Thermochemical Properties of Methyl-Substituted Cyclic Alkyl Ethers

Article pubs.acs.org/JPCA

Thermochemical Properties of Methyl-Substituted Cyclic Alkyl Ethers and Radicals for Oxiranes, Oxetanes, and Oxolanes: C−H Bond Dissociation Enthalpy Trends with Ring Size and Ether Site Itsaso Auzmendi-Murua,†,‡ Sumit Charaya,§,‡ and Joseph W. Bozzelli†,§,* †

Department of Chemical, Biological and Pharmaceutical Engineering and §Department of Chemistry and Environmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102, United States S Supporting Information *

ABSTRACT: Cyclic ethers are an important product from the gas-phase reactions of hydrocarbon radicals with molecular oxygen in the atmospheric chemistry of diolefins and in low to moderate temperature combustion and oxidation reaction systems. They are also important in organic synthesis. Structures, and fundamental thermochemical parametersenthalpy (ΔH°f,298), entropy (S°298), and heat capacity (Cp(T))have been calculated for a series of cyclic alkyl ethers and their carbon centered radicals. Enthalpies of formation (ΔH°f,298) are determined at the B3LYP/6-31G(d,p), B3LYP/6-31G(2d,2p), and CBS-QB3 levels using several work reactions for each species. Entropy (S) and heat capacity (Cp(T)) values from vibration, translational, and external rotational contributions are calculated using the rigid-rotor−harmonic-oscillator approximation based on the vibration frequencies and structures obtained from the density functional studies. Contributions from the internal methyl rotors are substituted for torsion frequencies. Calculated enthalpies of formation for a series of 12 cyclic ethers and methyl substituted cyclic ethers are in good agreement with available literature values. C−H bond dissociation enthalpies are reported for 28 carbon sites of 3 to 5 member ring cyclic ethers for use in understanding effects of the ring and the ether oxygen on kinetics and stability. Trends in carbon−hydrogen bond energies for the ring and methyl substituents relative to ring size and to distance from the ether group are described.

■

INTRODUCTION Epoxides, other cyclic ethers and lactones are formed in combustion (oxidation) of hydrocarbons at temperatures up to 1200 K from hydrocarbon radical association reactions with molecular oxygen. The reaction forms a peroxy radical with typically 20− 50 kcal mol−1 of initial chemical activation energy. The energized or stabilized peroxy radical can undergo an intramolecular hydrogen-atom transfer reaction forming a hydroperoxy alkyl radical. The formed alkyl radical has a low reaction barrier for addition to the peroxy oxygen atom adjacent to the carbon (carbon−oxygen bond formation). This forms the C−O sigma (σ) bond (forms the cyclic ether) and cleaves the weak (45 kcal mol−1) RO−OH bond. Formation of the stronger C−O bond is exothermic and the accompanying generation of •OH radical results in propagation and sometimes in generation of multi radical products (chain branching). This peroxy chemistry is critical to ignition in the developing HCCI (homogeneous charge compression ignition) engines, which are being developed for lower NOx emissions.1 Experimental data of Jones et al.2 show that the vapor-phase oxidation of C6−C16 hydrocarbons yields 11−25 wt % heterocyclic oxygenates as products. From n-hexane, the cyclic ether fraction contained 59% oxolanes (five-membered rings, tetrahydrofuran, THF), 35% oxetanes (four-membered rings), and 6% oxiranes (three-membered rings). From n-heptane, the cyclic ether fraction contained 68% oxolanes, 26% oxetanes, and 6% © 2012 American Chemical Society

oxiranes. Moderate-temperature (580−600 K) oxidation of primary reference fuels n-heptane and isooctane (2,2,4-trimethylpentane) with air in a jet-stirred-flow reactor3,4 at pressures as high as 40 bar yielded, 10 and 60 mol % cyclic ethers respectively, plus aldehydes and olefins. The 2-methyl-5-ethyloxolane and 2,2,4,4-tetramethyloxolane were the most abundant cyclic ethers from n-heptane and isooctane, respectively. Recent studies have highlighted the importance of the epoxides on the formation of the secondary organic aerosol (SOA) in the atmosphere, since polyols and organic sulfates have recently been identified in the secondary organic aerosol (SOA). The acidcatalyzed ring-opening of the epoxide, followed by the reaction with water and sulfate lead to the formation of the final diol and hydroxy sulfate products.5,6 Epoxides can also be formed from atmospheric reactions of olefins, when they are oxidized by (i) •OH addition, (ii) O2 association, (iii) loss of NO2 by reaction with NO, and (iv) cyclization by O• addition to the secondary π bond. This leads to the formation of the cyclic ether, as indicated in Figure 1 for isoprene. In addition, epoxides are important compounds in synthetic organic chemistry, and recent advances have provided the Received: July 21, 2012 Revised: November 27, 2012 Published: November 29, 2012 378

