Thermochemistry and Bond Dissociation Energies of Ketones - The

Article pubs.acs.org/JPCA

Thermochemistry and Bond Dissociation Energies of Ketones Jason M. Hudzik and Joseph W. Bozzelli* Chemistry, Chemical Engineering, and Environmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102, United States S Supporting Information *

ABSTRACT: Ketones are a major class of organic chemicals and solvents, which contribute to hydrocarbon sources in the atmosphere, and are important intermediates in the oxidation and combustion of hydrocarbons and biofuels. Their stability, thermochemical properties, and chemical kinetics are important to understanding their reaction paths and their role as intermediates in combustion processes and in atmospheric chemistry. In this study, enthalpies (ΔH°f 298), entropies (S°(T)), heat capacities (Cp°(T)), and internal rotor potentials are reported for 2butanone, 3-pentanone, 2-pentanone, 3-methyl-2-butanone, and 2-methyl-3-pentanone, and their radicals corresponding to loss of hydrogen atoms. A detailed evaluation of the carbon−hydrogen bond dissociation energies (C−H BDEs) is also performed for the parent ketones for the first time. Standard enthalpies of formation and bond energies are calculated at the B3LYP/6-31G(d,p), B3LYP/6-311G(2d,2p), CBS-QB3, and G3MP2B3 levels of theory using isodesmic reactions to minimize calculation errors. Structures, moments of inertia, vibrational frequencies, and internal rotor potentials are calculated at the B3LYP/6-31G(d,p) density functional level and are used to determine the entropies and heat capacities. The recommended ideal gas-phase ΔH°f 298, from the average of the CBS-QB3 and G3MP2B3 levels of theory, as well as the calculated values for entropy and heat capacity are shown to compare well with the available experimental data for the parent ketones. Bond energies for primary, secondary, and tertiary radicals are determined; here, we find the C−H BDEs on carbons in the α position to the ketone group decrease significantly with increasing substitution on these α carbons. Group additivity and hydrogen-bond increment values for these ketone radicals are also determined.

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and distribution using laser-induced fluorescence17−19 and as fuel additives in reducing soot emissions.20,21 Detailed chemical kinetic models have been developed and are readily available for hydrocarbon combustion22 with some, but far fewer, studies for ketones. Some chemical kinetic models have been developed involving smaller ketones such as for the oxidation of acetone23−25 and several reactions involving acetonyl radicals.26−28 Chemical kinetic models for 2-butanone and 3-pentanone oxidation have recently been reported29,30 where properties for radicals formed from hydrogen abstraction had to be estimated using group additivity and comparisons to acetone. The value used for the secondary carbon−hydrogen bonds was several kcal mol−1 higher than the actual value, and this could affect both unimolecular dissociation and abstraction kinetics in the model. Sebbar et al.31 in kinetic analysis of butanone oxidation have recently reported weak carbon− hydrogen bond dissociation energies in 2-butanone for the carbons adjacent to the carbonyl group to support this. Rate

INTRODUCTION The role of ketones in the chemistry of the earth’s atmosphere has been studied experimentally using field measurements and has been incorporated into modeling studies.1−5 Sources of atmospheric acetone, for example, include emissions from dead plant matter, burning of biomass, oxidation of hydrocarbons, and anthropogenic emissions.6−10 Acetone and the acetonyl radical, formed by OH abstraction,11 have been shown to play an important role in atmospheric chemistry by influencing ozone production through withdrawing nitrogen oxides in the form of peroxyacyl nitrates (PANs) and generating HOx free radicals.2−6,12−14 Important atmospheric loss processes for ketones involve hydrogen abstractions by OH radicals, a process that is partially controlled by carbon−hydrogen bond dissociation energies (C−H BDEs) and by photolysis.8,15,16 Besides their importance in the atmosphere, ketones are a major class of organic compounds. They make up a significant portion of organic cleaning solvents, paint thinners, nail polish removers, and as solvents in chemical processes. Ketones have also been used as fuel tracers for monitoring fuel properties such as concentration, temperature, density, pressure, velocity, © 2012 American Chemical Society

Received: March 24, 2012 Revised: May 9, 2012 Published: June 5, 2012 5707

dx.doi.org/10.1021/jp302830c | J. Phys. Chem. A 2012, 116, 5707−5722

The Journal of Physical Chemistry A

Figure 1. Nomenclature, recommended ΔH°f ketones in this study.

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298

(bold, kcal mol−1), and carbon−hydrogen bond dissociation energies (italic, kcal mol−1) for

constants for abstraction reactions in modeling atmospheric and combustion chemistry are commonly estimated using well-studied smaller compounds having similar bond dissociation energies. There have been previous microwave spectroscopy studies on the molecular geometry of several smaller ketones.32−35 Yet to the best of our knowledge, there are no comprehensive studies on bond energies of ketones and radicals corresponding to loss of H atom as a class of compounds with the exception of acetone, which has reported C−H bond energies of 92− 101 kcal mol−1.36−45 The more recent theoretical and experimental studies however seem to converge on a value of 96 ± 1 kcal mol−1.36,38,39,43 Although ketones have many applications and involvement in different chemical systems, basic thermochemical properties for several representative compounds are not available. Accurate and reliable enthalpies of formation and bond dissociation energies for these species are necessary for improvement in understanding ketonyl radicals, transition states, reaction paths, and in developing detailed chemical kinetic models.46−48

The objective of this study is to provide a set of thermochemical properties including enthalpies (ΔH°f 298), entropies (S°(T)), and heat capacities (Cp°(T)), along with primary, secondary, and tertiary C−H BDEs adjacent to the carbonyl group for five small ketone species, presented in Figure 1, to enhance the accuracy of modeling combustion systems. Our calculated ΔH°f 298 values for 2-butanone, 3-pentanone, 2-pentanone, 3-methyl-2-butanone, and 2-methyl3-pentanone show good agreement as compared to available literature values. We also determine ΔH°f 298 for all of the radicals corresponding to the loss of hydrogen atom (J represents the radical site on a preceding carbon atom). Bond energies are also determined from the parent and radical species and are compared to the available literature values and conventional normal primary, secondary, and tertiary bond energies from alkane hydrocarbons.

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COMPUTATIONAL METHODS Optimized geometries for the parent and radicals were initially calculated at the B3LYP/6-31G(d,p) level of theory.49,50 5708



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By summing the TVR and IR contributions, total entropy and heat capacity values are determined for all of the compounds in this study for the 100−5000 K temperature range. Individual TVR and IR contributions for each species are presented in the Supporting Information. The group additivity (GA) method, as developed by Benson,66 is also implemented as a comparison for our determined ΔH°f 298, S°298, and Cp°(T) values. The success of this method is based on the accurate knowledge of the contributions of representative groups from smaller molecules and their established linear consistency in thermochemical property contribution. Group additivity for the thermochemical properties of ketones along with the hydrogen-bond increment (HBI) values for the primary, secondary, and tertiary positions adjacent to the carbonyl group in ketones will be useful in the development of their kinetic modeling.66,67

Potential energy curves for the internal rotation barriers at this level of theory were created to verify the lowest energy conformation and for use in calculations of entropies and heat capacities. (These PE curves are available in the electronic version of the Supporting Information.) This B3LYP density functional theory (DFT) method combines the three-parameter Becke exchange functional, B3, with the Lee−Yang−Parr correlation functional, LYP. The moderate 6-31G(d,p) and the larger 6-311G(2d,2p), which includes additional polarization functions on carbon and hydrogen atoms, basis sets are employed with B3LYP, which we have shown previously to provide acceptable thermochemical properties for hydrocarbons and oxygenates.51,52 Higher level ab initio and DFT-based composite methods are utilized to provide more accurate thermochemical properties53−55 and to compare and gauge the accuracy of the lower level DFT calculations. G3MP2B354,56 is a modified version of the G3MP257 method where the geometries and zero-point vibration energies are from B3LYP calculations with QCISD(T), MP2, and high-level correction for the total energy. CBSQB358,59 is a complete basis set method that uses geometries and frequencies from the B3LYP level followed by single point energy calculations at the CCSD(T), MP4SDQ, and MP2 levels. The final energies are determined with a CBS extrapolation. All calculations were performed using the Gaussian 03 program suite.60 Isodesmic reactions were implemented to achieve greater accuracy for the gas-phase enthalpies of formation. These are hypothetical reactions that incorporate similar bonding environments for both reactants and products, which allow for cancellation of error associated with each method of analysis. Comparison with experimental data or the higher level ab initio calculations allows us to validate the use of the lower level DFT methods for ΔH°f 298 analysis of these ketones and radicals. The carbon−hydrogen bond dissociation energies (C−H BDE) are derived using the calculated ΔH°f 298 energies and the established literature value of 52.10 kcal mol−1 for a hydrogen atom.61 A bond cleavage reaction is used to calculate each C−H BDE as the difference in our ΔH°f 298 for the parent compound (R−H) and the corresponding radical (R•) plus hydrogen atom (H•):

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NOMENCLATURE Throughout this Article, abbreviations are utilized as illustrated below: • C(O) represents a carbonyl group, • (C) represents a methyl substituent on the preceding carbon atom, • J represents a radical site on the preceding carbon atom, • TVR denotes translation, vibration, and external rotation, • IR denotes internal rotation.

