Thermochemical Properties of exo-Tricyclo[5.2.1.02,6]decane (JP-10

10.1021/jp1049556. Publication Date (Web): August 16, 2010. Copyright © 2010 American Chemical Society. Cite this:J. Phys. Chem. A 114, 35, 9545-...
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Thermochemical Properties of exo-Tricyclo[5.2.1.02,6]decane (JP-10 Jet Fuel) and Derived Tricyclodecyl Radicals Jason M. Hudzik, Rubik Asatryan, and Joseph W. Bozzelli* Chemistry, Chemical Engineering and EnVironmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102 ReceiVed: May 30, 2010; ReVised Manuscript ReceiVed: July 29, 2010

exo-Tricyclo[5.2.1.02,6]decane (TCD) or exo-tetrahydrodicyclopentadiene is the principal component of the high-energy density hydrocarbon fuel commonly identified as JP-10. Thermodynamic parameters for the parent TCD molecule and of all the tricyclodecyl radicals corresponding to the loss of hydrogen atoms from different carbons sites (TCD-Ri with i indicating the given carbon center) are determined using several density functional theory and G3MP2B3 and CBS-QB3 higher level composite computational chemistry methods. Five isodesmic work reactions, three involving bridged hydrocarbon reference molecules with similar ring strains, are employed to produce a cancelation of systematic calculation errors in evaluation of standard, gas-phase formation enthalpies at 298 K. ∆fH°298 for TCD is found to be -19.5 ( 1.3 kcal mol-1, which is several kcal mol-1 lower than the commonly used values. Ci-H bond energies for corresponding TCD carbon sites are evaluated as follows: TCD-R1, 107.2; TCD-R2, 100.1; TCD-R3, 98.0; TCD-R4, 98.5; TCD-R9, 98.7; TCD-R10, 104.1 kcal mol-1. Results from use of five different DFT methods are in very good agreement with composite level values for all work reactions used for the radicals. The exo and endo isomers of TCD are both determined to have chair and boat conformers. Introduction exo-Tricyclo[5.2.1.02,6]decane (TCD), alternately named exo-tetrahydrodicyclopentadiene, is the principal component of the high-energy density hydrocarbon fuel JP-10 synthetically produced from the hydrogenation of dicyclopentadiene.1 The compound’s strained cyclic geometry allows for efficient energy storage and high thermal stability leading to its use as a missile fuel.2-5 TCD is also a component in lubricating and cutting oils, paint solvents, waxes, and semiconductor washing agents.6,7 Although this is a single-component fuel, the compound’s size and intricacy, viz., three rings with several strained carbon sites, results in complexity in trying to understand its reactions. The need to properly account for all the important and multifaceted product channels in combustion, thermal decomposition, atmospheric chemistry, and pyrolysis models results in significant complexity. Several researchers have used molecular dynamics, multielement flux analysis, and experimental conditions including high-temperature thermal decomposition, and cracking of JP-10 at various temperatures and pressures using spectroscopic, GC, and mass spectrometric analysis procedures to try and identify the important, initial products.3-5,8-11 Somewhat controversial observations in different studies have resulted in a wide range of varied products. The knowledge of the accurate thermochemistry of TCD is an important initial data set to the understanding of its combustion chemistry and reaction kinetics. Screening of the literature reveals one experimental study reporting the enthalpy of combustion and formation for the gas phase,12 one study for liquid phase,13 one high-level ab initio computational study,14 and estimated bond energies interpreted as based as secondary and tertiary bond energies in

simple nonstrained hydrocarbons.9 The experimentally determined gas phase ∆fH°298(g) of TCD is -14.38 ( 0.90 kcal mol-1 as reported by Boyd et al.12 in 1971, which Chickos et al.15 indicates is the endo isomer. This value is used in the kinetic mechanisms used to model JP-10 pyrolysis by Herbinet et al.9 Chenowidth et al.3 used the Boyd et al. strain energy data in their force field dynamics modeling of pyrolysis. Smith and Good13 report a liquid phase enthalpy of -29.35 ( 0.35 kcal mol-1 for the exo isomer at 298.15 K. Chickos et al.15 have determined vaporization enthalpies of 12.0 and 11.7 kcal mol-1 at 298.15 K for endo- and exo-tetrahydrodicyclopentadiene (TCD) by correlation gas chromatography. They also report gas phase enthalpies of formation of -17.6 ( 0.6 kcal mol-1 for the exo and -14.8 ( 0.8 kcal mol-1 for the endo isomer. Zehe and Jaffe14 have recently determined gas-phase formation enthalpies, ∆fH°298, of -18.5 and -15.4 kcal mol-1 for the exo- and endo-TCD isomers from the averages generated using an isodesmic bond separation reaction G3(MP2), G3(MP2)// B3LYP, and CBS-QB3. These values with the heat of vaporization values from Chickos et al.15 yield liquid phase enthalpies of formation of -30.2 kcal mol-1 for the exo and -27.4 kcal mol-1 for the endo isomers. We are not aware of any reported or calculated bond dissociation energies (BDE) for TCD; we interpret the work of Herbinet et al. as possible use of generic primary, secondary, and tertiary bond energies (ca. 101.1, 98.5, 96.5 kcal mol-1, respectively). The bond energies are particularly interesting because of the high strain in the molecule. It is, for example, well established that the bond energy on cyclopropane16,17 at 106 kcal mol-1 is 8.5 kcal mol-1 higher than that of a normal secondary C-H bond energy (98.5 kcal mol-1) due to the strain

10.1021/jp1049556  2010 American Chemical Society Published on Web 08/16/2010

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Figure 3. Conformations of endo-TCD.

Figure 1. Numbering scheme for carbon and hydrogen sites of TCD.