dx.doi.org/10.1021/jp309775h | J. Phys. Chem. A 2013, 117, 378−392

The Journal of Physical Chemistry A

Article

Lee−Yang−Parr correlation functional, LYP. There is a general consensus that B3LYP methods provide excellent low-cost performance for structure optimizations.20 The B3LYP/6-31G(d,p) level of theory is a reliable computational method for the determination of geometries of small polar compounds16 as well as being widely used for the calculation of radical species.17,18 The higher level composite CBS-QB3 method19 was also used in these work reaction calculations. CBS-QB3 is a multilevel model chemistry that combines the results of several ab initio and DFT individual methods and empirical correction terms to predict molecular energies with high accuracy and reasonable computational cost. It is based on B3LYP/CBSB7 calculations for the geometry optimization and frequencies, followed by a single point energy calculation at the CCSD(T)/6-31G +(d′) and MP4SDQ/CBSB4 level of theory. It includes a total energy extrapolation to the infinite basis-set limit using pair natural-orbital energies at the MP2/CBSB3 level, and an additive correction at the CCSD(T) level of theory. All calculations were performed using the Gaussian 03 program.20 Standard enthalpies of formation for stable species were calculated using the total energies at B3LYP/6-31G(d,p), B3LYP/ 6-31G(2d,2p), and CBS-QB3 levels with work reactions that are isodesmic in most cases. Isodesmic reactions conserve the number and type of bonds on both sides of an equation. The use of work reactions with similar bonding on both sides of an equation results in a cancellation of calculation error and improves the accuracy for energy analysis.21,22 The reported enthalpy values are compared with the known literature enthalpies of several molecules in the system to further serve as a calibration of the calculation methods.

Figure 1. Oxidation of isoprene resulting in formation of cyclic ethers.

methodology to both synthesize and transform epoxides with high stereochemical and regiochemical selectivity. Ethers are widely used as solvents and because of the ease with which they form peroxides, they are considered extremely hazardous.7,8 Experimental bond dissociation enthalpies of the C−H bonds are available for a number of organic compounds9−12 and there are several theoretical studies that have focused on the determination of the thermochemical properties of the cyclic ethers. Agapito et al.13 studied bond dissociation enthalpies on tetrahydrofuran (THF) and 1,4-dioxane and postulated that hyper-conjugation and ring strain are the main factors that should be considered to understand their thermodynamic stabilization. The reported C−H bond dissociation enthalpies of THF (leading to β-furanyl) and 1,4-dioxane are 98.0 and 91.1 kcal mol−1 respectively at the CBS-Q level. 13 Hoshino et al.7 studied cyclopentyl methyl ether (CPME). The bond dissociation enthalpy of the C−H bond at the α-position in the ring adjacent to the ether oxygen was evaluated theoretically to be 94.0 kcal mol−1 by the isodesmic reaction method. 7 Thermochemical parameters are important in evaluating reaction paths and kinetic processes in the atmosphere and in combustion environments. These values also provide a base for estimation of equilibria and energies for ring-opening reactions and dissociation reactions for the formation of radicals via hydrogen abstraction reactions. This study provides heats of formation and C−H bond dissociation enthalpies for 12 cyclic ethers and methyl substituted cyclic ethers.

■

RESULT AND DISCUSSION

Enthalpies of Formation and Bond Dissociation Enthalpies. Enthalpies of formation (ΔH°f,298) for the parent molecules were determined using corresponding enthalpy of reactions (ΔH°rxn,298) in the isodesmic work reactions and calculated standard enthalpies of each species. Structures of target molecules and an abbreviated nomenclature are illustrated in Figures 2−4. The molecular structure (bond distances, angles, dihedrals, and moments of inertia) of each of the studied species is included in the Supporting Information. Nomenclature for position identification of the methyl groups: • meth represents a methyl group bonded to a carbon in the ring adjacent to the ether oxygen. • msec represents a methyl group bonded to a carbon in the ring that is NOT adjacent to an ether oxygen. • meth−meth represents that the ring has two methyl groups bonded to different carbons in the ring, both carbons adjacent to the ether oxygen. • meth2 represents that the ring has two methyl groups bonded to a same carbon in the ring adjacent to the ether oxygen. The methyl group for 2-methyl oxolane (meth) and 3-methyl oxolane (msec), can be placed in exo or endo positions, see Figure 5. The exo conformers are lower in energy by 0.65 kcal mol−1 for the 2-methyl oxolane; and 0.11 kcal mol−1 for the 3-methyl oxolane. The dihedral angles for carbons in the 2-methyl oxolane and 3-methyl oxolane are summarized in Table 1 (the numbering of the atoms corresponds to that in Figure 5).

■

COMPUTATIONAL METHODS Geometries, vibration frequencies, moments of inertia, and internal rotor barriers for molecules and related radical species were optimized at the B3LYP/6-31G(d,p)14 and B3LYP/631G(2d,2p) 15 level of theory. The B3LYP method combines the three parameter Becke exchange functional, B3, with 379



Article

Figure 2. Three member ring cyclic alkyl ethers with radical sites and their structures and abbreviated nomenclature.

B3LYP/6-31G(2d,2p), and CBS-QB3 levels (eq 3, where values for cyclic ether and radical (this work) are under the respective moieties). ΔH°f,298 of 52.1 kcal mol−1 was used for H• atom enthalpy.

Enthalpies were calculated at 298.15 K for all species in the work reaction and used to calculate ΔH°rxn, 298, eq 1. ΔH °rxn,298 =

∑ Hf products − ∑ Hf reactants

(1)

y(cco)−meth → y(c•co)−meth + H• −22 . 65

The two products and one reactant in the work reaction are reference species with evaluated literature standard enthalpies. The ΔH°f,298 of the reference species used in these work reactions are summarized in Table 2. As an example, the following equation is used to estimate ΔH°f,298 (given in kcal mol−1 under each moiety) for y(cco)−meth: y(cco)− meth + (CH3CH3) → y(cco) + (CH3CH 2CH3) target

−20.04

−12.63

−25.02

29.78

52.1

(3)

ΔH°rxn,298 = bond dissociation enthalpy = [29.78 + 52.1] − [−22.65] = 104.51 kcal mol−1. Figure 6 represents as example the work reactions used for the determination of y(cco)−meth, and the alkyl radical derived from it, y(c•co)−meth. The Supporting Information includes the detailed work reactions and data used for the determination of the heat of formation and the bond dissociation enthalpies. The CBS-QB3 values are recommended (bold in tables), as these are the higher level calculations and they present the best consistency between the isodesmic work reactions. The data are in good agreement with the available literature data as illustrated in Table 4. The calculated uncertainty for the CBS-QB3 method is ±0.56 kcal mol−1 for stable molecules and ±1.29 kcal mol−1 for