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RESULTS AND DISCUSSION Isodesmic work reactions were used to calculate the ΔH°f 298 for each target species at the B3LYP/6-31G(d,p), B3LYP/ 6-311G(2d,2p), CBS-QB3, and G3MP2B3 levels of theory and are presented in Table 2. Each of the ketone parent compounds was analyzed with four to five isodesmic work reactions where the parent compound is reacted with ethane, propane, acetaldehyde, or acetone and yields a small three- or four-carbon n-alkane and, in most cases, acetone or 2-butanone. Slightly larger species are generated for the 2-methyl-3-pentanone work reactions. The radical work reactions are slightly different where the compound is reacted with a small hydrocarbon and yields the parent ketone plus a hydrocarbon radical as seen in Scheme 1. The radical work reactions are presented in Table 3.

R−H → R• + H•

Scheme 1. Radical Isodesmic Work Reactions

Comparison between results from DFT and ab initio calculations using isodesmic reactions shows excellent agreement for enthalpy of formations and bond energies (vide infra) for the ketones in this study. Contributions to entropies and heat capacities from translations, vibrations, and external rotations, represented as TVR, are calculated using the Statistical Mechanics for Heat Capacity and Entropy (SMCPS) program62 using the B3LYP/ 6-31G(d,p) level of theory. The SMCPS program uses geometry, mass, electronic degeneracy, symmetry, frequencies, number of optical isomers, and moments of inertia as input parameters for each compound. Contributions from internal rotations (IR) are incorporated using the Pitzer−Gwinn63−65 approximation method. The B3LYP/6-31G(d,p) level of theory is used to determine potential energy barriers to internal rotation of each rotor at 10° intervals. Reduced moments of inertia are determined from moments of inertia for the rotational groups using their mass and radius of rotation.

All of the species in the work reactions, except for the target compound, have standard well-established ΔH°f 298 values;48,61,68,69 these are listed in Table 1. In some cases, the work reactions utilized generated a ketone compound that is analyzed in this study. The reference ΔH°f 298 values used in these cases are from literature values70−73 shown in Table 1. The optimized structure parameters, symmetry values, moments of inertia, vibrational frequencies, internal rotor potentials, and individual contributions to entropies and heat capacities from the B3LYP/6-31G(d,p) level of theory are presented in the Supporting Information for each species in this analysis. 5709



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We recommend the ΔH°f 298 values from the average of the CBS-QB3 and G3MP2B3 levels of theory for all of the parent and radical ketone species, which are presented in Figure 1 (in bold) and Table 4. Table 5 shows a comparison of our recommended ΔH°f 298 values to other values reported in the literature. Values for all of the parent ketones are listed, but we only found values for 2-butanone and 3-pentanone radicals in the literature for comparison. 2-Butanone is the smallest ketone in this study, and our value of −57.3 kcal mol−1 has a maximum derivation of 0.4 kcal mol−1 of the reported literature values. Literature values are reported for 2-butanone radicals for comparison along with values determined using group additivity (GA) and hydrogen-bond increment (HBI) methods.66,67 When comparing our calculated values to the literature values for the three radical sites on 2-butanone, there is very good agreement with a maximum difference of only 0.6 kcal mol−1. However, the current group additivity for the two radical sites adjacent to the carbonyl range in difference between 0.9 and 1.5 kcal mol−1. Our calculated value of −62.5 kcal mol−1 for 3-pentanone also shows agreement below 0.9 kcal mol−1 with the reported literature value. The primary methyl radical CJCC(O)CC (methyl not adjacent to carbonyl group) is also within 1.3 kcal mol−1 of the reported GA and literature values. There is, however, a wide (∼7 kcal mol−1) range in the reported bond energies for the secondary radical CCJC(O)CC, which creates a 5 kcal mol−1 difference in our ΔH°f 298 value as compared to the GA hydrogen-bond increment value while only a 1 kcal mol−1 difference from one recent literature value. The data suggest the previous estimates of secondary bond dissociation energies adjacent to the carbonyl group in ketones are high and that kinetic estimates to C−H bond scission and abstraction are underestimated. New group additivity data for the ketone radicals are provided below. Values for our other three ketone parent species are below 0.2 kcal mol−1, which is well within the chemical accuracy of 1 kcal mol−1. We suggest the average ΔH°f 298 values from the CBS-QB3 and G3MP2B3 methods with the respective work reactions. The agreement between these methods provides support for these values. Carbon−Hydrogen Bond Dissociation Energies (C−H BDEs). C−H BDEs are computed from the work reactions listed in Table 3. The calculated ΔH°f 298 values of the parent and radical molecules are combined with the well-established literature value of 52.10 kcal mol−1 for the hydrogen atom.61 Primary C−H BDEs for ethane, n-propane, and n-butane have been previously shown by multiple studies to be in the 100.5−101 kcal mol−1 range.69,75,76 These studies also all report similarly lower values for secondary C−H BDEs of approximately 98.5 kcal mol−1 for n-propane and n-butane. The standard tertiary C−H BDE of 96.5 kcal mol−1 is averaged from t-butyl reported values, which range 95.7−97.2 kcal mol−1.69,75,77 Our calculated C−H BDEs for the ketones in this study from the DFT and higher level calculations are listed in Table 4 with the recommended values from the CBS-QB3 and G3MP2B3 methods in italics in Figure 1. Analysis of the BDE for the ketones in this study can be broken down into five bond types or classes: (i) primary, (ii) primary adjacent to the carbonyl, (iii) secondary, (iv) secondary adjacent to the carbonyl, and (v) tertiary adjacent to the carbonyl. Table 6 has a summary of these different bond classes for each parent compound where the consistency

Table 1. Standard Enthalpies of Formation for Reference Species Used in This Study species

ΔH°f 298 (kcal mol−1)

reference

H CH4a CH3CH3 CH3CH2CH3 CH3CH2CH2CH3 (CH3)3CH CC(O) CC(O)C CC(O)CC CCC(O)CC CC(O)C(C)C CJH3a CH3CJH2 CH3CJHCH3 (CH3)3CJ CH3CJHCH2CH3 CC(=O)CJa

52.10 −17.8 ± 0.1 −20.0 ± 0.1 −25.0 ± 0.1 −30.0 ± 0.1 −32.1 ± 0.1 −39.72 ± 0.16 −51.9 ± 0.2 −57.02 ± 0.20 −62.25 ± 0.39 −62.76 ± 0.21 35.1 ± 0.2 29.0 ± 0.4 21.5 ± 0.4 12.3 ± 0.4 16.1 ± 0.5 −8.3 ± 0.5

61 68 68 68 68 68 48 68 70 b 73 94 69 69 69 69 36

a

Used in reference reactions in Scheme 2. bReported on NIST WebBook as the reanalyzed value of ref 71 by ref 72.

