reduction is considerable, amounting to 14−44 kJ mol−1, and is mirrored by the decrease in the barrier heights for H-abstraction by both H atom and CH3, vide infra. Ionization Potentials. The adiabatic ionization energies were determined at the CBS-QB3, G3, and G4 levels of theory, Table 6. In general, there is good agreement with the limited number of previous results. An early photoelectron spectroscopic measurement for 2(3H)-furanone or α-crotonolactone of 10.70 eV is probably incorrect.39 Although, in general, consistent results are obtained from CBS-QB3, G3, and G4 computations, in two cases there are substantial disagreements, viz. for 2(5H) and its 4-methyl derivative where the uncertainties are ∼0.3 eV. To resolve this situation, we carried out more extensive calculations with the composite methods CBS-APNO18 and W1BD21 for these particular species. For 2(5H) the results are 10.24 and 10.23 eV, respectively, which together with the CBS-QB3 value now 4176



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Table 8. H-Abstraction by •CH3; Barriers and Reaction Enthalpies and Arrhenius Parametersa species 2(3H)-furanone

3-methyl-

4-methyl-

5-methyl-

2(5H)-furanone

3-methyl-

4-methyl-

5-methyl-

3(2H)-furanone

2-methyl-

4-methyl-

5-methyl-

a

site

E‡

ΔRH

C3 C4 C5 C3 C4 C5 Me C3 C5 Me C3 C4 Me C3 C4 C5 C4 C5 Me C3 C5 Me C3 C4 C5 Me C2 C4 C5 C2 C4 C5 Me C2 C5 Me C2 C4 Me

29.4 81.6 78.8 22.3 80.5 78.5 54.3 28.0 78.0 42.6 29.9 81.7 45.6 80.2 74.6 33.5 74.4 34.2 42.6 80.1 33.4 40.3 79.4 73.6 28.3 56.0 36.1 84.1 72.0 28.6 82.9 71.0 56.4 35.6 71.7 43.5 37.4 82.5 42.5

−111.6 +58.3 +52.1 −128.2 +56.5 +51.2 −8.6 −111.4 +53.9 −70.6 −114.6 +57.9 −60.2 +60.5 +46.9 −104.5 +47.1 −103.6 −57.5 60.5 −95.6 −61.0 +58.9 +46.0 −119.5 −6.1 −74.7 +66.9 +39.3 −92.6 +64.9 +36.6 −3.2 −77.2 +39.2 −56.5 −71.0 +65.4 −51.5

A 3.25 1.32 7.13 8.83 1.57 4.69 6.04 6.57 1.16 5.97 4.04 2.44 9.52 2.74 1.04 4.61 9.20 3.81 1.68 3.13 8.47 1.71 2.28 1.25 1.34 1.23 1.02 9.79 5.13 4.50 1.42 1.72 4.08 1.44 3.74 6.11 3.55 1.60 2.49

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

100 101 101 100 102 10−5 10−1 102 102 100 102 102 10−1 101 101 10−1 101 100 100 102 10−2 10−1 102 102 101 101 100 101 100 10−5 103 101 102 101 101 100 10−7 100 10−2

n

Ea

3.731 3.671 3.678 3.228 3.087 5.180 3.514 2.849 3.179 3.269 2.961 3.065 3.544 3.518 3.651 3.950 3.144 3.447 3.628 3.032 3.859 3.858 3.058 3.157 3.289 3.298 3.880 3.438 3.734 5.222 2.976 3.265 3.227 3.388 3.243 3.521 5.942 3.840 4.249

14.14 68.42 66.13 6.81 68.65 56.93 36.92 13.62 65.94 26.26 16.08 69.39 28.93 64.80 61.55 16.00 61.85 17.50 27.18 69.22 14.77 14.77 68.36 60.92 13.68 41.07 19.17 73.79 58.11 7.55 72.89 57.12 43.11 19.18 58.19 28.73 15.11 69.67 23.17


average to 10.22 ± 0.05 eV, and for 4-methyl-2(5H) 10.15 and 9.99, respectively. Where literature data are available, our calculated ionization energy results generally agree well. Values reported for 2(3H) range from 9.28 to 10.70 eV, with our mean value of 9.32 ± 0.01 eV agreeing best with the theoretical G4 calculations of Rayne and Forest40 and less satisfactorily with measured He I photoelectron spectroscopic data from Wang et al.41 The mean IP of 8.93 ± 0.01 eV for 5-methyl-2(3H)-furanone is in excellent agreement with recent photoionization cross-section measurements reported by Czekner et al.11 Our computed value for 3(2H) agrees very well with calculated G4 values of Rayne and Forest.40 Kinetics. The zero-point corrected electronic energy barriers to reaction are calculated at the M06-2X level of theory with the 6-311++G(d,p) basis set. Such a model chemistry is considered to provide reasonable accuracy and is relatively computationally inexpensive.22 The partition functions needed for the computation of rate constants are