(2)

The use of these balanced work reactions eliminates a significant component of the systemic errors in the calculations. Bond energies for the formation of radicals by loss of H• atom at 298.15 K were calculated from the standard ΔH°f,298 values of the parent molecules and of the radicals at B3LYP/6-31G(d,p), 380



Article

Figure 3. Four member ring cyclic alkyl ethers with radical sites and their structures and abbreviated nomenclature.

radicals, as indicated in Table 3. There is consistency for the B3LYP method for ΔH°f,298 values between the 6-31G(d,p) and 6-31G(2d,2p) basis sets, and the calculated 95% confidence limits are ±1.12/1.35 and ±0.76/1.34 kcal mol−1, for stable/ radicals, respectively. The low uncertainity for stable molecule enthalpy results from the good agreement between our calculation results and the literature data. Table 3 contains a summary of the uncertainties calculated for the methods used, both for stable molecules and radicals. The determination of the uncertainties is based on reference reactions, which have heats of reaction that are well-defined. The heat of reaction for each of these reference species were calculated at the B3LYP/6-31G(d,p) and/6-31G(2d,2p), and CBS-QB3 levels of theory, and a statistical analysis was performed to determine confidence limits. Appendix A includes a description of the calculation method of the uncertainties. The enthalpies of formation for the methyl substituted oxirane, oxetane and oxolane are shown in the Table 4 at each level of theory and literature reference values are listed for comparison. Table 5−7 include the enthalpies of formation calculated for the alkyl radical species on each of the cyclic ether systems, as well as the C−H bond dissociation enthalpies. This set of methyl substituents on these cyclic ethers allow a comparative study of trends for the C−H bond dissociation enthalpies (BDEs) on ether and the nonether carbons combined with changes in ring size. The methyl groups permit evaluation of primary methyl group C−H BDEs (non ring carbons) bonded to ether and nonether carbons. Structures are illustrated in Figures 7−10. Overall the C−H bond dissociation enthalpies on the ring ether carbons are significantly lower than corresponding C−H bonds on nonether, ring carbons. This trend is similar to bond energies on normal alkane (noncyclic) ethers. The C−H bond

energies on C3 and C4 ether rings are higher than corresponding C−H bonds at similar carbon sites in normal alkanes and this is similar to trends on the C−H bonds of small cyclic hydrocarbons versus normal alkanes. A review of C−H bond dissociation enthalpies of linear alkanes, linear ethers and cyclic alkanes is summarized in Table 8 for use in comparisons. C−H bond dissociation enthalpies have been calculated for: • Primary (methyl, nonring) carbons bonded to ether ring carbons (C/C/H3) • Primary (methyl, nonring) carbons bonded to nonether ring carbons (C/C/H3) • Ring ether carbons, nonmethyl substituted (C/C/H2/O) • Secondary ring (nonether) carbons (C/C2/H2) • Methyl substituted ring ether carbons (C/C2/H/O) • Tertiary ring nonether carbons (C/C3/H) Figures 8, 9, and 10 illustrate the bond types and Table 9 shows a comparison for primary/secondary/tertiary C−H bond dissociation energies versus: • (i) Increasing ring size for methyl substituted oxirane, oxetane and oxolane (the figures also include a comparison with linear alkanes/ethers). • (ii) C−H bond enthalpies on methyl groups bonded to ether ring carbons (groups 2, 4, and 6 in Table 9) and methyl carbons bonded to nonether carbons (groups 1, 3, and 5 in Table 9).

■

TRENDS IN C−H BOND ENERGIES A. Trends observed for C−H bonds on primary (methyl, non ring) carbons (groups 1 and 2 in Table 9): • C−H bond dissociation enthalpies for methyl groups bonded to a central nonether carbon remain similar as the

381



Article

Figure 4. Five member ring cyclic alkyl ethers with radical sites and their structures and abbreviated nomenclature.

• BDEs increase as the number of central atoms in the ring increase for methyl groups bonded to an ether carbon (group 2 in Table 9) 98.7 → 101.1 → 102.8 kcal mol−1 (three to five member ring, respectively). • The C−H bonds on the methyl primary radicals of linear alkanes (CH2•CH2CH3,23 101.0 kcal mol−1) and linear ethers (CH2•CH2OCH3,24 102.7 kcal mol−1) are similar to the BDEs on five member ring ethers. • The C−H bonds on methyl groups bonded to a ring ether carbon (group 2 in Table 9), have higher BDEs by 1.5−2.5 kcal mol−1 (101.1 → 102.8 kcal mol−1, for four to five member rings, respectively), compared to the methyl groups bonded to the respective nonether ring carbon, 99.8→100.2 kcal mol−1 (group 2 in Table 9).

Figure 5. Exo and endo sites (a and b above, respectively), for the methyl group on oxolane, 2-methyl (meth) and oxolane, 3-methyl (msec).

number of central atoms in the ring increase (group 1 in Table 9): 99.8 → 100.2 kcal mol−1 (four to five member ring, respectively).