Heat of Formation ΔH°f 298. A summary of the averages from the DFT and the higher level composite methods for parent ketones and corresponding radicals from data in Tables 2 and 3 is found in Table 4 and Figure 1. Evaluation of error in these standard enthalpies is provided in several ways. Tables 2 and 3 list averages of the reference species uncertainty and the standard deviation from the individual calculated ΔH°f 298 values from the DFT and the combined CBS-QB3 and G3MP2B3 work reactions. In addition, we show five reference reactions, Scheme 2, involving standard (known enthalpy) species, given in Table 1, where standard deviations are determined from the difference of the literature versus our calculated ΔH°reaction values. The resulting standard deviations from the reference reactions show an average of 1.2 and 0.4 kcal mol−1 for the DFT and ab initio methods, respectively. These standard deviations coincide with the average standard deviations, on a per work reaction basis, determined in Tables 2 and 3. We recommend the values from the Scheme 2 for evaluation of accuracy, and note that the uncertainty in the reference species also needs to be considered. On the basis of the correlations in these different techniques, we provide error values in Table 4 using the standard deviation from the individual calculated ΔH°f 298 values. These data demonstrate good agreement for the ΔH°f 298 values between the DFT and the higher level methods, which results from the use of work reactions. The parent ketones show an average difference of 0.7 kcal mol−1. The maximum difference is 0.2 kcal mol−1 for the smaller ketones (2-butanone, 3-pentanone, and 2-pentanone), which shows that DFT provides an acceptable analysis as compared to the higher level calculation methods. For the two larger ketones, the average difference increases to 1.7 and 1.4 kcal mol−1, which supports the known problems of additive errors in DFT methods;55,74 this should be considered in applying these time and computation resource effective DFT methods. The radical compounds have an average enthalpy difference of 1.0 kcal mol−1. If we remove CC(O)CJ(C)C and CCJ(C)C(O)CC, which have differences over 2 kcal mol−1 from consideration, the average difference is reduced to 0.8 kcal mol−1. 5710



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Table 2. Isodesmic Work Reactions and Calculated ΔH°f 298 for Ketone Parent Species ΔH°f 298 (kcal mol−1) B3LYP

isodesmic reactions CC(O)CC CC(O)CC CC(O)CC CC(O)CC

+ + + +

CH3CH3 CH3CH3 CH3CH2CH3 CC(O)

→ → → →

CCC(O)CC CCC(O)CC CCC(O)CC CCC(O)CC

+ + + +

CH3CH3 CH3CH3 CH3CH2CH3 CC(O)

→ → → →

n-CC(O)CCC n-CC(O)CCC n-CC(O)CCC n-CC(O)CCC n-CC(O)CCC

+ + + + +

CH3CH3 CH3CH3 CH3CH2CH3 CC(O) CC(O)C

→ → → → →

CC(O)C(C)C CC(O)C(C)C CC(O)C(C)C CC(O)C(C)C CC(O)C(C)C

+ + + + +

CH3CH3 CH3CH3 CH3CH2CH3 CC(O) CC(O)C

→ → → → →

CC(C)C(O)CC CC(C)C(O)CC CC(C)C(O)CC CC(C)C(O)CC

+ + + +

CH3CH3 CH3CH3 CH3CH3 CC(O)

→ → → →

6-31G(d,p) 6-311G(2d,2p)

CC(O)CC System CC(O)C + CH3CH2CH3 CC(O) + CH3CH2CH2CH3 CC(O)C + CH3CH2CH2CH3 CC(O)C + CC(O)C average method std dev CCC(O)CC System CC(O)C + CH3CH2CH2CH3 CC(O)CC + CH3CH2CH3 CC(O)CC + CH3CH2CH2CH3 CC(O)CC + CC(O)C average method std dev n-CC(O)CCC System CC(O)CC + CH3CH2CH3 CC(O)C + CH3CH2CH2CH3 CC(O)CC + CH3CH2CH2CH3 CC(O)C + CC(O)CC CC(O)CC + CC(O)CC average method std dev CC(O)C(C)C System CC(O)C + CH3CH2CH2CH3 CC(O)CC + CH3CH2CH3 CC(O)CC + CH3CH2CH2CH3 CC(O)CC + CC(O)C CC(O)CC + CC(O)CC average method std dev CC(C)C(O)CC System CC(O)CC + CH3CH2CH2CH3 CC(O)C(C)C + CH3CH2CH3 CCC(O)CC + CH3CH2CH3 CC(O)CC + CC(O)CC average method std dev

CBS-QB3

G3MP2B3

average reference species uncertainty

−57.42 −57.86 −57.49 −57.05 −57.45 0.36

−57.31 −57.92 −57.46 −56.85 −57.39

−57.36 −57.21 −57.29 −57.45 −57.33 0.21

−57.24 −56.85 −57.19 −57.57 −57.21

0.13 0.12 0.13 0.19 0.14

−62.88 −62.41 −62.49 −62.05 −62.46 0.34

−62.75 −62.31 −62.46 −61.85 −62.34

−62.71 −62.44 −62.37 −62.53 −62.51 0.15

−62.53 −62.37 −62.31 −62.70 −62.48

0.13 0.13 0.13 0.19 0.15

−61.87 −62.34 −61.94 −61.50 −61.47 −61.82 0.34

−61.74 −62.18 −61.89 −61.29 −61.45 −61.71

−61.94 −62.21 −61.87 −62.02 −61.60 −61.93 0.21

−61.93 −62.10 −61.88 −62.26 −61.71 −61.98

0.13 0.13 0.13 0.19 0.20 0.16

−61.73 −61.26 −61.34 −60.89 −60.87 −61.22 0.34

−61.64 −61.21 −61.35 −60.75 −60.91 −61.17

−63.14 −62.87 −62.80 −62.95 −62.53 −62.86 0.21

−63.01 −62.84 −62.79 −63.17 −62.62 −62.89

0.13 0.13 0.13 0.19 0.20 0.16

−66.88 −68.31 −66.65 −66.05 −66.97 0.89

−66.79 −68.20 −66.58 −65.89 −66.87

−68.39 −68.35 −68.27 −68.21 −68.31 0.09

−68.29 −68.27 −68.23 −68.46 −68.31

0.13 0.14 0.20 0.19 0.17

alkane secondary carbon. There is only one secondary carbon that is at one or more carbons removed from the carbonyl group; it is n-CC(O)CCJC, which has a normal secondary bond energy of 98.8 kcal mol−1. Tertiary bond energies adjacent to the carbonyl are also strongly influenced with lower bond energies of 87.5 and 87.8 kcal mol−1, 9 kcal mol−1 lower than the 96.5 kcal mol−1 commonly observed for an alkyl tertiary bond. Comparison of our calculated BDEs to literature values is limited to 2-butanone and 3-pentanone and presented in Table 5. The bond energies for CJC(O)CC and CC(O)CCJ are within approximately 0.2 kcal mol−1 to the averages of the GA and literature values, while there is a difference of approximately 0.9 kcal mol−1 for CC(O)CJC. There is an 88−94.8 kcal mol−1 range of values for CCJC(O)CC from 3-pentanone in the literature; our calculated value of 90.9 kcal mol−1 falls within. Our value for the primary methyl on CJCC(O)CC is within 0.3 kcal mol−1 of the literature value.

between the species for each bond type can be seen. Recent theoretical and experimental studies for the C−H BDEs in acetone are also included for comparison. Primary C−H positions have at least one carbon atom between the primary carbon and the carbonyl group. BDEs for these ketones provide a tight range from 101.0 to 101.5 kcal mol−1 from primary methyl groups in six different locations with various other effects from each parent. This provides a good distribution where these six C−H BDE’s are of near identical strength to those in n-alkanes of 101.1 kcal mol−1. Bond energies decrease by about 6 kcal mol−1 when analyzing the three species that have primary groups directly adjacent to the carbonyl group. The determined values are 95.5−95.6 kcal mol−1 and compare with the C−H BDE of acetone. This lower bond energy results from resonance with the carbonyl group. The secondary bond energies on carbons adjacent to the carbonyl are another 4−5 kcal mol−1 lower at 90.6−91.3. Overall, this is an 8 kcal mol−1 bond energy reduction from an 5711


