Combined Experimental and Theoretical Study of the Reactivity of Î³

Article pubs.acs.org/JPCA

Combined Experimental and Theoretical Study of the Reactivity of γ‑Butyro- and Related Lactones, with the OH Radical at Room Temperature Ian Barnes,*,†,‡ Stefan Kirschbaum,† and John M. Simmie*,‡ †

Physikalische Chemie/FBC, Bergische Universität Wuppertal, 42119 Wuppertal, Germany School of Chemistry, National University of Ireland, Galway, Ireland

‡

ABSTRACT: The total rates of reaction between four cyclic esters (β-butyro-, γ-butyro-, γ-valeroand δ-valero-lactones) and the OH radical have been measured relative to the rate of reaction of a reference compound, ethene, at room temperatures. The measurements show that the rates increase with increasing ring size. Theoretical calculations on the four lactones with the inclusion of a fifth, α-methyl-γ-butyrolactone, are broadly in agreement with this picture but provide a more insightful view of the sites at which hydrogen atom abstraction occurs in each molecule.

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is illegal in many countries but is used as an electrolyte9,10 in lithium-ion batteries, as a cosolvent in the preparation of nanocomposites,11 and as a plasticizer.12 Its function here is to serve as a reference against which the work on GVL can be judged and to round out comparisons we include a fourmembered heterocycle, 4-methyl-2-oxetanone or β-butyrolactone (BBL). The latter can undergo ring-opening polymerization to produce poly(hydroxybutyrate), a naturally occurring biodegradable polymer with an impressive temperature resistance.13 In addition we have included a six-membered ring compound, tetrahydro-2H-pyran-2-one, more commonly known as δ-valerolactone (DVL). Schematic structures of the compounds are shown in Table 7. With the exception of a very recent measurement of the rate constant for GVL + •OH by Dóbé et al.14 of (1.17 ± 0.12) × 10−12 cm3 molecule−1 s−1, none of the species of interest here have had their reaction rates determined. Clearly before any of these compounds come into widespread use it would be useful to have some data relating to their atmospheric fate, which in this context arises from the hydrogen-abstraction reactions by OH.15 The outcomes of the H-abstraction reactions are of interest of course with regard to possible products, but this is beyond the scope of this work.

INTRODUCTION Dihydro-2(3H)-furanone and its 3- and 5-methyl derivatives, more commonly known as gamma-butyrolactone (GBL), αmethyl γ-butyrolactone or 2-methyl-4-butenolide (AMGBL), and gamma-valerolactone (GVL), respectively, are cyclic esters with somewhat unusual physical properties. Thus, for example, in comparison to acyclic esters they have high densities, large dielectric constants, and very high boiling points, as shown in a comparison between GBL and an acyclic methyl ester, methyl propionate (C2H5C(O)OCH3), outlined by Hesse and Suhm1 (Table 1). Table 1. Physical Properties Compared property

C2H5C(O)OCH3

GBL

Dielectric constant Density/g cm−3 ΔvH/kJ mol−1 Tb/K

6.19 0.913 35.9 353

39 1.125 55.2 478

All of these lactones exist as dimers in the liquid state (stabilized by some 25−50 kJ mol−1 relative to the monomers) thus accounting for the large enthalpy of vaporization, ΔvH, and their extended boiling point range; in the gas phase the monomers are preferred. GVL, produced from lignocellulosic biomass,2 has received much attention as a sustainable platform molecule, as first proposed by Horváth et al.3 It can be upgraded to various other chemicals4 and fuels5 and even used directly as a green solvent for biomass processing.6 It was chosen as one of the ten most promising potential biofuels and subjected to a comprehensive analysis of its environmental impact from a production perspective.7 GBL falls into a somewhat different categoryas a pro-drug8 of the so-called recreational drug γ-hydroxybutyrate (GHB)it © XXXX American Chemical Society

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EXPERIMENTAL METHODS Relative kinetic experiments on the reactions of OH radicals with BBL, GBL, GVL, and DVL were performed in a 1080 L reaction chamber at 298 ± 2 K and a total pressure of 760 ± 10 Torr of synthetic air (760 Torr = 101.325 kPa) using ethene as the reference hydrocarbon. A detailed description of the reactor can be found elsewhere16 and only a brief description is given Received: March 12, 2014 Revised: May 7, 2014