determined at the same level of theory assuming harmonic oscillators and rigid rotors, although where appropriate, relaxed potential energy scans of putative hindered rotors were also undertaken. Each transition state located, identified by a single imaginary frequency, was subjected to an intrinsic reaction coordinate calculation44,45 to ensure that it connected to specific reactants and products. The rate constants were then computed with the Thermo module of the application MultiWell,17 which employs canonical transition state theory including asymmetric Eckart tunnelling corrections. The results are presented in modified Arrhenius form, k/cm3 mol−1 s−1 = ATnexp(−Ea/RT), in Tables 7−Table 10 and span the range 500−2000 K. The entropies, specific heats at constant pressure, and enthalpy functions of each species are a byproduct of such calculations, and these data are summarized in the Supporting Information. 4177



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Table 9. H-Addition; Barriers and Reaction Enthalpies and Arrhenius Parametersa species 2(3H)-furanone 3-methyl4-methyl5-methyl2(5H)-furanone 3-methyl4-methyl5-methyl3(2H)-furanone 2-methyl4-methyl5-methyla

site

E‡

ΔRH

C4 C5 C4 C5 C4 C5 C4 C5 C3 C4 C3 C4 C3 C4 C3 C4 C4 C5 C4 C5 C4 C5 C4 C5

16.7 22.2 15.8 21.4 17.0 15.7 13.6 26.9 20.5 21.1 25.2 17.0 19.3 24.7 20.6 19.9 21.2 22.7 19.4 21.3 21.6 17.3 19.1 26.2

−146.6 −140.5 −145.9 −141.4 −139.0 −143.0 −143.3 −129.3 −133.4 −146.7 −116.9 −150.2 −128.2 −129.3 −134.2 −148.4 −113.8 −122.2 −113.2 −122.9 −104.8 −135.1 −106.0 −106.7

A 4.01 2.08 1.83 1.37 2.43 6.59 5.01 5.39 2.66 2.29 1.21 3.52 1.06 5.92 1.35 1.20 3.25 2.39 2.04 1.53 3.12 2.61 1.32 1.85

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

108 108 107 107 108 108 108 107 108 108 108 108 107 107 108 108 108 108 108 108 108 108 107 106

n

Ea

1.528 1.620 1.827 1.867 1.604 1.587 1.466 1.653 1.584 1.613 1.641 1.564 2.036 1.724 1.344 1.595 1.555 1.588 1.573 1.595 1.587 1.573 1.998 2.167

11.38 15.92 8.71 13.45 11.10 10.68 8.53 18.92 14.64 15.33 18.43 11.60 12.11 18.17 14.47 14.16 15.62 16.62 14.24 15.55 15.42 11.48 11.87 17.34


Table 10. Addition of •CH3; Barriers and Reaction Enthalpies and Arrhenius Parametersa species 2(3H)-furanone 3-methyl4-methyl5-methyl2(5H)-furanone 3-methyl4-methyl5-methyl3(2H)-furanone 2-methyl4-methyl5-methyla

site

E‡

ΔRH

C4 C5 C4 C5 C4 C5 C4 C5 C3 C4 C3 C4 C3 C4 C3 C4 C4 C5 C4 C5 C4 C5 C4 C5

33.5 35.0 32.5 34.4 36.9 29.7 32.0 43.2 29.6 27.8 36.8 26.5 30.9 35.7 28.9 27.3 37.5 31.0 37.2 30.8 40.0 26.2 40.0 40.1

−106.7 −122.6 −111.7 −112.5 −103.1 −116.3 −104.5 −102.0 −81.8 −106.2 −79.2 −114.1 −89.5 −93.5 −93.3 −109.6 −72.1 −92.9 −74.1 −92.6 −68.0 −110.1 −64.9 −78.0

A 7.56 5.75 3.85 5.07 3.06 2.33 2.09 2.46 7.79 8.58 2.94 9.70 4.12 4.28 4.96 3.22 1.79 1.27 7.31 5.19 3.08 2.82 1.68 5.51