Table 1. Dihedral Angles in Methyl-Substituted Oxolane and the Energy Difference of the Conformers degrees species

dihedral

(a)

(b)

y(cccco)−meth

D(1,2,3,5) D(2,1,4,5) D(1,2,3,5) D(2,1,4,5)

27.9242 −18.2829 (endo) −33.7289 −27.7374 (exo)

−35.0701 6.0493 (exo) −33.2648 13.0591 (endo)

y(cccco)−msec

382

Δ energy (kcal mol‑1) (ΔHf,a − ΔHf,b) 0.65 −0.11



Article

Table 2. Standard Enthalpies of Formation at 298.15 K of Reference Speciesa

a

species

ΔH°f,298

ref

species

ΔH°f,298

ref

y(CH2CH2CH2) y(CH2CH•CH2) y(CH2CH•CH2CH2) y(CH2CH2CH2CH2) y(CH2CH2CH2CH2CH2) y(CH2CH•CH2CH2CH2) y(CH2CH2O) y(CH•CH2O) y(CH2CH2CH2O) y(CH•CH2CH2O) y(CH2CH•CH2O) y(CH2CH2CH2CH2O) y(CH•CH2CH2CH2O) y(CH2CH•CH2CH2O) CH3CH2• CH3CH3 CH3CH2CH3 CH3CH2CH2• CH3CH2•CH3

12.74 ± 0.12 69.74 6.62 ± 0.26 54.88 −18.26 ± 0.17 26.09 −12.72 39.69 −19.16 24.59 30.87 −43.97 −2.02 2.51 28.4 ± 0.5 −20.04 ± 0.07 −25.02 ± 0.12 23.9 ± 0.5 22.00 ± 0.5

12 25 12 25 12 25 33 33 33 33 33 33 33 33 12 12 12 12 35

CH3CH2CH2CH3 CH3CH2CH2CH2• CH3CH2CH2•CH3 CH3OCH3 CH3CH2OCH3 CH3(CH3)CHCH3 CH3(CH3)CHCH2• CH3CH2CH2CH2CH3 CH3CH2CH2CH•CH3 2-methyl butane oxirane oxirane, 2-methyl oxetane oxolane oxetane, 2-methyl oxetane, 3-methyl oxirane, 2-dimethyl oxolane, 2-methyl oxirane, 2,3-dimethyoxirane, 2,3-trimethyl

−35.08 ± 0.14 −20.04 ± 0.07 16.00 ± 0.5 −43.99 ± 0.12 −51.73 ± 0.16 −32.07 ± 0.15 17.0 ± 0.5 −35.08 ± 0.14 11.16 ± 0.5 −36.73 ± 0.14 −12.58 ± 0.15 −22.63 ± 0.15 −19.25 ± 0.15 −44.03 ± 0.17 −30.67 −27.21 −33.89 −54.58 −32.6 −42.11

12 12 23 12 12 12 12 34 23 12 12 12 12 12 1 1 1 1 36 36

Units: kcal mol−1.

Figure 6. Sample work reactions used for the parent molecules and radicals.

Table 3. Calculated Uncertainties for Each Methoda

B. Results for C−H bonds on secondary ring and methyl substituted ether ring carbons (group 3 and 4 in Table 9). • Bond dissociation enthalpies decrease as the number of central atoms in the ring increase for secondary radical sites (nonether ring carbons, group 3 in Table 9): 102.2 → 98.5 kcal mol−1 (four to five member ring, respectively).

a

383

parameters

B3LYP/6-31G(d,p)

B3LYP/6-31G(2d,2p)

CBS-QB3

stable molecules radicals

±1.02 ±1.35

±0.76 ±1.34

±0.56 ±1.13

See Appendix A for details on calculation of error. dx.doi.org/10.1021/jp309775h | J. Phys. Chem. A 2013, 117, 378−392


Article

Table 4. Calculated Standard Enthalpies of Formation at 298 K versus Calculation Methods for Three Member Ring Target Moleculesa ΔH°f,298 B3LYP target molecules

6-31G(d,p)

y(cco)−meth

−22.32

y(cco)−meth−meth y(cco)−meth2 y(cco)−meth2−meth y(cco)−meth2−meth2

−31.45 −34.95 −41.91 −48.63

y(ccco)−meth y(ccco)−msec

−28.38 −24.91

y(cccco)−meth y(cccco)−msec

−51.98 −49.20

a

6-31G(2d,2p)

average DFT

CBS-QB3

literature

−22.67

−22.64

−31.71 −34.88 −41.97 −49.14

−32.76 −33.74 −41.94 −50.68

−22.6312 −23.321 −32.6036 −33.891

−28.72 −25.29

−29.53 −26.09

−30.671 −27.211

−52.23 −49.46

−53.58 −50.59

−54.581

Three Member Systems −23.01 −31.97 −34.80 −42.02 −49.64 Four Member Systems −29.05 −25.67 Five Member Systems −52.47 −49.72


Table 5. Calculated Standard Enthalpies of Formation and C−H Bond Dissociation Enthalpy at 298 K for Radicals in a Three Member Ringa ΔH°f,298 B3LYP target molecules

a

6-31G(d,p)

y(cc•o)−meth bond dissociation enthalpy y(c•co)−meth bond dissociation enthalpy y(cco)−m•eth bond dissociation enthalpy

27.34 102.08 29.16 103.90 23.88 98.62

y(c•co)−meth−meth bond dissociation enthalpy y(cco)−meth−m•eth bond dissociation enthalpy

16.10 100.96 12.13 96.99

y(c•co)−meth2 bond dissociation enthalpy y(cco)−meth2• bond dissociation enthalpy

17.72 103.56 11.82 97.66

y(c•co)−meth2−meth bond dissociation enthalpy y(cco)−meth2−m•eth bond dissociation enthalpy y(cco)−meth2•−meth bond dissociation enthalpy