TCD TS) for the interconversion between chair and boat conformers in the exo-TCD isomer is also calculated. exo-TCD TST is the first-order transition state with one relatively low negative (imaginary) frequency at -163 cm-1. The Supporting Information includes the optimized geometry parameters, moments of inertia, and vibrational frequencies calculated at the B3LYP/6-31G(d,p) level, for these isomers. The B3LYP/631G(d,p), CBS-QB3, and G3MP2B3 levels of theory were further used for the thermochemical enthalpy analysis of these isomers. The main compound of interest in this analysis, exo-TCD chair, is referred to as TCD throughout the rest of this paper. Computational Methods

Figure 2. Conformations of exo-TCD.

of the C3-ring. Analysis of these properties will enable a better understanding of reaction paths and detailed chemical kinetic mechanisms. In this study we determine the enthalpy of formation of the TCD parent molecule and the radicals corresponding to endo and exo positions at each carbon site. Bond energies determined for the TCD radicals are shown to follow trends known for molecules having carbons with similar ring strain and only a few sites follow conventional normal secondary and tertiary bond energies from smaller hydrocarbons. Entropy and heat capacity values, as a function of temperature, are also determined for each system. NASA polynomials of the thermodynamic data from TCD and tricyclodecyl radicals are calculated. Throughout this article abbreviations are utilized as illustrated below: y represents a cyclic structure of compound; yy represents a bicyclic ring structure; j represents the radical site on a preceding carbon atom; en (endo) represents the hydrogen position pointing toward the peak -ch2- group on the bridging carbon; ex (exo) is pointing away. Isomers of TCD TCD exists in either exo or endo form depending on the respective hydrogen atom/cyclopentane ring positions relative to the single CH2 bridge carbon of the cyclohexane moiety in the molecule. In addition, there are chair and boat conformations for each of these two isomers. This results from the CH2 group at C(4) position flop in this nonbridged cyclopentane ring; see Figure 1 for numbering scheme. Figures 2 and 3 illustrate the exo and endo isomers along with their respective chair/boat conformations. The energy of the transition state structure (exo-

Structural parameters for this set of compounds were optimized at the B3LYP/6-31G(d,p) level of theory.18,19 Bond dissociation energies and heats of formation are determined from isodesmic reactions at the B3LYP, BB1K,20 MPWB1K,21 and BMK22 levels of theory in conjunction with the moderate 6-31G(d,p) basis set. The larger 6-311G(2d,2p) basis set including additional polarization functions on carbon and hydrogen atoms is also employed with the B3LYP hybrid DFT functional. This popular method combines the threeparameter Becke exchange functional, B3, with the LeeYang-Parr correlation functional, LYP. BB1K is an abbreviation for Becke88-Becke95 one-parameter model for kinetics. MPWB1K is based on the modified Perdew and Wang 1991 exchange functional and Becke’s 1995 meta correlation functional. BMK, Boese-Martin for Kinetics, is a hybrid-meta generalized gradient approximation (HM-GGA) method which includes kinetic energy density. All selected in current work methods have been designed for thermochemical kinetics calculations. Higher level ab initio and DFT-based composite methods G3MP2B323,24 and CBS-QB325 are also utilized in work reaction calculations which are more reliable in predicting accurate energies as shown in our previous studies.26,27 G3MP2B3 is a modified version of the G3MP228 method where the geometries and zero-point vibration energies are from B3LYP/6-31G(d) calculations. CBS-QB3 uses the B3LYP/6-311G(2d,d,p) level to calculate geometries and frequencies followed by several single point energy calculations at the MP2, MP4SDQ, and CCSD(T) levels. The final energies are determined with a CBS extrapolation. CBS-QB3 is considered a complete basis set method that is practical for the molecules and radicals in this study. All calculations were performed using the Gaussian 03 program suite.29 Accurate calculation of the gas phase enthalpy of formation can be achieved with DFT and use of work reactions where the bonding environment for the products and reactions are

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TABLE 1: Isodesmic Reactions and Calculated Enthalpies of Formations for TCDa ∆fH°298 (kcal mol-1) B3LYP

isodesmic reactions TCD System TCD + yc4h8 f yyc7h12 + yyc7h12 TCD + yc5h10 f yyc7h12 + yyc8h14 TCD + yc6h12 f yyc8h14 + yyc8h14 TCD + 3 ch3ch3 f 3 yc4h8 + ch3ch2ch2ch3 TCD + 4 ch3ch3 f 2 ch3ch2ch2ch3 + yc4h8 + 2 yc4h8 average atomization Osmont et al. corrected atomization a

BB1K MPWB1K BMK 6-31G(d,p) 6-311G(2d,2p) 6-31G(d,p) 6-31G(d,p) 6-31G(d,p) CBS-QB3 G3MP2B3 -19.34 -19.01 -19.95

-19.28 -19.39 -20.12

-20.09 -20.06 -22.10

-19.97 -19.85 -21.90

-20.81 -20.56 -21.99

-17.50 -18.56 -20.19 -20.23 -20.96

-17.58 -18.59 -20.26 -20.00 -20.73

-19.43 -5.22 -15.0

-19.59

-20.75

-20.57

-21.12

-19.49 -14.92

-19.43 -18.35

Zehe and Jaffe14 value from work reaction analysis -18.5 kcal mol-1.

SCHEME 1

DFT/work reaction methods. Higher level computation methods are continually under development and modification for improved accuracy of calculated energies, and advances in computing power help offset the very high computational cost of these methods. Comparison between results of multilevel and single level DFT calculations for the set of carefully selected isodesmic reactions, which include similar strained ring species on both sides of the reactions, show excellent agreement for enthalpy of formations and bond energies (vide infra). The absolute enthalpy of formation for all C-H radical sites and the parent exo-TCD were separately determined in this study. The corresponding C-H bond enthalpies were then determined from the bond cleavage reaction

R-H f R• + H•

similar on both sides of the reaction equation for cancellation of systematic errors. This allows for a more accurate enthalpy of formation for the DFT methods.24 Composite G3, G3MP2B3, and CBS-QB3 high-level quantum chemistry methods also provide accurate thermochemical properties.30 While DFT methods are popular in this type of analysis due to lower computation costs, their accuracy is not as high as the results of multilevel methods.24,31-33 Errors, which may seem insignificant in small molecule systems, compound as the size of the molecule increases. To improve accuracy in use of DFT calculations, the isodesmic work reactions are routinely used. Comparison with experimental data or higher level calculations allows for the validation of these combined