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dx.doi.org/10.1021/jp502489k | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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ethene by reaction with the radical precursors H2O2 or CH3ONO, photolysis, and loss to the reactor surface. From other studies it is known that all of these losses are negligible for ethene.17 To test for wall loss of the lactones each lactone was allowed to stand in synthetic air for 1 h. For the lactones wall loss was observed. Adding H2O2 or CH3ONO to the lactone in the dark did not increase the wall loss, showing reaction of the radical precursors with the lactones is negligible. Switching on the fluorescent or UV photolysis lamps with only lactone and air in the reactor did not increase the wall loss, showing also that loss due to photolysis is also negligible and does not need to be considered in the kinetic analysis. The loss of lactone due to wall deposition was relatively minor, 2−7%, except for γ-butyrolactone for which it amounted to some 15− 20%so, only really substantial for GBL. The percentage wall losses are the percentage of the total loss of the lactone during the entire irradiation period which are due to wall loss and not reaction with OH. As mentioned previously the lactones are compounds with high boiling points and low vapor pressures. In addition the ester entity makes them quite polar. Thus, it is not unusual to have quite high loss rates in chambers for such compounds. Similar wall loss difficulties occur, for example, in investigations on cresols.18 The wall loss rate for GBL ranged (6−8) × 10−5 s−1 and those for the other lactones ranging (1−3) × 10−5 s−1. To take account of the wall loss of the lactones the following modified equation was used in the analysis of the experimental data:

here. The reactor consists of two connected quartz-glass tubes (each 3 m long and 60 cm in diameter) closed at the ends with aluminum flanges containing inlet and outlet ports. The system can be evacuated to 10−3 Torr with a turbo-molecular pump backed by a double stage rotary fore pump. Three magnetically coupled Teflon mixing fans are mounted inside the chamber to ensure homogeneous mixing of the reactants. The photolysis system consists of 32 low-pressure mercury vapor lamps (Philips TUV 40 W; λmax = 254 nm) and 32 superactinic fluorescent lamps (Philips TL05 40 W: 320−480 nm, λmax = 360 nm), which are spaced evenly around the reaction vessel and are individually switchable. A White-type multiple-reflection mirror system mounted within the reactor allows sensitive in situ long path infrared absorption monitoring of reactants in the spectral range 700−4000 cm−1. The White system has a base length of 5.91 ± 0.01 m and was operated at 82 traverses giving a total optical path length of 484.7 ± 0.8 m. Infrared spectra were recorded with a spectral resolution of 1 cm−1 using a Nicolet Nexus FT-IR spectrometer equipped with a liquid nitrogen cooled mercury−cadmium−telluride (MCT) detector. Hydroxyl radicals were generated by the photolysis at 254 nm of H2O2: H 2O2 + hν → 2•OH

(R1)

Experiments were performed on lactone/ethene/H2O2/air mixtures, which were irradiated for periods of 20−40 min during the course of which infrared spectra were recorded at 1 cm−1 resolution with the FTIR spectrometer. Typically 90 or 120 interferograms were coadded per spectrum over a period of approximately 1.5 or 2 min. Some experiments were also performed under similar conditions using the photolysis of methyl nitrite, CH3ONO, with the fluorescent lamps as the OH radical source. These experiments served as a check for any influence of the radiation/radical source on the kinetic investigations. The initial concentrations used in the experiments were 0.5− 1 for the lactones, 3−5 for ethene, and 10−20 for H2O2 all these in ppmV, where 1 ppmV is equal to 2.46 × 1013 molecules cm−3 at 298 K and 760 Torr of total pressure. The chemicals used in the experiments had the following purities as given by the manufacturer and were used as supplied: synthetic air (Air Liquide, 99.999%), GBL (Aldrich, 99%), BBL (Aldrich, 99%), GVL (Aldrich, 99%), DVL (Aldrich, 99%), and H2O2 (Interox, 85%). In the presence of OH radicals the lactone and the reference compound ethene decay through the following reactions and with associated rate constants kL and kR: lactone + •OH → products

(kL)

ethene + •OH → products

(kR)

ln{([L]0 /[L]t ) − k W (t − t0)} = (kL /kR )· ln{([R]0 /[R]t )} (2)

where kW is the first-order rate coefficient for loss of the lactone to the reactor surface. This rate coefficient was determined by monitoring lactone/ethene/OH source/air reaction mixtures in the dark for 10 min before switching on the photolysis lamps.

