Thermochemistry of C7H16 to C10H22 Alkane Isomers: Primary

Article pubs.acs.org/JPCA

Thermochemistry of C7H16 to C10H22 Alkane Isomers: Primary, Secondary, and Tertiary C−H Bond Dissociation Energies and Effects of Branching Jason M. Hudzik,† Joseph W. Bozzelli,*,† and John M. Simmie‡ †

Chemistry, Chemical Engineering, and Environmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102, United States ‡ Combustion Chemistry Centre, School of Chemistry, National University of Ireland, Galway 091, Ireland S Supporting Information *

ABSTRACT: Standard enthalpies of formation (ΔH°f 298) of methyl, ethyl, primary and secondary propyl, and n-butyl radicals are evaluated and used in work reactions to determine internal consistency. They are then used to calculate the enthalpy of formation for the tert-butyl radical. Other thermochemical properties including standard entropies (S°(T)), heat capacities (Cp(T)), and carbon−hydrogen bond dissociation energies (C− H BDEs) are reported for n-pentane, n-heptane, 2-methylhexane, 2,3dimethylpentane, and several branched higher carbon number alkanes and their radicals. ΔH°f 298 and C−H BDEs are calculated using isodesmic work reactions at the B3LYP (6-31G(d,p) and 6-311G(2d,2p) basis sets), CBSQB3, CBS-APNO, and G3MP2B3 levels of theory. Structures, moments of inertia, vibrational frequencies, and internal rotor potentials are calculated at the B3LYP/6-31G(d,p) level for contributions to entropy and heat capacities. Enthalpy calculations for these hydrocarbon radical species are shown to have consistency with the CBS-QB3 and CBS-APNO methods using all work reactions. Our recommended ideal gas phase ΔH°f 298 values are from the average of all CBS-QB3, CBS-APNO, and for G3MP2B3, only where the reference and target radical are identical types, and are compared with literature values. Calculated values show agreement between the composite calculation methods and the different work reactions. Secondary and tertiary C−H bonds in the more highly branched alkanes are shown to have bond energies that are several kcal mol−1 lower than the BDEs in corresponding smaller molecules often used as reference species. Entropies and heat capacities are calculated and compared to literature values (when available) when all internal rotors are considered.

■

INTRODUCTION

six) of species from representative chemical classes such as alkanes, cycloalkanes, alkenes, and aromatics. Over the years there has been significant progress in the development, experimentation, and modeling of diesel surrogate fuels.3 This is due in part to the progress that has been made in the chemical kinetic models of the representative species used in surrogate fuels, with a particular focus on nheptane.4−13 It is a primary reference fuel (PRF) for the octane scale, used in performance rating for gasolines, and an autoignition diesel surrogate. Stability, thermochemical and physical properties, along with chemical kinetics of alkane parent and radical species are important to understanding their overall reaction paths and mechanisms in combustion processes and in atmospheric chemistry. These properties strongly influence their roles in these systems where having accurate and reliable values would

Hydrocarbon alkanes are fundamental structures in chemistry and are at the center of many chemical systems. Their role in natural gas has created a push to gather valuable information from geochemical studies of small alkane hydrocarbons in the hopes of advancing natural gas exploration and development.1,2 Linear and branched hydrocarbons are also components in the vast majority of transportation fuels. The understanding of fuel combustion is important for improving engine and combustion efficiency while reducing emission. This requires accurate reaction mechanisms with correct treatment of kinetic paths in existing fuels under the wide range of reaction conditions experienced in combustion systems. This is not easily accomplished because jet fuel, diesel fuel, and gasoline contain complex mixtures of hundreds, in some cases even thousands, of species, which increases the difficulty of accurate modeling. To combat this, surrogate fuels are utilized to represent the physical and chemical properties of the desired fuel by incorporating only a handful (currently three to © 2014 American Chemical Society

Received: April 11, 2014 Revised: August 13, 2014 Published: September 2, 2014 9364

dx.doi.org/10.1021/jp503587b | J. Phys. Chem. A 2014, 118, 9364−9379

The Journal of Physical Chemistry A

Article

Figure 1. Nomenclature for C7H16 Parent and Radical Species in this Study.

capacitates are determined with corrections for internal rotations for parent and radical species.

offer improvement in understanding and developing reaction paths and detailed chemical kinetic models. Modeling work for rate constant expressions are dependent upon knowing such thermochemical properties as enthalpies, entropies, and heat capacities for all of the reacting species. The group additivity (GA) method, as developed by Benson,14 allows for the rapid estimation of thermochemical properties based on the accurate knowledge of the contributions of representative groups from smaller molecules and their established linear consistency in thermochemical property contribution. This method is commonly implemented to estimate properties for species that are not well-known.4,8,15−17 C7 and higher Cn alkanes, and their radicals, are major components of the surrogates and are involved in a variety of different chemical systems. To the best of our knowledge, basic gas phase thermochemical properties are not readily available or experimental and theoretical values have discrepancies. There have been some studies on liquid and solid phases for linear and branched heptanes.18,19 By employing several moderately high-level computational methods, we have evaluated the different carbon−hydrogen bonds, standard enthalpies, and thermochemical properties on these species with a target on the effects of branching. There has been previous success using theoretical calculation methods in determining key thermochemical properties for varying length linear and branched alkanes.20−22 The objectives of this study are twofold. The first objective is to provide a set of consistent thermochemical properties, including standard enthalpies of formation and carbon− hydrogen bond dissociation energies (C−H BDEs), for small C1 to C5 primary, secondary, and tertiary hydrocarbon radicals. Available literature values and a series of work reactions are utilized in this study to determine consistent thermochemical properties for model species which are commonly utilized as reference species in work reactions for larger hydrocarbons as well as oxygen and nitrogen substituted hydrocarbons. The second objective is to use this internally consistent set of radical enthalpies 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 for a number of larger, highly branched C7 to C10 hydrocarbon isomers and their corresponding carbon-centered radicals. Our calculated ΔH°f 298 for parent species shows consistency and good agreement compared to available literature values. Bond energies for radical formation are also determined from the parent species and are compared to conventional normal primary, secondary, and tertiary bond energies from alkane hydrocarbons. Entropies and heat

■

COMPUTATIONAL METHODS Optimized geometries for all of the species were initially calculated at the B3LYP/6-31G(d,p) density function theory (DFT) method.23,24 This combines the three parameter Becke exchange functional, B3, with Lee−Yang−Parr correlation functional, LYP. The moderate 6-31G(d,p) and the larger 6311G(2d,2p) basis sets are employed with B3LYP which we have shown previously to provide acceptable thermochemical properties for hydrocarbons and oxygenates.25,26 Potential energy curves using the 6-31G(d,p) basis set, presented in the Supporting Information, for the internal rotation barriers were used to verify that our optimized structures were the lowest energy conformation. To verify both the accuracy and use of the DFT method, we employ higher level composite methods. G3MP2B327,28 is a modified version of the G3MP229 method where the geometries and zero-point vibration energies are from B3LYP/6-31G(d) calculations. CBS-QB330,31 is a complete basis set method that uses geometries and frequencies from the B3LYP/6-311G(2d,d,p) level followed by single-point energy calculations at the CCSD(T), MP4SDQ, and MP2 levels. The final energies are determined with a CBS extrapolation. The CBS-APNO32 method was also used for several key reference species of importance in this study which uses a HF/6311G(d,p) geometry optimization for reference force constants to help in optimization in the structure calculation at the QCISD/6-311G(d,p) level of theory. Single point energy calculations are then done using the QCISD(T), MP2(Full), and MP2 methods with a CBS-APNO extrapolation for the final energies. The QCISD(T) structure is considered the most accurate. All calculations were performed using the Gaussian 0333 and Gaussian 0934 program suites. For both the DFT and the composite methods, isodesmic work reactions were implemented for the gas phase enthalpies of formation (ΔH°f 298) to achieve greater accuracy. These reactions incorporate similar bonding environments for both reactants and products creating a cancellation of error associated with each calculation method of analysis. Agreement between the different methods is presented. There is also agreement for the C−H BDEs determined from the calculated ΔH°f 298 energies. Enthalpies of both parent and radical species are calculated and a bond cleavage reaction is used to calculate each C−H BDE as the difference in the ΔH°f 298 energies of the parent compound (RH) and the corresponding radical (R•) and hydrogen atom (H•): R − H → R• + H• 9365



Article

The dot (•) represents a radical site on the preceding carbon atom, and a parentheses with a carbon (C) represents a methyl substituent on the previous atom, as shown in Figure 1. In larger molecules, two carbons (C2) represent two methyl substituents on the previous atom. Two different methods are used for the calculation of entropies and heat capacities. Both begin using the rigid-rotor harmonic-oscillator (HO) approximation as calculated by the Statistical Mechanics for Heat Capacity and Entropy (SMCPS35) program. This calculates the contributions from translation, vibrations, and external rotations to entropy and heat capacities by using the geometry, frequencies, and moments of inertia, from the B3LYP/6-31G(d,p) method, with the mass, electronic degeneracy, symmetry, and number of optical isomers for each species. Zero- point vibration energies (ZPVE) are scaled by 0.9806 as recommended by Scott and Radom.36 Because of the error that exists with applying the HO approximation to the low-frequency vibrational (torsion) modes of internal rotations, we have removed these frequencies and replaced them with entropy and heat capacity contributions from single bond hindered rotor analysis. We have previously shown the accuracy issues in entropy calculations associated with only using the HO approximation and adjusting for only terminal methyl rotations37 for these species. In this study we replaced contributions from all internal rotations in the HO approximation with those from the ROTATOR hindered rotor analysis denoted SMCPS/ROTATOR. The ROTATOR38 code models the internal rotational potential energy curves calculated at the B3LYP/6-31G(d,p) level of theory. It then expands the hindrance potential in the Fourier series (see eq I), calculates the Hamiltonian matrix in the basis of wave functions of free internal rotor, and calculates the energy levels by direct diagonalization of the Hamiltonian matrix. Here the internal rotor potential calculated at discrete torsion angles is represented by a truncated Fourier series: V (ϕ) = ao +

Table 1. Standard Enthalpies of Formation used as Reference Species in Isodesmic Reactions ΔH°f 298 (kcal mol−1)

species H CH4 CH3CH3 CH3CH2CH3 CH3CH2CH2CH3 (CH3)3CH n-C5H12 CH3CH(CH3)CH2CH3 (CH3)4C n-C6H14 CC(C)C(C)C CC(C2)CC CC(C2)CCC CC(C2)C(C)C CC(C2)C(C)CC CC(C2)CC(C)C C•H3 CH3C•H2 CH3C•HCH3 C•H2CH2CH3 (CH3)3C• CH3C•HCH2CH3 C•H2CH2CH2CH3 C•H2CH2CH2CH2CH3 CH3C•HCH2CH2CH3 CH3CH2C•HCH2CH3

52.103 −17.8 −20.0 −25.0 −30.0 −32.1 −35.1 −36.7 −40.2 −39.9 −42.6 −44.4 −49.2 −48.9 −52.6 −54.40 35.01 29.0 21.2 24.3 12.6 16.6 19.3 14.3 11.4 11.7

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

0.001 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.4 0.36 0.02 0.4 0.9 0.9 1.3 0.9 0.9 1.2 1.2 1.2

reference 44 45 45 45 45 45 45 45 45 45 45 45 45 45 45 46 47 48 49 49 a 49 49 a a a

a

Derived in this study (Table 2) and used for reference species enthalpies.

