Bond Energies and Thermochemical Properties of Ring-Opened

Article pubs.acs.org/JPCA

Bond Energies and Thermochemical Properties of Ring-Opened Diradicals and Carbenes of exo-Tricyclo[5.2.1.02,6]decane Jason M. Hudzik, Á lvaro Castillo, and Joseph W. Bozzelli*

Chemistry, Chemical Engineering and Environmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102, United States

Downloaded by UNIV OF MANITOBA on September 11, 2015 | http://pubs.acs.org Publication Date (Web): September 10, 2015 | doi: 10.1021/acs.jpca.5b05564

S Supporting Information *

ABSTRACT: Exo-tricyclo[5.2.1.02,6]decane (TCD) or exo-tetrahydrodicyclopentadiene is an interesting strained ring compound and the single-component high-energy density hydrocarbon fuel known as JP-10. Important initial reactions of TCD at high temperatures could cleave a strained carbon−carbon (C−C) bond in the ring system creating diradicals also constrained by the remaining ring system. This study determines the thermochemical properties of these diradicals (TCD-H2 mJ-nJ where m and n correspond to the cleaved carbons sites) including the carbon−carbon bond dissociation energy (C−C BDE) corresponding to the cleaved TCD site. Thermochemical properties including enthalpies (ΔH°f298), entropies (S(T)), heat capacities (Cp(T)), and C−H and C−C BDEs for the parent (TCD-H2 m-n), radical (TCD-H2 mJ-n and m-nJ), diradical (TCD-H2 mJ-nJ), and carbene (TCD-H2 mJJ-n and m-nJJ) species are determined. Structures, vibrational frequencies, moments of inertia, and internal rotor potentials are calculated at the B3LYP/6-31G(d,p) level of theory. Standard enthalpies of formation in the gas phase for the TCD-H2 m-n parent and radical species are determined using the B3LYP density functional theory and the higher level G3MP2B3 and CBS-QB3 composite methods. For singlet and triplet TCD diradicals and carbenes, M06-2X, ωB97X-D, and CCSD(T) methods are included in the analysis to determine ΔH°f298 values. The C−C BDEs are further calculated using CASMP2(2,2)/aug-cc-pvtz//CASSCF(2,2)/cc-pvtz and with the CASMP2 energies extrapolated to the complete basis set limit. The bond energies calculated with these methods are shown to be comparable to the other calculation methods. Isodesmic work reactions are used for enthalpy analysis of these compounds for effective cancelation of systematic errors arising from ring strain. C−C BDEs range from 77.4 to 84.6 kcal mol−1 for TCD diradical singlet species. C−H BDEs for the parent TCD-H2 m-n carbon sites range from 93 to 101 kcal mol−1 with a similar range seen for loss of the second hydrogen to generate the diradical singlet species. A wider range for C−C BDEs is seen for the carbenes from about 77 to 100 kcal mol−1 as compared to the diradicals. Results from the DFT methods for the parents, radicals, diradicals, and carbenes are in good agreement with results from the composite methods using our sets of work reactions.

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INTRODUCTION Exo-tricyclo[5.2.1.02,6]decane (TCD), also named exo-tetrahydrodicyclopentadiene, is the single-component high-energy density hydrocarbon fuel known as JP-10. The strained cyclic geometry allows for energy storage and a high thermal stability.1−3 This may be advantageous for a high energy fuel but results in complexity when analyzing its reaction pathways in combustion, thermal decomposition, and atmospheric chemistry. This complexity is seen in the wide range of initial products, along with some conflicting data, for pyrolysis, combustion, and cracking of TCD by several research groups.1,3−12 Carbon−carbon (C−C) bonds in cyclic and linear hydrocarbons are typically weaker than corresponding carbon−hydrogen (C−H) bonds by about 10 kcal mol−1. C−C bonds also have a higher entropy gain in the cleavage of these bonds and will cleave faster under high-temperature unimolecular dissociation conditions versus C−H bonds. This cleavage reaction creates two radical species, and while reverse reaction is also rapid and highly competitive with further reaction such as chain branching, the forward reactions are important to the initiation of combustion and pyrolysis. © XXXX American Chemical Society

Thermodynamic data for diradicals, including their carbon− carbon bond dissociation energies (C−C BDEs) are valuable for evaluation of ring strain and for understanding reaction pathways of complex hydrocarbon fuels and in petroleum and other cracking reactors.13,14 Accurate thermochemical data also provide a basis for understanding the initiation and reaction kinetics. The initial ring-opening reactions in strained ring systems result in release of strain energy, where the initial ring-opened structure rearranges to a lower energy than that of the open ring initially formed. Intramolecular reactions of ring-opened, cyclic hydrocarbons often rapidly undergo an intramolecular hydrogen transfer where a H atom from a carbon adjacent to one radical moves to the opposite radical leading to a stable olefin via the exothermic double bond formation. Previous experimental and computational studies15−19 have determined gas- and liquid-phase formation enthalpies for TCD Received: June 10, 2015 Revised: August 21, 2015

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DOI: 10.1021/acs.jpca.5b05564 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A which have been used to model pyrolysis and combustion.4,7 In a previous computational study19 we determined thermodynamic parameters including enthalpies (ΔH°f298), entropies (S(T)), and heat capacities (Cp(T)) for TCD and tricyclodecyl radicals with their corresponding C−H BDEs. The role of diradical species created from breaking C−C bonds in ring-opening processes for cyclic and polycyclic compounds has been previously studied.7,14,20−27 Williams and co-workers11 suggested a mechanism where breaking the central C−C bond shared by two five-membered rings or a C−H bond of a CH2 group would likely be the initiation step in the unimolecular decomposition of TCD. The significant study by Herbinet et al.7 presented some thermochemistry and a comprehensive detailed kinetic model including diradical species created from initial unimolecular cleavage of the C−C bonds in TCD. They compared their model with experimental results for the thermal decomposition of TCD. Xing et al.10 similarly developed a probable diradical mechanism for the thermal cracking of TCD under elevated pressures. S. Anderson and co-workers8 studied pyrolysis of TCD in a flow reactor where they observed decomposition around 1000 K and complete decomposition at approximately 1350 K. They also determined important products by mass spectrometry analysis indicating that cyclopentadiene was a major initial product but is transient at these conditions and begins to decompose at approximately 1350 K. The computational studies (molecular dynamics simulations at several thousand degrees K) of W. Goddard’s research group4 reported C−C bond cleavage forming either ethylene with a C8 hydrocarbon or two C5 hydrocarbons from initial thermal decomposition. As modeling of reactive combustion chemical systems continues to advance, research on the involvement of diradicals and on carbenes as reactive intermediates in combustion will continue, and the need for their thermochemical properties will also increase. Research involving carbenes has increased as theoretical computations are aligned with experimental results. Computational studies for carbenes include heats of formation for small species such as ethylidene28 and hydroxyl-substituted carbenes29 to larger saturated and unsaturated diaminocarbenes30 and phenylcarbene.31 Carbene singlet versus triplet state stabilities have been studied computationally for trifluoromethyl and ammonium cationic ligand substitutions,32 mono- and diaryl substituents,33 and monoheteroatom substitution for acyclic and cyclic carbenes.34 Electronic structure effects from ortho-, meta-, and para-substitutions for phenylcarbene35 have also been investigated. In this study, each of the seven Cm−Cn bond energies are studied (m and n denote carbons according to numbering in Figure 1). Each of the C−C bonds in TCD is cleaved and the

mJ-nJ), and carbene (TCD-H2 mJJ-n and m-nJJ) species, J represents a radical site from the loss of a hydrogen atom on the preceding carbon atom. Standard enthalpies of formation of each parent, radical, diradical, and carbene species are calculated. The C−H BDEs corresponding to loss of H at the capped sites are determined for the radicals, while the C−C BDEs are calculated as the difference between the enthalpy of TCD and the diradical and carbene species. Entropies (S(T)) and heat capacities (Cp(T)) are also determined for each species.

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COMPUTATIONAL METHODS Density functional theory (DFT) and composite methods are used and compared in this study using calculations performed with the Gaussian 0336 and Gaussian 0937 program suites. The first DFT method is B3LYP38,39 which combines the three-parameter Becke exchange functional, B3, with the Lee− Yang−Parr correlation functional (LYP). Initial structural parameters including geometries, vibrational frequencies, moments of inertia, and internal rotor potentials were analyzed using B3LYP/6-31G(d,p). The second method is the long-range corrected hybrid density function of Chai and Head-Gordon, ωB97X-D,40,41 which includes empirical atom−atom dispersion corrections. Lastly, the hybrid meta-GGA exchange-correlation functional M06-2X42,43 by Zhao and Truhlar is employed. These methods use the 6-31G(d,p) basis set; the larger 6-311G(2d,2p) basis set was also used with B3LYP as a comparison. Higher level composite methods G3MP2B344,45 and CBSQB346,47 were used to assess DFT performance. G3MP2B3 is a modified version of the G3MP248 method where the geometries and zero-point vibration energies are from B3LYP calculations followed by QCISD(T), MP2, and higher level corrections to determine the total energy. CBS-QB3 is a complete basis set method where the B3LYP level geometries and frequencies are followed by single-point energy calculations at the CCSD(T), MP4SDQ, and MP2 levels of theory. The final energies are determined with a CBS extrapolation. Single-point energies using the coupled cluster method with single, double, and perturbative triple excitation calculations, CCSD(T),49−55 were calculated for the diradicals and carbenes based on optimized B3LYP/ 6-31G(d,p) geometries. The calculated atomic spin densities on singlet radical systems provide a verification of the density on the carbon atom radical sites. Singlet diradical spin densities for the species of interest are presented in the Supporting Information. A similar procedure was carried out for the triplet states. The spin-projection method developed by Yamaguchi and coworkers56 was applied to the energies for the singlet diradicals and carbenes from the DFT methods. This correction aims to remove the spin contamination error from the triplet state in the open-shell singlet calculations. Ess and Cook57 showed that DFT methods give inadequate singlet−triplet (S−T) energies without spin correction and that only corrected M06-2X and ωB97X-D give reasonable accuracy for S−T gap energies for open-shell singlet diradicals. Our CBS-QB3 singlet diradical values are further corrected to remove error from strong spin contamination. The method recommended by Sirjean et al.58 was used, where the error was calculated based on singlet−triplet gaps for hydrocarbon diradicals from CASSCF calculations and shown to produce acceptable formation enthalpies for 22 hydrocarbon and heteroatomic diradicals. C−C BDEs were further calculated using CASMP2(2,2)/aug-cc-pvtz//CASSCF(2,2)/cc-pvtz and CASMP2 extrapolated to the complete basis set limit. HF-SCF energies were calculated with the augmented correlation consistent

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

radical sites capped with a H atom (completion of valence) resulting in seven stable parent compounds, TCD-H2 m-n. For the radical (TCD-H2 mJ-n and m-nJ), diradical (TCD-H2 B


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The Journal of Physical Chemistry A basis set (X = D, T, Q)59−61 and extrapolated as suggested by Feller62

optimized, and the bond energy reported needs to be considered tentative. It may reflect that the TCD-H2 2J-6J ring opening may not occur as an initial step in this system. In order to provide a geometry for the singlet TCD-H2 2J-6J species, singlet single-point energy was calculated from the optimized triplet geometry at a C2−C6 distance of 3.26 Å. This procedure provided one negative frequency in the −51.31 to −104.76 cm−1 range, which, as noted above, corresponded to the 2J-6J bond reformation for each of the calculation methods. In order to estimate the energy, the inverse of the negative frequency was used to calculate the zero-point vibrational energy (ZPVE) contribution. All remaining singlet and all triplet diradicals had all positive frequencies. All the frequencies were scaled by 0.9806 for B3LYP, as recommended by Scott and Radom,64 and 0.967 for M06-2X and 0.975 for ωB97X-D, as recommended by Truhlar and co-workers.65 The calculated enthalpy values include this ZPVE contribution as well as the spin correction. A similar procedure was followed for the composite methods with adjusting for the negative frequency ZPVE correction. Errors in DFT methods seem insignificant in small molecules, but they increase linearly with increasing molecule size. To improve the accuracy of the calculated ΔH°f298 values, isodesmic work reactions, which have similar bonding environments for the products and reactants, were employed. Incorporation of similar bridged structures (similar ring strain environments) on both sides of the work reaction is important for accuracy in parent species enthalpy calculations.19 Our work reactions incorporate this for minimization of error. The Statistical Mechanics for Heat Capacity and Entropy (SMCPS) program66 is utilized to calculate the entropy and heat capacities for all of the compounds using the B3LYP/6-31G(d,p) level of theory. The SMCPS program applies the rigid-rotor harmonic-oscillator (HO) approximation using geometry, mass, electronic degeneracy, symmetry, frequencies, number of optical isomers, and moments of inertia as input parameters for each compound. Zero-point vibration energies (ZPVE) are scaled by 0.9806 for B3LYP/6-31G(d,p) as recommended by Scott and Radom.64 These contributions, noted as TVR, incorporate translations, vibrations, and external rotations. The HO approximation to low frequency vibrational modes of internal rotations creates error treating an internal rotor as a vibration. This is remedied by replacing these frequencies with entropy and heat capacity contributions from internal hindered rotor analysis. The contributions of the internal rotors, noted as IR, are incorporated using the Pitzer and Gwinn67−69 approximation method where the potential energy barriers to rotation are calculated at the B3LYP/6-31G(d,p) level. Internal rotor torsions below 4.5 kcal mol−1 are removed and are replaced with entropy and heat capacity contributions as hindered rotors. Reduced moments of inertia are determined from moments of inertia for the rotational groups using their mass and radius of rotation. Total entropy and heat capacity values, determined by summing the TVR and IR contributions, for the 50−5000 K temperature range for the singlet diradical compounds, are presented in the Appendix Table A1 and for all of the species in the Supporting Information.