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

103 103 102 102 103 104 104 104 103 103 103 103 10−4 101 103 103 104 104 103 103 106 105 102 101

n

Ea

2.463 2.466 2.788 2.705 2.526 2.452 2.397 2.226 2.436 2.426 2.508 2.406 4.562 3.014 2.439 2.462 2.421 2.410 2.430 2.402 1.561 1.903 2.996 3.042

26.71 27.57 24.23 25.51 29.91 23.13 25.53 37.51 22.64 21.17 29.94 19.61 14.87 27.03 22.45 20.84 30.88 23.95 30.68 23.97 36.44 19.80 31.84 31.09


Species Geometries. Not many of the geometries of the species of interest here have been determined previously. We do find in agreement with Legon14 that the non-methylene atoms in 2(5H)-furanone all lie on a plane and our computed rotational constants for 2(5H)-furanone are within 1% of their

experimentally measured values. We also agree with Alonso et al. that angelica lactone contains a planar ring.46 Breda and colleagues have obtained the vibrational spectrum of 2(5H)-furanone in an argon matrix at 10 K and discussed the details of the electronic structure and of intramolecular 4178



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interactions through natural bond analysis.42 Their computed geometries at DFT(B3LYP)/6-311++G(d,p) are in very good agreement with those found here. Hesse and Suhm47 have discussed the volatility differences between open and cyclic esters and shown in FTIR studies of supersonic jets that γ-butyrolactone (the saturated analogue of 2(5H)-furanone) is dimeric with computed dissociation energies of approximately 25 kJ mol−1. We find that similar dimers are formed for both 2(3H)- and 5-methyl-2(5H)furanones but have not explored the matter further. Barrier Heights and Reaction Enthalpies. To estimate the uncertainties in the rate constant calculations arising from inaccuracy of the barrier heights higher-level calculations were performed for a small number of reactions which involved the lowest barriers. Thus, for hydrogen addition to the C4 and C5 sites in 5-methyl-2(3H)-furanone, and for H-abstraction from the C3 site in 3-methyl-2(3H)-furanone, explicitly correlated coupled cluster48 calculations, CCSD(T)-F12/VDZ-F12// M06-2X/6-311++G(d,p), were carried out. The relevant numbers are: for C4 13.6 and 12.2, for C5 26.9 and 24.9, and for C3 21.4 and 19.1, respectively for DFT and CCSD(T) barriers in kJ mol−1. The results show that the DFT method used gives a satisfactory account of itself compared to the computationally more demanding CCSD(T). In terms of the computed rate constants, adopting the CCSD(T) lower barriers gives rise to a maximum increase of 38% for hydrogen addition to the C4 and C5 sites in 5-methyl-2(3H)-furanone and 41% for the abstraction from the C3 site in 3-methyl2(3H)-furanonethese diminish at high temperatures. In Tables 7−10 we show the site of attack, the zero-point corrected electronic energy, the reaction enthalpies at 0 K, and the modified Arrhenius parameters, all computed at the M062x/6-311++G(d,p) level of theory. H-Abstraction. The barrier heights for H-abstraction by •H and •CH3 have been computed, Tables 7 and 8. Abstraction of H by •H from an sp2 carbon faces a higher barrier than abstraction by •CH3 in all 12 molecules under investigation and is shown for the three basic furanones in Figure 4. Barriers for abstraction from an sp3 carbon by •CH3

A correlation between barrier heights and reaction enthalpies is shown, as an example for H-abstraction by •H and •CH3 for all molecules under investigation, see Figure 5.

Figure 5. H-abstraction by •H (■) and •CH3 (□).

A comparison of rate constants from the sp2, sp3, and methyl carbon in 5-methyl-2(3H)-furanone and 2(3H)-furanone is shown in Figure 6. Abstraction from the sp3 carbon dominates whereas that from the sp2 carbon is slowest, with H-abstraction from the methyl group intermediate in all cases. The presence of the methyl group on the furanone molecule affects the rate constant minimally. A comparison of the rate constants of the three basic furanones shows a very similar rate constant for abstraction

Figure 4. Barriers of abstraction by •H (a) and •CH3 (b).

are either identical to abstraction by •H or slightly higher. The barrier for H-abstraction from the methyl group by •CH3 is higher than that by •H in all cases, except 3-methyl-2(5H)furanone, for which it is identical. Despite the higher barriers for H-abstraction by H at most sites, abstraction of H by •H is considerably faster than abstraction by •CH3 at equivalent sites due to a significantly higher A-factor. Abstraction of H by both •H and •CH3 from the sp3 ring carbon is unsurprisingly dominant for all molecules.