(1)

using the respective parent and radical site ∆fH°298 along with the established literature value of 52.1 kcal mol-1 for the hydrogen atom.34 Differences in bond energy for a compound are important to determine the reaction pathways and kinetics at the specific radical sites. The radical’s stability often determines the relative energy needed to cleave a C-H or a C-C bond in beta scission reactions. The Statistical Mechanics for Heat Capacity and Entropy (SMCPS) program35 is utilized to calculate the entropy and heat capacities for the JP-10 (TCD) molecule and corresponding tricyclodecyl radicals using the B3LYP/6-31G(d,p) level of theory. The SMCPS program uses geometry, mass, electron degeneracy, symmetry, frequencies, number of optical isomers, and moments of inertia as input parameters for each compound. Entropy and heat capacity values are

TABLE 2: Reaction Enthalpies for Isodesmic Reactions Used in TCD Analysis ∆H°rxn

isodesmic reactions TCD System TCD + yc4h8 f yyc7h12 + yyc7h12 TCD + yc5h10 f yyc7h12 + yyc8h14 TCD + yc6h12 f yyc8h14 + yyc8h14 TCD + 3 ch3ch3 f 3 yc4h8 + ch3ch2ch2ch3 TCD + 4 ch3ch3 f 2 ch3ch2ch2ch3 + yc4h8 + 2 yc3h6

B3LYP BB1K MPWB1K BMK 6-31G(d,p) 6-311G(2d,2p) 6-31G(d,p) 6-31G(d,p) 6-31G(d,p) CBS-QB3 G3MP2B3 -13.48 0.51 2.10

-13.54 0.89 2.27

-12.73 1.56 4.25

-12.85 1.35 4.05

-12.01 2.06 4.14

-15.32 0.06 2.34 70.14 73.10

-15.24 0.09 2.41 69.91 72.87

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SCHEME 2

Hudzik et al. TABLE 3: Standard Enthalpies of Formation for Reference Species in Isodesmic Reactions

determined from temperatures of 1-5000 K and presented in the Appendix. Results and Discussion A series of hypothetical, isodesmic work reactions containing similar bond environments on both sides of the equations were utilized to reduce systematic errors from each level of theory in calculating the enthalpies of formation for target compounds. ∆f H°298 has been calculated using the B3LYP, BB1K, MPWB1K, and BMK methods with the 6-31G(d,p) basis set. The larger basis set, 6-311G(2d,2p), is also utilized with B3LYP functional. These results are compared with the results from the G3MP2B3 and CBS-QB3 levels of theory. Figure 1 illustrates the numbering for carbon atoms in TCD, where carbon 1 represents the highly strained bridge carbons to the three rings. Table 1 describes five work reactions for the TCD parent compound where three equations have near identical bond environments with similar strained bridged molecules on each side and lists the calculated standard enthalpy values. The last two reactions use smaller molecules, where the reactions do not incorporate bridged hydrocarbons in the products. These latter two reactions using smaller molecules are more common in the published literature for enthalpy determination studies.36,37 The work reactions for enthalpy determination are illustrated in Scheme 1. Enthalpies for the TCD work reactions are listed in Table 2. Equations for the analysis of target radical enthalpy values include given radical and the parent on both sides along with the smaller, representative hydrocarbon molecules and their corresponding radicals with accurately known enthalpies. Here the TCD radical (TCD-Ri with i indicating the given carbon center) plus a hydrocarbon (HC) molecule is set equal to a HC radical plus the TCD parent. Thus the absolute value of the radical enthalpy is calculated separately. The reactions for the tricyclodecyl radicals are illustrated in Scheme 2. The well established heat of formation literature values for the reference species are listed in Table 3. Table 4 has a summary of the abbreviations for the cyclic compound nomenclature also found in the work reactions. Supporting Information has the optimized geometry parameters, moments of inertia, and vibrational frequencies at the B3LYP/6-31G(d,p) level for TCD and Tricyclodecyl radicals from this study. Heat of Formation ∆f H°298. Tables 1 and 5 show that there is a good correlation for the ∆fH°298 values between each of the DFT methods and the higher level calculations for TCD and its radicals, when using the work reactions that contain a balance of ring strain on each side. The radicals formed do not reveal differences in energy for the exo and endo positions for any of the calculation methods, which indicates that the radical formed from loss of either the endo or exo H atom site is identical in structure. For the DFT methods it is seen that there is a maximum difference of 0.26 kcal mol-1 for the B3LYP method when comparing the average results at the 6-31G(d,p) and the triple-ζ 6-311G(2d,2p) basis sets for the parent and radicals. For the

b

species

∆fH°298 (kcal mol-1)

ref

h ch4 ch3ch3 ch3ch2ch3 (ch3)3ch ch3ch2ch2ch3 yc3h6 yc4h8 yc5h10 yc6h12 yyc7h12 yyc8h14 ch3cjh2 ch3cjhch3 (ch3)3cj ch3cjhch2ch3 yycj7h11

52.10 ( 0.001 -17.78 ( 0.1 -20.03 ( 0.07 -25.02 ( 0.12 -32.07 ( 0.14 -30.04 ( 0.14 12.74 ( 0.12 6.62 ( 0.26 -18.26 ( 0.17 -29.47 ( 0.19 -13.1 ( 1.1 -23.66 ( 0.26 29.0 ( 0.4 21.5 ( 0.4 12.3 ( 0.4 16.1 ( 0.5 33.9b

34 38 38 38 38 38 38 38 38 38 38 38 39 39 39 39 a

a See Supporting Information for the enthalpy calculation data. Error not reported.