5712

+ + + +

+ + + +

CJCC(O)CC CJCC(O)CC CJCC(O)CC CJCC(O)CC

CCJC(O)CC CCJC(O)CC CCJC(O)CC CCJC(O)CC

+ + + +

+ + + +

CC(O)CJC CC(O)CJC CC(O)CJC CC(O)CJC

CC(O)CCJ CC(O)CCJ CC(O)CCJ CC(O)CCJ

+ + + +

CJC(O)CC CJC(O)CC CJC(O)CC CJC(O)CC

CH3CH3 CH3CH2CH3 (CH3)3CH CH3CH2CH2CH3







→ → → →

→ → → →

CC(O)CC CC(O)CC CC(O)CC CC(O)CC


→ → → →

→ → → →


→ → → →

isodesmic reactions

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

CJC(O)CC System CH3CJH2 CH3CJHCH3 (CH3)3CJ CH3CJHCH2CH3 average method std dev bond energy CC(O)CJC System CH3CJH2 CH3CJHCH3 (CH3)3CJ CH3CJHCH2CH3 average method std dev bond energy CC(O)CCJ System CH3CJH2 CH3CJHCH3 (CH3)3CJ CH3CJHCH2CH3 average method std dev bond energy CJCC(O)CC System CH3CJH2 CH3CJHCH3 (CH3)3CJ CH3CJHCH2CH3 average method std dev bond energy CCJC(O)CC System CH3CJH2 CH3CJHCH3 (CH3)3CJ CH3CJHCH2CH3 average method std dev bond energy −26.12 −24.73 −23.80 −25.34 −25.00 0.91 89.60

−13.21 −11.82 −10.88 −12.43 −12.08 0.86 102.51

−7.97 −6.58 −5.64 −7.19 −6.85 0.86 102.52

−20.88 −19.49 −18.55 −20.10 −19.75 0.90 89.62

−14.61 −13.21 −12.28 −13.82 −13.48 0.91 95.89

6-31G(d,p)

B3LYP

90.14

−25.49 −24.20 −23.42 −24.71 −24.46

102.50

−13.14 −11.84 −11.07 −12.35 −12.10

102.50

−7.91 −6.62 −5.84 −7.13 −6.87

90.13

−20.28 −18.99 −18.21 −19.50 −19.24

96.45

−13.96 −12.67 −11.89 −13.18 −12.92

6-311G(2d,2p)

−23.76 −23.51 −23.93 −24.11 −23.83 0.37 90.77

−12.81 −12.56 −12.99 −13.16 −12.88 0.41 101.71

−7.54 −7.29 −7.72 −7.90 −7.61 0.43 101.76

−18.59 −18.35 −18.77 −18.95 −18.67 0.37 90.70

−13.65 −13.40 −13.83 −14.01 −13.72 0.35 95.65

CBS-QB3


Table 3. Isodesmic Work Reactions, Calculated ΔH°f 298, and Bond Dissociation Energies for Ketone Radical Species

91.00

−23.10 −23.29 −24.07 −23.91 −23.59

101.31

−12.79 −12.98 −13.77 −13.61 −13.29

101.31

−7.56 −7.75 −8.53 −8.38 −8.06

90.90

−17.98 −18.17 −18.95 −18.80 −18.47

95.64

−13.24 −13.42 −14.21 −14.05 −13.73

G3MP2B3

0.23 0.23 0.23 0.27 0.24

0.23 0.23 0.23 0.27 0.24

0.23 0.23 0.23 0.27 0.24

0.23 0.23 0.23 0.27 0.24

0.23 0.23 0.23 0.27 0.24


The Journal of Physical Chemistry A Article


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+ + + +

+ + + +

n-CC(O)CCCJ n-CC(O)CCCJ n-CC(O)CCCJ n-CC(O)CCCJ

CJC(O)C(C)C CJC(O)C(C)C CJC(O)C(C)C CJC(O)C(C)C

+ + + +

+ + + +

n-CC(O)CJCC n-CC(O)CJCC n-CC(O)CJCC n-CC(O)CJCC

n-CC(O)CCJC n-CC(O)CCJC n-CC(O)CCJC n-CC(O)CCJC

+ + + +

n-CJC(O)CCC n-CJC(O)CCC n-CJC(O)CCC n-CJC(O)CCC

Table 3. continued






n-CC(O)CCC n-CC(O)CCC n-CC(O)CCC n-CC(O)CCC

CC(O)C(C)C CC(O)C(C)C CC(O)C(C)C CC(O)C(C)C

→ → → →

→ → → →



→ → → →

→ → → →


→ → → →

isodesmic reactions

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

n-CJC(O)CCC CH3CJH2 CH3CJHCH3 (CH3)3CJ CH3CJHCH2CH3 average method std dev bond energy n-CC(O)CJCC CH3CJH2 CH3CJHCH3 (CH3)3CJ CH3CJHCH2CH3 average method std dev bond energy n-CC(O)CCJC CH3CJH2 CH3CJHCH3 (CH3)3CJ CH3CJHCH2CH3 average method std dev bond energy n-CC(O)CCCJ CH3CJH2 CH3CJHCH3 (CH3)3CJ CH3CJHCH2CH3 average method std dev bond energy CJC(O)C(C)C CH3CJH2 CH3CJHCH3 (CH3)3CJ CH3CJHCH2CH3 average method std dev bond energy System

System

System

System

System

−20.69 −19.29 −18.36 −19.90 −19.56 0.90 95.41

−12.78 −11.38 −10.45 −11.99 −11.65 0.86 102.40

−16.78 −15.38 −14.45 −15.99 −15.65 0.86 98.40

−25.05 −23.65 −22.72 −24.26 −23.92 0.89 90.13

−19.31 −17.91 −16.98 −18.52 −18.18 0.91 95.87

6-31G(d,p)

B3LYP

95.93

−20.08 −18.79 −18.01 −19.30 −19.04

102.27

−12.82 −11.52 −10.75 −12.03 −11.78

98.48

−16.61 −15.32 −14.54 −15.83 −15.57

90.56

−24.52 −23.23 −22.46 −23.74 −23.49

96.42

−18.66 −17.37 −16.59 −17.88 −17.63

6-311G(2d,2p)

−19.49 −19.24 −19.66 −19.84 −19.56 0.37 95.41

−12.66 −12.41 −12.84 −13.01 −12.73 0.40 101.32

−15.18 −14.94 −15.36 −15.54 −15.25 0.35 98.80

−22.86 −22.62 −23.04 −23.22 −22.93 0.39 91.12

−18.35 −18.10 −18.53 −18.70 −18.42 0.35 95.63

CBS-QB3


95.63

−18.85 −19.04 −19.82 −19.67 −19.34

100.96

−12.59 −12.78 −13.57 −13.41 −13.09

98.80

−14.76 −14.95 −15.73 −15.58 −15.26

91.41

−22.15 −22.34 −23.12 −22.97 −22.65

95.63

−17.92 −18.11 −18.90 −18.74 −18.42

G3MP2B3

0.23 0.23 0.23 0.27 0.24

0.23 0.23 0.23 0.27 0.24

0.23 0.23 0.23 0.27 0.24

0.23 0.23 0.23 0.27 0.24

0.23 0.23 0.23 0.27 0.24




5714

+ + + +

+ + + +

CCJ(C)C(O)CC CCJ(C)C(O)CC CCJ(C)C(O)CC CCJ(C)C(O)CC

CC(C)C(O)CJC CC(C)C(O)CJC CC(C)C(O)CJC CC(C)C(O)CJC

+ + + +

+ + + +

CC(O)C(C)CJ CC(O)C(C)CJ CC(O)C(C)CJ CC(O)C(C)CJ

CJC(C)C(O)CC CJC(C)C(O)CC CJC(C)C(O)CC CJC(C)C(O)CC

+ + + +

CC(O)CJ(C)C CC(O)CJ(C)C CC(O)CJ(C)C CC(O)CJ(C)C

Table 3. continued








→ → → →

→ → → →



→ → → →

→ → → →


→ → → →

isodesmic reactions

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

CC(O)CJ(C)C System CH3CJH2 −31.21 CH3CJHCH3 −29.82 (CH3)3CJ −28.88 CH3CJHCH2CH3 −30.43 average −30.08 method std dev 0.95 bond energy 84.89 CC(O)C(C)CJ System CH3CJH2 −14.47 CH3CJHCH3 −13.08 (CH3)3CJ −12.14 CH3CJHCH2CH3 −13.69 average −13.35 method std dev 0.86 bond energy 101.63 CJC(C)C(O)CC System CH3CJH2 −19.82 CH3CJHCH3 −18.42 (CH3)3CJ −17.49 CH3CJHCH2CH3 −19.04 average −18.69 method std dev 0.86 bond energy 101.72 CCJ(C)C(O)CC System CH3CJH2 −36.26 CH3CJHCH3 −34.86 (CH3)3CJ −33.93 CH3CJHCH2CH3 −35.47 average −35.13 method std dev 0.96 bond energy 85.28 CC(C)C(O)CJC System CH3CJH2 −32.43 CH3CJHCH3 −31.03 (CH3)3CJ −30.10 CH3CJHCH2CH3 −31.64 average −31.30 method std dev 0.90 bond energy 89.11