6.43 100.47 4.40 98.44 4.99 99.03

y(cco)−meth2−meth2• bond dissociation enthalpy

−4.44 98.34

6-31G(2d,2p) Oxirane, 2-Methyl 27.50 102.24 29.09 103.83 23.81 98.55 Oxirane, 2,3-Methyl 16.21 101.07 12.07 96.93 Oxirane, 2,2-Dimethyl 17.59 103.43 11.97 97.81 Oxirane, 2,2-Dimethyl, 3-Methyl 6.49 100.53 3.65 97.69 4.28 98.32 Oxirane, 2,2-Dimethyl, 3,3-Methyl −4.57 98.21

average DFT

CBS-QB3

27.42 102.16 29.13 103.87 23.85 98.59

28.16 102.90 29.77 104.51 23.98 98.72

16.15 101.01 12.10 96.96

17.76 102.62 13.59 98.45

17.66 103.50 11.90 97.74

18.39 104.23 13.35 99.19

6.46 100.50 4.02 98.06 4.64 98.68

7.47 101.51 4.59 98.63 5.09 99.13

−4.51 98.27

−4.29 98.49


• The bond dissociation enthalpies on ring ether carbons decrease as the number of central atoms in the ring increase. This is most significant for non substituted ring carbons (group 4 in Table 9): 104.5 → 95.0 → 94.0 kcal mol−1 (three to five member ring respectively).

• C−H bond dissociation enthalpies on secondary and on nonsubstituted ether carbons are higher for cyclic ethers compared to the linear ethers and alkanes. This is similar for alkanes and we attribute this to the influence of the ring strain. 384



Article

Table 6. Calculated Standard Enthalpies of Formation and C−H Bond Dissociation Enthalpy at 298 K for Radicals in a Four Member Ring ΔH°f,298 B3LYP target molecules

6-31G(d,p)

y(c•cco)−meth bond dissociation enthalpy y(cc•co)−meth bond dissociation enthalpy y(ccc•o)−meth bond dissociation enthalpy y(ccco)−m•eth bond dissociation enthalpy

12.06 93.69 20.73 102.36 13.86 95.49 19.37 101.0

y(cc•co)−msec bond dissociation enthalpy y(c•cco)−msec bond dissociation enthalpy y(ccco)−m•sec bond dissociation enthalpy

20.01 98.20 17.40 95.59 21.79 99.98

6-31G(2d,2p) Oxetane, 2-Methyl 12.04 93.67 20.81 102.44 13.82 95.45 16.27 100.90 Oxetane, 3-Methyl 20.04 98.23 17.33 95.52 21.78 99.97

average DFT

CBS-QB3

12.05 93.68 20.77 102.40 13.84 95.47 19.32 100.95

12.77 94.41 20.61 102.24 13.88 95.51 19.43 101.06

20.03 98.22 17.36 95.55 21.78 99.97

21.21 99.40 17.52 95.71 21.56 99.75

Units: kcal mol−1 Table 7. Calculated Standard Enthalpies of Formation and C−H Bond Dissociation Enthalpy at 298 K for Radicals in a Five Member Ringa ΔH°f,298 B3LYP work reactions

a

6-31G(d,p)

y(c•ccco)−meth bond dissociation enthalpy y(cc•cco)−meth bond dissociation enthalpy y(ccc•co)−meth bond dissociation enthalpy y(cccc•o)−meth bond dissociation enthalpy y(cccco)−m•eth bond dissociation enthalpy

−13.29 92.39 −6.26 99.42 −7.36 98.32 −12.11 93.57 −2.92 102.76

y(c•ccco)−msec bond dissociation enthalpy y(cc•cco)−msec bond dissociation enthalpy y(ccc•co)−msec bond dissociation enthalpy y(cccc•o)−msec bond dissociation enthalpy y(cccco)−m•sec bond dissociation enthalpy

−9.09 93.57 −7.37 95.29 −4.06 98.60 −8.53 94.13 −2.10 100.56

6-31G(2d,2p) Oxolane, 2-methyl −13.75 91.93 −7.24 98.44 −7.75 97.93 −11.48 94.20 −2.86 102.82 Oxolane, 3-Methyl −9.19 93.47 −7.68 94.98 −4.10 98.56 −8.74 93.92 −2.09 100.57

average DFT

CBS-QB3

−13.52 92.16 −6.75 98.93 −7.55 98.13 −11.79 93.89 −2.89 102.79

−12.51 93.17 −7.20 98.48 −6.72 98.96 −11.34 94.34 −2.83 102.75

−9.14 93.52 −7.53 95.13 −4.08 98.58 −8.63 94.03 −2.10 100.56

−9.16 93.50 −6.36 96.30 −4.33 98.33 −9.04 93.62 −2.50 100.16


• Secondary C−H bond dissociation enthalpies on methyl substituted nonether, ring carbons (group 3 in Table 9) are higher than C−H bonds in corresponding sites of cyclic alkanes. The BDEs are 102.2 and 98.5 kcal mol−1 for the four member ring (y(cc•co)−meth) and five member ring (y(cc•cco)−meth). These are ∼2 kcal mol−1 higher than the corresponding secondary C−H bond dissociation enthalpies on cyclobutyl and cyclopentyl: 100.4 and 96.8 kcal mol−1 [y(c•ccc) and y(c•cccc)] respectively.25

Figure 7. Radical sites on ether carbons (a) and nonether carbons (b). 385



Article

Table 8. C−H Bond Dissociation Enthalpies for Linear Alkanes, Linear Ethers, and Cyclic Alkanes for Comparison to the Bond Dissociation Enthalpies on the Cyclic Ethersa C−H bond dissociation enthalpies bond type primary secondary tertiary a

C−H bond dissociation enthalpies

linear alkanes

linear ethers

bond type

cyclic alkanes

101.0223 (CH2•CH2CH3) 99.1223 (CH3CH•CH3) 96.3037 (CH3)3C•

102.6524 (CH2•CH2OCH3) 95.0124 (CH3CH•OCH3) 94.9024 (CH3)2C•OCH3

cyclopropane

109.125

cyclobutane

100.425

cyclopentane

96.825

aUnits: kcal mol−1.