X ∞ E HF = E HF + ae−bX

with EXHF being the three calculated HF-SCF energies using the ∞ aug-cc-pVXZ basis sets. The EHF extrapolated energy and parameters a and b can then be calculated with X as the cardinal number of the basis set (D:2, T:3, and Q:4). CASMP2 correlation energies where calculated with the aug-cc-pVXZ (X = T, Q), and extrapolated following the atomic partial wave expansion of Helgaker et al.63


X ∞ −3 Ecorr CASMP2 = Ecorr CASMP2 + AX

where EXcorr CASMP2 are the CASMP2 correlation energies using the aug-cc-pVXZ basis sets. The E∞ corr CASMP2 and parameter A can then be calculated with simple algebra as for the HF-SCF energies. To provide an initial geometry for the singlet TCD-H2 diradical species, singlet single-point energies were calculated from the optimized triplet geometries. Optimization of the singlet diradicals resulted in sets of all positive vibration frequencies with the exception of the TCD-H2 2J-6J singlet diradical, which corresponds to a single bond bridge between two cyclopentane structures. Geometry optimization of the singlet TCD-H2 2J-6J species with each of the methods used in this study resulted in one negative frequency that corresponded to a ring reformation movement of the TCD-H2 2J-6J ring-opened structure. A stable singlet structure with no imaginary frequencies was obtained using the semiempirical methods PM3 and PM6, but optimization with the other methods in our analysis yielded ring closure back to TCD. B3LYP bond scans of relative energy versus the C2−C6 bond length were calculated using B3LYP/6-31G(d,p) and M06-2X/ 6-31G(d,p) methods; these are illustrated in the Supporting Information. The scans began at the optimized C2−C6 TCD bond length (from B3LYP/6-31G(d,p)) of 1.58 Å and were incremented by 0.05 Å for 50 steps up to 4.08 Å. This length included the optimized bond lengths of 3.26 and 3.19 Å for TCD-H2 2J-6J triplet diradical and the TCD-H2 2-6 parent species, respectively. These methods did not show a definitive maximum around 2.2−2.3 Å which was shown in the optimized semiempirical methods but rather increasing relative energies from 1.58 to 2.69 Å and then a more gradual increase through the further bond lengthening to 3.7 Å. It may be that the increasing energy relative to the bond distance is a result of increasing stain, where the radical sites often have near sp2 geometry, relative to sp3 of alkyl carbons. Frequencies from the B3LYP/6-31G(d,p) calculations were calculated for each step of the C2−C6 bond scan. No imaginary frequencies were observed between 1.58 and 2.03 Å and then again between 3.78 and 4.08 Å. One single negative frequency was observed at all scan positions from 2.13 to 3.68 Å with exception of 3.33 and 3.43 Å where multiple negative frequencies were observed. The presence of the negative frequency in the TCD-H2 2J-6J singlet is also noted in the tabular data below. This 2J-6J bond in TCD is the only bond in the TCD moiety that results in a ring expansion, and it generates an expanded ring with no internal rotors for structure change. We further note that bond distances around 3 Å are commonly found in variational transition state analysis for single, alkyl carbon−carbon bond dissociation transition states. Vibration movement to reform the bond between two paired radicals with only ring structure movement is probably not unreasonable, and the singlet TCD-H2 2J-6J diradical may not exist. The presence of the negative frequency for the optimized TCD-H2 2J-6J singlet diradical suggests the system is not properly

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NOMENCLATURE The following abbreviations are utilized: • = represents a double bond between two atoms, • Y represents a cyclic ring structure, C


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The Journal of Physical Chemistry A


• YY represents a bicyclic ring structure, • J or • represents a radical site on the preceding carbon atom, • JJ or : represents a carbene site on the preceding carbon atom, • (s) or (t) represents a singlet or triplet state species, • m and n denote carbon atoms according to numbering in Figure 1, • TCD and JP-10 denote exo-tricyclo[5.2.1.02,6]decane or exo-tetrahydrodicyclopentadiene. Figure 2 shows an example of the nomenclature used in this study for the parent, radical, diradical, and carbene species based

Figure 4. Stepwise calculation of radicals and bond dissociation energies by single-step hydrogen atom removal from TCD-H2 parent species.

TCD-H2 mJ-n and the TCD-H2 m-nJ species. Then from the monoradicals the hydrogen on the second carbon of the bond cleavage was removed to create the diradical, for both the singlet and triplet states. This diradical was denoted TCD-H2 mJ-nJ, and the structure was optimized. A separate calculation beginning with the monoradicals removed a second H atom from the first radical site to create the carbene, for both the singlet and triplet states, denoted TCD-H2 mJJ-n and TCD-H2 m-nJJ. The calculation and validation of the enthalpies of formation (ΔH°f298) for the lowest energy conformer of the parent compounds is completed with two sets of isodesmic work reactions to reduce systematic errors from the calculation methods. The first set of four work reactions, Scheme I, is used to calculate ΔH°f298

Figure 2. Example nomenclature for TCD-H2 1-2 parent, radical, diradical, and carbene species.

on the numbering in Figure 1. The structures in this figure were kept close to the geometry of the parent structure for ease of identification and do not reflect their optimized geometries.

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Scheme I. Work Reactions for Calculating ΔH°f298 of Parent TCD-H2 m-n

RESULTS The primary objectives of this study are to determine the BDEs for the seven different C−C bonds in TCD and to calculate the thermochemical properties of the singlet diradicals. Diradicals and carbenes can be formed from the cleavage of the TCD C−C bonds, as illustrated in Figure 3. These species have different

values. The first three contain reference species with similar strained− bridged cyclic bonding environments on both sides of the equations. The fourth reaction uses smaller molecules, which are not bridged, but their enthalpies are known to higher accuracy. This allows for some comparison of calculation errors where ring strain is not canceled. The reactions are similar to ones which provided good precision previously for TCD.19 The standard enthalpies of formation for the reference species used in the work reactions are in Table 1. A second set of work reactions for the parent compounds, illustrated in Scheme II, incorporate ring-opened species and the parent TCD compound. These are used to validate the Scheme I work reaction ΔH°f298 calculation and mimic the TCD to TCD-H2 m-n ring opening we have set out to study. The first two reactions in this set have strained-bridged bicyclic compounds, which open to their single cyclic counterparts. The third and fourth reactions involve cyclic ring opening to normal straight-chain alkanes. The nomenclature of the cyclic species used in these work reactions is presented in Figure 5, while the eight work reactions for the parent compounds are illustrated in the Appendix. Work reactions used to calculate ΔH°f298 for the lowest energy conformer of the TCD-H2 mJ-n and m-nJ radicals are listed in Scheme III. These work reactions use smaller radical and parent compounds as reference species where their heats of formation are accurately known; they also use a near TCD structure on both sides for strain cancelation. The work reactions for the singlet and triplet diradicals are illustrated in Scheme IV; they involve one reference species radical and one TCD-H2 m-n radical. Since there are two TCDH2 m-n single radical sites, one for m and one for n of each

Figure 3. Calculated carbon−carbon bond dissociation energies for ring opening of TCD to diradicals and carbenes.

relative stabilities which affect their C−C BDEs and thus the ringopening kinetics. The thermochemical properties determine initial decomposition kinetics and reaction pathways. With the main focus on the TCD diradicals, Figure 4 shows the stepwise calculations for the intermediate radical species and bond dissociation energies calculated in this study. The TCD-H2 m-n nomenclature corresponds to a starting TCD structure that has had the m-n bond cleaved and a H atom added to each carbon radical, as shown in Figures 3 and 4. The Cm−Cn bond corresponds to the TCD numbering in Figure 1. The structure with this m-n opened bond and each carbon radical site capped with H atoms was optimized. A monoradical was created (doublet species), denoted TCDH2 mJ-n or TCD-H2 m-nJ, from the optimized TCD-H2 m-n. The standard enthalpy and bond energy were calculated for the D


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smaller species with carbene (singlet and triplet) species. Three other work reactions are also used incorporating small n-alkane hydrocarbons and their olefins as illustrated in Scheme V. Optimized structures, moments of inertia, and vibration frequencies at the B3LYP/6-31G(d,p) level for all of the TCDH2 m-n parent, radical, diradical (triplet), and carbene (triplet) species are included in the Supporting Information.


Table 1. Standard Enthalpies of Formation for Reference Species in Work Reactions

a

species

ΔH°f298 (kcal mol−1)

reference

H CH4 CH3CH3 CH3CH2CH3 (CH3)3CH CH3CH2CH2CH3 CH3CH2CH2CH2CH3 CH2CH2 CH2CHCH3 CH3CHCHCH3 CH3CH2OH YC4H8 YC5H10 YC6H12 YC7H14 YYC7H12 YC8H16 YYC8H14 TCD CH3CJH2 CH3CJHCH3 (CH3)3CJ CH3CJHCH2CH3 :CH2 (s) :CH2 (t) CH3C:OH (s) CH3C:OH (t) YYCJ7H11

52.103 ± 0.001 −17.8 ± 0.1 −20.0 ± 0.1 −25.0 ± 0.1 −32.1 ± 0.1 −30.0 ± 0.1 −35.1 ± 0.2 12.5 ± 0.1 4.8 ± 0.2 −2.7 ± 0.2 −56.2 ± 0.1 6.6 ± 0.3 −18.3 ± 0.2 −29.5 ± 0.2 −37.0 ± 0.2 −13.1 ± 1.1 −44.1 ± 0.4 −23.7 ± 0.3 −19.5 ± 1.3 29.0 ± 0.4 21.5 ± 0.4 12.3 ± 0.4 16.1 ± 0.5 102.31 ± 0.20 93.31 ± 0.20 11.2 ± 1 42.3a 33.9 ± 1.1

70 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 19 72 72 72 72 73 73 29 29

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HEATS OF FORMATION ΔH°f298 1. Parents: TCD-H2 m-n. The work reactions for calculation of the ΔH°f298 for the lowest energy conformer of the TCD-H2 m-n parent species are listed in the Appendix. There is good consistency between the two sets of work reactions and the different levels of theory which serves as a check on our calculated ΔH°f298 values. The validation of these values from a second set of reactions is important as these parent species serve in the subsequent radical, diradical, and carbene work reactions. A summary of the ΔH°f298 values is provided in Table 2. The values from the B3LYP methods using the 6-31G(d,p) and 6-311G(2d,2p) basis sets are averaged and then compared to the average of the two composite methods CBS-QB3 and G3MP2B3. Our recommendation is the data from the composite methods which will be used in the subsequent reactions. Error analysis for the ΔH°f298 values incorporates uncertainties in the work reaction reference species and is calculated by taking the root-mean-square (RMS) of the sum of these uncertainties. The procedure is described in detail in the Supporting Information. 2. Radicals: TCD-H2 mJ-n and TCD-H2 m-nJ. Calculated ΔH°f298 and corresponding C−H BDE values for the lowest energy conformer of the radicals created from the loss of a single hydrogen atom from the TCD parent species are given in the Appendix. As expected, the heats of formation for the radicals at the 2-6 and 9-8 positions are nearly identical. In a similar fashion for the parent species, there is excellent precision in the ΔH°f298 values, so we average the B3LYP and composite methods and provide a summary in Table 2. We recommend the composite method average values and further use them as the standard reference ΔH°f298 values in the diradical work reactions. 3. Diradicals: TCD-H2 mJ-nJ. Table 3 lists the two sets of work reactions used to determine the heat of formation for the lowest energy conformer of the singlet and triplet diradicals using the calculated ΔH°f298 from respective TCD-H2 mJ-n and m-nJ radicals. The M06-2X and ωB97X-D functionals are also included in the diradical analysis to show the applicability of other DFT methods for these highly strained cyclic species. Use of work reactions and the spin-correction methods of Yamaguchi et al.56 and Sirjean et al.58 show that satisfactory results can be obtained from the less time and computationally demanding DFT methods compared to higher level results. The single-point energies from the CCSD(T) calculations, based on optimized B3LYP geometries, are also in line with the these methods. A summary of the singlet and triplet ΔH°f298 values is presented in Table 4. For the differences in the singlet and triplet energies for the diradicals, the majority falls below 1 kcal mol−1. The DFT methods

b

b

Error not reported. See Appendix for enthalpy calculation.

Scheme II. Work Reactions Using TCD Species for Validation of ΔH°f298 for Parent TCD-H2 m-n

Figure 5. Nomenclature of cyclic species as used in work reactions.

Cm−Cn location, we average all ten work reactions for the diradical ΔH°f298 values. For calculation of the ΔH°f298 for the lowest energy conformer of the TCD-H2 carbenes, we employ two work reactions that use

Scheme III. Work Reactions for Calculating ΔH°f298 of Single Radicals (Doublets)

E


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The Journal of Physical Chemistry A Scheme IV. Work Reactions for Calculating ΔH°f298 of Diradicals

Scheme V. Work Reactions for Calculating ΔH°f298 of Carbenes


Table 2. Summary of ΔH°f298 and C−H Bond Dissociation Energies for the Lowest Energy Conformer of TCD-H2 m-n Parent and Radical Speciesa,b B3LYPc species

ΔH°f298

TCD-H2 1-2 TCD-H2 1J-2 TCD-H2 1-2J TCD-H2 2-3 TCD-H2 2J-3 TCD-H2 2-3J TCD-H2 3-4 TCD-H2 3J-4 TCD-H2 3-4J TCD-H2 2-6 TCD-H2 2J-6 TCD-H2 2-6J TCD-H2 1-10 TCD-H2 1J-10 TCD-H2 1-10J TCD-H2 1-9 TCD-H2 1J-9 TCD-H2 1-9J TCD-H2 9-8 TCD-H2 9J-8 TCD-H2 9-8J

−33.9 ± 1.4 13.5 ± 2.4 13.9 ± 2.4 −31.4 ± 1.4 15.9 ± 2.4 19.5 ± 2.4 −29.1 ± 1.4 18.8 ± 2.4 19.2 ± 2.4 −25.1 ± 1.4 17.2 ± 2.4 17.2 ± 2.4 −32.2 ± 1.4 11.6 ± 2.4 17.2 ± 2.4 −35.7 ± 1.4 10.9 ± 2.4 15.5 ± 2.4 −38.2 ± 1.4 13.8 ± 2.4 13.8 ± 2.4

composited

C−H BDE

C−H BDEe

96.1 96.4

96.4 96.0

98.8 102.4

102.5 98.9

101.3 101.7

100.5 100.0

93.3 93.3

90.2 90.2

95.1 100.7

101.0 95.4

97.2 101.7

101.0 96.4

102.2 102.2

100.1 100.1

ΔH°f298 −30.5 ± 1.4 13.4 ± 2.4 13.9 ± 2.4 −30.8 ± 1.4 15.9 ± 2.4 18.3 ± 2.4 −30.4 ± 1.4 18.2 ± 2.4 18.3 ± 2.4 −24.1 ± 1.4 17.1 ± 2.4 17.1 ± 2.4 −31.5 ± 1.4 12.0 ± 2.4 16.5 ± 2.4 −34.2 ± 1.4 11.5 ± 2.4 14.5 ± 2.4 −36.3 ± 1.4 12.8 ± 2.4 12.8 ± 2.4