6-31G(d,p)

B3LYP

89.59

−31.86 −30.56 −29.79 −31.07 −30.82

86.07

−35.38 −34.08 −33.31 −34.59 −34.34

101.66

−19.78 −18.49 −17.71 −19.00 −18.75

101.58

−14.43 −13.14 −12.36 −13.65 −13.39

85.66

−30.35 −29.06 −28.28 −29.57 −29.31

6-311G(2d,2p)

−29.92 −29.67 −30.10 −30.27 −29.99 0.43 90.42

−32.81 −32.56 −32.99 −33.16 −32.88 0.46 87.53

−19.16 −18.92 −19.34 −19.52 −19.24 0.37 101.17

−13.76 −13.51 −13.94 −14.11 −13.83 0.38 101.14

−27.69 −27.44 −27.87 −28.04 −27.76 0.45 87.21

CBS-QB3


90.87

−29.04 −29.23 −30.01 −29.86 −29.54

88.09

−31.83 −32.01 −32.80 −32.64 −32.32

100.94

−18.98 −19.16 −19.95 −19.79 −19.47

100.89

−13.58 −13.77 −14.56 −14.40 −14.08

87.73

−26.75 −26.94 −27.72 −27.57 −27.25

G3MP2B3

0.20 0.20 0.20 0.23 0.21

0.20 0.20 0.20 0.23 0.21

0.20 0.20 0.20 0.23 0.21

0.23 0.23 0.23 0.27 0.24

0.23 0.23 0.23 0.27 0.24




Table 4. Summary of Average ΔH°f 298 and Bond Dissociation Energies from This Studya

0.20 0.20 0.20 0.23 0.21

DFT

CC(O)CC CJC(O)CC CC(O)CJC CC(O)CCJ CCC(O)CC CJCC(O)CC CCJC(O)CC n-CC(O)CCC n-CJC(O)CCC n-CC(O)CJCC n-CC(O)CCJC n-CC(O)CCCJ CC(O)C(C)C CJC(O)C(C)C CC(O)CJ(C)C CC(O)C(C)CJ CC(C)C(O)CC CJC(C)C(O)CC CCJ(C)C(O)CC CC(C)C(O)CJC CC(C)C(O)CCJ

102.41

101.25

−18.67 −18.85 −19.64 −19.48 −19.16

−18.69 −18.44 −18.87 −19.04 −18.76 0.41 101.65 −19.03 −17.74 −16.96 −18.25 −18.00

G3MP2B3

−57.4 −13.2 −19.5 −6.9 −62.4 −12.1 −24.7 −61.8 −17.9 −23.7 −15.6 −11.7 −61.2 −19.3 −29.7 −13.4 −66.9 −18.7 −34.7 −31.1 −18.0

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.4 0.9 0.9 0.9 0.3 0.9 0.9 0.3 0.9 0.9 0.9 0.9 0.3 0.9 1.0 0.9 0.9 0.9 1.0 0.9 0.9

CBS-QB3/G3MP2B3 C−H BDE 96.2 89.9 102.5 102.5 89.9 96.1 90.3 98.4 102.3 95.7 85.3 101.6 101.7 85.7 89.3 102.4

ΔH°f 298 −57.3 −13.7 −18.6 −7.8 −62.5 −13.1 −23.7 −62.0 −18.4 −22.8 −15.3 −12.9 −62.9 −19.4 −27.5 −14.0 −68.3 −19.4 −32.6 −29.8 −19.0

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.2 0.4 0.4 0.4 0.2 0.4 0.4 0.2 0.4 0.4 0.4 0.4 0.2 0.4 0.4 0.4 0.1 0.4 0.5 0.4 0.4

C−H BDE 95.6 90.8 101.5 101.5 90.9 95.6 91.3 98.8 101.1 95.5 87.5 101.0 101.1 87.8 90.6 101.4

Units in kcal mol−1. Error is standard deviation from work reaction tables; see also Scheme 2 for error analysis on reference reactions and Table 1 for reference species uncertainties. a


→ → → →


+ + + +

Figure 1 and Table 4 have the recommended bond energies from this study from the average of the CBS-QB3 and G3MP2B3 levels of theory. Internal Rotor Potential Analysis. Potential energy curves for internal rotations within the parent and radical species were determined using the B3LYP/6-31G(d,p) level of theory. Relaxed scans at 10° intervals were used to determine the lowest energy geometries. If a lower energy conformation was found, previous scans were rerun to ensure we had located the lowest energy conformation. These potential energy curves are used in the determination of contributions of the internal rotors to entropies and heat capacities, where the total values are in Appendix Table A1 and the separate contributions are in the Supporting Information. All of the parent ketone terminal methyl (not adjacent to the carbonyl) groups exhibit 3-fold symmetry with energy barriers between 2 and 3 kcal mol−1. The 3-fold barriers are 0.5 kcal mol−1 for methyl rotations adjacent to the carbonyl group. Upon radical formation at the methyl site, there is a decrease to 2-fold symmetry and a decrease in the barrier energy ranging from below 0.1 to 3.0 kcal mol−1 except for the groups adjacent to the carbonyl. Radical sites adjacent to the carbonyl group, regardless of primary, secondary, or tertiary, have energy barriers over 10 kcal mol−1 upon radical formation; this is a result of the resonance with the carbonyl group. A comparison of our determined barrier heights to those of Nickerson et al.78 and Sinke et al.79 is illustrated in Figure 2. Overall, we can see that there is reasonable agreement for the ethyl and methyl rotations adjacent to the carbonyl. There are slightly larger deviations between the values with the terminal methyl group barrier. This is a 1 kcal mol−1 range in the values for the terminal methyl group on 2-butanone. Our B3LYP

CC(C)C(O)CCJ CC(C)C(O)CCJ CC(C)C(O)CCJ CC(C)C(O)CCJ

+ + + +

isodesmic reactions

Table 3. continued

ΔH°f 298

species

CBS-QB3 6-311G(2d,2p) 6-31G(d,p)

Article

CC(C)C(O)CCJ System CH3CJH2 −19.10 CH3CJHCH3 −17.70 (CH3)3CJ −16.77 CH3CJHCH2CH3 −18.32 average −17.97 method std dev 0.86 bond energy 102.44

B3LYP




5715



Article

Scheme 2. Reference Reactions for Comparison of Literature and Calculated ΔH°reaction Values

Table 5. Comparison of ΔH°f 298 and Carbon−Hydrogen Bond Dissociation Energy for Ketones and Radicals to Literature Values ΔH°f 298 (kcal mol−1) species

a

C−H BDE (kcal mol−1)

this study

literature

ref

CC(O)CC

−57.3

CJC(O)CC

−13.7

−57.02 ± 0.20 −57.05 ± 0.23 −56.90 −57.0 ± 0.2 −56.88b −14.60b −13.3

70 a 79 68 30 30 36

CC(O)CJC

−18.6

−17.08b −18.6

30 36

90.8

CC(O)CCJ

−7.8

−7.88b −7.2

30 36

101.5

CCC(O)CC

−62.5

CJCC(O)CC

−13.1

CCJC(O)CC

−23.7

n-CC(O)CCC

−62.0

CC(O)C(C)C CC(C)C(O)CC

−62.9 −68.3

−61.65 ± 0.20 −62.25 ± 0.39 −62.20b −13.20b −11.8 −18.25b −22.7

73 a 29 29 36 29 36

−61.91 ± 0.26 −61.9 ± 0.2 −62.76 ± 0.21 −68.4 ± 0.2 −68.4 ± 0.2

73 68 73 98 68

this study

literature

ref

95.6

96.5 95.48b 95.8 95.55 92.3 93.2 93.8 91.3 90.3 90.50b 90.29 101.09b 102.1 100.65