Figure 8. C−H bond dissociation enthalpies for primary (methyl radical) carbons, bonded to a nonether carbon (Δ) and ether carbon (□).

Figure 10. C−H bond dissociation enthalpies for tertiary nonether carbons (Δ) and methyl substituted ether carbons (□).

Table 9. Comparison of C−H Bond Dissociation Enthalpies for Methyl-Substituted C3−C5 Cyclic Ethersa

Figure 9. C−H bond dissociation enthalpies for secondary nonether carbons (Δ) and ether carbons (□).

• Secondary radical sites on ether carbons (group 4 in Table 9) have 5 to 7 kcal mol−1 lower C−H bond enthalpies relative to secondary radical sites on comparable ring nonether carbons (group 3 in Table 9), due to resonance with the adjacent oxygen. • The secondary C−H bond dissociation enthalpies in the five member methyl substituted nonether ring carbons (group 3 in Table 9, third column) are similar to the values reported for the corresponding radicals of linear alkanes (CH3CH2•CH3,23 99.1 kcal mol−1).

a

aUnits: kcal mol−1.

• The secondary C−H bond dissociation enthalpies in the five member methyl substituted ether ring carbons (group 4 in Table 9, third column) are similar to the values reported for the corresponding radicals of linear ethers (CH3CH•OCH3,24 95.0 kcal mol−1). 386



Article

Table 10. Comparison of C−H Bond Dissociation Enthalpies for Methyl-Substituted Three Member Ring Ethersa

a


Table 11. Ideal Gas-Phase Thermodynamic Property vs. Temperaturea Cp(T)

a

species

S° at 298 K

300 K

400 K

500 K

600 K

800 K

1000 K

1500 K

y(cco)−meth y(cco)−meth2 y(cco)−meth−meth y(cco)−meth2−meth y(cco)−meth2−meth2 y(ccco)−meth y(ccco)−msec y(cccco)−meth y(cccco)−mb y(c•co)−meth y(cc•o)−meth y(cco)−m•eth y(c•co)−meth−meth y(cco)−meth−m•eth y(c•co)−meth2 y(cco)−meth2• y(c•co)−meth2−meth y(cco)−meth2−m•eth y(cco)−meth2•−meth y(cco)−meth2−meth2• y(c•cco)−meth y(cc•co)−meth y(ccc•o)−meth y(ccco)−m•eth y(c•cco)−msec y(cc•co)−msec y(ccco)−m•sec y(c•ccco)−meth y(cc•cco)−meth y(ccc•co)−meth y(cccc•o)−meth y(cccco)−m•eth y(c•ccco)−msec y(cc•cco)−msec y(ccc•co)−msec y(cccc•o)−msec y(cccco)−msec•

63.92 66.40 65.24 67.50 86.15 68.41 67.24 73.04 74.38 63.09 64.11 65.05 69.49 68.35 72.51 72.37 70.33 79.22 79.28 86.43 70.44 69.30 69.31 70.19 69.40 71.66 71.04 73.95 74.47 75.09 73.77 75.10 73.95 76.98 75.09 74.39 76.61

17.03 23.27 22.57 28.65 32.52 20.65 20.55 24.66 22.74 14.70 14.76 15.76 20.35 20.59 20.45 21.41 24.49 27.35 27.35 33.38 19.43 18.67 18.67 19.42 18.60 18.83 19.38 22.75 23.02 23.35 22.88 23.38 22.75 22.93 23.35 22.86 23.58

21.76 29.32 28.32 35.54 32.70 27.42 27.25 33.17 30.95 19.03 18.94 20.18 25.97 26.38 20.55 21.53 31.47 27.50 27.50 33.55 19.55 18.79 18.79 19.55 18.72 18.95 19.50 22.91 23.17 23.50 23.03 23.54 22.91 23.08 23.50 23.02 23.73

25.98 34.61 33.62 41.88 41.67 33.44 33.25 40.76 38.63 22.86 22.71 23.92 31.05 31.48 26.02 27.23 37.76 34.61 34.60 42.10 25.53 24.93 24.93 25.70 24.79 24.79 25.56 30.75 31.02 31.16 30.88 31.46 30.75 30.62 31.16 30.78 31.46

29.57 39.11 38.23 47.43 49.87 38.50 38.33 47.19 45.20 26.08 25.92 26.98 35.40 35.79 31.08 32.27 43.18 40.90 40.88 49.64 30.94 30.45 30.45 31.15 30.29 30.22 30.98 37.86 38.10 38.17 37.97 38.53 37.86 37.65 38.17 37.84 38.45

35.16 46.20 45.58 56.36 62.92 46.29 46.18 57.11 55.42 31.01 30.88 31.62 42.22 42.49 39.09 39.99 51.74 50.64 50.62 61.38 39.25 38.90 38.90 39.40 38.77 38.75 39.26 48.84 48.98 49.06 48.90 49.31 48.84 48.70 49.06 48.79 49.22

39.28 51.49 51.04 63.05 72.48 51.94 51.88 64.32 62.84 34.59 34.49 34.98 47.22 47.40 44.91 45.51 58.06 57.69 57.66 69.92 45.13 44.85 44.85 45.19 44.76 44.85 45.09 56.60 56.67 56.80 56.64 56.90 56.60 56.60 56.80 56.55 56.84