C−H BDE

C−H BDEe

96.0 96.4

96.8 96.3

98.8 101.2

101.6 99.2

100.7 100.8

100.8 100.7

93.2 93.2

94.4 94.4

95.6 100.1

100.0 95.5

97.8 100.7

100.8 97.8

101.2 101.2

100.8 100.8

Units kcal mol−1. bUncertainties for C−H BDEs are reported as ±2.4 kcal mol−1. cAverage from 6-31G(d,p) and 6-311G(2d,2p) basis sets. Average from CBS-QB3 and G3MP2B3 methods. eC−H BDE for the loss of the second hydrogen from the radical species generating diradical singlet species. a

d

For the DFT methods the largest difference occurs for the 2-6 position which ranges between 2.2 and 3.0 kcal mol−1. The other locations are all approximately 1 kcal mol−1 or less. In the CBSQB3 method, spin correction shows a substantial difference ranging from 5.6 to 5.9 kcal mol−1 where the 2-6 location is again the largest difference. 4. Comparison of ΔH°f298 TCD-H2 mJ-nJ to the Literature. Herbinet et al.7 also estimated thermochemical properties for these TCD diradicals. They used a combination of the THERGAS software,74 which we interpret as based on group additivity,75 and estimated corrections assuming no interaction between the two radical sites. A comparison between the Herbinet values and this study is presented in Table 4. Our singlet diradical values, regardless of the method, show that the TCD-H2 1J-2J, 2J-6J, 1J-10J, and 1J-9J positions are the lowest energy structures and fall within an approximate 4 kcal mol−1 range. These sites reflect the ring strain relief upon

predict larger differences for TCD-H2 9J-8J with a maximum of 2.4 kcal mol−1 from the B3LYP calculations. All of the methods show much larger differences for TCD-H2 2J-6J. Differences in singlet and triplet energies range from 5 to 6 kcal mol−1 from the DFT methods, while the higher level methods predict a lower 2−3 kcal mol−1 difference. For all of the methods, except CBSQB3, it is shown that the singlet is preferred to the triplet state. There is one exception from G3MP2B3 for TCD-H2 2J-3J where the triplet is favored by only 0.1 kcal mol−1. For the CBS-QB3 calculations it is seen that the triplet is lower in energy except for TCD-H2 2J-6J and 9J-8J where there are 2.2 and 0.3 kcal mol−1 differences, respectively. This could be from the spin-correction method applied to these values. On the basis of the results from the DFT, CCSD(T), and G3MP2B3 methods, we interpret that the singlet state is preferred for these TCD diradicals. ΔH°f298 singlet values using spin-uncorrected values are presented in Table 5 for comparison to spin-corrected values. F


G

1J-2J 1J-2J 1J-2J 1J-2J 1J-2J

2J-3J 2J-3J 2J-3J 2J-3J 2J-3J

2J-3J 2J-3J 2J-3J 2J-3J 2J-3J

3J-4J 3J-4J 3J-4J 3J-4J 3J-4J

TCD-H2 TCD-H2 TCD-H2 TCD-H2 TCD-H2




TCD-H2 3J-4J TCD-H2 3J-4J

1J-2J 1J-2J 1J-2J 1J-2J 1J-2J


1J-2 1J-2 1J-2 1J-2 1J-2

+ CH3CJH2 + CH3CJHCH3 + (CH3)3CJ + CH3CJHCH2CH3 + YYCJ7H11 Average C−H Bond Energy → TCD-H2 1-2J + CH3CJH2 + CH3CH3 → TCD-H2 1-2J + CH3CJHCH3 + CH3CH2CH3 → TCD-H2 1-2J + (CH3)3CJ + (CH3)3CH + CH3CH2CH2CH3 → TCD-H2 1-2J + CH3CJHCH2CH3 → TCD-H2 1-2J + YYCJ7H11 + YYC7H12 Average C−H Bond Energy TCD C1−C2 Bond Energy TCD-H2 2J-3J System → TCD-H2 2J-3 + CH3CJH2 + CH3CH3 → TCD-H2 2J-3 + CH3CJHCH3 + CH3CH2CH3 → TCD-H2 2J-3 + (CH3)3CJ + (CH3)3CH + CH3CH2CH2CH3 → TCD-H2 2J-3 + CH3CJHCH2CH3 → TCD-H2 2J-3 + YYCJ7H11 + YYC7H12 Average C−H Bond Energy → TCD-H2 2-3J + CH3CJH2 + CH3CH3 → TCD-H2 2-3J + CH3CJHCH3 + CH3CH2CH3 → TCD-H2 2-3J + (CH3)3CJ + (CH3)3CH + CH3CH2CH2CH3 → TCD-H2 2-3J + CH3CJHCH2CH3 → TCD-H2 2-3J + YYCJ7H11 + YYC7H12 Average C−H Bond Energy TCD C2−C3 Bond Energy TCD-H2 3J-4J System → TCD-H2 3J-4 + CH3CJH2 + CH3CH3 → TCD-H2 3J-4 + CH3CJHCH3 + CH3CH2CH3 → TCD-H2 3J-4 + (CH3)3CJ + (CH3)3CH + CH3CH2CH2CH3 → TCD-H2 3J-4 + CH3CJHCH2CH3 → TCD-H2 3J-4 + YYCJ7H11 + YYC7H12 Average C−H Bond Energy → TCD-H2 3-4J + CH3CJH2 + CH3CH3 → TCD-H2 3-4J + CH3CJHCH3 + CH3CH2CH3

TCD-H2 1J-2J system → TCD-H2 + CH3CH3 → TCD-H2 + CH3CH2CH3 → TCD-H2 + (CH3)3CH + CH3CH2CH2CH3 → TCD-H2 → TCD-H2 + YYC7H12

isodesmic reactions 56.65 57.95 58.78 57.42 58.06 57.8 96.5 56.79 58.09 58.92 57.56 58.20 57.9 96.1 77.3 65.03 66.33 67.16 65.80 66.44 66.2 102.4 64.05 65.35 66.18 64.82 65.46 65.2 99.0 85.1 65.32 66.62 67.45 66.09 66.74 66.4 100.4 64.95 66.25

56.38 57.78 58.76 57.15 58.03 57.6 96.3 56.48 57.88 58.86 57.25 58.13 57.7 95.9 77.1 65.09 66.49 67.48 65.86 66.74 66.3 102.5 63.83 65.23 66.21 64.60 65.48 65.1 98.9 85.2 65.49 66.89 67.88 66.26 67.14 66.7 100.7 65.12 66.52

66.25 67.05 66.95 66.02 67.16 66.7 100.6 66.12 66.91

65.20 65.99 65.90 64.96 66.11 65.6 101.8 64.72 65.51 65.42 64.48 65.63 65.2 98.9 84.9 66.48 67.40 67.76 66.59 67.40 67.1 101.1 66.66 67.57

64.90 65.82 66.18 65.01 65.83 65.5 101.8 64.57 65.48 65.84 64.67 65.49 65.2 99.0 84.8

Singlets 57.34 57.21 58.13 58.12 58.03 58.49 57.10 57.31 58.25 58.13 57.8 57.9 96.5 96.6 57.29 56.96 58.08 57.87 57.99 58.24 57.05 57.06 58.20 57.88 57.7 57.6 95.9 95.8 77.2 77.2 58.33 58.59 58.21 57.96 59.20 58.5 97.2 58.36 58.61 58.24 57.99 59.23 58.5 96.7 77.9

58.07 57.89 57.16 57.24 58.34 57.7 96.4 58.04 57.86 57.13 57.21 58.32 57.7 95.9 77.2

67.03 67.15 66.76 67.04 67.41 66.59 66.52 67.03 65.85 66.25 66.78 65.94 67.20 68.02 67.04 66.8 67.3 66.4 100.7 101.2 100.4 67.04 67.09 66.83 67.06 67.34 66.65

65.42 65.81 65.24 65.44 66.07 65.06 64.92 65.70 64.33 64.64 65.45 64.41 65.59 66.68 65.52 65.2 65.9 64.9 101.4 102.2 101.1 65.67 65.52 65.53 65.68 65.78 65.36 65.16 65.41 64.62 64.89 65.16 64.71 65.84 66.39 65.81 65.4 65.7 65.2 99.2 99.4 99.0 84.8 85.3 84.5

58.38 58.40 57.88 57.60 58.55 58.2 96.9 58.04 58.05 57.54 57.26 58.21 57.8 96.0 77.5

66.75 68.14 69.13 67.51 68.40 68.0 101.9 66.37 67.77

65.10 66.50 67.48 65.87 66.75 66.3 102.5 63.83 65.23 66.21 64.60 65.48 65.1 98.9 85.2

56.38 57.77 58.76 57.14 58.02 57.6 96.3 56.47 57.87 58.85 57.24 58.12 57.7 95.9 77.1

66.72 68.02 68.84 67.49 68.13 67.8 101.8 66.35 67.65

65.02 66.32 67.15 65.79 66.43 66.1 102.4 64.04 65.34 66.17 64.81 65.45 65.2 98.9 85.1

56.65 57.95 58.78 57.43 58.07 57.8 96.5 56.79 58.09 58.92 57.57 58.21 57.9 96.1 77.3

66.60 67.39 67.30 66.36 67.51 67.0 101.0 66.47 67.26

65.21 66.00 65.90 64.97 66.12 65.6 101.9 64.73 65.52 65.42 64.49 65.63 65.2 98.9 84.9

66.82 67.74 68.10 66.93 67.74 67.5 101.4 67.00 67.91

65.36 66.28 66.64 65.47 66.29 66.0 102.2 65.03 65.94 66.30 65.13 65.95 65.7 99.5 85.3

Triplets 57.33 57.21 58.12 58.13 58.02 58.49 57.09 57.32 58.24 58.14 57.8 57.9 96.5 96.6 57.28 56.96 58.08 57.88 57.98 58.24 57.04 57.07 58.19 57.89 57.7 57.6 95.9 95.8 77.2 77.2

57.60 57.86 57.48 57.23 58.47 57.7 96.4 57.63 57.89 57.51 57.26 58.50 57.8 96.0 77.2

67.05 66.94 67.06 67.20 66.54 66.83 66.27 66.58 67.22 67.81 66.8 67.1 100.8 101.0 67.06 66.88 67.08 67.14

65.49 65.15 65.51 65.40 64.99 65.03 64.71 64.78 65.66 66.02 65.3 65.3 101.5 101.5 65.74 64.86 65.75 65.11 65.23 64.74 64.96 64.49 65.91 65.73 65.5 65.0 99.3 98.8 84.9 84.6

58.38 58.39 57.87 57.60 58.55 58.2 96.9 58.04 58.05 57.53 57.25 58.20 57.8 96.0 77.4

67.02 66.85 66.11 66.20 67.30 66.7 100.6 67.09 66.91

65.20 65.02 64.29 64.37 65.48 64.9 101.1 65.49 65.32 64.58 64.67 65.77 65.2 99.0 84.5

58.09 57.91 57.18 57.26 58.36 57.8 96.5 58.06 57.88 57.15 57.23 58.34 57.7 96.0 77.2

B3LYP/ B3LYP/ M06-2X/ ωB97X-D/ CBSB3LYP/ B3LYP/ M06-2X/ ωB97X-D/ CBS6-31G(d,p) 6-311G(2d,2p) 6-31G(d,p) 6-31G(d,p) CCSD(T) QB3 G3MP2B3 6-31G(d,p) 6-311G(2d,2p) 6-31G(d,p) 6-31G(d,p) CCSD(T) QB3 G3MP2B3


Table 3. Isodesmic Reactions, Calculated ΔH°f298, and Bond Dissociation Energies for the Lowest Energy Conformer of TCD-H2 mJ-nJ Diradicals


The Journal of Physical Chemistry A Article


isodesmic reactions

TCD-H2 3J-4J System → TCD-H2 3-4J + (CH3)3CJ TCD-H2 3J-4J + (CH3)3CH TCD-H2 3J-4J + CH3CH2CH2CH3 → TCD-H2 3-4J + CH3CJHCH2CH3 → TCD-H2 3-4J + YYCJ7H11 TCD-H2 3J-4J + YYC7H12 Average C−H Bond Energy TCD-H2 C3−C4 Bond Energy TCD-H2 2J-6J System → TCD-H2 2J-6 + CH3CJH2 TCD-H2 2J-6J + CH3CH3 → TCD-H2 2J-6 + CH3CJHCH3 TCD-H2 2J-6J + CH3CH2CH3 → TCD-H2 2J-6 + (CH3)3CJ TCD-H2 2J-6J + (CH3)3CH TCD-H2 2J-6J + CH3CH2CH2CH3 → TCD-H2 2J-6 + CH3CJHCH2CH3 → TCD-H2 2J-6 + YYCJ7H11 TCD-H2 2J-6J + YYC7H12 Average C−H Bond Energy → TCD-H2 2-6J + CH3CJH2 TCD-H2 2J-6J + CH3CH3 → TCD-H2 2-6J + CH3CJHCH3 TCD-H2 2J-6J + CH3CH2CH3 → TCD-H2 2-6J + (CH3)3CJ TCD-H2 2J-6J + (CH3)3CH TCD-H2 2J-6J + CH3CH2CH2CH3 → TCD-H2 2-6J + CH3CJHCH2CH3 → TCD-H2 2-6J + YYCJ7H11 TCD-H2 2J-6J + YYC7H12 Average C−H Bond Energy TCD C2−C6 Bond Energy TCD-H2 1J-10J System → TCD-H2 1J-10 + CH3CJH2 TCD-H2 1J-10J + CH3CH3 → TCD-H2 1J-10 + CH3CJHCH3 TCD-H2 1J-10J + CH3CH2CH3 → TCD-H2 1J-10 + (CH3)3CJ TCD-H2 1J-10J + (CH3)3CH TCD-H2 1J-10J + CH3CH2CH2CH3 → TCD-H2 1J-10 + CH3CJHCH2CH3 → TCD-H2 1J-10 + YYCJ7H11 TCD-H2 1J-10J + YYC7H12 Average C−H Bond Energy → TCD-H2 1-10J + CH3CJH2 TCD-H2 1J-10J + CH3CH3 → TCD-H2 1-10J + CH3CJHCH3 TCD-H2 1J-10J + CH3CH2CH3 → TCD-H2 1-10J + (CH3)3CJ TCD-H2 1J-10J + (CH3)3CH TCD-H2 1J-10J + CH3CH2CH2CH3 → TCD-H2 1-10J + CH3CJHCH2CH3 → TCD-H2 1-10J + YYCJ7H11 TCD-H2 1J-10J + YYC7H12 Average C−H Bond Energy TCD C1−C10 Bond Energy TCD-H2 1J-9J System → TCD-H2 1J-9 + CH3CJH2 TCD-H2 1J-9J + CH3CH3 → TCD-H2 1J-9 + CH3CJHCH3 TCD-H2 1J-9J + CH3CH2CH3

Table 3. continued

67.08 65.73 66.37 66.1 99.9 85.7 54.19 55.50 56.32 54.97 55.61 55.3 90.4 54.20 55.50 56.32 54.97 55.61 55.3 90.4 74.8 59.68 60.98 61.81 60.46 61.10 60.8 100.9 58.67 59.97 60.80 59.44 60.08 59.8 95.4 79.8 59.19 60.49

67.50 65.89 66.77 66.4 100.2 86.0 53.76 55.16 56.14 54.52 55.41 55.0 90.0 53.76 55.16 56.14 54.53 55.41 55.0 90.0 74.5 59.71 61.11 62.10 60.48 61.36 61.0 101.1 58.54 59.94 60.93 59.31 60.19 59.8 95.4 79.8

H

59.23 60.63

59.00 59.79

58.99 59.78 59.69 58.75 59.90 59.4 99.5 58.73 59.52 59.43 58.49 59.64 59.2 94.7 78.8