TABLE 4: Nomenclature of Cyclic Species As Used in Work Reactions

BB1K, MPWB1K, and BMK there is a larger difference of 0.94 kcal mol-1 between the averages of these methods using the same 6-31G(d,p) basis set. The difference between the average energy values for all five DFT methods is consistent within 1 kcal mol-1 with the exception of the parent compound which is slightly higher at 1.7 kcal mol-1 due to an overestimate by the BMK method. The CBS-QB3 and G3MP2B3 higher level calculations are significantly more consistent with a maximum difference of 0.45 kcal mol-1 where a majority of the calculations are approximately 0.1 kcal mol-1. The close agreement between these two high level composite methods also suggests accuracy in addition to the obvious precision. Table 6 lists the average values for the combined five DFT methods and for the combined CBS-QB3 and G3MP2B3 methods. It can be seen overall that the DFT level of theory provides an acceptable analysis result, as compared to higher level calculations with a maximum difference of 1.2 kcal mol-1, when the work reaction includes balance of ring strain. ∆H(298) values for the radical work reactions vs calculation method are listed in the Supporting Information. We recommend the following enthalpy of formation values of -19.5, 35.7, 28.5, 26.4, 27.0, 27.1, and 32.5 kcal mol-1 for TCD, TCD-R1, TCD-R2, TCD-R3, TCD-R4, TCD-R9, and TCD-R10, respectively, which are the averages of the CBSQB3 and G3MP2B3 values. Recommended standard formation enthalpies are listed in Table 6.

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TABLE 5: Isodesmic Reactions and Calculated Enthalpies of Formations for Tricyclodecyl Radicals (TCD-Ri) ∆fH°298 (kcal mol-1) B3LYP

isodesmic reactions TCD-R1 System TCD-R1 + ch3ch3 f TCD + ch3cjh2 TCD-R1 + ch3ch2ch3 f TCD + ch3cjhch3 TCD-R1 + (ch3)3ch f TCD + (ch3)3cj TCD-R1 + ch3ch2ch2ch3 f TCD + ch3cjhch2ch3 TCD-R1 + yyc7h12 f TCD + yycj7h11 average bond energy TCD-R2 System TCD-R2 + ch3ch3 f TCD + ch3cjh2 TCD-R2 + ch3ch2ch3 f TCD + ch3cjhch3 TCD-R2 + (ch3)3ch f TCD + (ch3)3cj TCD-R2 + ch3ch2ch2ch3 f TCD + ch3cjhch2ch3 TCD-R2 + yyc7h12 f TCD + yycj7h11 average bond energy TCD-R3EX System TCD-R3EX + ch3ch3 f TCD + ch3cjh2 TCD-R3EX + ch3ch2ch3 f TCD + ch3cjhch3 TCD-R3EX + (ch3)3ch f TCD + (ch3)3cj TCD-R3EX + ch3ch2ch2ch3 f TCD + ch3cjhch2ch3 TCD-R3EX + yyc7h12 f TCD + yycj7h11 average bond energy TCD-R3EN System TCD-R3EN + ch3ch3 f TCD + ch3cjh2 TCD-R3EN + ch3ch2ch3 f TCD + ch3cjhch3 TCD-R3EN + (ch3)3ch f TCD + (ch3)3cj TCD-R3EN + ch3ch2ch2ch3 f TCD + ch3cjhch2ch3 TCD-R3EN + yyc7h12 f TCD + yycj7h11 average bond energy TCD-R4EX System TCD-R4EX + ch3ch3 f TCD + ch3cjh2 TCD-R4EX + ch3ch2ch3 f TCD + ch3cjhch3 TCD-R4EX + (ch3)3ch f TCD + (ch3)3cj TCD-R4EX + ch3ch2ch2ch3 f TCD + ch3cjhch2ch3 TCD-R4EX + yyc7h12 f TCD + yycj7h11 average bond energy TCD-R4EN System TCD-R4EN + ch3ch3 f TCD + ch3cjh2 TCD-R4EN + ch3ch2ch3 f TCD + ch3cjhch3 TCD-R4EN + (ch3)3ch f TCD + (ch3)3cj TCD-R4EN + ch3ch2ch2ch3 f TCD + ch3cjhch2ch3 TCD-R4EN + yyc7h12 f TCD + yycj7h11 average bond energy TCD-R9EX System TCD-R9EX + ch3ch3 f TCD + ch3cjh2 TCD-R9EX + ch3ch2ch3 f TCD + ch3cjhch3 TCD-R9EX + (ch3)3ch f TCD + (ch3)3cj TCD-R9EX + ch3ch2ch2ch3 f TCD + ch3cjhch2ch3 TCD-R9EX + yyc7h12 f TCD + yycj7h11 average bond energy TCD-R9EN System TCD-R9EN + ch3ch3 f TCD + ch3cjh2 TCD-R9EN + ch3ch2ch3 f TCD + ch3cjhch3 TCD-R9EN + (ch3)3ch f TCD + (ch3)3cj TCD-R9EN + ch3ch2ch2ch3 f TCD + ch3cjhch2ch3 TCD-R9EN + yyc7h12 f TCD + yycj7h11 average bond energy TCD-R10EX System TCD-R10EX + ch3ch3 f TCD + ch3cjh2 TCD-R10EX + ch3ch2ch3 f TCD + ch3cjhch3 TCD-R10EX + (ch3)3ch f TCD + (ch3)3cj TCD-R10EX + ch3ch2ch2ch3 f TCD + ch3cjhch2ch3 TCD-R10EX + yyc7h12 f TCD + yycj7h11 average bond energy TCD-R10EN System TCD-R10EN + ch3ch3 f TCD + ch3cjh2 TCD-R10EN + ch3ch2ch3 f TCD + ch3cjhch3 TCD-R10EN + (ch3)3ch f TCD + (ch3)3cj TCD-R10EN + ch3ch2ch2ch3 f TCD + ch3cjhch2ch3 TCD-R10EN + yyc7h12 f TCD + yycj7h11 average bond energy

BB1K MPWB1K BMK 6-31G(d,p) 6-311G(2d,2p) 6-31G(d,p) 6-31G(d,p) 6-31G(d,p) CBS-QB3 G3MP2B3 34.47 35.86 36.80 35.25 36.09 35.70 107.26