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RESULTS Figure 1 shows exemplary plots of the kinetic data according to eq 2, obtained with H2O2 as the OH radical source, for the

Provided that the lactone and ethene are lost only by the above reactions, it can be shown that ln([L]0 /[L]t ) = (kL /kR ) ln([R]0 /[R]t )

Figure 1. Plots of kinetic data according to eq 2 for the reactions of OH with lactones versus ethene reference.

(1)

where the subscripts 0 and t refer to the concentrations at t = 0 and at time t, respectively. The relative rate technique relies on the assumption that both the lactone and the reference ethene are removed solely by reaction with the oxidant species, in this case OH radicals. To verify this assumption, various tests were performed to assess possible contributions to the decay of the lactone and

reactions of OH with the lactones measured relative to OH with ethene. Reasonable linear plots with zero intercept were obtained for all of the lactones using both OH radical sources. The averaged rate coefficient ratios (kL/kR) obtained from the slopes of these plots from a minimum of three experiments B



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are given in Table 7. The values of the rate coefficients for the reactions of OH with the lactones listed here have been put on an absolute basis using values for the reference reaction19,20 back-calculated from the Arrhenius equation: kR = 1.96 × 10−12 e(438/T)cm3 molecule−1 s−1. The uncertainties given for the rate coefficients are the 2σ errors from the linear regression analyses of the plots plus an additional 10% to take into account the uncertainty in the rate coefficient for the reference ethene. The penultimate column shows the rate coefficient, kSAR, predicted from a structure− activity relationship (SAR). The current IUPAC recommendation21 for OH plus ethene is 7.9 × 10−12 cm3 molecule−1 s−1 for 298 K and 1 bar of air; this is some 7% lower than the value obtained using the Arrhenius expression. Apart from the reaction of OH with GVL there are no other rate coefficients reported in the literature which compare to the present experimentally determined values. Dóbé and colleagues have measured the reaction of OH radicals with GVL at room temperature using two experimental techniques: a low-pressure discharge flow and pulsed laser photolysis with OH detection via resonance fluorescence. They reported22 a preliminary value for the rate constant of (3.24 ± 0.24) × 10−12 cm3 molecule−1 s−1 at 300 K in a helium buffer, but most recently (1.17 ± 0.11) × 10−12 cm3 molecule−1 s−1 for the reaction at 298 K and at pressures of 2.95−91 mbar in helium.14 This latter value is significantly lower than the value of (2.81 ± 0.34) × 10−12 cm3 molecule−1 s−1 determined experimentally in this study at 303 ± 2 K and in synthetic air at 740 Torr through the use of the relative kinetic technique. At present we have no explanation for this large discrepancy. However, preliminary investigations indicate that the rate coefficients for the reactions of OH with the lactones are quite strongly temperature dependent which when coupled with the experimental shortcoming of the experimental methods employed may account for at least some of the discrepancy. Work is in progress to determine the temperature dependencies of the rate coefficients for the reactions of the OH radical with the lactones. Structure activity relationships (SAR) exist with which rate coefficients for the reaction of OH with gas phase organic compounds can be estimated. Values of the rate coefficients for the reactions of OH radicals with the lactones have been estimated using the AOPWIN module of the Estimation Program Interface suite.23 AOPWIN estimates the room temperature gas-phase reaction rate for the reaction between OH radicals and a compound utilizing the SAR developed by Kwok and Atkinson.24 As can be seen in Table 7 the SAR predicted values for the rate coefficients are in reasonable agreement with the experimentally determined values. This agreement cannot, however, be interpreted as an endorsement for the experimentally determined values in this work, since there are known limitations with SAR predictions for cyclic compounds due to uncertainties, for example, in parameters such as ring strain.