45.67 59.78 59.56 73.57 87.28 60.60 60.59 75.31 74.10 40.07 40.03 40.20 54.91 54.99 53.78 53.99 67.85 68.58 68.56 83.17 53.96 53.78 53.78 53.91 53.74 53.93 53.88 68.22 68.22 68.38 68.23 68.32 68.22 68.36 68.38 68.19 68.30

Units: S (cal mol−1) and Cp (cal mol−1 K−1). 387



Article

• Similarly, BDEs for ether carbons with a methyl substituent decrease as the number of central atoms in the ring increase (group 6 in Table 9): 102.9 → 94.4 → 93.2 kcal mol−1 (three to five member ring, respectively). • Bond dissociation enthalpies are increased on the 3 and 4 member rings compared to corresponding C−H sites on linear ether and alkyl radicals due to the ring strain. • Radical sites on methyl substituted ether carbons (group 6 in Table 9) have 3−4 kcal mol−1 lower C−H bond dissociation enthalpies compared to tertiary radical sites in nonether carbons (group 5 in Table 9), due to the adjacent oxygen. This is a similar effect to that in noncyclic ethers and is due to resonance of the radical with the ether group. Table 10 shows a comparison between the primary methyl C−H bond dissociation enthalpies of the different methyl substituted oxirane species, where both carbons of the ring are ether carbons and have one or more methyl substituents. It also shows the ether carbon BDEs where there is a H atom available.

Table 12. Comparison of the Enthalpies of Formation at 298 K Obtained Using CBS-QB3, and the Entropy at 298 K Obtained Using SMCPS and Rotator, with the Values Obtained Using Group Additivity ΔH°f,298

S°298

species

DFT

group additivity

DFT

group additivity

y(cco)−meth y(cco)−meth2 y(cco)−meth−meth y(cco)−meth2−meth y(cco)−meth2−meth2 y(ccco)−meth y(ccco)−msec y(cccco)−meth y(cccco)−mb y(c•co)−meth y(cc•o)−meth y(cco)−m•eth y(c•co)−meth−meth y(cco)−meth−m•eth y(c•co)−meth2 y(cco)−meth2• y(c•co)−meth2−meth y(cco)−meth2−m•eth y(cco)−meth2•−meth y(cco)−meth2−meth2• y(c•cco)−meth y(cc•co)−meth y(ccc•o)−meth y(ccco)−m•eth y(c•cco)−msec y(cc•co)−msec y(ccco)−m•sec y(c•ccco)−meth y(cc•cco)−meth y(ccc•co)−meth y(cccc•o)−meth y(cccco)−m•eth y(c•ccco)−msec y(cc•cco)−msec y(ccc•co)−msec y(cccc•o)−msec y(cccco)−msec•

−22.64 −33.74 −32.76 −41.94 −50.68 −29.53 −26.09 −53.58 −50.59 29.77 28.16 23.98 17.76 13.59 18.39 13.35 7.47 4.59 5.09 −4.29 12.77 20.61 13.88 19.43 17.52 21.21 21.56 −12.51 −7.20 −6.72 −11.34 −2.83 −9.16 −6.36 −4.33 −9.04 −2.50

−21.87 −31.47 −31.17 −40.77 −50.37 −28.54 −26.41 −53.50 −51.37 24.01 20.93 28.68 11.63 19.38 12.33 19.08 2.03 9.78 9.78 0.18 14.26 17.81 14.37 22.01 16.50 17.99 22.59 −10.70 −7.15 −7.15 −10.59 −2.95 −8.46 −6.97 −5.02 −8.46 −2.37

63.92 66.40 65.24 67.50 86.15 68.41 67.24 73.04 74.38 63.09 64.11 65.05 69.49 68.35 72.51 72.37 70.33 79.22 79.28 86.43 70.44 69.30 69.31 70.19 69.40 71.66 71.04 73.95 74.47 75.09 73.77 75.10 73.95 76.98 75.09 74.39 76.61

66.79 69.45 68.84 70.88 86.17 72.68 72.99 78.07 78.38 68.42 69.22 72.25 76.64 79.68 74.88 75.73 82.31 85.34 85.34 91.01 76.11 78.12 75.31 79.14 74.62 78.23 77.78 83.50 85.51 85.51 82.70 86.53 82.01 85.62 84.82 82.01 85.17

■

ENTROPY AND HEAT CAPACITY DATA The entropy and heat capacity data for the parent molecules were determined from the optimized structures, number of optical isomers, moments of inertia, vibrational frequencies, symmetries, mass of the molecule, internal rotor contributions for methyl rotors and electronic (spin) degeneracy. The calculations use standard formulas from statistical mechanics for the contributions of translation, external rotation and vibrations.26,27 Contributions to the entropy and the heat capacity from translation, vibrations and external rotation are calculated using the “SMCPS” program.28 This program utilizes the rigid-harmonic oscillator approximation from the optimized structures obtained at B3LYP/6-31G(d,p) level. The number of optical isomers and the spin degeneracy of unpaired electrons are also incorporated for the calculation of S°298. Contributions from hindered internal methyl rotors to S°298 and Cp(T) were determined using the “VIBIR” program.29 This program utilizes the method of Pitzer and Gwinn30,31 the potential barriers from the internal rotor analysis, foldness and the respective internal rotor moments of inertia, which were obtained at B3LYP/6-31G(d,p) level. The internal rotor data was combined with the S(T) and Cp(T) data from frequency, mass, moment of inertia; symmetry and electronic degeneracy from the statistical mechanics program SMCPS.28 Table 11 summarizes the data for entropy at 298 K and Cp(T) 300−1500K, and the Supporting Information includes data for the studied species from 50 to 5000K. The results obtained for ΔH°f,298 and S°298 are compared to the results obtained by using group additivity methods.32 Group additivity with corrections for rings is a straightforward and reasonably accurate calculation method to estimate thermodynamic properties of hydrocarbons and oxygenated hydrocarbons;32 it is particularly useful for application to larger