■

RESULTS AND DISCUSSION The isodesmic work reactions used in this analysis utilize reference species with the ΔH°f 298 values listed in Table 1. Species larger than five carbons do not have explicit hydrogens shown for readability. Enthalpies of formation for the tert-butyl radical and for the primary and two secondary radicals of npentane were determined using a series of six to nine work reactions with the CBS-QB3, CBS-APNO, and G3MP2B3 methods. The isodesmic reactions and the calculation results are provided in Table 2. Averages for each of the calculation methods are given as well as the method averages from the average of these three composite methods. Table 3 has the recommended values along with a number of available literature enthalpy values. This illustrates the range in literature values for each species; the range of the tert-butyl radical (2.6 kcal mol−1) was one focus of this study. The values shown in bold were selected and used in the work reactions in this study. Evaluation of the G3MP2B3 method for these radicals shows that it only provides consistency within a set of calculations on a given radical when the same class of radical is used for both the target and the reference radicals. Effectively a primary radical needed to be used as the reference for a primary radical target, etc. Typical differences between a primary with a secondary reference or inverse is ∼0.5 kcal mol−1. G3MP2B3 does not show the same agreement as CBS-QB3 or CBSAPNO for these radicals when a primary radical is a reference for a secondary or tertiary radical calculation. One illustration of this is shown in the calculated enthalpies and the standard deviations (std) from the work reactions in Table 2 for tert-butyl radical. The G3MP2B3 enthalpy values

∑ aicos(iϕ) + ∑ bisin(iϕ), where i = 1 − 7 (I)

Values of the coefficients (ao, ai, and bi) are calculated to provide the minima and maxima of the torsion potentials with allowance for a shift of the theoretical extreme angular positions. Previous studies have shown good agreement for entropy and heat capacity for a series of alkanes37 and for ketones39 between 298 and 1500 K using SMCPS/ROTATOR. Calculated values for the larger branched alkanes and radicals represent the lowest energy conformer. The GA method, as developed by Benson,14 was also used as a comparison for our determined parent ΔH°f 298, S°(T), and Cp(T) values. This successful method is based on the accurate knowledge of the contributions of representative groups from similar molecules and their established linear consistency in thermochemical property contribution. Thermodynamic properties of larger species, such as those in this study, can be accurately approximated based on the sum of the smaller representative groups where there are corrections for rotors, symmetry, electron degeneracy, optical isomers, and gauche and other interactions. We show below that this method compares well for these properties. 9366



Article

Table 2. Work Reactions and ΔHf °298 Valuesa for (CH3)3C•, C•H2CH2CH2CH2CH3, CH3C•HCH2CH2CH3, and CH3CH2C•HCH2CH3 Radicals ΔH°f 298 (kcal mol−1) isodesmic reactions (CH3)3C• system (CH3)3C• + CH4 → C•H3 + (CH3)3CH (CH3)3C• + CH3CH3 → CH3C•H2 + (CH3)3CH (CH3)3C• + CH3CH2CH3 → CH3C•HCH3 + (CH3)3CH (CH3)3C• + CH3CH2CH3 → C•H2CH2CH3 + (CH3)3CH (CH3)3C• + CH3CH2CH2CH3 → C•H2CH2CH2CH3 + (CH3)3CH (CH3)3C• + CH3CH2CH2CH3 → CH3C•HCH2CH3 + (CH3)3CH (CH3)3C• + n-C5H12 → C•H2CH2CH2CH2CH3 + (CH3)3CH (CH3)3C• + n-C5H12 → CH3C•HCH2CH2CH3 + (CH3)3CH (CH3)3C• + n-C5H12 → CH3CH2C•HCH2CH3 + (CH3)3CH average method average standard deviationb CH bond dissociation energy C•H2CH2CH2CH2CH3 system C•H2CH2CH2CH2CH3 + CH4 → C•H3 + n-C5H12 C•H2CH2CH2CH2CH3 + CH3CH3 → CH3C•H2 + n-C5H12 C•H2CH2CH2CH2CH3 + CH3CH2CH3 → CH3C•HCH3 + n-C5H12 C•H2CH2CH2CH2CH3 + CH3CH2CH3 → C•H2CH2CH3 + n-C5H12 C•H2CH2CH2CH2CH3 + CH3CH2CH2CH3 → C•H2CH2CH2CH3 + n-C5H12 C•H2CH2CH2CH2CH3 + CH3CH2CH2CH3 → CH3C•HCH2CH3 + n-C5H12 average method average standard deviationb CH bond dissociation energy CH3C•HCH2CH2CH3 system CH3C•HCH2CH2CH3 + CH4 → C•H3 + n-C5H12 CH3C•HCH2CH2CH3 + CH3CH3 → CH3C•H2 + n-C5H12 CH3C•HCH2CH2CH3 + CH3CH2CH3 → CH3C•HCH3 + n-C5H12 CH3C•HCH2CH2CH3 + CH3CH2CH3 → C•H2CH2CH3 + n-C5H12 CH3C•HCH2CH2CH3 + CH3CH2CH2CH3 → C•H2CH2CH2CH3 + n-C5H12 CH3C•HCH2CH2CH3 + CH3CH2CH2CH3 → CH3C•HCH2CH3 + n-C5H12 average method average standard deviationb CH bond dissociation energy CH3CH2C•HCH2CH3 system CH3CH2C•HCH2CH3 + CH4 → C•H3 + n-C5H12 CH3CH2C•HCH2CH3 + CH3CH3 → CH3C•H2 + n-C5H12 CH3CH2C•HCH2CH3 + CH3CH2CH3 → CH3C•HCH3 + n-C5H12 CH3CH2C•HCH2CH3 + CH3CH2CH3 → C•H2CH2CH3 + n-C5H12 CH3CH2C•HCH2CH3 + CH3CH2CH2CH3 → C•H2CH2CH2CH3 + n-C5H12 CH3CH2C•HCH2CH3 + CH3CH2CH2CH3 → CH3C•HCH2CH3 + n-C5H12 average method average

CBS-QB3

CBSAPNO

G3MP2B3

W1(RO)

W1U

W1Usc

W1BD

12.52 12.42 12.37 12.44 12.19

12.66 12.48 12.36 12.46 12.51

(13.75) (13.21) 12.73 (13.19) (13.23)

12.78 12.58

12.81 12.60

12.80 12.59

12.76 12.57

12.55

12.49

12.88

12.26

12.60

(13.33)

12.49

12.44

12.80

12.53

12.44

12.84

12.4

12.8

12.7

12.7

12.7

12.7

0.125 96.6

12.5 12.6 ± 1.3 0.091 96.7

0.064 (0.325) 97.0

14.55 14.45 14.41

14.36 14.18 14.06

14.72 14.19 (13.71)

14.47

14.15

14.16

14.22

14.20

14.20

14.59

14.18

(13.86)

14.4

14.3

0.129 101.6

14.2 14.3 ± 1.2 0.098 101.4

0.271 (0.350) 101.5

11.43 11.33 11.29

11.62 11.44 11.32

(12.35) (11.81) 11.33

11.35

11.42

(11.79)

11.10

11.47

(11.82)

11.46

11.45

11.48

11.3

11.4

0.129 98.5

11.5 11.4 ± 1.2 0.098 98.7

0.106 (0.350) 98.6

11.69 11.59 11.54

11.92 11.74 11.62

(12.53) (12.07) 11.59

11.61

11.72

(12.05)

11.36

11.77

(12.09)

11.72

11.75

11.74

11.6

11.8 11.7 ± 1.2

11.7

9367



Article

Table 2. continued ΔH°f 298 (kcal mol−1) isodesmic reactions CH3CH2C•HCH2CH3 system standard deviationb CH bond dissociation energy

CBS-QB3

CBSAPNO

G3MP2B3

0.129 98.8

0.098 99.0

0.106 (0.324) 98.9

W1(RO)

W1U

W1Usc

W1BD

a Values in parentheses are not utilized in calculation of the enthalpies of formation. bStandard deviation values in parentheses include enthalpy values for all work reactions.

average 13.1 kcal mol−1 with a std of 0.325 compared to 12.4 (std of 0.125) and 12.5 (std of 0.091) kcal mol−1 for CBS-QB3 and CBS-APNO, respectively. If one omits the work reactions where a primary radical is the reference radical, the average G3MP2B3 enthalpy is closer at 12.8 kcal mol−1 with a significantly lower std of 0.064. Use of a methyl radical for a reference species in a G3MP2B3 work reaction shows larger errors, in excess of 1 kcal mol−1. Similar deviations are seen with the secondary pentane radicals. Enthalpies for the secondary radicals CH3C•HCH2CH2CH3 and CH3CH2C•HCH2CH3 of 11.8 and 12.0 kcal mol−1 with std of 0.350 and 0.324 are moved to 11.4 and 11.7 kcal mol−1 with std of 0.106 and 0.106 with use of only secondary radicals giving better agreement with the CBS methods. As result of this, our recommended enthalpy values use data in Table 2 from G3MP2B3 work reactions only when the reference and target radical are of identical types. The values in parentheses are not used. The determined hydrocarbon radical values are highly consistent. This can be seen in looking at the enthalpy values in Table 3. We show differences between primary and secondary radicals of 3.1, 2.7, 2.9, and 2.6 kcal mol−1 for C3, C4, and the two secondary C5 radicals utilized in this study. This consistency in enthalpy values translates directly into the parent hydrocarbon C−H BDEs. All of the primary C−H bonds show a bond energy of 101.4−101.5 kcal mol−1. Secondary bonds are 98.3, 98.7, 98.6, and 98.9 kcal mol−1 for n-propane, n-butane, and n-pentane, second and third carbon sites, respectively. The range of literature values for tert-butyl radical is from 10.6 to 13.2 kcal mol−1 and the value we obtain is 12.6 kcal mol−1 which is close to most other reported literature values (see Table 3); this results in a tertiary C−H BDE of 96.8 kcal mol−1. For comparison, enthalpies for the primary radical site are given in Table 3 which shows a small range of values leading to an average primary C−H BDE of 101.7 kcal mol−1 (bold denotes recommended). The lowest value of 10.6 kcal mol−1 is reported by Leplat and Rossi40 who recently experimentally determined this value from the kinetics of metathesis reactions involving tert-butyl radical reactions with HBr. Geometry parameters for both the optimized and frozen tert-butyl radical are presented in the Supporting Information. To further verify the tertiary butyl radical standard enthalpy, higher level methods of the Weizmann-1 theories:41−43 W1 (denoted W1(RO)), unrestricted W1 (denoted W1U), spin corrected W1U (denoted W1Usc), and unrestricted Brueckner doubles W1 (denoted W1BD) are utilized for the two work reactions involving methane and ethane. Work reaction analysis with these methods show a consistent 12.7 kcal mol−1 value