39 30 36 31 95 39 96 97 36 30 31 30 36 31

101.5

101.8

36

90.9

93.4 94.8 88.4 90.8 88

39 96 45 36 37

Reported on NIST WebBook as the reanalyzed value of ref 71 by ref 72. bValues calculated using group additivity.

calculations show 1.98 kcal mol−1, while Nickerson and Sinke determined 2.4 and 2.95 kcal mol−1, respectively, which are typical barrier heights for terminal methyl rotation.80−83 While relaxed scans are needed to determine the lowest energy configuration, they do not necessarily represent the accurate internal rotation barrier. Entropy (S°(T)) and Heat Capacities (Cp°(T)). Contributions from each compound’s translations, vibration frequencies, and external rotations, represented as TVR, are calculated using the rigid-rotor harmonic-oscillator approximation SMCPS62

code with the zero-point vibration energies (ZVPE) scaled by 0.9806 for B3LYP/6-31G(d,p) as recommended by Scott and Radom.84 The optical isomers’ contribution to entropy for the radicals CC(O)C(C)CJ and CJC(C)C(O)CC code resulting from the chiral center created at the tertiary carbon center upon methyl radical formation is included in the SMCPS calculation. The contributions from internal rotations, represented by IR, are determined using the calculated potential energy rotational barriers (relaxed scan), moments of inertia for each group in 5716



Article

Table 6. Summary of Carbon−Hydrogen Bond Dissociation Energiesa for Noncyclic Ketone Radical Species carbon−hydrogen bond dissociation classes species CC(O)C CC(O)CC CCC(O)CC n-CC(O)CCC CC(O)C(C)C CC(C)C(O)CC a

primary

primary adjacent to carbonyl

secondary

secondary adjacent to carbonyl

98.8

90.8 90.9 91.3

96 ± 1 95.6

tertiary adjacent to carbonyl

b

101.5 101.5 101.1 101.0 101.1, 101.4

95.6 95.5

90.6

87.5 87.8

Recommended values from CBS-QB3/G3MP2B3 average (units in kcal mol−1). bAverage of literature values from refs 36, 38, 39, and 43.

It is known that a torsion frequency estimate of the contributions to heat capacity contribute a full R (ideal gas constant) to Cp°(T) at high temperatures, while a free rotor contributes only R/2. The computer code THERM, which is often used to extrapolate Cp°(T) data to higher temperatures and generate NASA polynomials, allows one to incorporate the number of internal rotors in the target Cp°(T) (infinity) value. This allows some adjustment for anharmonic effects by under-representing the number of rotors, one can add R/2 to Cp°(T)(infinity), where each rotor omitted would be counted by THERM as frequency contribution. Our recommendation is to underestimate the number of rotors contribution to Cp°(T)(infinity) by one-half. The individual contributions to the total entropies and heat capacities, TVR and IR, in the 100−5000 K temperature range for the ketone parents and radicals from the B3LYP/6-31G(d,p) level of theory are presented in the Supporting Information. The total entropies and heat capacities values versus temperature are tabulated in Appendix Table A1. For the radical ketone species, all of the single bond rotations were included except for the radical sites directly adjacent to the carbonyl group. The energy barriers for these primary, secondary, and tertiary locations are all in excess of 10 kcal mol−1 where contributions were treated as torsion frequencies. These barriers result from resonance between the radical site and the adjacent, electronegative carbonyl group. The resonance also accounts for the low bond dissociation energies. Potential barriers for rotors, where S°(T) and Cp°(T) values were determined from torsion frequencies, are denoted in the potential energy diagrams in the Supporting Information with asterisks. Group Additivity Values. The group additivity (GA) method, as developed by Benson,66 is a rapid estimation method for ΔH°f 298, S°298, and Cp°(T) of stable species. The hydrogen-bond increment method (HBI) for group additivity of radical species, as developed by this research group,67 is implemented for the ketone radical species. The HBI method allows calculation of the thermochemical properties of radicals with only one group in addition to that of the parent species. Thermodynamic properties of larger species can then be accurately approximated as the sum of the smaller representative groups due to their contributions’ linear consistency with corrections for rotors, symmetry, electron degeneracy, optical isomers, and other interactions taken into account. Group additivity for the thermochemical properties of ketones will be useful in the development of their chemical kinetic modeling. The known groups that are used in the GA method calculation are listed in Table 8. As we have described above, the bond dissociation energies for primary, secondary, and

Figure 2. Comparison of determined rotational barriers to literature values for 2-butanone: (a) ref 78; (b) ref 79.

the rotor, and barrier foldness. Internal rotor torsion frequencies, including terminal methyl groups, are identified using visual inspection in GaussView and are removed from vibration contribution. In cases where identification of a frequency was uncertain due to coupling to other motions, the lower frequency was selected. These are replaced with entropy and heat capacity contributions from the Pitzer−Gwinn method for hindered rotor analysis. Our use of the Pitzer− Gwinn methods is described in detail in ref 67. Table 7 illustrates results from several different assumptions for inclusion of internal rotor versus torsion frequency contributions for the molecules in this study; it also provides comparison with experimental data for the species where it is available. We also calculated and included the entropy and heat capacities for acetone, CC(O)C, to show the agreement between our calculated values and other available values. Values from the group additivity (GA) method are also included, which coincide well with the experimental data providing some support for considering the GA data as reference in the comparisons. For this limited set of ketones, we observed that contributions to entropy and heat capacity from all of the internal rotors in each of the parent ketones need to be included to match the literature data from Stull.85 In Table 7, we see that entropy is significantly underestimated when only the low barrier methyl rotors are considered, in one case by more than 5 cal mol−1 K−1, relative to the data in Stull. There is much better agreement to Stull for acetone, 2-butanone, and 2pentanone when all of the rotors are considered where there are maximum absolute differences of 0.8 cal mol−1 K−1 for S°298 and 1.2 cal mol−1 K−1 for Cp°(T) between 300 and 1000 K. Similar agreement for 2-butanone to data from Chao70 is also observed. We note that the sp3 carbon bonds of the smaller ketones have slightly lower barriers than those in alkane hydrocarbons, and these internal rotors should have important contributions, but there are also internal rotors in the larger ketones that have barriers higher than 6 kcal mol−1. There are a number of studies on methods and the importance for calculating contributions from internal rotations to obtain more accurate entropies and heat capacity estimates.86−93 We look forward to further analysis using several of these methods. 5717



Article

Table 7. Comparison of Entropies and Heat Capacities for Ketone Parent Species from B3LYP/6-31G(d,p) Level of Theory to Other Available Methods Cp°(T) (cal mol−1 K−1) −1

S°298 (cal mol

species CC(O)C σ = 18

70.09 70.49 71.72 70.67 80.88 80.81 81.11 80.60 80.55 77.68 81.58 89.29 86.37 86.30 81.69 89.58 90.48 89.91 88.37 88.31 84.14 90.41 87.99 85.53 85.46 83.52 88.70 97.59 93.02 92.95 88.42 96.40

CC(O)CC σ=9

CCC(O)CC σ = 18

n-CC(O)CCC σ=9

CC(O)C(C)C σ = 27

CC(C)C(O)CC σ = 27

−1

K )