34.84 36.13 36.91 35.62 36.22 35.94 107.50

32.82 35.10 36.63 34.44 35.80 34.96 106.52

32.93 35.17 36.60 34.46 35.84 35.00 106.56

34.31 34.89 35.51 34.62 35.55 34.98 106.54

35.49 35.73 35.31 35.13 36.33 35.60 107.16

36.05 35.86 35.08 35.23 36.30 35.71 107.27

26.14 27.53 28.47 26.92 27.76 27.37 98.93

26.52 27.81 28.59 27.30 27.91 27.63 99.19

24.76 27.04 28.57 26.38 27.74 26.90 98.46

24.93 27.17 28.61 26.47 27.84 27.00 98.56

27.17 27.75 28.37 27.48 28.41 27.84 99.40

28.16 28.41 27.98 27.80 29.00 28.27 99.83

29.07 28.88 28.10 28.25 29.31 28.72 100.28

24.62 26.02 26.95 25.40 26.25 25.85 97.41

24.75 26.04 26.82 25.53 26.13 25.85 97.41

23.77 26.05 27.58 25.39 26.75 25.91 97.47

23.87 26.11 27.54 25.40 26.78 25.94 97.50

25.88 26.46 27.08 26.19 27.12 26.55 98.11

26.27 26.52 26.09 25.92 27.11 26.38 97.94

26.84 26.65 25.87 26.02 27.09 26.49 98.05

24.62 26.02 26.95 25.40 26.25 25.85 97.41

24.75 26.04 26.82 25.53 26.13 25.85 97.41

23.77 26.06 27.58 25.39 26.75 25.91 97.47

23.87 26.11 27.54 25.40 26.78 25.94 97.50

25.88 26.46 27.08 26.19 27.12 26.55 98.11

26.27 26.52 26.09 25.91 27.11 26.38 97.94

26.84 26.65 25.87 26.02 27.09 26.49 98.05

25.17 26.56 27.50 25.95 26.79 26.39 97.95

25.27 26.56 27.34 26.05 26.66 26.38 97.94

24.38 26.66 28.18 25.99 27.35 26.51 98.07

24.40 26.64 28.08 25.94 27.31 26.47 98.03

26.47 27.05 27.67 26.77 27.71 27.13 98.69

26.83 27.08 26.66 26.48 27.67 26.95 98.51

27.35 27.16 26.37 26.53 27.59 27.00 98.56

25.17 26.56 27.50 25.95 26.79 26.39 97.95

25.27 26.56 27.34 26.06 26.66 26.38 97.94

24.38 26.66 28.18 25.99 27.35 26.51 98.07

24.40 26.64 28.08 25.94 27.31 26.47 98.03

26.47 27.04 27.66 26.77 27.71 27.13 98.69

26.83 27.08 26.66 26.48 27.67 26.95 98.51

27.35 27.16 26.37 26.53 27.59 27.00 98.56

26.12 27.52 28.45 26.91 27.75 27.35 98.91

26.37 27.66 28.44 27.16 27.76 27.48 99.04

24.86 27.14 28.67 26.48 27.84 27.00 98.56

24.94 27.18 28.62 26.48 27.86 27.01 98.57

26.56 27.14 27.76 26.87 27.80 27.23 98.79

26.96 27.21 26.79 26.61 27.80 27.07 98.63

27.55 27.36 26.58 26.73 27.79 27.20 98.76

26.12 27.52 28.45 26.91 27.75 27.35 98.91

26.37 27.66 28.44 27.16 27.76 27.48 99.04

24.86 27.15 28.67 26.48 27.84 27.00 98.56

24.94 27.18 28.62 26.48 27.86 27.01 98.57

26.57 27.14 27.76 26.87 27.81 27.23 98.79

26.96 27.21 26.79 26.61 27.80 27.07 98.63

27.55 27.36 26.58 26.73 27.79 27.20 98.76

31.09 32.49 33.42 31.88 32.72 32.32 103.88

31.23 32.52 33.29 32.01 32.61 32.33 103.89

30.45 32.73 34.26 32.07 33.43 32.59 104.15

30.61 32.85 34.28 32.14 33.52 32.68 104.24

31.78 32.36 32.98 32.08 33.02 32.44 104.00

32.40 32.65 32.23 32.05 33.24 32.51 104.07

32.92 32.73 31.95 32.10 33.16 32.57 104.13

31.09 32.49 33.42 31.88 32.72 32.32 103.88

31.23 32.52 33.30 32.01 32.61 32.33 103.89

30.45 32.73 34.26 32.07 33.43 32.59 104.15

30.61 32.85 34.28 32.14 33.52 32.68 104.24

31.78 32.35 32.97 32.08 33.02 32.44 104.00

32.40 32.65 32.22 32.04 33.24 32.51 104.07

32.92 32.73 31.95 32.10 33.16 32.57 104.13

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TABLE 6: Recommended ∆fH°298 and Bond Dissociation Energy Values for TCD and Radicals DFT species

TABLE 8: Recommended ∆fH°298 for TCD Isomers

CBS-QB3/G3MP2B3

BDE ∆fH°298 BDE ∆fH°298 (kcal mol-1) (kcal mol-1) (kcal mol-1) (kcal mol-1)

TCD -20.3 ( 1.0 TCD-R1 35.3 ( 1.1 TCD-R2 27.3 ( 1.0 TCD-R3 26.0 ( 1.0 TCD-R4 26.6 ( 1.0 TCD-R9 27.2 ( 1.0 TCD-R10 32.5 ( 1.0

106.9 98.9 97.6 98.1 98.8 104.0

-19.5 ( 1.3 35.7 ( 0.5 28.5 ( 0.5 26.4 ( 0.5 27.0 ( 0.5 27.1 ( 0.5 32.5 ( 0.5

107.2 100.1 98.0 98.5 98.7 104.1

SCHEME 3

Heat of Formation ∆fH°298 Calculated by Atomization Reaction Methods. An atomization reaction method is also utilized to determine the enthalpy of formation for TCD at the B3LYP/6-31G(d,p), CBS-QB3, and G3MP2B3 levels of theory. Calculation details have been described previously.26,40 In this method, ∆Hf(o+tc), a hypothetical atomization reaction is employed in a similar fashion to the above isodesmic work reactions. The target molecule, TCD, is balanced with its constituent atoms, C and H, in the gas phase with revised temperature correction values. For TCD the reaction is