Figure 2. Geometries of (top) pre-reaction complex, (middle) transition state, and (bottom) post-reaction complex formed during the H-abstraction reaction in GBL + •OH from the C3 equatorial site.

Figure 3. Numbering system employed shown for equatorial GVL.

Table 2. H-Abstraction by •OH from GBLa site

E‡

ΔrH

C3a C3e C4a C4e C5a C5e

3.05 3.58 4.21 9.72 −2.70 3.81

−93.2 −93.2 −79.9 −79.9 −85.5 −85.5

k/cm3 s−1 1.45 6.61 8.93 2.41 2.86 1.19 7.30

× 10−13 × 10−14 × 10−14 × 10−14 × 10−13 × 10−13 × 10−13

a

0 K zero-point corrected electronic energies relative to reactants, kJ mol−1, at M06-2X/6-311++G(d,p).

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H 2 CO, CH 3 CHO, CH 3 COCH 3 , CH 3 OCH 3 , HCOOH, CH3COOH, and HCOOCH3 (VOCs) with •OH. It is a widely used functional for generating potential energy surfaces in the study of reaction mechanisms.27−30 Energetics. All equilibrium and transition state geometries were optimized with the application Gaussian0931 with intrinsic reaction coordinate calculations being used to connect reactants, transition states, and products. In most cases both pre- and post-reaction complexes were found whose stabilization energies relative to reactants, or products, as the case may

COMPUTATIONAL METHODS The M06-2X functional25 with a 6-311++G(d,p) basis set was employed in all the calculations of energetics and kinetics. This combination has been tested by Elm et al.26 and shown to perform quite well in comparison with much more computationally demanding CCSD(T)-F12a/VTZ-F12//BH&HLYP/ aug-cc-pVTZ calculations over a number of H atom abstraction reactions between the oxygenates CH3OH, CH3CH2OH, C



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Table 3. H-Abstraction by •OH from GVLa site

E‡

C3a C3e C4a C4e C5a CH3

2.72 3.71 4.16 9.69 −6.63 2.33

C3a C3e C4a C4e C5e CH3

0.11 3.01 4.69 7.30 −2.24 1.33

ΔrH Equatorial −92.6 −92.6 −78.4 −78.4 −92.3 −61.0 Total Axial −94.64 −94.64 −80.9 −80.9 −94.8 −63.9 Total

Table 6. H-Abstraction by •OH from DVLa k/cm3 s−1 −13

1.73 5.19 4.10 1.54 3.22 1.38 3.63

× 10 × 10−14 × 10−14 × 10−14 × 10−12 × 10−13 × 10−12

1.06 7.32 7.72 3.57 9.42 5.84 1.29

× 10−13 × 10−14 × 10−14 × 10−14 × 10−13 × 10−14 × 10−12

C3a C4a C4e C5a C5e CH3

−3.71 2.89 9.30 −2.37 3.42 −3.61

C3e C4a C4e C5a C5e CH3

−3.36 4.49 9.38 −2.78 3.42 −0.89

Equatorial −113.1 −77.7 −77.6 −83.0 −85.6 −64.6 Total Axial −116.4 −80.9 −80.9 −83.7 −85.5 −66.4 Total