Figure 6. Rate constants for H-abstraction from sp2 (●○), sp3 (■□), and methyl carbons (▲Δ) from 2(3H) (open) and 5-methyl-2(3H) (closed). 4179



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from the sp3 carbon, Figure 7. A slightly larger variation is seen for abstraction from the sp2 carbon with the fastest rate observed for H-abstraction from C5 in 3(2H).

important at the higher temperatures due to the absence of low barriers to reaction. The trends in total reactivity as regards H-abstraction by • CH3 remain unchanged throughout the temperature range studied with 2-methyl-3(2H) dominating due to the low barrier at the C2 site. Addition of H Atom. In a similar vein, Table 9 shows the data for hydrogen atom addition to the unsaturated bonds in each molecule. The barriers are typically 20 kJ mol−1 and slightly influenced by the location of the methyl group at either C4 and C5 but not at C3. The same is true for methyl addition, Table 10, except that the barriers are higher at ∼33 kJ mol−1 and highest for addition to C5 in the 5-methyl species. The presence of the methyl group on saturated bonds raises the barrier of addition to the methylated carbon and lowers it for nonmethylated one. Addition of •CH3. Addition of H and CH3. Addition of •H and • CH3 was computed for all 12 molecules under investigation, Tables 9 and 10. A comparison of the rate constants for •H addition is shown in Figure 8 for α-angelica lactone as an example. Addition of H dominates over addition of CH3. Addition to the C4 site is consistently faster due to less steric effects on the C4 site.

Figure 7. Rate constants for H-abstraction by •H from C3 (■), C4 (▲), and C5 (●) for 2(3H) (solid) and 2(5H) (dashed) and C2 (■), C4 (▲), and C5 (●) for 3(2H) (dotted).

The barriers obtained in this study are comparable to those for similar reactions, for example, in a previous study of 2,5dimethylfuran Simmie and Metcalfe49 calculated the barrier of H abstraction by H from the ring structure (sp2 carbon) as 88 kJ/mol. Our comparable values for 5-methyl-2(3H)-furanone and 5-methyl-3(2H)-furanone are 78 and 90, respectively; our systems of course contain a carbonyl group on the ring structure which will affect the barriers. Furthermore, Simmie’s study30 of H abstraction by H from tetrahydrofuran reported a barrier from an sp3 carbon of 56 kJ/ mol, whereas in this paper it is considerably lower at 30 kJ/mol for analogue systems due to the formation of the superallylic radical which is stabilized by delocalization. Total Reactivity of Abstraction. A comparison of the total reactivity of each species as regards H-abstraction by •H has revealed that at the lower temperatures 3-methyl-2(3H)furanone is most reactive largely due to the enhanced reactivity of the C3 site as a result of the ease of formation of a superallylic radical and the additional enhancement provided by the methyl group at C3. In the first case this is supported by the very low BDE for C−CH3, Table 5, and by weakening of the C−H bond, seen in the two leftmost structures in Figure 3, by the presence of a methyl group. The least reactive species is 5-methyl-3(2H)-furanone and remains so at all temperatures, largely due to the large energy barrier to abstraction at the C2 site. The only other standout feature in this comparison is the change in relative reactivity shown by 3(2H)-furanone, which becomes progressively more

Figure 8. α-Angelica lactone addition of •H (■) and •CH3 (▲) to C4 () and C5 (---).

Abstraction versus Addition. A comparison of rate constants for abstraction and addition of •H shows that the dominant path is H addition to the C4 site in α-angelica lactone, Figure 9, followed by H-abstraction from methyl group. The slowest rate in this comparison is abstraction of H from C4 (sp2). Comparison of all abstraction and addition reactions of 2(3H)-furanone, the non-methylated derivative of α-angelica lactone, shows that addition of •H to the C4 and C5 sites dominates, followed by •H abstraction by H atom from the C3 site (sp3), Figure 10. Addition of •CH3 to the C4 and 4180



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investigated. H atom addition to 5-methyl-2(5H)-furanone dominates followed by addition to 4-methyl-2(3H). The same two species dominate with regard to addition of CH3, but in reverse order. H• and •CH3 shifts. After addition at a particular site the possibility arises of 1,2-X shifts, where X = •H or •CH3; both circumstances were investigated. Exactly similar behavior is seen for H atom shifts after addition of hydrogen to all 12 species except that the barrier heights are now considerably lower, averaging 150 versus 200 kJ mol1. Xu et al.50 pyrolyzed 2(3H)-furanone in a low pressure flow reactor and followed the progress of reaction by photoelectron spectroscopy. They showed that 2(5H)-furanone was formed and was 80% complete by 550 °C but at 600 °C both acrolein and carbon monoxide were detected. They suggested that 1,2 hydrogen shifts interconvert 2(3H) with 2(5H), Figure 11, and that only the 2(3H)-furanone decarbonylates, Figure 12.