which supports the 12.6 kcal mol−1 value obtained from the CBS-QB3, CBS-APNO, and selected G3MP2B3 methods. The bold values in Table 3 are utilized in calculations for each of the parent C7H16 compounds with four to five work reactions where the parent compound is reacted with a straight chain alkane yielding smaller linear and branched alkanes. The work reactions with the calculated ΔH°f 298 for each of the C7 parent species using the CBS-QB3, CBS-APNO, and G3MP2B3 methods are presented in Table 4. The Supporting Information has these calculations at the B3LYP method with the 6-31G(d,p) and 6-311G(2d,2p) basis sets. The work reactions for the alkane radicals have the radical species reacted with a small hydrocarbon yielding the parent species plus a hydrocarbon radical. The work reactions incorporate primary, secondary, and tertiary species as seen in Table 5. For the B3LYP and G3MP2B3 methods there is decreased precision in the calculated enthalpies when work reactions are included that do not match the radical site location for the C7 radicals. This is most easily seen with the DFT methods and is consistent with our findings for the smaller tert-butyl and n-pentane hydrocarbon radicals with G3MP2B3. Statistical analysis for comparison for the B3LYP and G3MP2B3 methods, provided in Supporting Information, illustrates the enthalpy calculated between work reactions for a given radical with identical reference and target radical type (primary (p), secondary (s), and tertiary (t)), results in significantly better consistency than enthalpy values from work reactions incorporating different radical type in reactant/ product pairings. B3LYP, regardless of basis set, shows an enthalpy increase of ∼0.8 kcal mol−1 for target primary radicals and a ∼0.8 kcal mol−1 decrease in enthalpy for target tertiary radicals when not considering the same class of radical for the target and reference radical. G3MP2B3 by comparison shows a ∼0.3 kcal mol−1 decrease and a ∼0.3 kcal mol−1 increase for the respective radical sets. In B3LYP calculations, secondary target radicals decrease slightly by ∼0.5 kcal mol−1, when a different radical type (p, s, or t) is used for reference and here, G3MP2B3 shows an increase of ∼0.2 kcal mol−1 To improve overall precision work reactions where only the reference and target radical are identical type (p, s, or t) are utilized for the B3LYP/6-31G(d,p), B3LYP/6-311G(2d,2p), and G3MP2B3 methods. The values for other work reactions are provided in parentheses to illustrate the significant deviation(s). Table 5 has our recommended ΔH°f 298 for each radical species considering the radical site location. For the species with tertiary radical site locations, both secondary and tertiary work reaction species are used. Properties for all species including optimized structure parameters, symmetry, moments of inertia, vibration frequencies, and internal rotor potentials from the B3LYP/6-31G(d,p) level of theory are presented in the Supporting Information. 9368



Article

Table 3. Recommended ΔHf °298 values for (CH3)3C•, C•H2CH2CH2CH2CH3, CH3C•HCH2CH2CH3, and CH3CH2C•HCH2CH3 Radicals with Comparison to Other Available Literature Values species

ΔH°f 298 (kcal mol−1)

reference

35.01 ± 0.02 35.2 ± 0.2 35.0 34.8 ± 0.2 35.05 ± 0.07 29.0 ± 0.4 28.9 ± 0.4 28.9 28.66 ± 0.10 28.4 ± 0.5 29.1 ± 0.6 21.2 ± 0.9 21.5 21.5 ± 0.4 21.6 ± 0.5 22. ± 0.5 20.7 ± 0.5 24.3 ± 0.9 24.0 24.2 ± 0.2 23.9 ± 0.5 24.1 ± 0.5 24.0 ± 0.5 12.6 ± 1.3 13.0 ± 0.9 12.3 12.3 ± 0.4 13.2 ± 1.9 11. ± 0.7 12.1 ± 0.8 12.4 ± 0.4 12.4 ± 0.5 10.6 ± 0.4 17.8 ± 0.9 17.4 17.6 ± 1.9 17. ± 0.5 16.6 ± 0.9 16.1 ± 0.5 16.8 ± 1.9 16. ± 0.5 16.1 ± 0.5 17.0 ± 0.4 19.3 ± 0.9 19.2 19.6 ± 1.9 19.3 ± 0.5 14.3 ± 1.2 11.4 ± 1.2 11.7 ± 1.2

47 49 50 51 48 48 49 50 47 52 53 49 50 48 47 52 54 49 50 47 52 54 55 a 49 50 48 47 52 53 54 55 40 49 50 47 52 49 48 47 52 56 55 49 50 47 54 a a a

C•H3

CH3C•H2

CH3C•HCH3

C•H2CH2CH3

(CH3)3C•

(CH3)2CHC•H2

CH3C•HCH2CH3

C•H2CH2CH2CH3

C•H2CH2CH2CH2CH3 CH3C•HCH2CH2CH3 CH3CH2C•HCH2CH3 a

31G(d,p) and 6-311G(2d,2p) basis sets, are included in the Supporting Information. The error analysis incorporates uncertainties in the work reaction reference species and the work reactions at each calculation method. They are calculated by summing the uncertainties of the reference species and adding the std of the calculated enthalpies of formation. The root-mean-square (RMS) of these values is taken at each calculation method and then another RMS is taken to determine the overall uncertainty in the DFT and composite values. This procedure is described in detail in the Supporting Information. We find surprisingly good agreement for the ΔH°f 298 values between the DFT and composite resulting from the use of the error canceling work reactions and work reactions where the reference and target radical are identical types. The parent species show that the lower level DFT methods provide acceptable analysis compared to the higher level composite methods with an average absolute difference of 0.4 kcal mol−1. We note that differences between the methods increased as the amount of branching increased and this should be considered when applying these DFT methods. There is a slightly higher average absolute difference for the radical species. The recommend ΔH°f 298 values for the parent species from the average of the CBS-QB3, CBS-APNO, and selected G3MP2B3 methods are included in Table 6 for comparison to available literature values. Our calculated values of −45.1 and −46.7 kcal mol−1 for nC7H16 and CC(C)CCCC, respectively, are within the small ranges of the reported available literature values. This good consistency suggests our work reactions and calculation methods are appropriate for these types of hydrocarbons. Our value of −47.0 kcal mol−1 for CC(C)C(C)CC is in the middle of the range provided by the literature, but is still within chemical accuracy, defined as 1 kcal mol−1. Comparison to the group additivity (GA) method shows an excellent agreement for n-heptane with a slight increase of approximately 0.2 kcal mol−1 in derivation as the chain branching increases while incorporating gauche interaction and 1,5 hydrogen repulsions. Enthalpies, entropies, and heat capacities for the groups used in the GA method14 are provided in the Supporting Information. Carbon−Hydrogen Bond Dissociation Energies (C−H BDEs). C−H BDEs are computed from the work reactions listed in Table 5. The calculated ΔH°f 298 of the parent and radical molecules are combined with the established value of 52.103 kcal mol−1 for the hydrogen atom.44 The data from CBS-QB3, CBS-APNO, and selected G3MP2B3 methods show good agreement to standard reference C−H BDEs of 101.1, 98.5, and 96.5 kcal mol−1 for primary, secondary, and tertiary alkanes, respectively. These values are confirmed by multiple studies where primary C−H BDEs for ethane, n-propane, and n-butane in the 100−101 kcal mol−1 range and secondary C−H BDEs of approximately 98 kcal mol−1 for n-propane and nbutane.48,60,61 Tertiary C−H BDE from tert-butyl reported values range 95.7−97.2 kcal mol−1.48,60,62 Our calculated primary C−H BDEs for these alkanes fall within a 1 kcal mol−1 range from 100.7 to 101.7 kcal mol−1. Our secondary and tertiary C−H BDEs give a slightly larger range of 97.7 to 98.9 and 95.4 to 96.6 kcal mol−1, respectively. Uncertainties reported match those assigned for the enthalpy calculations since they already incorporate uncertainties from the calculated enthalpies and reference species for the parent

Calculated in this study (Table 2).

Standard Enthalpy of Formation ΔH°f 298. Tables 4 and 5 list the work reactions used to determine the ΔH°f 298 values for the parent and radical C7H16 species from the CBS-QB3, CBS-APNO, and G3MP2B3 methods. The work reactions from Tables 4 and 5 using the DFT B3LYP method, with the 69369



Article

Table 4. Isodesmic Work Reactions and Calculated ΔHf °298 for C7H16 Parent Species ΔHf°298 (kcal mol−1) isodesmic reactions n-C7H16 system → CH3CH2CH3 → CH3CH2CH2CH3 → n-C5H12 → CH3CH2CH2CH3 → n-C5H12

CBS-QB3

CBS-APNO

G3MP2B3

+ + + + +

n-C6H14 n-C5H12 n-C5H12 n-C6H14 n-C6H14 average method average

−44.97 −45.22 −45.23 −44.88 −44.99 −45.06

−44.97 −45.23 −45.24 −44.87 −44.98 −45.06 −45.1 ± 0.6

−44.95 −45.17 −45.21 −44.86 −44.98 −45.03

CC(C)CCCC system CH3CH3 → (CH3)3CH CH3CH2CH3 → (CH3)3CH CH3CH3 → CH3CH(CH3)CH2CH3 CH3CH2CH3 → CH3CH(CH3)CH2CH3 CH3CH2CH2CH3 → CH3CH(CH3)CH2CH3

+ + + + +

n-C5H12 n-C6H14 CH3CH2CH2CH3 n-C5H12 n-C6H14 average method average

−46.88 −46.53 −46.88 −46.89 −46.65 −46.77

−46.81 −46.45 −46.86 −46.87 −46.61 −46.72 −46.7 ± 0.6

−46.87 −46.56 −46.84 −46.88 −46.65 −46.76

CC(C)C(C)CC system CH3CH3 → CC(C)C(C)C CH3CH2CH3 → CC(C)C(C)C CH3CH2CH2CH3 → CC(C)C(C)C n-C5H12 → CC(C)C(C)C

+ + + +

CH3CH2CH3 CH3CH2CH2CH3 n-C5H12 n-C6H14 average method average

−47.06 −46.96 −47.07 −46.72 −46.95

−47.07 −46.97 −47.08 −46.71 −46.96 −47.0 ± 0.6

−47.05 −46.96 −47.08 −46.73 −46.96

n-C7H16 n-C7H16 n-C7H16 n-C7H16 n-C7H16

+ + + + +

CH3CH3 CH3CH3 CH3CH2CH3 CH3CH2CH3 CH3CH2CH2CH3

CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC

+ + + + +

CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC

+ + + +

and radical species. The error introduced from H• in the bond dissociation reaction is not included due to its comparatively small contribution. Work by Snitsiriwat and Bozzelli 46 on isooctane, CC(C2)CC(C)C, depicts the trend of decreasing C−H BDEs for tertiary and adjacent secondary locations with increasing size and number of branching groups within the species. For additional comparisons, we have calculated secondary and tertiary BDEs for three larger branched alkanes given in Figure 2. Enthalpies of formations for the parent and studied radicals are calculated using B3LYP/6-31G(d,p), B3LYP/6-311G(2d,2p), CBS-QB3, and G3MP2B3 methods. The DFT calculations are presented in the Supporting Information and the composite methods are listed in Table 7. These larger molecules could not be calculated using the resource demanding CBS-APNO method. There is a good comparison for the ΔHf °298 and the BDEs between the DFT and composite methods but it is important to ensure that the work reactions chosen have good cancellation of error. This is seen especially for DFT calculations, in the Supporting Information, for the calculated values in parentheses, specifically for CC(C2)C(C)C(C2)C. The radicals for these larger hydrocarbons exhibit a similar deviation in precision, as the smaller C7 species, when all of the work reactions are utilized: please see the comparison presented in the Supporting Information. Work reactions where the reference and target radical are of identical type (p, s, or t) are the only ones utilized for reporting from the DFT and G3MP2B3 methods. The values for work reactions in parentheses are provided to illustrate the deviation and are not included in the calculation of the enthalpies of formation. One may observe that, as with the C7 isomers, the differences between the methods increased as the amount of branching increased. We note that while there is only a 0.4 kcal mol−1