C. Results for C−H bonds on tertiary ring and methyl substituted ether ring carbons (group 5 and 6 in Table 9): • Bond dissociation enthalpies for tertiary radical sites on central nonether carbons decrease as the number of central atoms in the ring increase (group 5 in Table 9): 99.4 → 96.3 kcal mol−1 (four to five member ring, respectively). Table 13. Reactions Used for Stable Molecules

Reactions for Stable Molecules reaction 1 reaction 2 reaction 3 reaction 4 reaction 5 reaction 6

y(CH3OCH3) + CH3CH2CH3 → Y(CH3CH2CH3) + CH3OCH3 y(CH3OCH3) + CH3CH2CH2CH3 → Y(CH3CH2CH3) + CH3CH2OCH3 y(CH3OCH2CH3) + CH3CH2CH3 → y(CH3CH2CH2CH3) + CH3OCH3 y(CH3OCH2CH3) + CH3CH2CH2CH3 → y(CH3CH2CH2CH3) + CH3CH2OCH3 y(CH3OCH2CH2CH3) + CH3CH2CH3 → y(CH3CH2CH2CH2CH3) + CH3OCH3 y(CH3OCH2CH2CH3) + CH3CH2CH2CH3 → y(CH3CH2CH2CH2CH3) + CH3CH2OCH3 388



Article

Table 14. Reactions Used for Radicals Reactions for Radicals Y(CH2•CH2CH3) → CH3CH2CH3 + y(CH3CH2CH3) + CH3CH•CH3 Y(CH2•CH2CH3) → CH3CH2CH2CH3 + y(CH3CH2CH3) + CH3CH2CH•CH3 Y(CH2•CH2CH3) → CH3CH2CH2CH2CH3 + y(CH3CH2CH3) + CH3CH2CH2CH•CH3 y(CH •CH2CH2CH3) → CH3CH2CH3 + y(CH3CH2CH2CH3) + CH3CH•CH3 y(CH2•CH2CH2CH3) → CH3CH2CH2CH3 + y(CH3CH2CH2CH3) + CH3CH2CH•CH3 y(CH2•CH2CH2CH3) → CH3CH2CH2CH2CH3 + y(CH3CH2CH2CH3) + CH3CH2CH2CH•CH3 y(CH2•CH2CH2CH2CH3) → CH3CH2CH3 + y(CH3CH2CH2CH2CH3) + CH3CH•CH3 y(CH2•CH2CH2CH2CH3) → CH3CH2CH2CH3 + y(CH3CH2CH2CH2CH3) + CH3CH2CH•CH3 y(CH2•CH2CH2CH2CH3) → CH3CH2CH2CH2CH3 + y(CH3CH2CH2CH2CH3) + CH3CH2CH2CH•CH3

reaction 1 reaction 2 reaction 3 reaction 4 reaction 5 reaction 6 reaction 7 reaction 8 reaction 9

Table 15. Calculated Enthalpy of Reaction, ΔHrxn, for Parent Ether Reactionsa ΔHrxn298

Δ(calcd − ref)

B3LYP

a

B3LYP

reactions

6-31g(d,p)

6-31g(2d,2p)

CBS-QB3

literature

6-31g(d,p)

6-31g(2d,2p)

CBS-QB3

1 2 3 4 5 6)

6.53 4.70 6.97 5.14 6.82 4.99

6.09 2.75 6.78 3.44 7.01 3.67

6.62 3.44 7.33 4.15 7.30 4.12

6.35 3.62 6.90 4.17 6.80 4.07

0.18 1.08 0.07 0.97 0.03 0.93

−0.26 −0.87 −0.12 −0.73 0.21 −0.40

0.28 −0.18 0.43 −0.02 0.50 0.05


Table 16. Enthalpy of Reaction, ΔHrxn, for Radical Species Reactionsa ΔHrxn298

Δ(calcd − ref)

B3LYP

a

B3LYP

reactions

6-31g(d,p)

6-31g(2d,2p)

CBS-QB3

literature

6-31g(d,p)

6-31g(2d,2p)

CBS-QB3

1 2 3 4 5 6 7 8 9

−10.17 −9.95 −10.01 −0.96 −0.73 0.80 1.84 2.07 2.00

−10.21 −10.00 −10.06 −0.93 −0.72 −0.78 1.81 2.02 1.97

−10.34 −10.11 −10.15 −1.50 −1.28 −1.31 2.43 2.65 2.62

−9.74 −10.73 −10.52 −0.36 −1.35 −1.14 3.06 2.07 2.28

−0.43 0.78 0.51 −0.60 0.62 0.34 −1.22 0.00 −0.28

−0.47 0.73 0.46 −0.57 0.63 0.36 −1.25 −0.05 −0.31

−0.60 0.62 0.37 −0.14 0.07 −0.17 −0.63 0.08 0.34


sites. Results for methyl-substituted oxirane, oxetane and oxolane show the following points. • Primary methyl radicals:

molecules and in codes or databases for the estimation of thermochemical properties in reaction mechanism generation. Table 12 summarizes the comparison of the results obtained, and Appendix B summarizes the groups used for the Group Additivity calculations. For the parent molecules, there is very good agreement for the heat of formation between the values obtained by the ab initio and Group additivity calculations (

Thermochemical Properties of Methyl-Substituted Cyclic Alkyl Ethers

Recommend Documents