Figure 11. Interconversion of 2(3H)- and 2(5H)-furanones.

Figure 9. α-Angelica lactone abstraction of H (■) by •H from C3 (), C4 (---), and Me (···) vs addition of •H (▲) to C4 (), and C5 (---).

C5 sites is intermediate, and H abstraction by •H and •CH3 are slowest for the entire temperature range. Total Reactivity of Addition. The total reactivity of each species as regards to H-addition and methyl addition was Figure 12. Decarbonylation of 2(3H)-furanone.

However, the barrier heights encountered for the first 1 → 2 shift are ∼240 kJ mol−1, as against 220 kJ mol−1 for the elimination of CO, and thus this scheme is unlikely to be kinetically significant under their experimental conditions. We find that the direct decarbonylation of the 2(5H)-furanone is even more energetically unfeasible at ∼510 kJ mol−1 but concerted elimination to CH2O + HCCH + CO faces a barrier of 400 kJ mol−1. A sequence of H-addition/elimination reactions would, however, be feasible because, as shown above in Table 9, H-addition at C5 faces a barrier of only 22 kJ mol−1; given the “catalytic” nature of this scheme, 2(3H) + •H ⇆ 2(5H) + •H, only impurity levels of an H atom source would be required to interconvert the furanones.

■

CONCLUSIONS A systematic analysis of the enthalpies of formation, bond dissociation, ionization potential. and the kinetics of reaction with hydrogen and methyl radicals of three basic furanones and their methyl derivatives has been conducted. Where possible. bond dissociation energies have been compared to literature data and broadly fall in line with similar molecular systems. The presence of a methyl group on a ring-carbon was found to reduce the C−H bond energy at the same site, mirrored by a decrease in barrier heights of H-abstraction by H atom and CH3. Ionization potentials, calculated at the CBS-QB3 and G3 levels of theory were compared to limited experimental data, and the G3 method was found unreliable for 2 species out of 12

Figure 10. Comparison of abstraction and addition reactions of 2(3H)-furanone. 4181