difference for CC(C2)C(C)C(C2)C where several added work reaction on this molecule did not have good cancelation of error. These work reactions, along with their larger error, are illustrated in the Supporting Information. This serves as an example of the importance in selecting appropriate work reactions. We also illustrated this in a study on thermochemistry of tricyclodecane radicals.25 A summary of the secondary and tertiary BDEs for the C7 isomers, isooctane, and the larger branched alkanes is given in Table 8. These values result in average C−H BDEs for the branched alkanes of 98.3 and 95.3 kcal mol−1 for secondary and tertiary sites, respectively. The values show an approximate decrease of 0.2 and 1.2 kcal mol−1 from smaller alkane BDEs. A decrease is observed in the BDEs as the size and number of the branching groups increase within a species. Internal Rotors. Potential energy curves for internal rotation of single bonds for 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 scan were rerun to ensure we had located the lowest energy conformation. These potential energy curves are available in the Supporting Information and are used to determined entropy and heat capacity contributions. Entropy (S°(T)) and Heat Capacities (Cp(T)). Entropies and heat capacities are calculated using our SMCPS/ ROTATOR method and are compared to available literature and calculated group additivity (GA) values in an attempt to gauge our accuracy. Calculation of entropy and heat capacity data includes scaling of the frequencies, in SMCPS, as recommended by Scott and Radom.36 Table 9 shows consistency between our values and both the GA and literature data. There is good agreement for the three parent species with literature for heat capacities between 300 and 1500 K. 9370



Article

Table 5. Isodesmic Work Reactions, Recommended ΔHf °298, and Bond Dissociation Energies for C7H16 Radical Speciesa ΔH°f 298 (kcal mol−1) isodesmic reactions C•CCCCCC C•CCCCCC C•CCCCCC C•CCCCCC C•CCCCCC C•CCCCCC C•CCCCCC C•CCCCCC C•CCCCCC C•CCCCCC

+ + + + + + + + + +

C•CCCCCC system CH4 → C•H3 CH3CH3 → CH3C•H2 CH3CH2CH3 → CH3C•HCH3 CH3CH2CH3 → C•H2CH2CH3 (CH3)3CH → (CH3)3C• CH3CH2CH2CH3 → C•H2CH2CH2CH3 CH3CH2CH2CH3 → CH3C•HCH2CH3 n-C5H12 → C•H2CH2CH2CH2CH3 n-C5H12 → CH3C•HCH2CH2CH3 n-C5H12 → CH3CH2C•HCH2CH3

+ + + + + + + + + +

n-C7H16 n-C7H16 n-C7H16 n-C7H16 n-C7H16 n-C7H16 n-C7H16 n-C7H16 n-C7H16 n-C7H16 average

CBS-QB3

CBS-APNO

G3MP2B3

4.28 4.18 4.14 4.20 4.37 3.95 4.32 4.03 4.25 4.30 4.2

4.40 4.22 4.10 4.20 4.34 4.25 4.23 4.35 4.18 4.18 4.2 4.3 ± 1.8 101.4 ± 1.8

4.76 4.23 (3.75) 4.20 (3.61) 4.24 (3.90) 4.34 (3.82) (3.85) 4.4

1.46 1.36 1.31 1.38 1.54 1.12 1.49 1.20 1.43 1.47 1.4

1.68 1.50 1.38 1.47 1.61 1.52 1.50 1.62 1.45 1.45 1.5 1.4 ± 1.8 98.6 ± 1.8

(2.35) (1.81) 1.33 (1.79) (1.20) (1.83) 1.48 (1.92) 1.40 1.44 1.4

1.66 1.56 1.52 1.58 1.74 1.33 1.70 1.41 1.63 1.67 1.6

1.93 1.75 1.63 1.73 1.87 1.78 1.76 1.88 1.71 1.71 1.8 1.7 ± 1.8 98.8 ± 1.8

(2.60) (2.06) 1.58 (2.04) (1.45) (2.08) 1.74 (2.18) 1.66 1.69 1.7

1.66 1.56 1.52 1.58 1.74 1.33 1.69 1.41 1.63 1.67 1.6

1.88 1.70 1.58 1.68 1.82 1.73 1.71 1.83 1.66 1.66 1.7 1.7 ± 1.8 98.8 ± 1.8

(2.60) (2.06) 1.58 (2.04) (1.45) (2.07) 1.73 (2.17) 1.65 1.69 1.7

2.83 2.73

2.89 2.71

3.45 2.91

method average C−H bond dissociation energy CC•CCCCC CC•CCCCC CC•CCCCC CC•CCCCC CC•CCCCC CC•CCCCC CC•CCCCC CC•CCCCC CC•CCCCC CC•CCCCC

+ + + + + + + + + +

CC•CCCCC system CH4 → C•H3 CH3CH3 → CH3C•H2 CH3CH2CH3 → CH3C•HCH3 CH3CH2CH3 → C•H2CH2CH3 (CH3)3CH → (CH3)3C• CH3CH2CH2CH3 → C•H2CH2CH2CH3 CH3CH2CH2CH3 → CH3C•HCH2CH3 n-C5H12 → C•H2CH2CH2CH2CH3 n-C5H12 → CH3C•HCH2CH2CH3 n-C5H12 → CH3CH2C•HCH2CH3

+ + + + + + + + + +


method average C−H bond dissociation energy CCC•CCCC CCC•CCCC CCC•CCCC CCC•CCCC CCC•CCCC CCC•CCCC CCC•CCCC CCC•CCCC CCC•CCCC CCC•CCCC

+ + + + + + + + + +

CCC•CCCC system CH4 → C•H3 CH3CH3 → CH3C•H2 CH3CH2CH3 → CH3C•HCH3 CH3CH2CH3 → C•H2CH2CH3 (CH3)3CH → (CH3)3C• CH3CH2CH2CH3 → C•H2CH2CH2CH3 CH3CH2CH2CH3 → CH3C•HCH2CH3 n-C5H12 → C•H2CH2CH2CH2CH3 n-C5H12 → CH3C•HCH2CH2CH3 n-C5H12 → CH3CH2C•HCH2CH3

+ + + + + + + + + +


method average C−H bond dissociation energy CCCC•CCC CCCC•CCC CCCC•CCC CCCC•CCC CCCC•CCC CCCC•CCC CCCC•CCC CCCC•CCC CCCC•CCC CCCC•CCC

+ + + + + + + + + +

CCCC•CCC system CH4 → C•H3 CH3CH3 → CH3C•H2 CH3CH2CH3 → CH3C•HCH3 CH3CH2CH3 → C•H2CH2CH3 (CH3)3CH → (CH3)3C• CH3CH2CH2CH3 → C•H2CH2CH2CH3 CH3CH2CH2CH3 → CH3C•HCH2CH3 n-C5H12 → C•H2CH2CH2CH2CH3 n-C5H12 → CH3C•HCH2CH2CH3 n-C5H12 → CH3CH2C•HCH2CH3

+ + + + + + + + + +


method average C−H bond dissociation energy C•C(C)CCCC C•C(C)CCCC

+ +

CH4 CH3CH3

C•C(C)CCCC system → C•H3 → CH3C•H2 9371

+ +

CC(C)CCCC CC(C)CCCC



Article

Table 5. continued ΔH°f 298 (kcal mol−1) isodesmic reactions C•C(C)CCCC C•C(C)CCCC C•C(C)CCCC C•C(C)CCCC C•C(C)CCCC C•C(C)CCCC C•C(C)CCCC C•C(C)CCCC

+ + + + + + + +

C•C(C)CCCC system CH3CH2CH3 → CH3C•HCH3 CH3CH2CH3 → C•H2CH2CH3 (CH3)3CH → (CH3)3C• CH3CH2CH2CH3 → C•H2CH2CH2CH3 CH3CH2CH2CH3 → CH3C•HCH2CH3 n-C5H12 → C•H2CH2CH2CH2CH3 n-C5H12 → CH3C•HCH2CH2CH3 n-C5H12 → CH3CH2C•HCH2CH3

+ + + + + + + +

CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC average

CBS-QB3

CBS-APNO

G3MP2B3

2.69 2.75 2.91 2.50 2.86 2.58 2.80 2.84 2.7

2.59 2.69 2.83 2.74 2.72 2.84 2.67 2.67 2.7 2.8 ± 1.8 101.7 ± 1.8

(2.43) 2.89 (2.30) 2.93 (2.58) 3.03 (2.50) (2.54) 3.0

−2.29 −2.38 −2.43 −2.37 −2.20 −2.62 −2.25 −2.54 −2.31 −2.27 −2.4

−2.25 −2.43 −2.55 −2.46 −2.32 −2.41 −2.43 −2.31 −2.48 −2.48 −2.4 −2.2 ± 1.8 96.6 ± 1.8

(−0.97) (−1.51) −1.99 (−1.53) −2.12 (−1.49) −1.84 (−1.40) −1.92 −1.88 −1.9

0.11 0.01 −0.04 0.03 0.19 −0.23 0.14 −0.15 0.08 0.12 0.0

0.20 0.02 −0.10 0.00 0.14 0.05 0.03 0.15 −0.02 −0.02 0.0 0.1 ± 1.8 98.9 ± 1.8

(1.11) (0.57) 0.09 (0.55) (−0.04) (0.58) 0.24 (0.68) 0.16 0.20 0.2

−0.46 −0.56 −0.60 −0.54 −0.38 −0.79 −0.42 −0.71 −0.49 −0.45 −0.5

−0.31 −0.49 −0.61 −0.52 −0.37 −0.47 −0.48 −0.37 −0.54 −0.54 −0.5 −0.5 ± 1.8 98.4 ± 1.8

(0.49) (−0.04) −0.52 (−0.07) (−0.66) (−0.03) −0.37 (0.07) −0.45 −0.42 −0.4

−0.21 −0.31 −0.35 −0.29

−0.05 −0.23 −0.35 −0.25

(0.70) (0.16) −0.32 (0.14)

method average C−H bond dissociation energy CC•(C)CCCC CC•(C)CCCC CC•(C)CCCC CC•(C)CCCC CC•(C)CCCC CC•(C)CCCC CC•(C)CCCC CC•(C)CCCC CC•(C)CCCC CC•(C)CCCC