300 K

400 K

500 K

600 K

800 K

1000 K

1500 K

17.97 17.97

22.00 22.00

25.89 25.89

29.34 29.34

34.93 34.93

39.15 39.15

45.26

17.51 23.47 24.68 24.78

21.47 28.95 29.81 29.87

25.26 34.14 34.76 34.72

28.61 38.69 39.09 39.02

34.02 46.00 46.08 46.00

38.12 51.49 51.33 51.26

44.56 59.46

23.74 22.99 23.47 30.37

29.51 28.48 28.75 37.40

34.89 33.63 33.68 43.29

39.58 38.15 38.00 48.34

47.07 45.43 45.00 57.13

52.66 50.90 50.30 63.55

61.36 59.49 58.68 73.40

59.41

28.60 28.72 29.63 29.67 29.06

35.93 35.63 36.10 36.65 36.42

42.79 42.09 42.10 42.84 42.80

48.75 47.76 47.37 48.19 48.32

58.23 56.88 55.95 57.10 57.13

65.28 63.72 62.47 63.69 63.61

76.21 74.43 72.79 73.53

28.60 27.95 28.67 28.32

35.95 35.23 35.84 35.75

42.81 41.94 42.32 42.63

48.78 47.73 47.83 48.32

58.26 56.94 56.51 57.41

65.31 63.80 62.98 64.11

76.24 74.49 73.12 74.13

29.10 28.82 29.06 34.52 33.95 34.49 35.00

36.37 35.83 35.71 43.45 42.79 42.93 43.09

43.13 42.23 41.86 51.33 51.02 50.62 50.59

49.01 47.74 47.22 57.82 58.17 57.29 57.14

58.37 56.56 55.85 68.51

65.35 63.20 62.40 76.31

69.53 67.96 67.64

76.21 73.64 72.74 88.20

77.97 75.98 75.46

91.07 88.57 87.58

method GA Stull85 Gaussian SMCPS + GA Stull85 Chao70 Gaussian SMCPS SMCPS + SMCPS + GA Gaussian SMCPS SMCPS + SMCPS + GA Stull85 Gaussian SMCPS SMCPS + SMCPS + GA Gaussian SMCPS SMCPS + SMCPS + GA Gaussian SMCPS SMCPS + SMCPS +

rotors

VIBIR

0a 2c

VIBIR VIBIR

0a 0a 2b 3c

VIBIR VIBIR

0a 0a 2b 4c

VIBIR VIBIR

0a 0a 2b 4c

VIBIR VIBIR

0a 0a 3b 4c

VIBIR VIBIR

0a 0a 3b 5c

a

No rotors. Use of torsion frequencies for rotor contributions without reduction (correction) in entropy for equivalent hydrogen atoms in CH3 groups. bOnly methyl rotors. cAll internal rotors.

Table 8. Literature and Recommended Hydrogen-Bond Increment Group Values for Ketones Cp°(T) (cal mol−1 K−1) group C/CO/H3 CO/C2 C/C2/H2 C/C/H3 C/C/CO/H2 C/C2/CO/H KETOP KETOS KETOT

ΔH°f 298 (kcal mol−1) −10.08 −31.40 −4.93 −10.20 −5.20 −1.7 95.6 90.9 87.7

S°298 (cal mol−1 K−1)

300 K

400 K

Known Groups 30.41 6.19 7.84 15.01 5.59 6.32 9.42 5.50 6.95 30.41 6.19 7.84 9.60 6.20 7.70 −11.70 4.16 5.91 Recommended Hydrogen-Bond Increment Groups −2.37 −0.01 −0.43 −3.13 −1.68 −2.27 −4.59 −1.74 −2.74

500 K

600 K

800 K

1000 K

1500 K

9.40 7.09 8.25 9.40 8.70 7.34

10.79 7.76 9.35 10.79 9.50 8.19

13.02 8.89 11.07 13.02 11.10 9.46

14.77 9.61 12.34 14.77 12.20 10.19

17.58 10.10 14.20 17.58 14.07 11.29

−1.02 −2.61 −3.39

−1.58 −2.85 −3.61

−2.74 −3.64 −4.18

−3.58 −4.14 −4.55

−4.34 −4.54 −4.89

groups result in the thermochemical properties of the radical compounds when the entropy and heat capacities are added to the parent species. The bond group enthalpy corresponds to the average C−H BDE for the specific adjacent ketone classes in Table 6, while the entropy and heat capacities are averaged from the difference in the radical and parent compounds.

tertiary C−H bonds located adjacent to the carbonyl site have energies approximately 6−9 kcal mol−1 lower than those found for alkanes. This difference is a major concern, so we therefore suggest recommended ketone bond groups from the species in this study, where KETOP (CJC(O)), KETOS (CCJC( O)), and KETOT (C2CJC(O)) correspond to the ketone primary, secondary, and tertiary locations, respectively. These 5718



Article

Table A1. Calculated Entropya and Heat Capacitya for Ketone Parent and Radical Species from the B3LYP/6-31G(d,p) Level of Theory CC(O)CC

CJC(O)CC

CC(O)CJC

temp (K)

total Cp

total S

total Cp

total S

100 150 200 250 298 400 500 600 700 800 1000 1500 2000 2500 3000 3500 4000 4500 5000 zero-point energyb

14.060 16.178 18.459 20.883 23.362 28.753 33.675 37.996 41.746 45.000 50.304 58.682 63.028 65.435 66.875 67.791 68.409 68.841 69.155 68.787

65.551 70.431 74.524 78.239 81.585 88.323 94.601 100.574 106.250 111.631 121.592 142.531 159.202 172.878 184.397 194.317 203.011 210.742 217.698

12.709 15.577 18.347 21.000 23.516 28.686 33.223 37.115 40.433 43.285 47.903 55.188 58.978 61.086 62.349 63.154 63.695 64.075 64.352 60.749

62.790 67.672 71.960 75.888 79.437 86.489 92.933 98.969 104.631 109.947 119.672 139.811 155.681 168.640 179.532 188.898 197.102 204.392 210.948

CCC(O)CC

temp (K) 100 150 200 250 298 400 500 600 700 800 1000 1500 2000 2500

total S

total Cp

total S

13.106 15.065 17.098 19.396 21.804 27.105 31.899 36.036 39.559 42.578 47.436 54.991 58.875 61.023 62.306 63.124 63.673 64.058 64.339 60.733 CJCC(O)CC

62.641 67.517 71.549 75.156 78.413 84.973 91.094 96.912 102.423 107.635 117.226 137.237 153.066 166.007 176.889 186.250 194.450 201.738 208.292

14.570 16.873 18.985 21.141 23.338 28.163 32.548 36.345 39.606 42.423 47.012 54.262 58.034 60.128 61.378 62.177 62.717 63.095 63.371 59.389 CCJC(O)CC

68.274 73.404 77.688 81.483 84.850 91.505 97.590 103.316 108.704 113.776 123.081 142.448 157.760 170.284 180.819 189.884 197.823 204.880 211.228

total Cp

total S

total Cp

total S

total Cp

total S

16.571 20.039 23.244 26.397 29.487 36.100 42.102 47.374 51.962 55.952 62.472 72.794 78.157 81.127 82.905 84.038 84.800 85.333 85.720 86.273 n-CC(O)CCC

69.926 75.704 80.756 85.387 89.583 97.996 105.809 113.218 120.245 126.905 139.221 165.098 185.695 202.590 216.820 229.073 239.813 249.365 257.957

17.302 20.739 23.643 26.493 29.312 35.405 40.899 45.667 49.783 53.349 59.163 68.365 73.157 75.815 77.406 78.424 79.108 79.587 79.935 76.874 n-CC(O)CJCC

74.185 80.260 85.478 90.156 94.345 102.638 110.238 117.389 124.122 130.464 142.119 166.420 185.657 201.400 214.645 226.042 236.027 244.903 252.888

15.983 19.230 22.077 24.960 27.882 34.276 40.127 45.232 49.619 53.397 59.504 69.056 73.979 76.700 78.327 79.364 80.059 80.545 80.900 78.262 n-CC(O)CCJC

67.786 73.685 78.751 83.310 87.413 95.613 103.225 110.447 117.284 123.750 135.676 160.594 180.337 196.492 210.082 221.775 232.021 241.127 249.318

temp (K) 100 150 200 250 298 400 500 600 700 800 1000 1500 2000 2500 3000 3500 4000 4500 5000 zero-point energyb

CC(O)CCJ

total Cp

n-CJC(O)CCC

n-CC(O)CCCJ

total Cp

total S

total Cp

total S

total Cp

total S

total Cp

total S

total Cp

total S

14.107 18.681 21.752 25.086 28.514 35.844 42.320 47.833 52.506 56.511 62.984 73.123 78.368 81.273