k/cm3 s−1 1.74 5.43 2.65 9.13 1.31 3.26 3.19

× 10−12 × 10−14 × 10−14 × 10−13 × 10−13 × 10−13 × 10−12

4.44 5.85 1.02 5.94 1.36 1.13 1.36

× 10−13 × 10−14 × 10−14 × 10−13 × 10−13 × 10−13 × 10−12

a


Table 5. H-Abstraction by •OH from BBLa site

E‡

ΔrH

C3c C3t C4 CH3

10.01 10.71 0.93 3.77

−70.4 −70.4 −74.1 −64.4 Total

k/cm3 s−1 1.39 1.75 1.87 3.43 2.53

C3a C3e C4a C4e C5a C5e C6a C6e

−1.97 −1.80 1.93 5.20 0.12 8.61 −4.92 1.13

−107.4 −107.4 −86.0 −86.0 −82.4 −82.4 −91.3 −91.3 Total

k/cm3 s−1 8.44 4.61 2.24 3.30 1.30 4.52 3.19 5.45 5.77

× 10−13 × 10−13 × 10−13 × 10−13 × 10−13 × 10−14 × 10−12 × 10−13 × 10−12

GVL and AMGBL exist in two conformational forms with the methyl group axial and equatorial to the “plane” of the ring; both compounds are also chiral. The pseudo-equatorial form is shown in Figure 3; this conformer is slightly more stable and comprises 73.4% of the population at 298.15 K. A relaxed internal dihedral angle scan of C3−C4−C5−O shows an interconversion barrier of 6.3 kJ mol−1, while the comparable plot for GBL is symmetrical with a similar barrier to interconversion of ∼7 kJ mol−1 in agreement with microwave measurements.33 Kinetics. The Thermo module of the application MultiWell34 was used to calculate the H atom abstractions rate constants via transition state theory. The harmonic oscillator rigid rotor approximation was invoked for the determination of partition functions except where hindered rotors are involved when relaxed potential energy scans were performed to determine the rotational barriers. For methyl groups the scans show threefold symmetry, typically with barriers of 10− 15 kJ mol−1. The results for GBL are shown in Table 2 which lists the barrier height, E‡, and the enthalpy change at 0 K, ΔrH, and the computed rate constant, k, in cm3 molecule−1 s−1 at 298 K. Note that the reactivity is largely centered on the hydrogen atoms adjacent to the heterocyclic oxygen, that is, sites C3 and C5. This is a common feature in all the other systems studied. The results for GVL are summarized in Table 3, with the calculated rate constants at 298.15 K. There is a reasonable congruence between the GBL and GVL results for Habstraction from C3 and C4 sites, but abstraction from C5 is much faster when the methyl group is present in either an equatorial or an axial position. Thus, GVL is some 2 to 5 times more reactive than GBL, but this is not due to the reactivity of the methyl group per se, but rather to the influence that it has on the abstractable hydrogen at C5. These results are broadly in line with expectations based on bond dissociation energies for which C3H ≈ C5H ≪ C4H ≪ CH2H as 400 ≈ 402 ≪ 418 ≪ 435 kJ mol−1. In not unrelated examples the presence of a methyl group at C5 in 5-methyl-2(5H)-furanone results in a lowering of the barrier for H atom abstraction by •H from 30.6 for 2(5H)-furanone to 24.7 kJ mol−1 and a comparable decrease of 8 kJ mol−1 for the related system 3methyl-2(3H)-furanone.35 The dominant equatorial conformer (equatorial:axial = 73.4:26.6 at 298.15 K from computed Gibbs free energies) of GVL is more reactive than the axial conformer resulting in an overall rate constant of 3.02 × 10−12 cm3 molecule−1 s−1. The computed rate constants shown above must be treated with some caution as the results are dependent upon the

Table 4. H-Abstraction by •OH from AMGBLa ΔrH

ΔrH



E‡

E‡

a

a

site

site

× 10−14 × 10−14 × 10−13 × 10−14 × 10−13

a


be, are typical of values reported for similar systems by Galano et al.32 A typical set of pre-reaction and post-reaction complexes and the intervening transition state are shown (Figure 2) for abstraction of an equatorial H atom from site C3 in GBL + • OH. Although •OH addition to the carbon atom of the carbonyl group is feasible, the barrier to such addition exceeds 40 kJ mol−1 and so this avenue was not pursued further. D



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Figure 4. Nomenclature of H-abstraction sites.