56.06 56.85 56.75 55.82 56.96 56.5 91.5 56.06 56.85 56.75 55.82 56.97 56.5 91.5 75.9

59.44 60.36

59.59 60.51 60.87 59.70 60.52 60.2 100.3 58.66 59.58 59.94 58.77 59.59 59.3 94.9 79.2

54.91 55.82 56.18 55.01 55.83 55.6 90.6 54.91 55.82 56.19 55.01 55.83 55.6 90.6 75.0

Singlets 66.82 67.93 65.88 66.76 67.03 67.58 66.6 67.3 100.4 101.1 86.1 86.7 59.49 59.74 59.37 59.12 60.36 59.6 94.7 59.48 59.74 59.37 59.12 60.35 59.6 94.6 79.1

60.21 60.22

60.59 60.84

60.26 60.28 60.27 60.53 59.75 60.16 59.47 59.91 60.43 61.15 60.0 60.4 100.1 100.5 60.44 60.07 60.45 60.33 59.94 59.96 59.66 59.71 60.61 60.94 60.2 60.2 95.8 95.8 79.6 79.8

59.37 59.39 58.87 58.59 59.54 59.2 94.2 59.38 59.39 58.87 58.59 59.54 59.2 94.2 78.6

60.06 59.88

59.74 59.56 58.83 58.91 60.01 59.4 99.5 59.94 59.76 59.03 59.11 60.22 59.6 95.2 79.0

59.36 59.18 58.44 58.53 59.63 59.0 94.1 59.36 59.18 58.45 58.53 59.64 59.0 94.1 78.5

66.54 66.97 65.91 66.26 66.72 66.00 67.21 67.96 67.10 66.8 67.2 66.5 100.6 101.0 100.3 86.3 86.7 85.9

60.12 61.52

59.85 61.25 62.23 60.61 61.50 61.1 101.2 58.68 60.07 61.06 59.44 60.33 59.9 95.5 80.0

59.75 61.15 62.13 60.52 61.40 61.0 96.0 59.75 61.15 62.13 60.52 61.40 61.0 96.0 80.4

68.75 67.14 68.02 67.6 101.4 87.3

60.10 61.40

59.84 61.14 61.97 60.61 61.26 61.0 101.1 58.83 60.13 60.96 59.60 60.24 60.0 95.5 79.9

59.90 61.21 62.03 60.68 61.32 61.0 96.1 59.91 61.21 62.03 60.68 61.32 61.0 96.1 80.5

68.48 67.12 67.76 67.5 101.3 87.1

60.06 60.85

59.17 59.96 59.86 58.93 60.08 59.6 99.7 58.91 59.70 59.60 58.67 59.82 59.3 94.9 78.9

60.74 61.53 61.43 60.50 61.64 61.2 96.2 60.74 61.53 61.43 60.50 61.65 61.2 96.2 80.6

60.34 61.26

59.73 60.64 61.01 59.83 60.65 60.4 100.5 58.80 59.71 60.08 58.90 59.72 59.4 95.0 79.4

61.09 62.00 62.37 61.19 62.01 61.7 96.8 61.09 62.01 62.37 61.20 62.01 61.7 96.8 81.2

Triplets 67.16 68.27 66.23 67.10 67.38 67.92 66.9 67.6 100.7 101.5 86.4 87.0

61.64 61.90 61.52 61.27 62.51 61.8 96.8 61.64 61.90 61.52 61.27 62.51 61.8 96.8 81.2

60.49 60.50

60.37 60.63

60.38 59.75 60.39 60.01 59.87 59.63 59.59 59.38 60.54 60.62 60.2 59.9 100.3 100.0 60.56 59.55 60.57 59.80 60.05 59.43 59.78 59.18 60.73 60.42 60.3 59.7 95.9 95.3 79.7 79.2

61.93 61.94 61.42 61.14 62.09 61.7 96.7 61.93 61.94 61.42 61.14 62.10 61.7 96.7 81.2

66.56 66.76 66.28 66.52 67.23 67.75 66.8 67.0 100.7 100.8 86.3 86.5

60.44 60.26

59.97 59.80 59.06 59.15 60.25 59.6 99.7 60.18 60.00 59.26 59.35 60.45 59.8 95.4 79.2

62.23 62.05 61.31 61.40 62.50 61.9 96.9 62.23 62.05 61.31 61.40 62.50 61.9 96.9 81.4

66.18 66.26 67.36 66.8 100.6 86.2






isodesmic reactions

TCD-H2 1J-9J System → TCD-H2 1J-9 + (CH3)3CJ TCD-H2 1J-9J + (CH3)3CH TCD-H2 1J-9J + CH3CH2CH2CH3 → TCD-H2 1J-9 + CH3CJHCH2CH3 → TCD-H2 1J-9 + YYCJ7H11 TCD-H2 1J-9J + YYC7H12 Average C−H Bond Energy → TCD-H2 1-9J + CH3CJH2 TCD-H2 1J-9J + CH3CH3 → TCD-H2 1-9J + CH3CJHCH3 TCD-H2 1J-9J + CH3CH2CH3 → TCD-H2 1-9J + (CH3)3CJ TCD-H2 1J-9J + (CH3)3CH TCD-H2 1J-9J + CH3CH2CH2CH3 → TCD-H2 1-9J + CH3CJHCH2CH3 → TCD-H2 1-9J + YYCJ7H11 TCD-H2 1J-9J + YYC7H12 Average C−H Bond Energy TCD C1−C9 Bond Energy TCD-H2 9J-8J System → TCD-H2 9J-8 + CH3CJH2 TCD-H2 9J-8J + CH3CH3 → TCD-H2 9J-8 + CH3CJHCH3 TCD-H2 9J-8J + CH3CH2CH3 → TCD-H2 9J-8 + (CH3)3CJ TCD-H2 9J-8J + (CH3)3CH TCD-H2 9J-8J + CH3CH2CH2CH3 → TCD-H2 9J-8 + CH3CJHCH2CH3 → TCD-H2 9J-8 + YYCJ7H11 TCD-H2 9J-8J + YYC7H12 Average C−H Bond Energy → TCD-H2 9-8J + CH3CJH2 TCD-H2 9J-8J + CH3CH3 → TCD-H2 9-8J + CH3CJHCH3 TCD-H2 9J-8J + CH3CH2CH3 → TCD-H2 9-8J + (CH3)3CJ TCD-H2 9J-8J + (CH3)3CH TCD-H2 9J-8J + CH3CH2CH2CH3 → TCD-H2 9-8J + CH3CJHCH2CH3 → TCD-H2 9-8J + YYCJ7H11 TCD-H2 9J-8J + YYC7H12 Average C−H Bond Energy TCD C9−C8 Bond Energy

Table 3. continued

61.32 59.96 60.60 60.3 100.9 57.64 58.95 59.77 58.42 59.06 58.8 96.4 79.0 59.43 60.73 61.56 60.20 60.85 60.6 99.9 59.43 60.73 61.56 60.20 60.85 60.6 99.9 80.0

61.61 60.00 60.88 60.5 101.1 57.60 59.00 59.98 58.37 59.25 58.8 96.5 79.1 59.67 61.07 62.05 60.44 61.32 60.9 100.2 59.67 61.07 62.05 60.44 61.32 60.9 100.2 80.4

61.04 61.83 61.73 60.80 61.94 61.5 100.8 61.04 61.83 61.73 60.80 61.94 61.5 100.8 80.9

60.88 61.79 62.15 60.98 61.80 61.5 100.9 60.88 61.79 62.15 60.98 61.80 61.5 100.9 81.0

Singlets 59.69 60.72 58.76 59.55 59.91 60.36 59.4 60.1 100.0 100.7 58.67 58.67 59.47 59.58 59.37 59.95 58.44 58.77 59.58 59.59 59.1 59.3 96.7 96.9 78.7 79.2 62.35 61.75 61.41 62.36 62.01 61.23 61.85 61.63 60.50 61.57 61.39 60.58 62.52 62.62 61.68 62.1 61.9 61.1 101.5 101.2 100.4 62.35 61.75 61.41 62.36 62.01 61.23 61.85 61.63 60.50 61.57 61.39 60.58 62.52 62.62 61.68 62.1 61.9 61.1 101.5 101.2 100.4 81.6 81.3 80.5

59.71 60.47 59.14 59.43 60.22 59.23 60.38 61.46 60.33 60.0 60.7 59.7 100.6 101.3 100.3 60.33 60.32 60.32 60.34 60.58 60.14 59.82 60.21 59.41 59.54 59.96 59.49 60.49 61.19 60.59 60.1 60.5 60.0 97.7 98.1 97.6 79.5 80.0 79.3 61.99 63.39 64.37 62.75 63.64 63.2 102.6 61.99 63.39 64.37 62.75 63.64 63.2 102.6 82.7

62.50 60.89 61.77 61.4 102.0 58.49 59.89 60.87 59.26 60.14 59.7 97.4 80.0 61.91 63.21 64.04 62.69 63.33 63.0 102.4 61.91 63.21 64.04 62.69 63.33 63.0 102.4 82.5

62.23 60.87 61.52 61.2 101.8 58.56 59.86 60.68 59.33 59.97 59.7 97.3 79.9 62.32 63.11 63.02 62.08 63.23 62.8 102.1 62.32 63.11 63.02 62.08 63.23 62.8 102.1 82.2

62.68 63.60 63.96 62.79 63.61 63.3 102.7 62.68 63.60 63.96 62.79 63.61 63.3 102.7 82.8

Triplets 60.75 61.62 59.82 60.45 60.96 61.27 60.5 61.0 101.1 101.6 59.73 59.57 60.52 60.48 60.43 60.85 59.49 59.67 60.64 60.49 60.2 60.2 97.8 97.8 79.8 80.1

62.75 62.10 62.76 62.36 62.25 61.98 61.97 61.74 62.92 62.97 62.5 62.2 101.9 101.6 62.75 62.10 62.76 62.36 62.25 61.98 61.97 61.74 62.92 62.97 62.5 62.2 101.9 101.6 82.0 81.7

59.98 60.25 59.70 60.01 60.65 61.24 60.3 60.5 100.9 101.1 60.60 60.11 60.61 60.37 60.10 59.99 59.82 59.74 60.77 60.98 60.4 60.2 98.0 97.9 79.8 79.8

62.34 62.16 61.43 61.51 62.61 62.0 101.3 62.34 62.16 61.43 61.51 62.61 62.0 101.3 81.5

59.52 59.61 60.71 60.1 100.7 60.70 60.52 59.79 59.87 60.98 60.4 98.0 79.7





I


Article


Table 4. Summary of Calculated ΔH°f298 for the Lowest Energy Conformer of TCD-H2 mJ-nJ Diradicals with Comparison to Literature Valuesa,b B3LYPc

ωB97X-D

M06-2X

CCSD(T)

CBSQB3

G3MP2B3

species

singlet

triplet

singlet

triplet

singlet

triplet

singlet

triplet

singlet

triplet

singlet

triplet

literaturee

TCD-H2 1J-2J TCD-H2 2J-3J TCD-H2 3J-4J TCD-H2 2J-6Jd TCD-H2 1J-10J TCD-H2 1J-9J TCD-H2 9J-8J

57.8 65.7 66.4 55.2 60.3 59.6 60.7

57.8 65.7 67.7 61.0 60.5 60.5 63.1

57.7 65.4 66.6 56.5 59.3 59.3 61.5

57.7 65.4 67.0 61.2 59.5 60.3 62.8

57.7 65.4 67.2 55.6 59.8 59.7 61.5

57.7 65.8 67.6 61.7 59.9 60.6 63.3

58.0 65.3 66.8 59.2 60.1 60.0 62.1

58.0 65.4 66.8 61.7 60.2 60.3 62.5

58.5 65.8 67.2 59.6 60.3 60.6 61.9

57.7 65.1 67.0 61.8 59.8 60.4 62.2

57.7 65.1 66.5 59.0 59.5 59.9 61.1

57.7 65.0 66.7 61.9 59.7 60.2 62.0

57.41 67.80 68.14 72.21 61.79 67.49 67.39

Units kcal mol−1 bUncertainties are reported as ±3.3 kcal mol−1. cAverage from 6-31G(d,p) and 6-311G(2d,2p) Basis Sets; dhad one negative frequency corresponding to bond reformation converted to positive for each method, accuracy is uncertain. eRef 7.

a

Table 5. Comparison of Spin-Corrected and -Uncorrected ΔH°f298 Values for Singlet TCD-H2 m-n Diradicals and Carbenesa


B3LYP

a

ωB97X-D

M06-2X

CBS-QB3

species

corrected

uncorrected

corrected

uncorrected

corrected

uncorrected

corrected

uncorrected

TCD-H2 1J-2J TCD-H2 2J-3J TCD-H2 3J-4J TCD-H2 2J-6J TCD-H2 1J-10J TCD-H2 1J-9J TCD-H2 9J-8J TCD-H2 1JJ-2 TCD-H2 1-2JJ TCD-H2 2JJ-3 TCD-H2 2-3JJ TCD-H2 3JJ-4 TCD-H2 3-4JJ TCD-H2 2JJ-6 TCD-H2 1JJ-10 TCC-H2 1-10JJ TCD-H2 1JJ-9 TCD-H2 1-9JJ TCD-H2 9JJ-8

57.8 65.7 66.4 55.2 60.3 59.6 60.7 60.0 60.2 62.3 75.2 72.6 74.5 65.4 57.8 68.5 57.9 71.2 69.5

57.8 65.7 67.0 57.7 60.4 60.0 61.9 60.5 60.3 62.3 74.3 71.9 73.8 65.5 58.4 68.5 58.7 70.2 68.7

57.7 65.4 66.6 56.5 59.3 59.3 61.5 61.2 61.3 62.6 77.2 77.0 77.0 66.7 60.3 70.1 60.7 73.1 73.1

57.7 65.4 66.8 58.7 59.4 59.8 62.1 61.2 61.3 62.6 76.0 75.2 75.7 66.7 60.3 70.1 60.7 71.9 71.0

57.7 65.4 67.2 55.6 59.8 59.7 61.5 60.7 61.4 63.7 76.1 74.3 75.6 67.0 60.0 70.5 59.8 72.0 70.9

57.7 65.6 67.4 58.5 59.8 60.1 62.4 60.9 61.4 63.7 74.7 73.2 74.2 66.8 60.1 70.0 60.3 70.6 69.7

58.5 65.8 67.2 59.6 60.3 60.6 61.9

52.9 60.2 61.5 53.7 54.7 55.0 56.2

Units kcal mol−1.