+ + + + + + + + + +

CC(C)C•CCC CC(C)C•CCC CC(C)C•CCC CC(C)C•CCC CC(C)C•CCC CC(C)C•CCC CC(C)C•CCC CC(C)C•CCC CC(C)C•CCC CC(C)C•CCC

+ + + + + + + + + +

CC(C)CC•CC CC(C)CC•CC CC(C)CC•CC CC(C)CC•CC CC(C)CC•CC CC(C)CC•CC CC(C)CC•CC CC(C)CC•CC CC(C)CC•CC CC(C)CC•CC

+ + + + + + + + + +

CC(C)CCC•C CC(C)CCC•C CC(C)CCC•C CC(C)CCC•C

+ + + +

CC•(C)CCCC system CH4 → C•H3 + CC(C)CCCC CH3CH3 → CH3C•H2 + CC(C)CCCC CH3CH2CH3 → CH3C•HCH3 + CC(C)CCCC CH3CH2CH3 → C•H2CH2CH3 + CC(C)CCCC (CH3)3CH → (CH3)3C• + CC(C)CCCC CH3CH2CH2CH3 → C•H2CH2CH2CH3 + CC(C)CCCC CH3CH2CH2CH3 → CH3C•HCH2CH3 + CC(C)CCCC n-C5H12 → C•H2CH2CH2CH2CH3 + CC(C)CCCC n-C5H12 → CH3C•HCH2CH2CH3 + CC(C)CCCC n-C5H12 → CH3CH2C•HCH2CH3 + CC(C)CCCC average method average C−H bond dissociation energy CC(C)C•CCC system CH4 → C•H3 + CC(C)CCCC CH3CH3 → CH3C•H2 + CC(C)CCCC CH3CH2CH3 → CH3C•HCH3 + CC(C)CCCC CH3CH2CH3 → C•H2CH2CH3 + CC(C)CCCC (CH3)3CH → (CH3)3C• + CC(C)CCCC CH3CH2CH2CH3 → C•H2CH2CH2CH3 + CC(C)CCCC CH3CH2CH2CH3 → CH3C•HCH2CH3 + CC(C)CCCC n-C5H12 → C•H2CH2CH2CH2CH3 + CC(C)CCCC n-C5H12 → CH3C•HCH2CH2CH3 + CC(C)CCCC n-C5H12 → CH3CH2C•HCH2CH3 + CC(C)CCCC average method average C−H bond dissociation energy CC(C)CC•CC system CH4 → C•H3 + CC(C)CCCC CH3CH3 → CH3C•H2 + CC(C)CCCC CH3CH2CH3 → CH3C•HCH3 + CC(C)CCCC CH3CH2CH3 → C•H2CH2CH3 + CC(C)CCCC (CH3)3CH → (CH3)3C• + CC(C)CCCC CH3CH2CH2CH3 → C•H2CH2CH2CH3 + CC(C)CCCC CH3CH2CH2CH3 → CH3C•HCH2CH3 + CC(C)CCCC n-C5H12 → C•H2CH2CH2CH2CH3 + CC(C)CCCC n-C5H12 → CH3C•HCH2CH2CH3 + CC(C)CCCC n-C5H12 → CH3CH2C•HCH2CH3 + CC(C)CCCC average method average C−H bond dissociation energy CC(C)CCC•C system CH4 → C•H3 + CC(C)CCCC CH3CH3 → CH3C•H2 + CC(C)CCCC CH3CH2CH3 → CH3C•HCH3 + CC(C)CCCC CH3CH2CH3 → C•H2CH2CH3 + CC(C)CCCC 9372



Article

Table 5. continued ΔH°f 298 (kcal mol−1) isodesmic reactions CC(C)CCC•C CC(C)CCC•C CC(C)CCC•C CC(C)CCC•C CC(C)CCC•C CC(C)CCC•C

CC(C)CCCC• CC(C)CCCC• CC(C)CCCC• CC(C)CCCC• CC(C)CCCC• CC(C)CCCC• CC(C)CCCC• CC(C)CCCC• CC(C)CCCC• CC(C)CCCC•

C•C(C)C(C)CC C•C(C)C(C)CC C•C(C)C(C)CC C•C(C)C(C)CC C•C(C)C(C)CC C•C(C)C(C)CC C•C(C)C(C)CC C•C(C)C(C)CC C•C(C)C(C)CC C•C(C)C(C)CC

CC•(C)C(C)CC CC•(C)C(C)CC CC•(C)C(C)CC CC•(C)C(C)CC CC•(C)C(C)CC CC•(C)C(C)CC CC•(C)C(C)CC CC•(C)C(C)CC CC•(C)C(C)CC CC•(C)C(C)CC

CC(C)C•(C)CC CC(C)C•(C)CC CC(C)C•(C)CC CC(C)C•(C)CC CC(C)C•(C)CC CC(C)C•(C)CC

+ + + + + +

+ + + + + + + + + +

+ + + + + + + + + +

+ + + + + + + + + +

+ + + + + +

CC(C)CCC•C system (CH3)3CH → (CH3)3C• + CH3CH2CH2CH3 → C•H2CH2CH2CH3 + CH3CH2CH2CH3 → CH3C•HCH2CH3 + n-C5H12 → C•H2CH2CH2CH2CH3 + n-C5H12 → CH3C•HCH2CH2CH3 + n-C5H12 → CH3CH2C•HCH2CH3 + average method average C−H bond dissociation CC(C)CCCC• system CH4 → C•H3 + CH3CH3 → CH3C•H2 + CH3CH2CH3 → CH3C•HCH3 + CH3CH2CH3 → C•H2CH2CH3 + (CH3)3CH → (CH3)3C• + CH3CH2CH2CH3 → C•H2CH2CH2CH3 + CH3CH2CH2CH3 → CH3C•HCH2CH3 + n-C5H12 → C•H2CH2CH2CH2CH3 + n-C5H12 → CH3C•HCH2CH2CH3 + n-C5H12 → CH3CH2C•HCH2CH3 + average method average C−H bond dissociation C•C(C)C(C)CC system CH4 → C•H3 + CH3CH3 → CH3C•H2 + CH3CH2CH3 → CH3C•HCH3 + CH3CH2CH3 → C•H2CH2CH3 + (CH3)3CH → (CH3)3C• + CH3CH2CH2CH3 → C•H2CH2CH2CH3 + CH3CH2CH2CH3 → CH3C•HCH2CH3 + n-C5H12 → C•H2CH2CH2CH2CH3 + n-C5H12 → CH3C•HCH2CH2CH3 + n-C5H12 → CH3CH2C•HCH2CH3 + average method average C−H bond dissociation CC•(C)C(C)CC system CH4 → C•H3 + CH3CH3 → CH3C•H2 + CH3CH2CH3 → CH3C•HCH3 + CH3CH2CH3 → C•H2CH2CH3 + (CH3)3CH → (CH3)3C• + CH3CH2CH2CH3 → C•H2CH2CH2CH3 + CH3CH2CH2CH3 → CH3C•HCH2CH3 + n-C5H12 → C•H2CH2CH2CH2CH3 + n-C5H12 → CH3C•HCH2CH2CH3 + n-C5H12 → CH3CH2C•HCH2CH3 + average method average C−H bond dissociation CC(C)C•(C)CC system CH4 → C•H3 + CH3CH3 → CH3C•H2 + CH3CH2CH3 → CH3C•HCH3 + CH3CH2CH3 → C•H2CH2CH3 + (CH3)3CH → (CH3)3C• + CH3CH2CH2CH3 → C•H2CH2CH2CH3 + 9373

CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC

CBS-QB3

CBS-APNO

G3MP2B3

−0.13 −0.54 −0.17 −0.46 −0.24 −0.19 −0.3

−0.11 −0.20 −0.22 −0.10 −0.27 −0.27 −0.2 −0.2 ± 1.8 98.6 ± 1.8

(−0.45) (0.18) −0.17 (0.28) −0.25 −0.21 −0.2

2.61 2.52 2.47 2.53 2.70 2.28 2.65 2.36 2.59 2.63 2.5

2.72 2.54 2.42 2.52 2.66 2.57 2.55 2.66 2.50 2.50 2.6 2.6 ± 1.8 101.5 ± 1.8

3.11 2.57 (2.09) 2.55 (1.96) 2.59 (2.24) 2.68 (2.16) (2.20) 2.7

1.93 1.83 1.78 1.85 2.01 1.60 1.96 1.67 1.90 1.94 1.8

2.15 1.96 1.84 1.94 2.08 1.99 1.97 2.09 1.92 1.92 2.0 2.0 ± 1.8 101.0 ± 1.8

2.49 1.95 (1.47) 1.93 (1.34) 1.96 (1.62) 2.06 (1.54) (1.58) 2.1

−3.69 −3.79 −3.83 −3.77 −3.61 −4.02 −3.66 −3.94 −3.72 −3.68 −3.8

−3.62 −3.80 −3.92 −3.82 −3.68 −3.77 −3.79 −3.67 −3.84 −3.84 −3.8 −3.6 ± 1.8 95.4 ± 1.8

(−2.30) (−2.84) −3.32 (−2.87) −3.46 (−2.83) −3.17 (−2.73) −3.25 −3.21 −3.3

−2.76 −2.85 −2.90 −2.84 −2.67 −3.09

−2.78 −2.96 −3.08 −2.99 −2.85 −2.94

(−1.33) (−1.87) −2.35 (−1.89) −2.48 (−1.86)

energy CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC CC(C)CCCC

energy CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC


energy CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC



Article

Table 5. continued ΔH°f 298 (kcal mol−1) isodesmic reactions CC(C)C•(C)CC CC(C)C•(C)CC CC(C)C•(C)CC CC(C)C•(C)CC

CC(C)C(C•)CC CC(C)C(C•)CC CC(C)C(C•)CC CC(C)C(C•)CC CC(C)C(C•)CC CC(C)C(C•)CC CC(C)C(C•)CC CC(C)C(C•)CC CC(C)C(C•)CC CC(C)C(C•)CC

CC(C)C(C)C•C CC(C)C(C)C•C CC(C)C(C)C•C CC(C)C(C)C•C CC(C)C(C)C•C CC(C)C(C)C•C CC(C)C(C)C•C CC(C)C(C)C•C CC(C)C(C)C•C CC(C)C(C)C•C

CC(C)C(C)CC• CC(C)C(C)CC• CC(C)C(C)CC• CC(C)C(C)CC• CC(C)C(C)CC• CC(C)C(C)CC• CC(C)C(C)CC• CC(C)C(C)CC• CC(C)C(C)CC• CC(C)C(C)CC•

a

+ + + +

+ + + + + + + + + +

+ + + + + + + + + +

+ + + + + + + + + +

CC(C)C•(C)CC system CH3CH2CH2CH3 → CH3C•HCH2CH3 + n-C5H12 → C•H2CH2CH2CH2CH3 + n-C5H12 → CH3C•HCH2CH2CH3 + n-C5H12 → CH3CH2C•HCH2CH3 + average method average C−H bond dissociation CC(C)C(C•)CC system CH4 → C•H3 + CH3CH3 → CH3C•H2 + CH3CH2CH3 → CH3C•HCH3 + CH3CH2CH3 → C•H2CH2CH3 + (CH3)3CH → (CH3)3C• + CH3CH2CH2CH3 → C•H2CH2CH2CH3 + CH3CH2CH2CH3 → CH3C•HCH2CH3 + n-C5H12 → C•H2CH2CH2CH2CH3 + n-C5H12 → CH3C•HCH2CH2CH3 + n-C5H12 → CH3CH2C•HCH2CH3 + average method average C−H bond dissociation CC(C)C(C)C•C system CH4 → C•H3 + CH3CH3 → CH3C•H2 + CH3CH2CH3 → CH3C•HCH3 + CH3CH2CH3 → C•H2CH2CH3 + (CH3)3CH → (CH3)3C• + CH3CH2CH2CH3 → C•H2CH2CH2CH3 + CH3CH2CH2CH3 → CH3C•HCH2CH3 + n-C5H12 → C•H2CH2CH2CH2CH3 + n-C5H12 → CH3C•HCH2CH2CH3 + n-C5H12 → CH3CH2C•HCH2CH3 + average method average C−H bond dissociation CC(C)C(C)CC• system CH4 → C•H3 + CH3CH3 → CH3C•H2 + CH3CH2CH3 → CH3C•HCH3 + CH3CH2CH3 → C•H2CH2CH3 + (CH3)3CH → (CH3)3C• + CH3CH2CH2CH3 → C•H2CH2CH2CH3 + CH3CH2CH2CH3 → CH3C•HCH2CH3 + n-C5H12 → C•H2CH2CH2CH2CH3 + n-C5H12 → CH3C•HCH2CH2CH3 + n-C5H12 → CH3CH2C•HCH2CH3 + average method average C−H bond dissociation

CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC CC(C)C(C)CC

CBS-QB3

CBS-APNO

G3MP2B3

−2.72 −3.01 −2.78 −2.74 −2.8

−2.96 −2.84 −3.01 −3.01 −2.9 −2.7 ± 1.8 96.4 ± 1.8

−2.20 (−1.76) −2.28 −2.24 −2.3

1.63 1.53 1.48 1.55 1.71 1.29 1.66 1.37 1.60 1.64 1.5

1.63 1.45 1.33 1.42 1.56 1.47 1.45 1.57 1.40 1.40 1.5 1.6 ± 1.8 100.7 ± 1.8

2.26 1.72 (1.24) 1.70 (1.11) 1.73 (1.39) 1.83 (1.31) (1.35) 1.8

−1.34 −1.44 −1.48 −1.42 −1.26 −1.67 −1.30 −1.59 −1.37 −1.32 −1.4

−1.20 −1.38 −1.50 −1.41 −1.26 −1.36 −1.37 −1.26 −1.43 −1.43 −1.4 −1.3 ± 1.8 97.7 ± 1.8

(−0.31) (−0.84) −1.32 (−0.87) (−1.46) (−0.83) −1.17 (−0.73) −1.25 −1.22 −1.2

1.66 1.56 1.52 1.58 1.74 1.33 1.69 1.41 1.63 1.67 1.6

1.78 1.60 1.48 1.57 1.72 1.63 1.61 1.72 1.56 1.56 1.6 1.7 ± 1.8 100.7 ± 1.8

2.21 1.67 (1.19) 1.65 (1.06) 1.69 (1.34) 1.79 (1.26) (1.30) 1.8




energy

Values in parentheses are not utilized in calculation of the enthalpies of formation.

carbon−hydrogen bond dissociation energies (C−H BDEs) for n-heptane, 2-methylhexane, 2,3-dimethylpentane, and their carbon centered radicals are calculated. Internal rotor potentials are determined using B3LYP/6-31G(d,p) to verify we have the lowest energy structure and for calculating contributions to entropies and heat capacities. ΔH°f 298 values are calculated using isodesmic work reactions with density functional theory

Entropies and heat capacities for the radical species over the same temperature are included in Table 10 using our SMCPS/ ROTATOR method.

■

SUMMARY A set of thermochemical properties including enthalpies (ΔH°f 298), entropies (S°(T)), heat capacities (Cp(T)), and 9374



Article

Table 6. Comparison of Calculated ΔH°f 298 Values for C7H16 Isomers to Available Literature Values this study

literature

species

ΔH°f 298a

ΔH°f 298b

reference

n-C7H16

−45.1 ± 0.6

−44.8 ± 0.3 −44.89 ± 0.19 −44.9 −44.88 −44.74 −44.84 −45.05 −46.5 ± 0.2 −46.60 ± 0.30 −46.59 −46.43 −46.48 −46.49 −47.5 ± 0.3 −47.62 ± 0.30 −46.39 −47.23

45 57 58 19 21 59 c 45 57 19 21 59 c 45 57 59 c

CC(C)CCCC

−46.7 ± 0.6

CC(C)C(C)CC

−47.0 ± 0.6

for the internal rotor potentials, groups used in the GA method calculations, details on our error analysis calculations, work reactions using B3LYP calculations, statistics on comparison of calculated radical enthalpies using different sets of work reactions, and complete citations for abbreviated references. This information is available in the supplemental electronic material, free of charge via the Internet at http://pubs.acs.org.

■

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors acknowledge STTR funding from the U.S. Navy (Contract No. 68335-09-C-0376).

■

REFERENCES

(1) Chen, X. H.; Zhang, M.; Huang, G. H.; Hu, G. Y.; Wang, X.; Xu, G. J. Geochemical Characteristics of Light Hydrocarbons in Cracking Gases from Chloroform Bitumen A, Crude Oil and Its Fractions. Sci. China, Ser. D: Earth Sci. 2009, 52, 26−33. (2) Zhang, M.; Huang, G. H.; Hu, G. Y.; Zhao, H. J. Geochemical Study on Oil-Cracked Gases and Kerogen-Cracked Gases (I)Experimental Simulation and Products Analysis. Sci. China, Ser. D: Earth Sci. 2010, 52, 1−9. (3) Pitz, W. J.; Mueller, C. J. Recent Progress in the Development of Diesel Surrogate Fuels. Prog. Energy Combust. Sci. 2011, 37, 330−350. (4) Westbrook, C. K.; Pitz, W. J.; Herbinet, O.; Curran, H. J.; Silke, E. J. A Comprehensive Detailed Chemical Kinetic Reaction Mechanism for Combustion of n-Alkane Hydrocarbons from nOctane to n-Hexadecane. Combust. Flame 2009, 156, 181−199. (5) Simmie, J. M. Detailed Chemical Kinetic Models for the Combustion of Hydrocarbon Fuels. Prog. Energy Combust. Sci. 2003, 29, 599−634. (6) Curran, H. J.; Gaffuri, P.; Pitz, W. J.; Westbrook, C. K. A Comprehensive Modeling Study of n-Heptane Oxidation. Combust. Flame 1998, 114, 149−177. (7) Curran, H. J.; Gaffuri, P.; Pitz, W. J.; Westbrook, C. K. A Comprehensive Modeling Study of iso-Octane Oxidation. Combust. Flame 2002, 129, 253−280. (8) Curran, H. J.; Pitz, W. J.; Westbrook, C. K.; Callahan, C. V.; Dryer, F. L. Oxidation of Automotive Primary Reference Fuels at Elevated Pressures. Symp. (Int.) Combust., [Proc.] 1998, 27, 379−387. (9) Yuan, T.; Zhang, L.; Zhou, Z.; Xie, M.; Ye, L.; Qi, F. Pyrolysis of n-Heptane: Experimental and Theoretical Study. J. Phys. Chem. A 2011, 115, 1593−1601. (10) Pant, K. K.; Kunzru, D. Pyrolysis of n-Heptane: Kinetics and Modeling. J. Anal. Appl. Pyrolysis 1996, 36, 103−120. (11) Held, T. J.; Marchese, A. J.; Dryer, F. L. A Semi-Empirical Reaction Mechanism for n-Heptane Oxidation and Pyrolysis. Combust. Sci. Technol. 1997, 123, 107−146. (12) Chakraborty, J. P.; Kunzru, D. High Pressure Pyrolysis of nHeptane. J. Anal. Appl. Pyrolysis 2009, 86, 44−52.

a

Lowest energy conformer. b Corresponds to the Boltzmann distribution of conformers. cCalculated using Group Additivity with Gauche and 1,5 interactions.

and higher level composite computational methods. Precision in calculated enthalpies for the B3LYP/6-31G(d,p), B3LYP/6311G(2d,2p), and G3MP2B3 methods was achieved using only work reactions with the same class of radical (primary, secondary, tertiary) for both the target and reference radical. The CBS-QB3 and CBS-APNO methods did not show a decrease in precision when work reactions with all radical classes were utilized. Comparisons of our recommended enthalpies for the parent species with referenced literature data are within chemical accuracy of 1 kcal mol−1. Calculated C−H bond dissociation energies for the radicals are within acceptable limits compared to standard n-alkane primary, secondary, and tertiary bonds but secondary and tertiary C− H bonds in the more highly branched alkanes are shown to have bond energies that are several kcal mol−1 lower than these standard alkanes. Entropies and heat capacities are determined. There is good agreement for our calculation methods to the referenced available literature values when corrections for all internal rotations are accounted for.

■

AUTHOR INFORMATION

Notes

ASSOCIATED CONTENT

S Supporting Information *

Data for the optimized structures, symmetry values, moments of inertia, unscaled vibration frequencies, internal rotor potential energy curves, coefficients for Fourier series used

Figure 2. Nomenclature for Larger Branching Alkanes for Comparison of Bond Dissociation Energies. 9375



Article

Table 7. Isodesmic Work Reactions, Calculated ΔHf °298, and Bond Dissociation Energies for Larger Branching Alkanesa,b ΔH°f 298 (kcal mol−1) isodesmic reactions

CBS-QB3

CC(C2)CC(C2)C CC(C2)CC(C2)C CC(C2)CC(C2)C CC(C2)CC(C2)C CC(C2)CC(C2)C

+ + + + +

CC(C2)CC(C2)C system CH3CH3 → CC(C2)CC CH3CH2CH3 → CC(C2)CC CH3CH2CH3 → CC(C2)CCC CH3CH2CH2CH3 → CC(C2)CC n-C5H12 → CC(C2)CCC

CC(C2)C•C(C2)C CC(C2)C•C(C2)C CC(C2)C•C(C2)C CC(C2)C•C(C2)C CC(C2)C•C(C2)C CC(C2)C•C(C2)C CC(C2)C•C(C2)C CC(C2)C•C(C2)C CC(C2)C•C(C2)C CC(C2)C•C(C2)C

+ + + + + + + + + +

CC(C2)C•C(C2)C system CH4 → C•H3 CH3CH3 → CH3C•H2 CH3CH2CH3 → CH3C•HCH3 CH3CH2CH3 → C•H2CH2CH3 (CH3)3CH → (CH3)3C• CH3CH2CH2CH3 → C•H2CH2CH2CH3 CH3CH2CH2CH3 → CH3C•HCH2CH3 n-C5H12 → C•H2CH2CH2CH2CH3 n-C5H12 → CH3C•HCH2CH2CH3 n-C5H12 → CH3CH2C•HCH2CH3

CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C

+ + + + +

CC(C2)C•(C)C(C)C CC(C2)C•(C)C(C)C CC(C2)C•(C)C(C)C CC(C2)C•(C)C(C)C CC(C2)C•(C)C(C)C CC(C2)C•(C)C(C)C CC(C2)C•(C)C(C)C CC(C2)C•(C)C(C)C CC(C2)C•(C)C(C)C CC(C2)C•(C)C(C)C