Although the ring in β-butyrolactone or 4-methyl-2oxetanone (BBL) is planar,36 the molecule is chiral and the two hydrogens on C3 are different, one being cis to the methyl group and the other trans; see Table 5. An exhaustive investigation of the conformational structure of δ-valerolactone or DVL has been carried out by Weber and Brückner37 at the B3LYP/def2-TZVPP level. In addition they summarize many previous studies and conclude that a half-chair form is the most stable structure which faces an inversion barrier of some 12 kJ mol−1. Here we employ the half-chair conformer, labeled HClac by them, as the basis for all computations. The barrier heights for H-abstraction by •OH are reported in Table 6; the nomenclature follows exactly the same format as that shown for GBL in Figure 4, except that two additional sites are now available at C6. The overall reactivity at each site shows roughly the same trend as the C−H BDEs, namely, C3:379, C4:402, C5:405, and C6:395 kJ mol−1. So the more remote sites at C4 and C5 are the least reactive, while the sites adjacent to the heterocyclic oxygen or the ketonic carbon are more reactive. Based on the above calculations the total reactivity computed follows the pattern BBL < GBL < AMGBL ∼ GVL < DVL,

energetics such as the barrier heights. Although the model chemistry employed here is recommended for kinetics calculations it falls short of the current “gold standard”, in computational quantum chemistry of coupled cluster calculations in the complete basis set limit. Calculations at the CCSD(T) level were tried for the most important channel, namely, C5a, with both cc-pVDZ and cc-pVTZ basis sets at M06-2X/6-311++G(d,p) geometries. The zero-point corrected electronic energy differences, or barrier heights, become −1.30 at VDZ, −4.40 at VTZ, and finally −3.61 kJ mol−1 using explicitly correlated coupled cluster method CCSD(T)-F12/ VDZ-F12//M06-2X/6-311++G(d,p). Given that the DFT calculated barrier was −2.7 kJ mol−1 the additional computational expense is probably unwarranted at this stage. H-abstraction from α-methyl γ-butyrolactone or 2-methyl-4butanolide (AMGBL) shares many of the same characteristics as H-abstraction from GVL; thus, equatorial and axial conformers of AMGBL exist with the equatorial dominating at 76.6:23.4. The energetics are summarized in Table 4 and the total rate constant of 2.76 × 10−12 cm3 molecule−1 s−1 differs very little, not unexpectedly, from that found for GVL. There are no experimental measurements for this compound that we are aware of. E



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Table 7. Rate Constant Ratios and Rate Constants for the Reaction of OH Radicals with Lactones

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which is in agreement with the experimental ranking of BBL < GBL ∼ GVL < DVL; see Table 7. Numerically the calculations are in good agreement with the experiments for both GVL and DVL but seem to consistently underestimate the total reactivity of GBL and BBLthe reasons for this are unclear at this moment. The trend that increasing ring size increases the reactivity of each lactone is, however, well captured by both experiment and theory (Table 7). A not dissimilar trend is seen in going from cyclobutanone to cyclopentanone where a 3-fold increase in the rate constant38 from 8.70 × 10−13 to 2.94 × 10−12 cm3 molecule−1 s−1 occurs. It is to be noted that SAR predictions24 for these two cyclic species differ by factors of 2.3−5.2 from the experimental values. Note that there is good agreement between the computed reactivities for the isomeric pair, GVL and AMGBL, which differ only in the location of the exocyclic methyl group. Thus, for γ-valerolactone where the methyl group occupies the C5 site the total reactivity of the equatorial conformer is 3.63 × 10−12 and that of the axial conformer is 1.29 × 10−12 cm3 molecule−1 s−1 (Table 3). For α-methyl-γ-butyrolactone or AMGBL, the methyl group is now at C3 but the total reactivities are very similar at 3.19 × 10−12 and 1.36 × 10−12 cm3 molecule−1 s−1 for the equatorial and axial conformers, respectively (Table 4).

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Computational resources were provided by the Irish Centre for High-End Computing, ICHEC.

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REFERENCES

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CONCLUSIONS Experiment and theory have been used to determine the room temperature reaction rate constants toward the OH radical for four cyclic ethers or lactones. The four membered ring compound, 4-methyl-2-oxetanone, is the least reactive and the six membered ring species, δ-valerolactone, is the most reactive. The three 5-membered rings exhibit an intermediate position and have comparable reactivities. The reactivity of each compound is mainly controlled by the carbon site adjacent to the heterocyclic oxygen, that is, C5 in the case of GBL, AMGBL, and GVL; C4 in the case of BBL; and C6 for DVL. F



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Combined Experimental and Theoretical Study of the Reactivity of Î³

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