bond breakage into a more relaxed geometry and are consistent with the TCD-H2 1J-2J and 1J-10J values determined by Herbinet, while the 1J-9J position is over 7 kcal mol−1 higher in energy suggesting less relief of ring strain upon bond cleavage. They also determined that the 2J-6J position has the highest ΔH°f298 for these diradicals, while we determine it to be one of the lowest for both the singlet and triplet states. Li et al.11 suggested that cleavage of the 2-6 bond could be the first ringopening position, and Davidson et al.5 noted that this 2-6 location might also be most susceptible to bond reformation. The TCD-H2 2J-3J, 3J-4J, and 9J-8J diradicals all have reported enthalpies within less than 1 kcal mol−1 to each other in the Herbinet study. Our calculations show good correlation to these values for the 2-3 and 3-4 positions, but our 9-8 position is approximately 6 kcal mol−1 lower in energy. 5. Carbenes: TCD-H2 mJJ-n and TCD-H2 m-nJJ. We have also calculated some initial ΔH°f298 values for the lowest energy conformer of the TCD carbene species for comparison to the diradicals. Optimization of the triplet state carbenes was straightforward, similar to the triplet diradicals, while careful singlet optimization was necessary. Singlet carbenes with terminal alkane locations (for example 2-3JJ, 3-4JJ, 1-9JJ, and 9JJ-8) would quickly converge to more stable bicyclic olefins via a hydrogen

transfer from an adjacent carbon. Keeping this in mind, we determined ΔH°f298 values for all singlet and triplet species using work reactions shown in Table 6. Since the same enthalpy values were seen for the radicals and diradicals for 2-6 and 9-8, we have only analyzed one carbene species for each location. All of the DFT methods have been corrected using the same spin-projection method that we used for the diradicals. A summary of the calculated ΔH°f298 values is presented in Table 7 where we see, in general, that there are similar values for the DFT methods, while the values from CCSD(T), CBS-QB3, and G3MP2B3 are higher. In the subsequent analysis, we consider the range of values determined from all the calculation methods. The singlet−triplet gaps for these carbenes have a much larger range as compared to the diradicals from under 1 to over 10 kcal mol−1. This is expected due to the proximity of the two electrons on the single carbon. Except for two cases, TCD-H2 2JJ-6 and 1-10JJ, all of the methods show agreement in preference for either the singlet or triplet state. The singlets are more stable for secondary cyclic positions, while the triplets show favorable stability for the terminal methyl locations. From these methods, we see that some of the carbenes are similar in energy to the diradicals. TCD-H2 1JJ-2, 1-2JJ, 2JJ-3, 1JJ-10, and 1JJ-9 singlet species all have energies between J


1JJ-2 1JJ-2 1JJ-2 1JJ-2 1JJ-2

1-2JJ 1-2JJ 1-2JJ 1-2JJ 1-2JJ

2JJ-3 2JJ-3 2JJ-3 2JJ-3 2JJ-3

2-3JJ 2-3JJ 2-3JJ 2-3JJ 2-3JJ

3JJ-4 3JJ-4 3JJ-4 3JJ-4 3JJ-4





K


+ + + + +

+ + + + +

+ + + + +

+ + + + +

+ + + + +

1-2 1-2 1-2 1-2 1-2

+ + + + +

:CH2 CH3C:OH CH2CH2 CH2CHCH3 CH3CHCHCH3 Average TCD C1−C2 Bond Energy TCD-H2 1-2JJ System → TCD-H2 1-2 + :CH2 CH4 → TCD-H2 1-2 + CH3C:OH CH3CH2OH → TCD-H2 1-2 + CH2CH2 CH3CH3 → TCD-H2 1-2 + CH2CHCH3 CH3CH2CH3 CH3CH2CH2CH3 → TCD-H2 1-2 + CH3CHCHCH3 Average TCD C1−C2 Bond Energy TCD-H2 2JJ-3 System → TCD-H2 2-3 + :CH2 CH4 → TCD-H2 2-3 + CH3C:OH CH3CH2OH → TCD-H2 2-3 + CH2CH2 CH3CH3 → TCD-H2 2-3 + CH2CHCH3 CH3CH2CH3 CH3CH2CH2CH3 → TCD-H2 2-3 + CH3CHCHCH3 Average TCD C2−C3 Bond Energy TCD-H2 2-3JJ System → TCD-H2 2-3 + :CH2 CH4 → TCD-H2 2-3 + CH3C:OH CH3CH2OH → TCD-H2 2-3 + CH2CH2 CH3CH3 → TCD-H2 2-3 + CH2CHCH3 CH3CH2CH3 CH3CH2CH2CH3 → TCD-H2 2-3 + CH3CHCHCH3 Average TCD C2−C3 Bond Energy TCD-H2 3JJ-4 System → TCD-H2 3-4 + :CH2 CH4 → TCD-H2 3-4 + CH3C:OH CH3CH2OH → TCD-H2 3-4 + CH2CH2 CH3CH3 → TCD-H2 3-4 + CH2CHCH3 CH3CH2CH3 CH3CH2CH2CH3 → TCD-H2 3-4 + CH3CHCHCH3 Average TCD C3−C4 Bond Energy

TCD-H2 1JJ-2 system → TCD-H2 CH4 → TCD-H2 CH3CH2OH → TCD-H2 CH3CH3 → TCD-H2 CH3CH2CH3 CH3CH2CH2CH3 → TCD-H2

isodesmic reactions 60.49 61.58 58.64 59.64 60.39 60.1 79.6 60.61 61.71 58.76 59.77 60.51 60.3 79.7 62.47 63.57 60.62 61.63 62.37 62.1 81.6 75.57 76.67 73.72 74.73 75.47 75.2 94.7 72.91 74.00 71.06 72.06 72.81 72.6 92.0

60.17 61.17 58.33 59.51 60.50 59.9 79.4 60.26 61.26 58.42 59.60 60.59 60.0 79.5 62.68 63.68 60.83 62.02 63.01 62.4 81.9 75.46 76.46 73.61 74.80 75.79 75.2 94.7 72.82 73.82 70.98 72.16 73.15 72.6 92.0

74.28 78.99 76.64 77.45 77.53 77.0 96.4

74.45 79.16 76.82 77.62 77.71 77.2 96.6

59.95 64.65 62.31 63.12 63.20 62.6 82.1

58.59 63.30 60.96 61.77 61.85 61.3 80.8

58.53 63.24 60.90 61.70 61.79 61.2 80.7

73.96 76.76 73.22 73.73 74.06 74.3 93.8

75.76 78.56 75.02 75.53 75.87 76.1 95.6

63.28 66.08 62.54 63.05 63.38 63.7 83.1

61.04 63.84 60.30 60.81 61.15 61.4 80.9

Singlet 60.30 63.09 59.56 60.07 60.40 60.7 80.1

82.39 75.83 73.46 73.36 73.53 75.7 95.2

84.24 77.67 75.31 75.20 75.37 77.6 97.0

70.87 64.31 61.94 61.83 62.01 64.2 83.7

69.16 62.60 60.23 60.12 60.30 62.5 81.9

70.14 63.57 61.21 61.10 61.27 63.5 82.9

81.46 74.10 74.08 74.07 73.90 75.5 95.0

82.87 75.52 75.49 75.48 75.31 76.9 96.4

70.05 62.70 62.67 62.66 62.50 64.1 83.6

69.46 62.11 62.08 62.07 61.90 63.5 83.0

67.98 60.63 60.60 60.60 60.43 62.0 81.5

82.79 78.49 78.45 78.33 77.96 79.2 98.7

84.06 79.76 79.72 79.60 79.23 80.5 99.9

67.29 62.99 62.95 62.82 62.45 63.7 83.2

68.61 64.30 64.27 64.14 63.77 65.0 84.5

68.77 64.47 64.43 64.31 63.94 65.2 84.6

69.87 76.19 67.94 69.12 70.12 70.6 90.1

71.83 78.15 69.90 71.09 72.08 72.6 92.1

69.44 75.76 67.51 68.70 69.69 70.2 89.7

67.21 73.52 65.27 66.46 67.45 68.0 87.4

67.22 73.53 65.28 66.47 67.46 68.0 87.5

69.85 75.78 69.19 70.20 70.94 71.2 90.7

71.82 77.75 71.16 72.16 72.91 73.2 92.6

69.82 75.75 69.16 70.17 70.91 71.2 90.6

67.58 73.50 66.91 67.92 68.67 68.9 88.4

67.68 73.61 67.02 68.03 68.77 69.0 88.5

71.67 73.55 67.00 67.81 67.89 69.6 89.0

73.76 75.64 69.09 69.90 69.98 71.7 91.1

72.91 74.79 68.25 69.05 69.13 70.8 90.3

70.55 72.43 65.89 66.69 66.78 68.5 87.9

70.31 72.19 65.65 66.45 66.54 68.2 87.7

72.16 77.19 68.28 68.79 69.13 71.1 90.6

73.15 78.18 69.28 69.79 70.12 72.1 91.6

72.39 77.42 68.51 69.03 69.36 71.3 90.8

69.77 74.80 65.89 66.40 66.74 68.7 88.2

Triplet 68.95 73.98 65.07 65.58 65.91 67.9 87.4

74.58 74.24 67.01 66.90 67.08 70.0 89.4

75.74 75.40 68.17 68.06 68.23 71.1 90.6

76.01 75.66 68.44 68.33 68.50 71.4 90.8

73.85 73.51 66.28 66.17 66.35 69.2 88.7

73.29 72.95 65.72 65.61 65.78 68.7 88.1

72.85 74.31 73.75 73.74 73.57 73.6 93.1

73.92 75.38 74.82 74.81 74.64 74.7 94.2

72.94 74.40 73.84 73.83 73.66 73.7 93.2

70.70 72.16 71.60 71.59 71.42 71.5 91.0

70.28 71.74 71.18 71.17 71.00 71.1 90.5

74.06 74.08 73.49 73.37 73.00 73.6 93.1

74.88 74.89 74.30 74.18 73.81 74.4 93.9

74.76 74.78 74.19 74.07 73.70 74.3 93.8

72.46 72.47 71.89 71.76 71.39 72.0 91.5

71.97 71.98 71.40 71.27 70.90 71.5 91.0



Table 6. Isodesmic Reactions, Calculated ΔH°f298, and Bond Dissociation Energies for the Lowest Energy Conformer of TCD-H2 m-n Carbenes




3-4JJ 3-4JJ 3-4JJ 3-4JJ 3-4JJ

2JJ-6 2JJ-6 2JJ-6 2JJ-6 2JJ-6

1JJ-10 1JJ-10 1JJ-10 1JJ-10 1JJ-10

1-10JJ 1-10JJ 1-10JJ 1-10JJ 1-10JJ

1JJ-9 1JJ-9 1JJ-9 1JJ-9 1JJ-9





L


+ + + + +

+ + + + +

+ + + + +

+ + + + +

+ + + + +

isodesmic reactions 3-4 3-4 3-4 3-4 3-4

+ + + + +

:CH2 CH3C:OH CH2CH2 CH2CHCH3 CH3CHCHCH3 Average TCD C3−C4 Bond Energy TCD-H2 2JJ-6 System → TCD-H2 2-6 + :CH2 CH4 → TCD-H2 2-6 + CH3C:OH CH3CH2OH → TCD-H2 2-6 + CH2CH2 CH3CH3 → TCD-H2 2-6 + CH2CHCH3 CH3CH2CH3 CH3CH2CH2CH3 → TCD-H2 2-6 + CH3CHCHCH3 Average TCD C2−C6 Bond Energy TCD-H2 1JJ-10 System → TCD-H2 1-10 + :CH2 CH4 → TCD-H2 1-10 + CH3C:OH CH3CH2OH → TCD-H2 1-10 + CH2CH2 CH3CH3 → TCD-H2 1-10 + CH2CHCH3 CH3CH2CH3 CH3CH2CH2CH3 → TCD-H2 1-10 + CH3CHCHCH3 Average TCD C1−C10Bond Energy TCD-H2 1−10JJ System → TCD-H2 1-10 + :CH2 CH4 → TCD-H2 1-10 + CH3C:OH CH3CH2OH → TCD-H2 1-10 + CH2CH2 CH3CH3 → TCD-H2 1-10 + CH2CHCH3 CH3CH2CH3 CH3CH2CH2CH3 → TCD-H2 1-10 + CH3CHCHCH3 Average TCD C1−C10 Bond Energy TCD-H2 1JJ-9 System → TCD-H2 1-9 + :CH2 CH4 → TCD-H2 1-9 + CH3C:OH CH3CH2OH → TCD-H2 1-9 + CH2CH2 CH3CH3 → TCD-H2 1-9 + CH2CHCH3 CH3CH2CH3 CH3CH2CH2CH3 → TCD-H2 1-9 + CH3CHCHCH3 Average TCD C1−C9 Bond Energy

TCD-H2 3-4JJ System → TCD-H2 CH4 → TCD-H2 CH3CH2OH → TCD-H2 CH3CH3 → TCD-H2 CH3CH2CH3 CH3CH2CH2CH3 → TCD-H2

Table 6. continued

74.79 75.89 72.94 73.95 74.70 74.5 93.9 65.76 66.86 63.91 64.92 65.66 65.4 84.9 58.04 59.14 56.19 57.19 57.94 57.7 77.2 68.86 69.96 67.01 68.02 68.77 68.5 88.0 58.18 59.28 56.33 57.34 58.09 57.8 77.3

74.81 75.81 72.97 74.15 75.15 74.6 94.0 65.58 66.59 63.74 64.93 65.92 65.4 84.8 58.23 59.23 56.39 57.58 58.57 58.0 77.5 68.61 69.61 66.77 67.95 68.95 68.4 87.8 58.26 59.26 56.42 57.60 58.59 58.0 77.5