+ + + + + + + + + +

CC(C2)C•(C)C(C)C system CH4 → C•H3 CH3CH3 → CH3C•H2 CH3CH2CH3 → CH3C•HCH3 CH3CH2CH3 → C•H2CH2CH3 (CH3)3CH → (CH3)3C• CH3CH2CH2CH3 → C•H2CH2CH2CH3 CH3CH2CH2CH3 → CH3C•HCH2CH3 n-C5H12 → C•H2CH2CH2CH2CH3 n-C5H12 → CH3C•HCH2CH2CH3 n-C5H12 → CH3CH2C•HCH2CH3

CC(C2)C(C)C•(C)C CC(C2)C(C)C•(C)C CC(C2)C(C)C•(C)C CC(C2)C(C)C•(C)C CC(C2)C(C)C•(C)C CC(C2)C(C)C•(C)C CC(C2)C(C)C•(C)C CC(C2)C(C)C•(C)C CC(C2)C(C)C•(C)C CC(C2)C(C)C•(C)C

+ + + + + + + + + +

CC(C2)C(C)C•(C)C system CH4 → C•H3 CH3CH3 → CH3C•H2 CH3CH2CH3 → CH3C•HCH3 CH3CH2CH3 → C•H2CH2CH3 (CH3)3CH → (CH3)3C• CH3CH2CH2CH3 → C•H2CH2CH2CH3 CH3CH2CH2CH3 → CH3C•HCH2CH3 n-C5H12 → C•H2CH2CH2CH2CH3 n-C5H12 → CH3C•HCH2CH2CH3 n-C5H12 → CH3CH2C•HCH2CH3

+ + + + +

+ + + + + + + + + +

(CH3)4C CC(C2)CC (CH3)4C CC(C2)CCC CC(C2)CCC average method average

CC(C2)CC(C2)C CC(C2)CC(C2)C CC(C2)CC(C2)C CC(C2)CC(C2)C CC(C2)CC(C2)C CC(C2)CC(C2)C CC(C2)CC(C2)C CC(C2)CC(C2)C CC(C2)CC(C2)C CC(C2)CC(C2)C average method average CH bond dissociation energy

CC(C2)C(C)C(C)C CH3CH3 → CH3CH2CH3 → CH3CH3 → CH3CH3 → CH3CH2CH3 →

system CC(C2)C(C)C CC(C2)C(C)C CC(C2)CC CC(C2)CC(C)C CC(C2)CC(C)C

9376

+ + + + +

CH3CH2CH2CH3 n-C5H12 n-C5H12 CH3CH2CH3 CH3CH2CH2CH3 average method average

G3MP2B3

−59.11 −59.36 −58.75 −59.10 −58.73 −59.0 −59.1 ±

−59.25 −59.49 −58.91 −59.23 −58.85 −59.1 1.0

−13.48 (−12.36) −13.58 (−12.90) −13.63 −13.38 −13.56 (−12.93) −13.40 (−13.52) −13.52 (−12.89) −13.45 −13.23 −13.74 (−12.79) −13.51 −13.31 −13.47 −13.27 −13.5 −13.3 −13.4 ± 2.2 97.8 ± 2.2 −57.50 −57.51 −58.09 −58.19 −58.09 −57.9 −57.9 ±

−57.59 −57.62 −58.23 −58.24 −58.15 −58.0 0.9

+ + + + + + + + + +

CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C average method average CH bond dissociation energy

−15.63 (−14.14) −15.73 (−14.68) −15.77 −15.16 −15.71 (−14.70) −15.55 −15.29 −15.67 (−14.67) −15.60 −15.01 −15.88 (−14.57) −15.66 −15.09 −15.62 −15.05 −15.7 −15.1 −15.4 ± 2.2 94.6 ± 2.2

+ + + + + + + + + +

−15.93 (−14.57) −16.03 (−15.11) −16.08 −15.59 −16.01 (−15.13) −15.85 −15.72 −15.97 (−15.09) −15.90 −15.44 −16.19 (−14.99) −15.96 −15.52 −15.92 −15.48 −16.0 −15.5 −15.8 ± 2.2 94.3 ± 2.2

CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C)C average method average CH bond dissociation energy



Article

Table 7. continued ΔH°f 298 (kcal mol−1) isodesmic reactions

a

CBS-QB3

CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C

+ + + + + + + + +

CC(C2)C(C)C(C2)C system CH3CH3 → CC(C2)CC CH3CH2CH3 → CC(C2)CC CH3CH2CH2CH3 → CC(C2)CCC CH3CH3 → CC(C2)CCC (CH3)3CH → CC(C2)C(C)CC (CH3)4C → CC(C2)C(C)CC CH3CH2CH2CH3 → CC(C2)C(C)C n-C5H12 → CC(C2)C(C)CC n-C6H14 → CC(C2)C(C)CC

CC(C2)C•(C)C(C2)C CC(C2)C•(C)C(C2)C CC(C2)C•(C)C(C2)C CC(C2)C•(C)C(C2)C CC(C2)C•(C)C(C2)C CC(C2)C•(C)C(C2)C CC(C2)C•(C)C(C2)C CC(C2)C•(C)C(C2)C CC(C2)C•(C)C(C2)C CC(C2)C•(C)C(C2)C

+ + + + + + + + + +

CC(C2)C•(C)C(C2)C system CH4 → C•H3 CH3CH3 → CH3C•H2 CH3CH2CH3 → CH3C•HCH3 CH3CH2CH3 → C•H2CH2CH3 (CH3)3CH → (CH3)3C• CH3CH2CH2CH3 → C•H2CH2CH2CH3 CH3CH2CH2CH3 → CH3C•HCH2CH3 n-C5H12 → C•H2CH2CH2CH2CH3 n-C5H12 → CH3C•HCH2CH2CH3 n-C5H12 → CH3CH2C•HCH2CH3

+ + + + + + + + + +

CC(C2)CC CC(C2)CCC CC(C2)CCC (CH3)4C CC(C2)CC CC(C2)C(C)C CC(C2)C(C)C CC(C2)C(C)C CC(C2)C(C)CC average method average

CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C CC(C2)C(C)C(C2)C average method average CH bond dissociation energy

−59.92 −59.56 −59.30 −59.31 −58.71 −58.33 −58.85 −58.27 −58.04 −58.9 −59.0 ±

−60.13 −59.78 −59.53 −59.55 −58.89 −58.46 −59.00 −58.39 −58.13 −59.1 1.5

−15.96 (−14.48) −16.05 (−15.02) −16.10 −15.50 −16.04 (−15.04) −15.87 −15.63 −15.99 (−15.00) −15.92 −15.35 −16.21 (−14.90) −15.98 −15.43 −15.94 −15.39 −16.0 −15.5 −15.7 ± 2.7 95.4 ± 2.7

Values in parentheses are not utilized in calculation of the enthalpies of formation. bLowest Energy Conformer. (19) Huffman, H. M.; Gross, M. E.; Scott, D. W.; McCullough, J. P. Low Temperature Thermodynamic Properties of Six Isomeric Heptanes. J. Phys. Chem. 1961, 65, 495−503. (20) Zheng, J.; Yu, T.; Truhlar, D. G. Multi-Structural Thermodynamics of C-H Bond Dissociation in Hexane and Isohexane Yielding Seven Isomeric Hexyl Radicals. Phys. Chem. Chem. Phys. 2011, 13, 19318−19324. (21) Karton, A.; Gruzman, D.; Martin, J. M. L. Benchmark Thermochemistry of the CnH2n+2 Alkane Isomers (n = 2−8) and Performance of DFT and Composite Ab Initio Methods for Dispersion-Driven Isomeric Equilibria. J. Phys. Chem. A 2009, 113, 8434−8447. (22) Gruzman, D.; Karton, A.; Martin, J. M. L. Performance of Ab Initio and Density Functional Methods for Conformational Equilibria of CnH2n+2 Alkane Isomers (n = 4−8). J. Phys. Chem. A 2009, 113, 11974−11983. (23) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (24) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (25) Hudzik, J. M.; Asatryan, R.; Bozzelli, J. W. Thermochemical Properties of exo-Tricyclo[5.2.1.02,6]decane (JP-10 Jet Fuel) and Derived Tricyclodecyl Radicals. J. Phys. Chem. A 2010, 114, 9545− 9553. (26) Hudzik, J. M.; Bozzelli, J. W. Structure and Thermochemical Properties of 2-Methoxyfuran, 3-Methoxyfuran, and Their CarbonCentered Radicals Using Computational Chemistry. J. Phys. Chem. A 2010, 114, 7984−7995. (27) Baboul, A. G.; Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-3 Theory Using Density Functional Geometries and ZeroPoint Energies. J. Chem. Phys. 1999, 110, 7650−7657.

Table 8. Summary of Calculated Secondary and Tertiary C−H BDEsa bond dissociation energy location

a

+ + + + + + + + +

G3MP2B3

species

secondary

tertiary

n-C7H16 CC(C)CCCC CC(C)C(C)CC CC(C2)CC(C)C CC(C2)CC(C2)C CC(C2)C(C)C(C)C CC(C2)C(C)C(C2)C

98.6, 98.8, 98.8 98.4, 98.6, 98.9 97.7 97.3 97.8

96.6 95.4, 96.4 94.2 94.3, 94.6 95.4

Units of kcal mol−1.

(13) Chaos, M.; Kazakov, A.; Zhao, Z.; Dryer, F. L. A HighTemperature Chemical Kinetic Model for Primary Reference Fuels. Int. J. Chem. Kinet. 2007, 39, 399−414. (14) Benson, S. W. Thermochemical Kinetics, 2nd ed.; WileyInterscience: New York, NY, 1976. (15) Westbrook, C. K.; Pitz, W. J.; Curran, H. J. Chemical Kinetic Modeling Study of the Effects of Oxygenated Hydrocarbons on Soot Emissions from Diesel Engines. J. Phys. Chem. A 2006, 110, 6912− 6922. (16) Silke, E. J.; Pitz, W. J.; Westbrook, C. K.; Ribaucour, M. Detailed Chemical Kinetic Modeling of Cyclohexane Oxidation. J. Phys. Chem. A 2007, 111, 3761−3775. (17) Westbrook, C. K.; Pitz, W. J.; Curran, H. C.; Boercker, J.; Kunrath, E. Chemical Kinetic Modeling Study of Shock Tube Ignition of Heptane Isomers. Int. J. Chem. Kinet. 2001, 33, 868−877. (18) Pitzer, K. S. The Thermodynamics of n-Heptane and 2,2,4Trimethylpentane, including Heat Capacities, Heats of Fusion and Vaporization and Entropies. J. Am. Chem. Soc. 1940, 62, 1224−1227. 9377



Article

Table 9. Comparison of Calculated Entropy and Heat Capacities for C7H16 Parent Species to Other Available Literature Valuesa Cp(T)b species n-C7H16 (18)

CC(C)CCCC (27)

CC(C)C(C)CC (81)

S°298

b

102.18 105.05 102.27 102.29 102.78c 100.87 103.70 100.38 100.48 101.33c 99.56 99.44 98.96 99.08

300 K

400 K

500 K

600 K

800 K

1000 K

1500 K

method

39.88 39.56 39.86 39.67 40.42 39.61 39.72 39.86 39.52 40.28 39.34 39.91 39.86 38.68

50.43 49.24 50.42 50.35 50.74 50.37 49.83 50.42 50.66 50.98 50.31 49.88 50.42 50.44