TCD f 10 C + 16 H Table 1 has the values for the atomization reaction where the B3LYP/6-31G(d,p) value of -5.22 kcal mol-1 is apparently not acceptable and the -14.92 kcal mol-1 value from CBS-QB3 is a significant 4.6 kcal mol-1 overestimate from the recommended -19.5 kcal mol-1 value from the isodesmic work reaction analysis at composite level. On the other hand, the G3MP2B3 value of -18.35 kcal mol-1 is only higher by 1.1 kcal mol-1. Hence, the G3MP2B3 atomization method appears to be a reliable alternative method with good accuracy for hydrocarbon systems. The Osmont et al. empirically corrected the atomization method for polycyclic hydrocarbons41 from a B3LYP/631G(d,p) calculation is also presented in Table 1. A calculated value of -15.0 kcal mol-1 is determined, 4.5 kcal mol-1 higher than our -19.5 kcal mol-1 recommended value. While the authors show good agreement of their method with noncyclic hydrocarbons and oxy-hydrocarbons, they do show the method performs less well for complex polycyclic hydrocarbons.42-45

species

∆fH°298 (kcal mol-1)

exo-TCD chair exo-TCD boat exo-TCD TS endo-TCD chair endo-TCD boat

-19.5 ( 1.3 -17.4 ( 1.3 -15.4 ( 1.3 -15.3 ( 1.3 -16.5 ( 1.3

Heat of Formation ∆fH°298 from Isomerization (Interconversion) Reaction Analysis. We use our detailed results for the heat of formation of the lower energy chair form of the exo-TCD, -19.5 kcal mol-1, combined with the isomerization work reactions in Scheme 3 to determine the standard enthalpies of formation for the boat and TS forms of exo-TCD and the chair and boat forms of endo-TCD. This reaction allows for a maximum degree of error cancellation because of the similar strain in the endo and exo isomer structures and systematic errors on specific atom groups will cancel. Table 7 has a summary of the values calculated for the work reactions. Data for each of the work reactions are available in the Supporting Information. Structures of the different exo and endo isomers are illustrated in Figures 2 and 3, respectively. The exo-TCD structure is more stable than the endo-TCD isomer by about 2.6 kcal mol-1. The exo-TCD chair is shown to be approximately 2 kcal mol-1 more stable than the exo-TCD boat conformation. For the exo-TCD TST (conversion of the chair form to the boat form) the transition state energy is calculated to be higher than the exo-TCD chair by a 4 kcal mol-1 barrier. The energies of the endo-TCD boat and chair conformations show a smaller energy difference, ca. 1 kcal mol-1 with the boat conformation lower in energy. Overall, there is good correlation between the data generated from the isomerization and isodesmic work reactions. Recommended values for these isomers, given in Table 8, are -19.5, -17.4, -15.4, -15.3, and -16.5 kcal mol-1 for the exo-TCD chair, exo-TCD boat, exo-TCD TS, endo-TCD chair, and endo-TCD boat, respectively. Errors are again assigned using the standard deviations from the isodesmic work reaction values. Our recommended values of -19.5 and -16.5 kcal mol-1 for exo and endo are within 1 kcal mol-1 to the Zehe and Jaffe14 values of -18.5 and -15.4 kcal mol-1 for the exo and endo isomers. The endo-TCD values of -15.3 and -16.5 kcal mol-1 for the chair and boat conformations are similar to the -14.38 kcal mol-1 reported by Boyd et al.12 Using our recommended values with the heat of vaporization values from Chickos et al.15 gives liquid phase enthalpies of -31.2 and -28.5 kcal mol-1 for exo- and endo-TCD. These values are within 2 kcal mol-1 of the reported liquid phase enthalpies of Zehe and Jaffe14 and Smith and Good.13 Entropy, S°298, and Heat Capacity, Cp(T). Entropy and heat capacities for TCD and tricyclodecyl radicals are calculated at the B3LYP/6-31G(d,p) level of theory using the Statistical Mechanics for Heat Capacity and Entropy (SMCPS) pro-

TABLE 7: TCD Isomers ∆fH°298 from Unimolecular Isomerization and Bimolecular Isodesmic Work Reactions isomerization work reaction (∆fH°298, kcal mol-1)

isodesmic work reaction (∆fH°298, kcal mol-1)

species

B3LYP/6-31G(d,p)

CBS-QB3

G3MP2B3

B3LYP/6-31G(d,p)