58.02 62.73 60.39 61.19 61.28 60.7 80.2

67.36 72.07 69.72 70.53 70.61 70.1 89.5

57.65 62.36 60.01 60.82 60.90 60.3 79.8

64.03 68.73 66.39 67.20 67.28 66.7 86.2

74.34 79.05 76.71 77.51 77.60 77.0 96.5

59.41 62.21 58.67 59.18 59.52 59.8 79.3

70.11 72.91 69.37 69.88 70.22 70.5 90.0

59.58 62.38 58.84 59.35 59.68 60.0 79.4

66.65 69.45 65.91 66.42 66.75 67.0 86.5

Singlet 75.17 77.97 74.43 74.94 75.28 75.6 95.0

69.48 62.92 60.55 60.44 60.62 62.8 82.3

78.77 72.21 69.84 69.73 69.91 72.1 91.6

69.74 63.18 60.81 60.70 60.88 63.1 82.5

76.33 69.76 67.40 67.29 67.46 69.6 89.1

83.80 77.24 74.87 74.76 74.94 77.1 96.6

67.44 60.08 60.06 60.05 59.88 61.5 81.0

77.35 69.99 69.97 69.96 69.79 71.4 90.9

67.07 59.72 59.69 59.68 59.52 61.1 80.6

73.63 66.27 66.25 66.24 66.07 67.7 87.2

82.41 75.06 75.03 75.03 74.86 76.5 95.9

68.59 64.29 64.25 64.12 63.75 65.0 84.5

78.92 74.62 74.58 74.46 74.09 75.3 94.8

68.77 64.47 64.43 64.31 63.94 65.2 84.6

75.27 70.97 70.93 70.80 70.43 71.7 91.1

83.71 79.40 79.36 79.24 78.87 80.1 99.6

64.10 70.42 62.17 63.35 64.35 64.9 84.3

68.36 74.67 66.42 67.61 68.60 69.1 88.6

61.30 67.61 59.36 60.55 61.54 62.1 81.5

65.85 72.17 63.92 65.11 66.10 66.6 86.1

71.54 77.85 69.61 70.79 71.78 72.3 91.8

64.24 70.17 63.58 64.59 65.33 65.6 85.0

68.40 74.33 67.74 68.74 69.49 69.7 89.2

61.57 67.50 60.91 61.91 62.66 62.9 82.4

66.15 72.08 65.49 66.49 67.24 67.5 86.9

71.54 77.47 70.88 71.89 72.63 72.9 92.3

67.79 69.67 63.12 63.93 64.01 65.7 85.2

69.60 71.48 64.93 65.74 65.82 67.5 87.0

65.22 67.10 60.56 61.36 61.45 63.1 82.6

69.12 71.00 64.45 65.26 65.34 67.0 86.5

73.29 75.17 68.62 69.43 69.51 71.2 90.7

66.76 71.79 62.88 63.40 63.73 65.7 85.2

70.55 75.58 66.68 67.19 67.52 69.5 89.0

63.77 68.79 59.89 60.40 60.73 62.7 82.2

68.53 73.56 64.65 65.16 65.50 67.5 86.9

Triplet 72.78 77.81 68.91 69.42 69.75 71.7 91.2

70.75 70.41 63.18 63.07 63.25 66.1 85.6

72.95 72.61 65.38 65.27 65.44 68.3 87.8

68.34 68.00 60.77 60.66 60.83 63.7 83.2

72.42 72.08 64.85 64.74 64.92 67.8 87.3

75.60 75.26 68.03 67.92 68.09 71.0 90.4

67.88 69.34 68.78 68.77 68.60 68.7 88.1

71.47 72.92 72.36 72.36 72.19 72.3 91.7

65.04 66.49 65.93 65.93 65.76 65.8 85.3

69.72 71.18 70.62 70.61 70.44 70.5 90.0

73.87 75.32 74.76 74.75 74.59 74.7 94.1

69.74 69.76 69.17 69.05 68.68 69.3 88.7

72.70 72.72 72.13 72.01 71.64 72.2 91.7

67.01 67.03 66.44 66.32 65.95 66.5 86.0

71.71 71.72 71.14 71.01 70.64 71.2 90.7

74.89 74.90 74.32 74.19 73.82 74.4 93.9






Article

69.48 69.50 68.91 68.78 68.41 69.0 88.5 70.64 70.29 63.06 62.96 63.13 66.0 85.5 67.87 72.90 63.99 64.50 64.83 66.8 86.3

CARBON−CARBON BOND DISSOCIATION ENERGIES (C−C BDE) 1. C−C BDE: Diradicals. The C−C BDEs were computed as the difference in energy of the ΔH°f298 for TCD,19 −19.5 kcal mol−1, and the ΔH°f298 for diradical species. For reference we note the C−C standard BDE for methyl groups in the C2−C6 n-alkanes are 88−90 kcal mol−1, while ethyl and propyl groups C−C BDEs in the C4−C8 and C6−C8 for n-alkanes are slightly lower in the 86−88 kcal mol−1 range.76 C−C BDE for several n-aldehydes has been shown to be 82−85 kcal mol−1 with larger energies of 88−90 kcal mol−1 for bond dissociations more than three carbon atoms away from the carbonyl group.77 We have estimated C−C BDEs for cyclopentane and cyclohexane using calculation ΔH°f298 values for the parent and corresponding diradicals as determined by Sirjean et al.14 We determined C−C BDE values of 81 and 88 kcal mol−1 for cyclopentane and cyclohexane in a similar fashion to our methods above, C−C BDE values calculated with each cyclic compound opening to a diradical with a normal alkane conformation. Sirjean et al.14 report rate parameters for unimolecular cyclopentane and cyclohexane ring opening to singlet diradicals with activation energies of approximately 85 (log A (s−1) of 18.11 and n −0.466) and 93 (log A (s−1) of 21.32 and n −0.972) kcal mol−1, respectively, at temperatures between 600 and 2000 K. A summary of the C−C BDEs, in Table 8, representing the TCD ring opening to singlet and triplet diradicals range from 77 to 85 kcal mol−1 with good correlations between the DFT and the higher level calculations. Included in this table are C−C BDEs, calculated as the energy difference from TCD ring opening to diradical formation, using CASMP2(2,2)/aug-ccpvtz//CASSCF(2,2)/cc-pvtz and also with the CASMP2 energies extrapolated to the complete basis set limit. These methods produce bond energies comparable to the other calculation methods we employed giving further verification to our results. The average differences between the singlet and triplet energies for all of the diradicals, except for TCD-H2 2J-6J, are less than 1 kcal mol−1 for values from the higher level calculations. This species has a large difference in the calculated ΔH°f298 which translates into large differences for the C−C BDEs. The TCD-H2 2J-6J singlet is unique and needs to be considered an estimate due to the negative vibration frequency, as noted above at the end of the methods section. We consider the singlet C−C BDEs values from the average of the CASMP2 values from Table 8, which provide good representative C−C BDEs for all of our methods, in the subsequent analysis. Our calculations show that five of the seven C−C BDEs fall within a tight 3.3 kcal mol−1 range. The 1-2 position is determined to be the most favorable site for initial ring-opening reactions which connects the two cyclopentane rings through the

71.48 72.58 69.63 70.64 71.38 71.1 90.6

69.74 70.83 67.89 68.89 69.64 69.4 88.9 69.90 70.90 68.06 69.24 70.23 69.7 89.1

70.41 75.12 72.77 73.58 73.66 73.1 92.6

70.50 73.29 69.75 70.27 70.60 70.9 90.3

79.13 72.57 70.20 70.09 70.27 72.4 91.9

76.83 69.47 69.45 69.44 69.27 70.9 90.4

78.28 73.97 73.93 73.81 73.44 74.7 94.1

66.07 72.38 64.14 65.32 66.31 66.8 86.3

66.01 71.94 65.35 66.36 67.10 67.4 86.8

68.37 70.25 63.70 64.51 64.59 66.3 85.7

68.27 69.73 69.17 69.16 68.99 69.1 88.5

70.95 70.96 70.37 70.25 69.88 70.5 89.9 69.93 71.39 70.83 70.82 70.65 70.7 90.2 71.65 71.31 64.08 63.97 64.15 67.0 86.5 Triplet 68.97 74.00 65.10 65.61 65.94 67.9 87.4 69.29 71.17 64.62 65.43 65.51 67.2 86.7 67.61 73.54 66.95 67.96 68.70 69.0 88.4 67.60 73.91 65.66 66.85 67.84 68.4 87.8 80.07 75.76 75.73 75.60 75.23 76.5 95.9 78.84 71.48 71.46 71.45 71.28 72.9 92.4 80.07 73.51 71.14 71.03 71.21 73.4 92.9 Singlet 71.63 74.43 70.89 71.40 71.74 72.0 91.5

■

:CH2 CH3C:OH CH2CH2 CH2CHCH3 CH3CHCHCH3 Average TCD C1−C9 Bond Energy TCD-H2 9JJ-8 System → TCD-H2 9-8 + :CH2 CH4 → TCD-H2 9-8 + CH3C:OH CH3CH2OH → TCD-H2 9-8 + CH2CH2 CH3CH3 → TCD-H2 9-8 + CH2CHCH3 CH3CH2CH3 CH3CH2CH2CH3 → TCD-H2 9-8 + CH3CHCHCH3 Average TCD C9−C8Bond Energy

71.44 72.44 69.60 70.78 71.77 71.2 90.7

70.38 75.09 72.75 73.55 73.64 73.1 92.5

approximately 58 and 65 kcal mol−1. All of the methods show 1JJ-9, 1JJ-10, and 1-2JJ are the lowest energy species. Energies for the most stable state of the other carbenes all begin close to the maximum diradical energy around 65 kcal mol−1 and continue up to about 75 kcal mol−1. The higher energy states for these carbenes show energies with an even higher maximum of about 80 kcal mol−1. In Table 5 a comparison of the singlet ΔH°f298 carbene values is presented. B3LYP shows the smallest difference with all values falling below 1 kcal mol−1, while M06-2X and ωB97X-D provide a wider range of 0.0−2.1 kcal mol−1, although several species do not undergo change.

9JJ-8 9JJ-8 9JJ-8 9JJ-8 9JJ-8 TCD-H2 TCD-H2 TCD-H2 TCD-H2 TCD-H2

+ + + + +

TCD-H2 1−9JJ System → TCD-H2 1-9 CH4 → TCD-H2 1-9 CH3CH2OH → TCD-H2 1-9 CH3CH3 → TCD-H2 1-9 CH3CH2CH3 CH3CH2CH2CH3 → TCD-H2 1-9 + + + + + 1-9JJ 1-9JJ 1-9JJ 1-9JJ 1-9JJ TCD-H2 TCD-H2 TCD-H2 TCD-H2 TCD-H2

Table 6. continued

isodesmic reactions

+ + + + +





M


Article

The Journal of Physical Chemistry A Table 7. Summary of Calculated ΔH°f298 for the Lowest Energy Conformer of TCD-H2 m-n Carbenesa,b B3LYPc


a

ωB97X-D

M06-2X

CCSD(T)

CBS-QB3

G3MP2B3

species

singlet

triplet

singlet

triplet

singlet

triplet

singlet

triplet

singlet

triplet

singlet

triplet

TCD-H2 1JJ-2 TCD-H2 1-2JJ TCD-H2 2JJ-3 TCD-H2 2-3JJ TCD-H2 3JJ-4 TCD-H2 3-4JJ TCD-H2 2JJ-6 TCD-H2 1JJ-10 TCD-H2 1-10JJ TCD-H2 1JJ-9 TCD-H2 1-9JJ TCD-H2 9JJ-8

60.0 60.2 62.3 75.2 72.6 74.5 65.4 57.8 68.5 57.9 71.2 69.5

68.5 68.4 70.7 72.9 70.9 72.6 67.1 62.5 69.4 65.2 68.7 67.1

61.2 61.3 62.6 77.2 77.0 77.0 66.7 60.3 70.1 60.7 73.1 73.1

68.2 68.5 70.8 71.7 69.6 71.2 67.0 63.1 67.5 65.7 67.2 66.3

60.7 61.4 63.7 76.1 74.3 75.6 67.0 60.0 70.5 59.8 72.0 70.9

67.9 68.7 71.3 72.1 71.1 71.7 67.5 62.7 69.5 65.7 67.9 66.8

63.5 62.5 64.2 77.6 75.7 77.1 69.6 63.1 72.1 62.8 73.4 72.4

68.7 69.2 71.4 71.1 70.0 71.0 67.8 63.7 68.3 66.1 67.0 66.0

62.0 63.5 64.1 76.9 75.5 76.5 67.7 61.1 71.4 61.5 72.9 70.9

71.1 71.5 73.7 74.7 73.6 74.7 70.5 65.8 72.3 68.7 70.7 69.1

65.2 65.0 63.7 80.5 79.2 80.1 71.7 65.2 75.3 65.0 76.5 74.7

71.5 72.0 74.3 74.4 73.6 74.4 71.2 66.5 72.2 69.3 70.5 69.0

Units kcal mol−1. bUncertainties are reported as ±1.9 kcal mol−1. cAverage from 6-31G(d,p) and 6-311G(2d,2p) basis sets.

Table 8. Summary of Calculated C−C Bond Dissociation Energies for the Lowest Energy Conformer of TCD-H2 mJ-nJ Diradicalsa,b B3LYPc

ωB97X-D

M06-2X

CCSD(T)

CBS-QB3

G3MP2B3

CASMP2d

CASMP2e

species

singlet

triplet

singlet

triplet

singlet

triplet

singlet

triplet

singlet

triplet

singlet

triplet

singlet

singlet

TCD-H2 1J-2J TCD-H2 2J-3J TCD-H2 3J-4J TCD-H2 2J-6Jf TCD-H2 1J-10J TCD-H2 1J-9J TCD-H2 9J-8J

77.2 85.1 85.9 74.6 79.8 79.1 80.2

77.2 85.1 87.2 80.5 79.9 80.0 82.6

77.2 84.9 86.1 75.9 78.8 78.7 80.9

77.2 84.9 86.4 80.6 78.9 79.8 82.2

77.2 84.8 86.7 75.0 79.2 79.2 81.0

77.2 85.3 87.0 81.2 79.4 80.1 82.8

77.5 84.8 86.3 78.6 79.6 79.5 81.6

77.4 84.9 86.3 81.2 79.7 79.8 82.0

77.9 85.3 86.7 79.1 79.8 80.0 81.3

77.2 84.6 86.5 81.2 79.2 79.8 81.7

77.2 84.5 85.9 78.5 79.0 79.3 80.5

77.2 84.5 86.2 81.4 79.2 79.7 81.5

77.7 84.6 85.7 77.9 79.5 79.4 80.9

77.1 81.8 83.5 77.9 79.9 80.2 80.5

a Units kcal mol−1 bUncertainties are reported as ±3.3 kcal mol−1. cAverage from 6-31G(d,p) and 6-311G(2d,2p) basis sets. dCASMP2(2,2)/augcc-pvtz//CASSCF(2,2)/cc-pvtz. eCASMP2(2,2)/CBS//CASSCF(2,2)/cc-pvtz extrapolated to complete basis set limit. fHad one negative vibrational frequency in each method corresponding to bond reformationconverted to positive, accuracy is uncertain.

Table 9. Summary of Calculated C−C Bond Dissociation Energies for the Lowest Energy Conformer of TCD-H2 m-n Carbenesa,b B3LYPc

a

M06-2X

ωB97X-D

CCSD(T)

CBS-QB3

G3MP2B3

species

singlet

triplet

singlet

triplet

singlet

triplet

singlet

triplet

singlet

triplet

singlet

triplet

TCD-H2 1JJ-2 TCD-H2 1-2JJ TCD-H2 2JJ-3 TCD-H2 2-3JJ TCD-H2 3JJ-4 TCD-H2 3-4JJ TCD-H2 2JJ-6 TCD-H2 1JJ-10 TCD-H2 1-10JJ TCD-H2 1JJ-9 TCD-H2 1-9JJ TCD-H2 9JJ-8

79.5 79.6 81.7 94.7 92.0 94.0 84.8 77.3 87.9 77.4 90.6 89.0

88.0 87.9 90.2 92.3 90.4 92.1 86.5 82.0 88.9 84.7 88.1 86.6

80.7 80.8 82.1 96.6 96.4 96.5 86.2 79.8 89.5 80.2 92.5 92.6

87.7 87.9 90.3 91.1 89.0 90.7 86.5 82.6 87.0 85.2 86.7 85.7

80.1 80.9 83.1 95.6 93.8 95.0 86.5 79.4 90.0 79.3 91.5 90.3

87.4 88.2 90.8 91.6 90.6 91.2 86.9 82.2 89.0 85.2 87.4 86.3

82.9 81.9 83.7 97.0 95.2 96.6 89.1 82.5 91.6 82.3 92.9 91.9

88.1 88.7 90.8 90.6 89.4 90.4 87.3 83.2 87.8 85.6 86.5 85.5

81.5 83.0 83.6 96.4 95.0 95.9 87.2 80.6 90.9 81.0 92.4 90.4

90.5 91.0 93.2 94.2 93.1 94.1 90.0 85.3 91.7 88.1 90.2 88.5

84.6 84.5 83.2 99.9 98.7 99.6 91.1 84.6 94.8 84.5 95.9 94.1

91.0 91.5 93.8 93.9 93.1 93.9 90.7 86.0 91.7 88.7 89.9 88.5

Units kcal mol−1. bUncertainties are reported as ±1.9 kcal mol−1. cAverage from 6-31G(d,p) and 6-311G(2d,2p) basis sets.