75.068 77.458 82.101 86.418 90.408 98.651 106.453 113.930 121.039 127.774 140.207 166.255 186.927 203.862

12.783 18.088 21.647 25.179 28.614 35.700 41.794 46.885 51.141 54.752 60.551 69.616 74.312 76.919

72.020 74.433 79.261 83.793 87.981 96.516 104.467 111.995 119.078 125.741 137.932 163.172 183.039 199.256

14.297 17.615 20.922 24.312 27.634 34.526 40.543 45.661 50.007 53.734 59.757 69.171 74.042 76.741

68.197 73.406 78.062 82.415 86.440 94.656 102.339 109.639 116.539 123.057 135.041 160.038 179.805 195.971

17.457 19.832 22.279 24.965 27.802 34.100 39.847 44.849 49.152 52.861 58.879 68.295 73.142 75.818

75.329 81.229 86.113 90.485 94.399 102.276 109.612 116.592 123.214 129.483 141.054 165.286 184.510 200.251

14.806 18.901 21.797 25.001 28.279 35.182 41.164 46.166 50.360 53.933 59.679 68.684 73.360 75.952

78.633 81.195 85.872 90.182 94.149 102.267 109.872 117.096 123.912 130.334 142.113 166.582 185.891 201.672

5719



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Table A1. continued n-CC(O)CCC

n-CJC(O)CCC

temp (K)

total Cp

total S

total Cp

total S

3000 3500 4000 4500 5000 zero-point energyb

83.010 84.113 84.859 85.384 85.763 86.259

218.113 230.384 241.133 250.688 259.285

78.481 79.474 80.143 80.615 80.958 78.218

212.880 224.596 234.855 243.969 252.166

CC(O)C(C)C temp (K) 100 150 200 250 298 400 500 600 700 800 1000 1500 2000 2500 3000 3500 4000 4500 5000 zero-point energyb

a

total Cp

total S

n-CC(O)CJCC

n-CC(O)CCJC

total Cp

total S

78.352 79.380 80.072 80.558 80.910 78.459 CJC(O)C(C)C

209.569 221.268 231.514 240.622 248.813

total Cp

15.857 69.781 14.483 19.373 75.267 18.561 22.572 80.132 22.142 25.751 84.615 25.594 28.915 88.704 28.903 35.708 96.983 35.671 41.862 104.716 41.523 47.217 112.095 46.470 51.841 119.099 50.662 55.851 125.747 54.262 62.396 138.042 60.098 72.737 163.894 69.300 78.116 184.475 74.103 81.101 201.362 76.772 82.884 215.588 78.373 84.020 227.840 79.393 84.785 238.578 80.082 85.322 248.126 80.566 85.714 256.716 80.918 85.982 78.033 CC(C)C(O)CC CJC(C)C(O)CC

total S

total Cp

77.412 78.427 79.112 79.592 79.940 76.852 CC(O)CJ(C)C

total S 213.496 224.896 234.881 243.758 251.743

total Cp

total S

15.865 18.565 21.094 23.834 26.720 33.207 39.215 44.471 48.989 52.873 59.142 68.886 73.881 76.638 78.283 79.331 80.034 80.528 80.886 77.981 CCJ(C)C(O)CC

67.017 72.761 77.584 81.907 85.801 93.679 101.069 108.140 114.869 121.262 133.085 157.898 177.603 193.740 207.321 219.009 229.250 238.354 246.543

66.899 72.343 77.321 81.957 86.202 94.778 102.695 110.161 117.176 123.773 135.855 160.940 180.732 196.910 210.511 222.213 232.460 241.568 249.760

n-CC(O)CCCJ total Cp

total S

77.506 214.937 78.496 226.349 79.163 236.343 79.632 245.225 79.972 253.213 76.942 CC(O)C(C)CJ total Cp

total S

16.434 72.435 20.102 78.181 23.504 83.280 26.766 87.990 29.857 92.251 36.125 100.739 41.574 108.496 46.232 115.764 50.234 122.569 53.692 128.967 59.357 140.681 68.396 165.025 73.153 184.265 75.807 200.004 77.398 213.247 78.413 224.643 79.099 234.628 79.579 243.503 79.929 251.486 76.899 CC(C)C(O)CJC CC(C)C(O)CCJ

temp (K)

total Cp

total S

total Cp

total S

total Cp

total S

total Cp

total S

total Cp

total S

100 150 200 250 298 400 500 600 700 800 1000 1500 2000 2500 3000 3500 4000 4500 5000 zero-point energyb

16.126 20.937 27.047 30.963 34.824 43.090 50.591 57.142 62.784 67.638 75.461 87.580 93.767 97.169 99.198 100.478 101.343 101.947 102.388 103.497

77.827 83.695 86.172 91.523 96.404 106.325 115.633 124.528 132.988 141.011 155.860 186.989 211.674 231.882 248.875 263.502 276.312 287.699 297.937

18.827 23.838 28.189 32.247 36.039 43.669 50.252 55.865 60.680 64.854 71.681 82.596 88.335 91.531 93.454 94.677 95.502 96.082 96.503 94.409

77.753 84.346 90.371 95.984 101.092 111.296 120.639 129.387 137.586 145.288 159.404 188.731 211.916 230.886 246.843 260.577 272.610 283.305 292.926

15.546 19.397 24.959 28.619 32.339 40.504 47.968 54.447 59.970 64.679 72.184 83.654 89.465 92.659 94.553 95.756 96.565 97.132 97.544 95.534

75.256 81.092 83.426 88.488 93.123 102.592 111.546 120.140 128.327 136.106 150.480 180.547 204.338 223.778 240.122 254.179 266.488 277.426 287.262

17.259 21.991 25.881 29.668 33.425 41.451 48.588 54.730 59.968 64.469 71.765 83.202 89.118 92.398 94.361 95.607 96.447 97.039 97.470 95.599

71.206 77.529 83.244 88.531 93.356 103.131 112.256 120.930 129.142 136.907 151.208 181.090 204.762 224.139 240.440 254.471 266.762 277.685 287.512

18.858 23.956 28.003 31.680 35.225 42.671 49.318 55.073 60.028 64.319 71.336 82.461 88.270 91.497 93.428 94.656 95.489 96.073 96.497 94.096

77.751 84.387 90.415 95.949 100.927 110.859 119.979 128.571 136.665 144.286 158.298 187.535 210.690 229.648 245.602 259.336 271.364 282.058 291.678

Units of cal mol−1 K−1. bUnits of kcal mol−1.

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SUMMARY

improve accuracy by canceling error associated with the levels of theory. Comparisons with literature data show the calculated enthalpies of formation for the ketone parent molecules are within 1 kcal mol−1 chemical accuracy. C−H BDEs for the ketones are determined and shown to be 6−9 kcal mol−1 lower than a corresponding alkane BDE for the respective primary,

Enthalpies of formation for five ketones and 16 radicals with their corresponding carbon−hydrogen bond dissociation energies (C−H BDEs) are analyzed using density functional theory and higher level ab initio computational methods, many for the first time. Isodesmic work reactions were used to 5720



Article

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secondary, and tertiary C−H bonds when adjacent to the electronegative and radical stabilizing carbonyl group. C−H bond energies on a carbon that is not adjacent to a carbonyl group are shown to be similar to the standard n-alkanes for primary and secondary bonds. Results from the enthalpies of formation and bond dissociation energies from the DFT calculation methods are in acceptable agreement with composite method values when used with work reactions that effectively cancel errors. Further calculation and analysis is needed on the determination of entropy and heat capacity contributions, where this study found that the inclusion of all internal rotors is required, to have agreement with accepted literature compendiums on thermochemical properties of organic molecules for the parent ketones.

■

APPENDIX Appendix Table A1 presents the total entropy and heat capacity values for the ketone parent and radical species over the temperature range of 100−5000 K from the B3LYP/ 6-31G(d,p) level of theory.

■

ASSOCIATED CONTENT

S Supporting Information *

Data on atom numbering for the optimized structures, z-matrices, symmetry values, moments of inertia, vibration frequencies, internal rotor potential energy curves, individual contributions to entropy and heat capacities, and complete author listings for abbreviated references. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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