60.05 58.49 60.07 60.25 60.25 60.12 59.16 60.07 60.66 60.46 60.19 59.11 60.07 60.64

68.33 66.62 68.33 68.7 68.41 68.47 67.24 68.33 69.2 68.59 68.61 67.14 68.33 69.3

81.39 79.70 81.43 81.8 81.40 81.58 80.18 81.43 82.6 81.49 81.77 80.04 81.43 83.1

91.24 89.60 91.20 91.2 91.18 91.38 89.96 91.20 92.4 91.20 91.52 89.81 91.20 93.5

106.16 105.20

GA SMCPS/ROTATOR ref 63 ref 59 ref 64 GA SMCPS/ROTATOR ref 63 ref 59 ref 64 GA SMCPS/ROTATOR ref 63 ref 59

106 106.52 106.52 105.39 108 106.48 106.88 105.28 110

Symmetry values are given in parentheses, values are for lowest energy conformers. bUnits of cal mol−1 K−1. cSubtracted 0.026 cal mol−1 K−1 from referenced value to convert from a standard pressure of 1 bar to 1 atm.

a

Table 10. Calculated Entropy and Heat Capacities for C7H16 Radical Species Cp(T)a

a

species

S°298

a

300 K

400 K

500 K

600 K

800 K

1000 K

1500 K

C•CCCCCC CC•CCCCC CCC•CCCC CCCC•CCC C•C(C)CCCC CC•(C)CCCC CC(C)C•CCC CC(C)CC•CC CC(C)CCC•C CC(C)CCCC• C•C(C)C(C)CC CC•(C)C(C)CC CC(C)C•(C)CC CC(C)C(C•)CC CC(C)C(C)C•C CC(C)C(C)CC•

111.59 111.06 111.44 110.88 107.08 106.93 106.72 105.78 106.40 107.25 102.42 103.60 103.90 102.16 100.27 102.51

38.60 37.54 37.02 37.74 40.11 36.80 38.72 38.83 38.80 38.98 39.99 37.40 36.85 40.48 40.05 40.49

48.12 46.99 46.76 47.37 49.38 46.09 48.25 48.51 48.15 48.73 49.57 46.86 46.51 49.84 49.67 49.75

57.02 55.96 55.84 56.34 58.00 55.03 57.03 57.37 56.92 57.64 58.31 55.77 55.48 58.47 58.33 58.29

64.73 63.78 63.69 64.09 65.48 62.90 64.61 65.00 64.55 65.29 65.81 63.55 63.27 65.91 65.76 65.69

76.99 76.30 76.22 76.47 77.43 75.58 76.74 77.14 76.81 77.42 77.74 76.04 75.74 77.77 77.60 77.53

86.21 85.72 85.63 85.80 86.47 85.15 85.92 86.30 86.06 86.53 86.73 85.46 85.17 86.73 86.58 86.52

100.73 100.50 100.42 100.49 100.81 100.17 100.48 100.75 100.65 100.89 100.97 100.31 100.07 100.95 100.85 100.81

Units of cal mol−1 K−1.

(28) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. Gaussian-3 (G3) Theory for Molecules Containing First and Second-Row Atoms. J. Chem. Phys. 1998, 109, 7764−7776. (29) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K.; Rassolov, V.; Pople, J. A. Gaussian-3 Theory Using Reduced Møller-Plesset Order. J. Chem. Phys. 1999, 110, 4703−4709. (30) Montgomery, J. A., Jr; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VI. Use of Density Functional Geometries and Frequencies. J. Chem. Phys. 1999, 110, 2822−2827. (31) Montgomery, J. A., Jr; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VII. Use of the Minimum Population Localization Method. J. Chem. Phys. 2000, 112, 6532−6542. (32) Ochterski, J. W.; Petersson, G. A.; Montgomery, J. A., Jr A Complete Basis Set Model Chemistry. V. Extensions to Six or More Heavy Atoms. J. Chem. Phys. 1996, 104, 2598−2619. (33) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr, ; Vreven, T.; Kudin, K. N.; Burant, J. C. et al. Gaussian 03, Revision D.01; Gaussian, Inc.: Wallingford, CT, 2003.

(34) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, Revision C.01; Gaussian, Inc.: Wallingford, CT, 2009. (35) Sheng, C. Ph.D. Dissertation. Department of Chemical Engineering, New Jersey Institute of Technology, Newark, NJ, 2002. (36) Scott, A. P.; Radom, L. Harmonic Vibrational Frequencies: An Evaluation of Hartree-Fock, Moller-Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors. J. Phys. Chem. 1996, 100, 16502−16513. (37) Hudzik, J. M.; Bozzelli, J. W. Calculated Entropies for nHeptane, 2-Methylhexane, 2,3-Dimethylpentane, and Radicals from the Loss of H Atoms. Adv. Phys. Chem. 2013, 2013, 7. (38) Lay, T. H.; Krasnoperov, L. N.; Venanzi, C. A.; Bozzelli, J. W.; Shokhirev, N. V. Ab Initio Study of α-Chlorinated Ethyl Hydroperoxides CH3CH2OOH, CH3CHClOOH, and CH3CCl2OOH: Conformational Analysis, Internal Rotation Barriers, Vibrational Frequencies, and Thermodynamic Properties. J. Phys. Chem. 1996, 100, 8240−8249. (39) Hudzik, J. M.; Bozzelli, J. W. Thermochemistry and Bond Dissociation Energies of Ketones. J. Phys. Chem. A 2012, 116, 5707− 5722. 9378



Article

(60) Luo, Y.-R. Comprehensive Handbook of Chemical Bond Energies; CRC Press: Boca Raton, FL, 2007. (61) Bauschlicher, C. W. The Bond Dissociation Energies of 1Butene. Chem. Phys. Lett. 1995, 239, 252−257. (62) Feng, Y.; Liu, L.; Wang, J. T.; Zhao, S. W.; Guo, Q. X.; Homolytic, C.-H.; Bond, N.-H. Dissociation Energies of Strained Organic Compounds. J. Org. Chem. 2004, 69, 3129−3138. (63) Stull, D. R.; Westrum, E. F., Jr.; Sinke, G. C. The Chemical Thermodynamics of Organic Compounds; Wiley: New York, NY, 1969. (64) Yu, T.; Zheng, J.; Truhlar, D. G. Statistical Thermodynamics of the Isomerization Reaction Between n-Heptane and iso-Heptane. Phys. Chem. Chem. Phys. 2012, 14, 482−494.

(40) Leplat, N.; Rossi, M. J. The Reinvestigation of the Kinetics of the Metathesis Reactions t-C4H9• + HBr (HI) → i-C4H10+ Br•(I•) and of the t-C4H9• Free Radical Thermochemistry. J. Phys. Chem. A 2014, 118, 5135−5148. (41) Martin, J. M. L.; De Oliveira, G. Towards Standard Methods for Benchmark Quality ab initio Thermochemistry - W1 and W2 Theory. J. Chem. Phys. 1999, 111, 1843−1856. (42) Parthiban, S.; Martin, J. M. L. Assessment of W1 and W2 Theories for the Computation of Electron Affinities, Ionization Potentials, Heats of Formation, and Proton Affinities. J. Chem. Phys. 2001, 114, 6014−6029. (43) Barnes, E. C.; Petersson, G. A.; Montgomery, J. A., Jr; Frisch, M. J.; Martin, J. M. L. Unrestricted Coupled Cluster and Brueckner Doubles Variations of W1 Theory. J. Chem. Theory Comput. 2009, 5, 2687−2693. (44) Cox, J. D.; Wagman, D. D.; Medvedev, V. A. CODATA Key Values for Thermodynamics; Hemisphere Publishing, Corp.: New York, NY, 1989. (45) Pedley, J. B. Thermochemical Data and Structures of Organic Compounds; Thermodynamics Research Center: College Station, TX, 1994. (46) Snitsiriwat, S.; Bozzelli, J. W. Thermochemical Properties for Isooctane and Carbon Radicals: Computational Study. J. Phys. Chem. A 2013, 117, 421−429. (47) Goos, E.; Burcat, A.; Ruscic, B.; Extended Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion with Updates from Active Thermochemical Tables, March 2014. http://garfield.Chem.elte.Hu/Burcat/burcat.html. (48) Blanksby, S. J.; Ellison, G. B. Bond Dissociation Energies of Organic Molecules. Acc. Chem. Res. 2003, 36, 255−263. (49) Goldsmith, C. F.; Magoon, G. R.; Green, W. H. Database of Small Molecule Thermochemistry for Combustion. J. Phys. Chem. A 2012, 116, 9033−9057. (50) Baulch, D. L.; Bowman, C. T.; Cobos, C. J.; Cox, R. A.; Just, T.; Kerr, J. A.; Pilling, M. J.; Stocker, D.; Troe, J.; Tsang, W.; et al. Evaluated Kinetic Data for Combustion Modeling: Supplement II. J. Phys. Chem. Ref. Data 2005, 34, 757−1397. (51) Chase, M. W., Jr. NIST-JANAF Thermochemical Tables. J. Phys. Chem. Ref. Data, Monogr. 1998, 9, 1−1951. (52) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. In Ion Energetics Data in NIST Chemistry WebBook, NIST Standard Reference Database Number 69; Linstrom, P. J., Mallard, W. G., Eds.; National Institute of Standards and Technology: Gaithersburg, MD, http://webbook.nist.gov. (53) Nicovich, J. M.; Van Dijk, C. A.; Kreutter, K. D.; Wine, P. H. Kinetics of the Reactions of Alkyl Radicals with Hydrogen Bromide and Deuterium Bromide. J. Phys. Chem. 1991, 95, 9890−9896. (54) Seetula, J. A.; Slagle, I. R. Kinetics and Thermochemistry of the R + HBr ⇄ RH + Br (R = n-C3H7, iso-C3H7, n-C4H9, iso-C4H9, secC4H9 or tert-C4H9) Equilibrium. J. Chem. Soc., Faraday Trans. 1997, 93, 1709−1719. (55) Tsang, W. The Stability of Alkyl Radicals. J. Am. Chem. Soc. 1985, 107, 2872−2880. (56) Seakins, P. W.; Pilling, M. J.; Niiranen, J. T.; Gutman, D.; Krasnoperov, L. N. Kinetics and Thermochemistry of R+HBr ⇄ RH +Br Reactions: Determinations of the Heat of Formation of C2H5, iC3H7, sec-C4H9, and t-C4H9. J. Phys. Chem. 1992, 96, 9847−9855. (57) Prosen, E. J.; Rossini, F. D. Heats of Combustion and Formation of the Paraffin Hydrocarbons at 25°C. J. Res. Natl. Bur. Stand. (U. S.) 1945, 34, 263−269. (58) Furka, Á . Relative Energy of Organic Compounds I. Hydrocarbons and Their Oxygen Derivatives. Struct. Chem. 2009, 20, 587−604. (59) Scott, D. W. Chemical Thermodynamic Properties of Hydrocarbons and Related Substances. Properties of the Alkane Hydrocarbons, C1 through C10 in the Ideal Gas State from 0 to 1500 K; Bulletin 666 for the U.S. Bureau of Mines, National Technical Information Service: Alexandria, VA, 1974. 9379


Thermochemistry of C7H16 to C10H22 Alkane Isomers: Primary

Recommend Documents