The two strongest BDEs are 83.2 and 84.6 kcal mol−1 for TCD-H2 2J-3J and 3J-4J. These correspond to opening a five carbon ring and do not show as great a relief from ring strain as the other locations on TCD. 2. C−C BDE: Carbenes. For comparison, the C−C BDEs for generating the singlet and triplet carbenes were determined and given in Table 9. The methods we have employed give consistent values with slightly lower values for the DFT methods and higher values for the composite methods. Several of the DFT methods predict C−C BDEs in a similar range as seen for the diradical BDEs and extending to over

C1 and C2 bridgehead carbons. Formation of this singlet diradical is the weakest relative C−C BDE of 77.4 kcal mol−1 for TCD. The next four bond energies have differences of about 3 kcal mol−1 with the 2-6 only slightly stronger than the 1-2 bond at 77.9 kcal mol−1. The next highest energies, 1-10 and 1-9, have only a 0.1 kcal mol−1 difference, 79.7 and 79.8 kcal mol−1, respectively, and involve breaking bonds to the same C1 bridgehead carbon. The final energy in this grouping is only approximately 1 kcal mol−1 higher at 80.7 kcal mol−1 for the 9-8 position. These four C−C BDEs are only slightly lower than the 81 kcal mol−1 we estimated for cyclopentane. N


Article

The Journal of Physical Chemistry A 90 kcal mol−1. The composite methods have a higher starting range for the carbene C−C BDEs and extend to almost 100 kcal mol−1. More work on these TCD carbenes will be investigated, and at this time, we see that some of these TCD carbene species have similar C−C BDEs to their diradical counterparts.

CASMP2 energies extrapolated to the complete basis set limit methods. The 1-2 position would be the most favorable C−C bond to break based on our findings which connects the two cyclopentane rings through the C1 and C2 bridgehead carbons. An initial analysis of the TCD carbene C−C BDEs shows a wider range from about 77 to 100 kcal mol−1 due to the variation in the singlet and triplet ΔH°f298 values for the individual methods. Future work will investigate these findings.

■


ENTROPIES (S(T)) AND HEAT CAPACITY (CP(T)) Entropies and heat capacities for the TCD-H2 mJ-nJ diradical singlet species at the B3LYP/6-31G(d,p) level of theory for the 50−5000 K temperature range (JANNAF format) are presented in the Appendix and correspond to the lowest energy conformer of the singlet electronic state. The entropy values determined from the diradical triplet species were reduced down by R ln(3) to account for the multiplicity difference. Total entropies and heat capacities for the other species in this study are presented in the Supporting Information.

■

APPENDIX

1. Total Entropy and Heat Capacity

Appendix Table A1 presents the total entropy and heat capacity values for the TCD-H2 mJ-nJ singlet diradical species over the temperature range of 50- 5000 K. 2. Calculation of the 2-Norbornyl Radical

■

No literature value currently exists for the gas-phase heat of formation for the 2-norbornyl radical. We determine a value for use in our isodesmic work reactions using the norbornane gas-phase heat of formation value of −13.1 ± 1.1 kcal mol−1,71 hydrogen atom gas-phase heat of formation value of 52.103 kcal mol−1,70 and the bond dissociation energy of 99.1 ± 1.3 kcal mol−1.78 These values allow for a derived heat of formation value of 33.9 ± 1.1 kcal mol−1 for 2-norbornyl used in this study.

SUMMARY The carboncarbon bond dissociation energies in exo-tricyclo[5.2.1.02,6]decane (TCD) corresponding to diradical and carbene formation are determined. We calculate ΔH°f298 values for the TCD-H2 m-n parent, radicals (TCD-H2 mJ-n and m-nJ), diradicals (TCD-H2 mJ-nJ), and carbenes (TCD-H2 mJJ-n and m-nJJ) which are used to determine C−H BDEs in going from parent to radical to diradical species. Density functional theory and composite methods in conjunction with a series of work reactions are employed to increase accuracy. The use of reactions to cancel error with use of similar bridged hydrocarbons shows that results from the use of DFT methods can result in accurate data. Entropies (S(T)) and heat capacities (Cp(T)) are also determined for all species. C−C BDEs range from 77.4 to 84.6 kcal mol−1 for TCD diradical singlet species, which are consistent with the CASMP2(2,2)/aug-cc-pvtz//CASSCF(2,2)/cc-pvtz and the

3. Internal Rotor Analysis

Internal rotor analysis is needed for determination of the lowest energy geometries and for internal rotor contributions to entropy and heat capacity. Potential curves at 298 K for internal rotors in the parent, radical, diradical, and carbene species were determined using relaxed scans at the B3LYP/6-31G(d,p) level of theory at 10° intervals. If a lower energy conformer was found, previous scans were re-run to insure that we had the lowest energy conformation. Figure 6 shows the bond numbering for

Table A1. Calculated Total Entropiesa and Heat Capacitiesa for the Lowest Energy Conformer of TCD-H2 mJ-nJ Singlet Diradical Species from B3LYP/6-31G(d,p) Level of Theory temp

TCD-H2 1J-2J

TCD-H2 2J-3J

TCD-H2 3J-4J

TCD-H2 2J-6J

TCD-H2 1J-9J

TCD-H2 9J-8J

(K)

Cp

S

Cp

S

Cp

S

Cp

S

Cp

S

Cp

S

Cp

S

12.35 18.25 23.38 28.76 35.07 41.88 56.79 69.86 80.75 89.76 97.29 109.12 126.93 135.87 140.76 143.66 145.51 146.75 147.61 148.24 143.197

60.93 71.35 79.72 87.15 94.21 100.93 115.32 129.40 143.10 156.23 168.70 191.72 239.72 277.57 308.45 334.38 356.67 376.19 393.52 409.11

12.92 17.86 22.75 28.24 34.75 41.70 56.72 69.71 80.45 89.29 96.67 108.27 125.87 134.79 139.69 142.61 144.46 145.71 146.59 147.22 143.034

61.36 71.37 79.10 86.08 92.83 99.32 113.39 127.23 140.71 153.62 165.89 188.52 235.72 272.98 303.40 328.95 350.93 370.17 387.27 402.64

12.82 18.43 23.55 29.10 35.54 42.37 57.07 69.77 80.26 88.92 96.16 107.58 124.98 133.83 138.72 141.63 143.48 144.72 145.60 146.23 142.180

63.38 73.23 80.85 87.78 94.49 100.94 114.87 128.53 141.82 154.54 166.61 188.89 235.36 272.06 302.04 327.24 348.91 367.89 384.75 399.91

10.53 15.57 21.30 27.36 34.10 41.11 56.17 69.30 80.23 89.28 96.85 108.75 126.69 135.71 140.65 143.58 145.45 146.70 147.58 148.21 144.605

56.98 65.72 73.10 80.03 86.83 93.39 107.58 121.53 135.13 148.18 160.59 183.52 231.39 269.19 300.04 325.96 348.23 367.74 385.07 400.65

11.41 16.94 22.22 27.95 34.50 41.39 56.23 69.15 79.91 88.82 96.28 108.02 125.79 134.76 139.68 142.60 144.46 145.71 146.59 147.22 143.726

59.69 68.92 76.37 83.22 89.91 96.36 110.31 124.03 137.41 150.24 162.45 185.01 232.15 269.39 299.81 325.36 347.34 366.58 383.67 399.05

12.81 18.32 23.26 28.71 35.09 41.90 56.70 69.59 80.31 89.17 96.59 108.26 125.91 134.83 139.73 142.64 144.49 145.73 146.60 147.24 142.868

60.85 71.10 79.04 86.16 92.99 99.54 113.64 127.46 140.91 153.81 166.06 188.68 235.89 273.16 303.59 329.15 351.13 370.37 387.47 402.85

13.41 18.30 23.44 29.14 35.58 42.32 56.81 69.42 79.91 88.59 95.88 107.37 124.88 133.78 138.68 141.60 143.46 144.71 145.59 146.23 142.406

62.09 72.03 79.58 86.50 93.23 99.68 113.56 127.16 140.38 153.04 165.08 187.30 233.71 270.39 300.36 325.55 347.22 366.20 383.06 398.22

50 100 150 200 250 298 400 500 600 700 800 1000 1500 2000 2500 3000 3500 4000 4500 5000 zero-point energyb a

TCD-H2 1J-10J

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


Article


barriers of 0.4−0.8 kcal mol−1 in the diradical species. The carbenes exhibit similarities to the parents, radicals, and diradicals with methyl rotation with barrier heights between 0.5 and 3.4 kcal mol−1. 3b. Methyl and Ethyl Group Rotors. Barriers that involve methyl and ethyl group rotors for TCD-H2 2-3 and 1-9 have a 5.6−6.3 kcal mol−1 range. These compare with similar values in n-alkane groups; for example, the central C−C rotor barrier in n-butane has been reported as between 5.0 and 5.5 kcal mol−1.83−85 The barrier increases to 10.8 kcal mol−1 for ethyl rotation (rotor 2) in TCD-H2 3-4 due to the closeness of the two methyls. In radical, diradical, and carbene formation we see a similar decrease in barrier height energy as occurred in the methyl radicals, but these barriers are still in excess of 4.3 kcal mol−1. This is seen in the 2.2 kcal mol−1 maximum barrier energy difference between the parent, radical, diradical, and carbene compounds for TCD-H2 2-3 and TCD-H2 1-9; the TCD-H2 3-4 compounds show a larger 3.2 kcal mol−1 maximum difference. 3c. Cyclopentane Rotation. TCD-H2 1-2 is unique in that it has rotation about the bond joining two cyclopentane rings. This barrier energy is similar to that for the methyl and ethyl substituent group rotors. The parent compound has a nonsymmetrical maximum barrier of 7.1 kcal mol−1. This barrier undergoes a small decrease to 6.1−7.0 kcal mol−1 upon radical,


compounds that have more than one internal rotor. Note that these structures do not reflect their optimized geometries. Plots of internal rotation potentials at 298 K are available in the Supporting Information. The following is a detailed discussion of the internal rotation potential barriers. 3a. Methyl Rotation. Rotational barriers in the parent TCDH2 m-n compounds exhibit 3-fold barrier heights between 2.4 and 3.4 kcal mol−1 which are near the typical rotor potential for methyl groups in hydrocarbons79−82 at ∼3 kcal mol−1. Locations which are more crowded, for example, rotor 1 in TCD-H2 3-4, have larger barriers, while less hindered rotors, rotor 3 in TCDH2 3-4 and in the TCD-H2 1-10 rotor, have lower barriers. When the methyl group is the radical site, the barriers have 2-fold barriers with reduced heights of 0.2−1.0 kcal mol−1 and

Figure 6. Internal rotor notation for species with multiple rotational bonds.

Table A2. Isodesmic Reactions and Calculated ΔH°f298 for the Lowest Energy Conformer of TCD-H2 m-n Parent Species ΔH°f298 (kcal mol−1) B3LYP isodesmic reactions TCD-H2 TCD-H2 TCD-H2 TCD-H2

1-2 1-2 1-2 1-2

+ + + +

YC4H8 YC5H10 YC6H12 3 CH3CH3

TCD-H2 1-2 System → YYC7H12 → YYC7H12 → YYC8H14 → 2 YC4H8

TCD-H2 TCD-H2 TCD-H2 TCD-H2

1-2 1-2 1-2 1-2

+ + + +

YYC7H12 YYC8H14 YC5H10 YC4H8

→ → → →

+ + + + + + + +

YC7H14 YC8H16 CH3CH2CH2CH2CH3 CH3CH2CH2CH3

+ + + + + + + +


2-3 2-3 2-3 2-3

+ + + +




2-3 2-3 2-3 2-3

+ + + +


→ → → →

+ + + + + + + +



3-4 3-4 3-4 3-4

+ + + +




3-4 3-4 3-4 3-4

+ + + +


→ → → →


YC7H14 YC8H16 YC8H16 2 CH3CH2CH2CH3 Average TCD TCD TCD TCD Average YC7H14 YC8H16 YC8H16 2 CH3CH2CH2CH3 Average TCD TCD TCD TCD Average YC7H14 YC8H16 YC8H16 2 CH3CH2CH2CH3 Average TCD TCD TCD TCD Average P

6-31G(d,p)

6-311G(2d,2p)

CBS-QB3

G3MP2B3

−33.77 −32.91 −33.90

−34.39 −33.68 −34.46

−33.5 −33.90 −33.36 −34.15

−34.2 −34.59 −33.76 −34.75

−33.8

−34.4

−30.07 −29.26 −30.94 −31.62 −30.5 −32.05 −30.16 −30.48 −30.74 −30.9

−30.07 −29.23 −30.95 −31.47 −30.4 −31.97 −30.10 −30.52 −30.82 −30.9

−31.49 −30.63 −31.63

−31.78 −31.07 −31.85

−31.2 −31.63 −31.08 −31.87

−31.6 −31.98 −31.14 −32.13

−31.5

−31.7

−30.47 −29.67 −31.35 −32.02 −30.9 −32.45 −30.57 −30.88 −31.15 −31.3

−30.44 −29.59 −31.31 −31.83 −30.8 −32.33 −30.46 −30.88 −31.18 −31.2

−29.22 −28.36 −29.36

−29.35 −28.64 −29.42

−29.0 −29.35 −28.81 −29.60

−29.1 −29.55 −28.71 −29.71

−29.3

−29.3

−30.02 −29.22 −30.89 −31.57 −30.4 −32.00 −30.11 −30.43 −30.69 −30.8

−30.03 −29.19 −30.91 −31.43 −30.4 −31.93 −30.06 −30.48 −30.78 −30.8


Article

The Journal of Physical Chemistry A Table A2. continued ΔH°f298 (kcal mol−1) B3LYP


isodesmic reactions TCD-H2 TCD-H2 TCD-H2 TCD-H2

2-6 2-6 2-6 2-6

+ + + +




2-6 2-6 2-6 2-6

+ + + +


→ → → →



+ + + + + + + +


1-10 1-10 1-10 1-10

+ + + +



1-10 1-10 1-10 1-10

+ + + +


→ → → →

+ + + + + + + +


+ + + +


1-9 1-9 1-9 1-9

+ + + +



1-9 1-9 1-9 1-9

+ + + +


→ → → →

+ + + + + + + +


9-8 9-8 9-8 9-8

+ + + +




9-8 9-8 9-8 9-8

+ + + +


→ → → →


YC7H14 YC8H16 YC8H16 2 CH3CH2CH2CH3 Average TCD TCD TCD TCD Average

+ + + +

TCD-H2 1-9 System → YYC7H12 → YYC7H12 → YYC8H14 → 2 YC4H8 YC7H14 YC8H16 CH3CH2CH2CH2CH3 CH3CH2CH2CH3

YC7H14 YC8H16 YC8H16 2 CH3CH2CH2CH3 Average TCD TCD TCD TCD Average

YC7H14 YC8H16 YC8H16 2 CH3CH2CH2CH3 Average TCD TCD TCD TCD Average YC7H14 YC8H16 YC8H16 2 CH3CH2CH2CH3 Average TCD TCD TCD TCD Average