CBS-QB3

G3MP2B3

exo-TCD chair exo-TCD boat exo-TCD TS endo-TCD chair endo-TCD boat

-17.5 -16.0 -15.6 -15.8

-17.4 -15.4 -15.3 -16.4

-17.4 -15.4 -15.3 -16.5

-19.4 -17.5 -16.0 -15.5 -15.7

-19.5 -17.5 -15.5 -15.4 -16.4

-19.4 -17.4 -15.4 -15.3 -16.5

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gram.35 Zero-point vibration energies (ZVPE) are scaled by 0.9806 for B3LYP/6-31G(d,p) as recommended by Scott and Radom.46 Contributions from each compound’s geometry, frequencies, moments of inertia, and internal rotors are considered and presented for the temperature range of 1-5000 K in the Appendix, Table 10. NASA Polynomials for use in kinetic and thermochemical calculations and modeling are presented in the Supporting Information. Bond Dissociation Energies. Bond dissociation energies corresponding to the loss of a hydrogen atom are computed from the work reactions listed in Table 5 using the ∆fH°298 of the parent molecule and carbon site radicals with the standard enthalpy of the hydrogen atom. Determining these bond energies facilitates understanding the initial reaction pathways and kinetics the compound will undergo with lower bond energies being more susceptible to hydrogen abstraction. Standard bond dissociation energies for primary, secondary, and tertiary alkanes of 101.1, 98.5, and 96.5 kcal mol-1 along with energies for secondary one- and two-carbon bridges and bridgeheads for norbornane47 of 104.9, 98.7, and 107.3 kcal mol-1 were used for values of the standard reference species. TCD has two tertiary bridgehead radical sites related to the carbon 1 and 2 atoms in the numbering scheme of Figure 1. TCD-R1 and TCD-R2 have bond energies of 107.2 and 100.1 kcal mol-1, which are significantly different from the common 96.5 kcal mol-1 for a tertiary alkane C-H bond. TCD-R1 is similar to the 107.3 kcal mol-1 for the bridgehead position of norbornane and 106 kcal mol-1 found both in cyclopropane16,17 and bicyclo[1.1.1]pentane48 resulting from the ring strain present. This strain also accounts for the relative difference in energy for the two tertiary sites, TCD-R1 and TCD-R2, where the more highly strained TCD-R1 has about a 7 kcal mol-1 higher bond energy than the less strained TCD-R2. The increasing strain and energy is caused by an unfavorable nonplanar geometry created upon radical formation. TCD-R3, TCD-R4, and TCD-R9 are all secondary carbons with energies of 98.0, 98.5, and 98.7 kcal mol-1; these values are slightly lower than the 98.5 kcal mol-1 for secondary alkanes C-H bonds. These TCD radical values are consistent with the 98.7 kcal mol-1 for the secondary two-carbon bridge bond energy for norbornane,47 97-98 kcal mol-1 for the secondary two- and three- carbon bridges of bicyclo[3.1.1]heptane, tricyclo[3.1.1.01,5]heptane, tricyclo[2.2.1.01,4]heptane, and bicyclo[2.2.2]octane,48 and 96-97 kcal mol-1 for cyclopentane.17,49-51 TCD-R10 is a strained, single bridging, carbon with strain that is probably similar to TCD-R1 and TCD-R2, although now in a secondary structure. The resulting bond energy for TCD-R10 of 104.1 kcal mol-1 is indicative of this strain and is similar to 104.9 kcal mol-1 found for the secondary onecarbon bridged bond energy in norbornane47 and 103-105 kcal mol-1 for the single bridging positions in bicyclo[2.1.1]hexane

and bicyclo[3.1.1]heptane.48 This can be compared to the 100 kcal mol-1 bond energy observed in cyclohexane, where there is little strain.17,49-51 The carbon sites for the exo and endo hydrogen atoms, see Figure 1, are shown to have identical bond energies, as illustrated in Table 5, and therefore are not separately discussed. Summary Standard enthalpy of formation of the parent TCD molecule and the different tricyclodecyl radicals corresponding to loss of H atoms from the carbons sites are evaluated using five density functional methods and the G3MP2B3 and CBS-QB3 composite computational methods. A series of five isodesmic, work reactions that include reference molecules of similar ring strain, is used to effect a cancelation of calculation errors. The enthalpy of formation for TCD of -19.5 kcal mol-1 is found to be several kcal mol-1 lower than the commonly used literature values. Carbon-hydrogen bond energies for the TCD carbon sites (TCD-Ri) are determined as follows: TCD-R1, 107.2; TCD-R2, 100.1; TCD-R3, 98.0; TCD-R4, 98.5; TCD-R9, 98.7; TCD-R10, 104.1 kcal mol-1. Results from use of five different DFT methods are in very good agreement with composite method values for work reactions that contain similar bridged hydrocarbons on both sides and for the radicals. NASA Polynomials for the thermodynamic data for TCD and tricyclodecyl radicals are presented in the Supporting Information. Acknowledgment. The authors acknowledge STTR funding from the US Navy (Contract Number 68335-09-C-0376). We also acknowledge Rick Burnes, the STTR contract monitor, and Brydger Van Otten, Chris Montgomery, and Michael Bockelie of Reaction Engineering International for helpful discussions. Supporting Information Available: Data on atom numbering, optimized structures and z-matrices, moments of inertia, vibration frequencies, determination of formation enthalpy for 2-Norbornyl radical, reaction enthalpies for radical isodesmic work reactions, NASA polynomial thermodynamic data for TCD and radicals, and isomerization and isodesmic work reactions for isomer enthalpies. This information is available free of charge via the Internet at http://pubs.acs.org. Appendix Table 9 lists enthalpy values from isodesmic work reactions that do not include similar bridged hydrocarbon species for cancellation of error resulting from strain and show significant deviations from our recommended value. Table 10 presents the entropy and heat capacity values for the parent TCD and the radicals over the temperature range of 1-5000 K typical of JANNAF tabulation.

TABLE 9: DFT Calculations of Standard Formation Enthalpy on TCD Using Small Molecule Work Reactions Do Not Show Acceptable Results ∆fH°298 (kcal mol-1) B3LYP isodesmic reactions

6-31G(d,p)

6-311G(2d,2p)

BB1K 6-31G(d,p)

MPWB1K 6-31G(d,p)

BMK 6-31G(d,p)

CBS-QB3

G3MP2B3

TCD System TCD + 14 ch4 f 12 ch3ch3 TCD + 4 ch4 f 2 yc5h10 + 2 ch3ch3 average

0.34 -9.91 -4.78

-1.60 -9.90 -5.75

-10.18 -15.31 -12.75

-8.89 -15.11 -12.00

-11.66 -14.08 -12.87

-20.08 -20.78 -20.43

-19.48 -20.51 -19.99

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TABLE 10: Calculated Entropiesa and Heat Capacitiesa for TCD and Tricyclodecyl Radicals from B3LYP/6-31G(d,p) Geometries, Frequencies, Moments of Inertia, and Internal Rotors TCD temp (K) 1 50 100 150 200 250 298 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 2000 2500 3000 3500 4000 4500 5000 zero point energyb

TCD-R1

TCD-R2

TCD-R3EX

TCD-R3EN

TCD-R4EX

TCD-R4EN

Cp

S

Cp

S

Cp

S

Cp

S

Cp

S

Cp

S

Cp

S

7.949 8.945 12.502 16.700 21.931 28.537 35.827 36.142 51.917 65.987 77.637 87.205 95.158 101.856 107.552 112.425 116.614 120.227 123.353 126.069 135.333 140.398 143.404 145.314 146.595 147.493 148.146 149.018