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Yield Synthesis of Branched C-7-C-10 Gasoline-like Hydrocarbons. Angew. Chem. Int. Ed. 2014, 53, 1854−1857. (5) Wolff, L. Ü ber einige Abkömmlinge der Lävulinsäure. Justus Liebigs Ann. Chem. 1885, 229, 249−285. (6) J. J. Bozell, G. R. P. Technology development for the production of biobased products from biorefinery carbohydratesthe US Department of Energy’s “Top 10” revisited. Green Chem. 2010, 539−554. (7) Simmie, J. M.; Würmel, J. Harmonising Production, Properties and Environmental Consequences of Liquid Transport Fuels from Biomass2,5-Dimethylfuran as a Case Study. ChemSusChem 2013, 6, 36−41. (8) Evans, R. J.; Milne, T. A. Molecular characterization of the pyrolysis of biomass. Energy Fuels 1987, 1, 123−137. (9) Branca, C.; Giudicianni, P.; Di, B. C. GC/MS characterization of liquids generated from low-temperature pyrolysis of wood. Ind. Eng. Chem. Res. 2003, 42, 3190−3202. (10) Dufour, A.; Weng, J.; Jia, L.; Tang, X.; Sirjean, B.; Fournet, R.; Gall, H. L.; Brosse, N.; Billaud, F.; Mauviel, G.; Qi, F. Revealing the chemistry of biomass pyrolysis by means of tunable synchrotron photoionisation-mass spectrometry. RSC Adv. 2013, 3, 4786−4792. (11) Czekner, J.; Taatjes, C. A.; Osborn, D. L.; Meloni, G. Absolute photoionization cross-sections of selected furanic and lactonic potential biofuels. Int. J. Mass Spectrom. 2013, 348, 39−46. (12) Hamilton, J. F.; Webb, P. J.; Lewis, A. C.; Hopkins, J. R.; Smith, S.; Davy, P. Partially oxidised organic components in urban aerosol using GCXGC-TOF/MS. Atmos. Chem. Phys. 2004, 4, 1279−1290. (13) Vasiliu, M.; Guynn, K.; Dixon, D. A. Prediction of the Thermodynamic Properties of Key Products and Intermediates from Biomass. J. Phys. Chem. C 2011, 115, 15686−15702. (14) Legon, A. C. Microwave spectra and ring configuration of gamma-butyrolactone and gamma-crotonolactone. J. Chem. Soc., Chem. Commun. 1970, 838−. (15) Rodriguez-Otero, J.; Cabaleiro-Lago, E. M.; Hermida-Ramon, J. M.; Pena-Gallego, A. DFT Study of Pericyclic and Pseudopericyclic Thermal Cheletropic Decarbonylations. Evaluation of Magnetic Properties. J. Org. Chem. 2003, 68, 8823−8830. (16) Frisch, M. J.; G. W. T, 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 D.1; Gaussian, Inc.: Wallingford, CT, 2009. (17) Montgomery, J. 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. (18) Ochterski, J. W.; Petersson, G. A.; Montgomery, J. A. A complete basis set model chemistry 0.5. Extensions to six or more heavy atoms. J. Chem. Phys. 1996, 104, 2598−2619. (19) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. Gaussian-3 (G3) theory for molecules containing first and second-row atoms. J. Chem. Phys. 1998, 109, 7764−7776. (20) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-4 theory using reduced order perturbation theory. J. Chem. Phys. 2007, 127, 124105−124108. (21) Barnes, E. C.; Petersson, G. A.; Montgomery, J. A.; Frisch, M. J.; Martin, J. M. L. Unrestricted Coupled Cluster and Brueckner Doubles Variations of W1 Theory. J. Chem. Theory Comput. 2009, 5, 2687− 2693. (22) Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other. Theor. Chem. Acc. 2008, 120, 215−241. (23) Nicolaides, A.; Rauk, A.; Glukhovtsev, M. N.; Radom, L. Heats of formation from G2, G2(MP2), and G2(MP2,SVP) total energies. J. Phys. Chem. 1996, 100, 17460−17464. (24) Goos, E.; Burcat, A.; Ruscic, B. Third Millennium Thermodynamic Database for Combustion and Air-Pollution Use with updates from Active Thermochemical Tables. 2013.

on the basis of an unacceptably high uncertainty value. Additional calculations using composite methods G4, CBSAPNO, and W1BD were found more suitable and resulting values were found in good agreement with literature values. An analysis of the kinetics of H-abstraction by H and CH3 and addition of H and CH3 has provided a comprehensive set of rate constants. Not surprisingly, H-abstraction from sp3carbons was found to be fastest, intermediate for abstraction from the methyl group and slowest for sp 2 -carbons. Comparison of abstraction by •H and •CH3 showed a higher barrier for abstraction by •H from an sp2-carbon, which was not seen for abstraction from sp3-carbons. Slower rates of abstraction by CH3 are contributed to a significantly lower Afactor. A comparison of rates of H-abstraction from the furanone 2(3H) and its methyl derivative angelica lactone indicates an insignificant effect of the methyl group. In terms of the total reactivity of H-abstraction by H atom, our conclusion is that 3methyl-2(3H)-furanone is the most reactive as a result of the ease of formation of a superallylic radical, giving rise to enhanced reactivity at the C3 site. In contrast 5-methyl-3(2H)furanone is the least reactive species as a result of the large energy barrier at the C2 site. Regarding H-abstraction by methyl, the dominant species was found to be 2-methyl-3(2H)furanone. Addition of H was found to be consistently faster than addition of CH3 for all species. The comparison of abstraction vs addition of angelica lactone showed that addition to the methylated sp2 carbon dominates, whereas abstraction from the sp2 carbon (C4) was least significant. Of all classes of reactions investigated, the H addition to both sides of the double bond was found to dominate in all species, whereas H abstraction by methyl was least dominant. The analysis of 1,2-X shifts resulting in the interconversion of the two basic furanone was found highly likely.

■

ASSOCIATED CONTENT

S Supporting Information *

Tables of thermodynamic data of entropy, specific heat, and enthalpy calculated using the Thermo module of Multiwell. This material is available free of charge via the Internet at http://pubs.acs.org.

■ ■

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS Computational resources were provided by the Irish Centre for High End Computing, ICHEC. We thank K. P. Somers (NUI Galway) for the provision of computational tools.

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REFERENCES

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