6-31G(d,p)

6-311G(2d,2p)

CBS-QB3

G3MP2B3

−25.27 −24.41 −25.41

−25.40 −24.69 −25.47

−25.0 −25.41 −24.86 −25.65

−25.2 −25.60 −24.76 −25.75

−25.3

−25.4

−23.50 −22.69 −24.37 −25.05 −23.9 −25.48 −23.59 −23.91 −24.17 −24.3

−23.85 −23.01 −24.72 −25.24 −24.2 −25.75 −23.88 −24.30 −24.60 −24.6

−32.35 −31.49 −32.49

−32.47 −31.76 −32.54

−32.1 −32.48 −31.94 −32.73

−32.3 −32.67 −31.84 −32.83

−32.4

−32.4

−31.01 −30.20 −31.88 −32.56 −31.4 −32.99 −31.10 −31.42 −31.68 −31.8

−31.14 −30.30 −32.02 −32.54 −31.5 −33.04 −31.17 −31.59 −31.89 −31.9

−35.79 −34.93 −35.93

−36.16 −35.45 −36.23

−35.6 −35.93 −35.39 −36.18

−35.9 −36.36 −35.52 −36.51

−35.8

−36.1

−33.74 −32.94 −34.62 −35.29 −34.1 −35.73 −33.84 −34.15 −34.42 −34.5

−33.82 −32.98 −34.69 −35.21 −34.2 −35.72 −33.85 −34.26 −34.56 −34.6

−38.22 −37.37 −38.36

−38.59 −37.88 −38.66

−38.0 −38.36 −37.82 −38.61

−38.4 −38.79 −37.96 −38.95

−38.3

−38.6

−35.95 −35.15 −36.83 −37.50 −36.4 −37.93 −36.04 −36.36 −36.63 −36.7

−35.94 −35.10 −36.82 −37.33 −36.3 −37.84 −35.97 −36.39 −36.69 −36.7

of formation values. C−H BDEs in Table 2 show the DFT methods provide acceptable values compared to the higher levels. Average values from the composite methods are referenced here. The secondary cyclic carbon radicals TCD-H2 1J-2, 1-2J, 2J-3, 1J-9, and 1J-10 have bond energies ranging from 95.6 to 98.8 kcal mol−1. These are consistent with the standard BDEs for secondary alkanes of 98.5 kcal mol−1 and the 97−99 kcal mol−1 range of the secondary cyclic carbon radicals of TCD19 (TCD-R3, TCD-R4, TCD-R9), norbornane,78 bicyclo[3.1.1]heptane,88 and bicyclo[2.2.2]octane.88 The TCD-H2 2-6 radicals have lower bond energies of 93.2 kcal mol−1 seemingly due to better radical stability with larger ring of eight or more carbons. This is consistent with bond

diradical, and carbene formation. Similar energy barriers are seen for the central O−O rotor in dimethyl tetraoxide86 and the central C−O rotor in methyl ethyl ether.87 4. Discussion on Carbon−Hydrogen Bond Dissociation Energies (C−H BDEs)

4a. C−H BDE: Parent to Radical. C−H BDEs are computed from the calculated parent and radical enthalpies listed in Table 2 with the standard enthalpy of the hydrogen atom in Table 1 according to the reaction TCD‐H2 m‐n Parent → TCD‐H2 m‐n Radical + H

When comparing the DFT and composite calculation, similar ranges are seen for the BDE as was previously seen with the heat Q


Article


Table A3. Isodesmic Reactions, Calculated ΔH°f298, and C−H Bond Dissociation Energies for the Lowest Energy Conformer of TCD-H2 m-n Radical Species ΔH°f298 (kcal mol−1) B3LYP


isodesmic reactions

6-31G(d,p)

6-311G(2d,2p)

CBS-QB3

G3MP2B3

CH3CJH2 CH3CJHCH3 (CH3)3CJ CH3CJHCH2CH3 YYCJ7H11 Average Bond Energy

12.17 13.57 14.55 12.94 13.82 13.4 96.0

12.48 13.78 14.61 13.25 13.90 13.6 96.2

13.25 13.51 13.13 12.88 14.12 13.4 95.9

13.75 13.57 12.84 12.92 14.03 13.4 96.0


1J-2 1J-2 1J-2 1J-2 1J-2

+ + + + +

TCD-H2 1J-2 System CH3CH3 → TCD-H2 CH3CH2CH3 → TCD-H2 (CH3)3CH → TCD-H2 CH3CH2CH2CH3 → TCD-H2 YYC7H12 → TCD-H2


1-2J 1-2J 1-2J 1-2J 1-2J

+ + + + +

TCD-H2 CH3CH3 CH3CH2CH3 (CH3)3CH CH3CH2CH2CH3 YYC7H12

1-2J System → TCD-H2 → TCD-H2 → TCD-H2 → TCD-H2 → TCD-H2

1-2 1-2 1-2 1-2 1-2

+ + + + +


12.56 13.95 14.94 13.32 14.21 13.8 96.3

12.82 14.12 14.95 13.60 14.24 13.9 96.5

13.70 13.96 13.58 13.34 14.57 13.8 96.4

14.26 14.08 13.35 13.43 14.54 13.9 96.5


2J-3 2J-3 2J-3 2J-3 2J-3

+ + + + +


2J-3 System → TCD-H2 → TCD-H2 → TCD-H2 → TCD-H2 → TCD-H2

2-3 2-3 2-3 2-3 2-3

+ + + + +


14.62 16.02 17.00 15.39 16.27 15.9 98.8

14.83 16.13 16.95 15.60 16.24 16.0 98.9

15.67 15.93 15.55 15.30 16.54 15.8 98.7

16.31 16.13 15.39 15.48 16.58 16.0 98.9


2-3J 2-3J 2-3J 2-3J 2-3J

+ + + + +



2-3 2-3 2-3 2-3 2-3

+ + + + +


18.31 19.71 20.69 19.08 19.96 19.6 102.5

18.23 19.53 20.36 19.00 19.65 19.4 102.3

18.38 18.64 18.27 18.02 19.25 18.5 101.4

18.44 18.26 17.53 17.61 18.72 18.1 101.0


3J-4 3J-4 3J-4 3J-4 3J-4

+ + + + +



3-4 3-4 3-4 3-4 3-4

+ + + + +


17.61 19.01 19.99 18.38 19.26 18.8 101.4

17.57 18.87 19.70 18.34 18.98 18.7 101.2

18.16 18.41 18.04 17.79 19.03 18.3 100.8

18.39 18.21 17.48 17.56 18.66 18.1 100.6


3-4J 3-4J 3-4J 3-4J 3-4J

+ + + + +



3-4 3-4 3-4 3-4 3-4

+ + + + +


18.08 19.48 20.46 18.85 19.73 19.3 101.8

18.04 19.34 20.16 18.81 19.45 19.2 101.7

18.32 18.58 18.20 17.95 19.19 18.4 101.0

18.42 18.25 17.51 17.60 18.70 18.1 100.6


2J-6 2J-6 2J-6 2J-6 2J-6

+ + + + +



2-6 2-6 2-6 2-6 2-6

+ + + + +


15.85 17.25 18.23 16.62 17.50 17.1 93.2

16.12 17.42 18.25 16.89 17.54 17.2 93.4

16.80 17.06 16.69 16.44 17.67 16.9 93.1

17.52 17.34 16.60 16.69 17.79 17.2 93.3

1-2 1-2 1-2 1-2 1-2

+ + + + +

R


Article

The Journal of Physical Chemistry A Table A3. continued ΔH°f298 (kcal mol−1) B3LYP


isodesmic reactions

6-31G(d,p)

6-311G(2d,2p)

CBS-QB3

G3MP2B3


2-6J 2-6J 2-6J 2-6J 2-6J

+ + + + +

TCD-H2 2-6J System CH3CH3 → TCD-H2 CH3CH2CH3 → TCD-H2 (CH3)3CH → TCD-H2 CH3CH2CH2CH3 → TCD-H2 YYC7H12 → TCD-H2


1J-10 1J-10 1J-10 1J-10 1J-10

+ + + + +



1-10 1-10 1-10 1-10 1-10

+ + + + +


10.31 11.70 12.69 11.07 11.95 11.5 95.1

10.46 11.76 12.59 11.23 11.88 11.6 95.1

11.79 12.05 11.67 11.42 12.66 11.9 95.5

12.42 12.24 11.50 11.59 12.69 12.1 95.6


1-10J 1-10J 1-10J 1-10J 1-10J

+ + + + +



1-10 1-10 1-10 1-10 1-10

+ + + + +


15.99 17.39 18.37 16.76 17.64 17.2 100.8

15.99 17.29 18.12 16.76 17.41 17.1 100.7

16.51 16.77 16.39 16.14 17.38 16.6 100.2

16.73 16.55 15.82 15.90 17.01 16.4 100.0


1J-9 1J-9 1J-9 1J-9 1J-9

+ + + + +



1-9 1-9 1-9 1-9 1-9

+ + + + +


9.69 11.09 12.07 10.46 11.34 10.9 97.2

9.74 11.04 11.87 10.51 11.16 10.9 97.1

11.29 11.55 11.18 10.93 12.16 11.4 97.7

11.90 11.73 10.99 11.08 12.18 11.6 97.8


1-9J 1-9J 1-9J 1-9J 1-9J

+ + + + +



1-9 1-9 1-9 1-9 1-9

+ + + + +


14.30 15.70 16.68 15.07 15.95 15.5 101.8

14.27 15.57 16.40 15.04 15.69 15.4 101.7

14.54 14.80 14.42 14.17 15.41 14.7 100.9

14.62 14.45 13.71 13.80 14.90 14.3 100.6


9J-8 9J-8 9J-8 9J-8 9J-8

+ + + + +



9-8 9-8 9-8 9-8 9-8

+ + + + +


12.66 14.05 15.04 13.42 14.30 13.9 102.3

12.58 13.88 14.71 13.35 13.99 13.7 102.1

12.75 13.00 12.63 12.38 13.62 12.9 101.3

12.99 12.81 12.08 12.17 13.27 12.7 101.1


9-8J 9-8J 9-8J 9-8J 9-8J

+ + + + +



9-8 9-8 9-8 9-8 9-8

+ + + + +


12.66 14.05 15.04 13.42 14.30 13.9 102.3

12.58 13.88 14.71 13.35 13.99 13.7 102.1

12.75 13.00 12.63 12.38 13.62 12.9 101.3

12.99 12.81 12.08 12.17 13.27 12.7 101.1

2-6 2-6 2-6 2-6 2-6

+ + + + +


15.85 17.25 18.23 16.62 17.50 17.1 93.2

16.12 17.42 18.25 16.89 17.54 17.2 93.4

16.81 17.07 16.69 16.44 17.68 16.9 93.1

17.52 17.34 16.61 16.69 17.79 17.2 93.3

S


Article


The Journal of Physical Chemistry A energies seen of 96−97 kcal mol−1 for cyclopentane, 99− 100 kcal mol−1 for cyclohexane, and 95.7 kcal mol−1 for cyclooctane.76,88−91 Radical formation on primary sites of an alkane branch for the TCD-H2 3-4, 9-8, 2-3J, 1-10J, and 1-9J has bond energies ranging from 100.1 to 101.2 kcal mol−1, with only a 1.1 kcal mol−1 difference in these on methyl, ethyl, or n-propyl groups. There is excellent agreement to a standard 101.1 kcal mol−1 primary alkane and the 100−101 kcal mol−1 primary C−H BDE range reported for ethane, n-propane, and n-butane.72,76,92 A search of the literature for substituted cycloalkane BDEs provided only values for the primary C−H BDE for the methyl group in methylcyclopropane ranging from 97 to 99 kcal mol−1.76,89 These values from primary alkanes and alkane-substituted cyclics are consistent with our findings. 4b. Second C−H BDE: Radical to Diradical. Table 2 also summarizes the energy required to remove the second hydrogen from each TCD-H2 m-n radical to generate the diradical singlet species using the reaction

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS 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 and Michael Bockelie of Reaction Engineering International for helpful discussions. (The SMCPS Program for entropy and heat capacity is available, free of charge, from the authors). The authors would also like to thank the editor and reviewers for their comments.

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TCD‐H2 m‐n Radical → TCD‐H2 m J‐n J Diradical + H

These second C−H BDEs are calculated based on the singlet diradical composite method average. As was the case for the hydrogen removal, the average from the B3LYP and the composite methods are in good agreement. Overall these species are not affected by the existence of the first radical site. The maximum difference for these second C−H BDEs as compared to the first is only 1.2 kcal mol−1 which allows us to draw the same conclusions for these BDEs as seen in the first energies. 5. ΔH°f298 of TCD-H2 m-n Parent Species

Appendix Table A2 have the Scheme I work reactions for the ΔH°f298 calculations and the Scheme II work reactions for comparison to validate these findings for the TCD-H2 m-n parent species. DFT provides comparable ΔH°f298 values to the higher level composite methods, and both sets of work reactions generate agreeable values giving us confidence for the enthalpies for these strained bicyclic hydrocarbons. 6. ΔH°f298 of TCD-H2 m-n Radical Species

Appendix Table A3 has the ΔH°f298 calculations using the five work reactions in Scheme III for the TCD-H2 m-n radicals and the corresponding C−H BDEs from the parent species. As seen in the parent species, there is good consistency between the DFT and composite methods where the lower level calculations provide acceptable enthalpy values for these bicyclic radical hydrocarbons including the C−H BDEs.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b05564. Uncertainty calculations, entropy and heat capacities, hindered internal rotor potential energy diagrams, optimized structures, moments of inertia, vibrational frequencies, TCD C2−C6 bond length scan, TCD C2− C6 bond length scan negative frequencies, Mulliken spin densities, and complete references (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. T


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Bond Energies and Thermochemical Properties of Ring-Opened

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