24.334 55.693 62.918 68.748 74.223 79.785 85.390 85.630 98.162 111.266 124.332 137.017 149.176 160.764 171.783 182.256 192.211 201.682 210.701 219.299 256.954 287.736 313.614 335.868 355.358 372.677 388.250

7.949 8.956 12.550 16.811 22.080 28.628 35.759 36.066 51.301 64.763 75.848 84.920 92.443 98.768 104.140 108.733 112.678 116.080 119.024 121.580 130.298 135.064 137.893 139.689 140.895 141.740 142.354 140.906

25.647 57.008 64.251 70.112 75.625 81.217 86.827 87.066 99.507 112.410 125.203 137.576 149.402 160.649 171.327 181.461 191.086 200.233 208.939 217.233 253.515 283.139 308.027 329.423 348.157 364.801 379.767

7.949 9.442 13.235 17.375 22.516 28.974 36.048 36.353 51.525 64.954 76.022 85.084 92.601 98.921 104.288 108.875 112.814 116.209 119.145 121.693 130.379 135.123 137.936 139.723 140.921 141.762 142.372 140.337

25.685 57.253 64.930 71.049 76.706 82.385 88.050 88.291 100.806 113.755 126.581 138.979 150.827 162.093 172.786 182.935 192.571 201.730 210.444 218.746 255.056 284.696 309.594 330.996 349.733 366.381 381.348

7.949 9.546 13.282 17.565 22.826 29.368 36.499 36.806 52.025 65.435 76.452 85.455 92.915 99.186 104.511 109.064 112.974 116.346 119.264 121.797 130.436 135.158 137.960 139.740 140.934 141.772 142.380 139.795

25.637 57.255 64.973 71.136 76.866 82.623 88.362 88.606 101.259 114.319 127.229 139.689 151.583 162.883 173.602 183.770 193.422 202.592 211.316 219.626 255.959 285.608 310.511 331.917 350.656 367.305 382.273

7.949 9.545 13.281 17.564 22.825 29.367 36.499 36.805 52.025 65.435 76.451 85.455 92.915 99.186 104.511 109.064 112.974 116.346 119.264 121.796 130.436 135.158 137.960 139.740 140.934 141.772 142.380 139.795

25.637 57.255 64.973 71.135 76.865 82.622 88.361 88.605 101.258 114.318 127.227 139.688 151.581 162.881 173.601 183.769 193.420 202.591 211.315 219.625 255.957 285.607 310.510 331.915 350.655 367.303 382.272

7.949 10.610 13.980 18.013 23.102 29.541 36.615 36.921 52.090 65.484 76.499 85.507 92.972 99.247 104.575 109.129 113.039 116.410 119.325 121.855 130.480 135.191 137.985 139.759 140.950 141.784 142.390 139.448

25.599 58.044 66.385 72.782 78.615 84.422 90.187 90.432 103.110 116.182 129.100 141.568 153.469 164.776 175.502 185.676 195.333 204.509 213.237 221.552 257.899 287.557 312.466 333.875 352.616 369.267 384.236

7.949 10.607 13.978 18.011 23.100 29.539 36.615 36.920 52.089 65.484 76.499 85.507 92.972 99.247 104.575 109.129 113.039 116.410 119.325 121.855 130.480 135.191 137.985 139.759 140.950 141.784 142.390 139.449

25.599 58.040 66.378 72.774 78.607 84.414 90.178 90.423 103.101 116.173 129.091 141.559 153.460 164.767 175.493 185.667 195.324 204.500 213.229 221.543 257.890 287.548 312.457 333.866 352.607 369.258 384.227

TCD-R9EX

TCD-R9EN

TCD-R10EX

TCD-R10EN

temp (K)

Cp

S

Cp

S

Cp

S

Cp

S

1 50 100 150 200 250 298 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 2000 2500 3000 3500 4000 4500 5000 zero point energyb

7.949 8.895 12.722 17.296 22.755 29.402 36.581 36.889 52.130 65.525 76.519 85.500 92.941 99.197 104.510 109.055 112.960 116.328 119.243 121.775 130.415 135.142 137.947 139.730 140.926 141.765 142.375 139.904

25.632 56.963 64.216 70.208 75.890 81.644 87.394 87.638 100.320 113.402 126.326 138.795 150.693 161.995 172.715 182.883 192.533 201.703 210.425 218.734 255.060 284.706 309.606 331.010 349.748 366.396 381.364

7.949 8.895 12.722 17.296 22.755 29.402 36.581 36.889 52.130 65.526 76.519 85.500 92.941 99.197 104.510 109.055 112.960 116.328 119.243 121.775 130.415 135.142 137.947 139.730 140.926 141.765 142.375 139.903

25.632 56.963 64.216 70.208 75.890 81.644 87.394 87.638 100.320 113.402 126.326 138.795 150.693 161.995 172.716 182.883 192.534 201.703 210.425 218.734 255.060 284.706 309.606 331.010 349.748 366.396 381.364

7.949 9.302 13.041 17.409 22.725 29.307 36.458 36.766 51.993 65.394 76.396 85.383 92.830 99.091 104.411 108.961 112.871 116.245 119.166 121.703 130.364 135.105 137.920 139.709 140.910 141.752 142.364 140.153

25.649 57.204 64.727 70.810 76.502 82.241 87.972 88.216 100.859 113.911 126.812 139.262 151.146 162.435 173.144 183.303 192.945 202.107 210.824 219.127 255.436 285.072 309.966 331.366 350.102 366.748 381.715

7.949 9.301 13.040 17.409 22.725 29.307 36.459 36.766 51.993 65.394 76.396 85.383 92.831 99.092 104.411 108.961 112.872 116.245 119.166 121.703 130.365 135.105 137.920 139.709 140.910 141.752 142.364 140.152

25.649 57.204 64.726 70.809 76.501 82.241 87.971 88.215 100.859 113.910 126.811 139.262 151.145 162.434 173.143 183.302 192.944 202.107 210.823 219.127 255.435 285.071 309.966 331.366 350.102 366.748 381.714

a

Units of cal mol-1 K-1. b Units of kcal mol-1.

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