Weakly Bound Carbon−Carbon Bonds in Acenaphthene Derivatives

J. Phys. Chem. A 2010, 114, 1161–1168

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Weakly Bound Carbon-Carbon Bonds in Acenaphthene Derivatives and Hexaphenylethane Enoch Dames, Baptiste Sirjean, and Hai Wang* Department of Aerospace and Mechanical Engineering, UniVersity of Southern California, Los Angeles, California 90089-1453 ReceiVed: October 8, 2009; ReVised Manuscript ReceiVed: NoVember 22, 2009

A class of acenaphthene derivatives is shown to contain weak central carbon-carbon bonds that may be easily cleaved at high temperatures or even at ambient conditions to yield persistent free diradicals. To demonstrate the weak C-C bond strength, density functional theory calculations were carried out at several levels of theory for both the parent molecules and the diradicals resulting from the C-C bond cleavage. To assess the accuracy of the calculations, hexaphenylethane was chosen as a model compound due to its similarity with the molecules studied here, its great resonance stabilization, and long-standing history within the chemistry community. The C-C bond dissociation energy of hexaphenylethane was determined to be 11.3 ( 1.4 kcal/ mol using a combination of isodesmic reactions and calculations at the M06-2X/6-31+G(d,p) level of theory. The types of molecules presented here are proposed as strong possibilities for the natural existence of free radicals in young and mature soot formed in hydrocarbon combustion. 1. Introduction Persistent free radicals (PFRs) in soot have been attributed to the existence of various oxygenated compounds.1,2 These are resonantly stabilized, free radicals of semiquinone, phenoxyl, and cyclopentadienyl origins. It is thought that the uptake of persistent free radicals through the respiratory system can lead to the production of hydroxyl radicals harmful to cellular components, subsequently increasing the risk of lung cancer.1,3 Soot, generally described as aggregates of roughly spherical, primary particles coexisting with graphite flakes, can serve also as nuclei for atmospheric aerosols.4,5 Although the most prominent atmospheric aerosol nucleation phenomena involve sulfuric acid, ammonia, or ionic particles, carbon-based aerosols are also known to act as cloud condensation nuclei. For example, soot exhaust from aircraft engines is thought to be responsible, at least partially, for contrail formation in the wake of an aircraft.6-8 Combustion soot has also been observed to show various wetting properties.7-10 More specifically, depending on the conditions of soot formation, the material may be either hydrophobic or hydrophilic, with the ability to uptake substantial amounts of water on both surface sites and internally within pores.8,11 What has not been adequately addressed though is the mechanism of water uptake by a soot surface traditionally thought to be hydrophobic. In particular, the potential role of free-radical species on the surface of a carbon particle and/or within its pores has not yet been considered. Although the oxidation of soot surfaces by ozone, OH and other oxidants can lead to the formation of polar sites capable of water uptake,5,12-28 persistent free radicals can also form tight hydrogen bonds with water molecules, thus acting as molecular sites for water uptake. Theoretically, the binding energy of hydrogen-like bonds between a methyl radical and water is 1.5 kcal/mol.29,30 This binding energy increases to over 2, 3, and 4 kcal/molforethyl,isopropyl,andtert-butylradicals,respectively.30,31 Likewise, some oxygenated hydrocarbon free radicals exhibit similar tendencies to form hydrogen bonds with water. For * To whom correspondence should be addressed. E-mail: [email protected]. Phone: (213) 740-0499.

example, the phenoxyl-water binding energy was reported to be ∼4 kcal/mol.32 Persistent free radicals may also impact the mechanism of soot nucleation and surface growth in hydrocarbon combustion. Currently, the modeling of soot formation in flames generally follows the hydrogen-abstraction-carbon-addition (HACA) mechanism.33,34 In this mechanism, soot surface growth requires the existence of gas-phase free radicals, notably the H atom. The addition of gas-phase, hydrocarbon species, for example, acetylene, to an aromatic carbon site requires H-atom abstraction of an aryl-H to produce a radical site, which subsequently reacts with acetylene or other hydrocarbon species. Experimental evidence suggests that soot can continue to grow in mass even in the absence of gas-phase free radicals (e.g., H•). In ethylene-air counterflow diffusion flames, the soot volume fraction observed toward the stagnation surface of the opposed jets can be predicted only if soot retains a free-radical characteristic while they are transported toward the stagnation surface.35 In more recent studies of burnerstabilized ethylene-oxygen-argon flames, the soot volume fraction was found to continually increase in the postflame region, where the temperature drops below 1500 K and few gas-phase free radicals can survive.36,37 Ample evidence suggests persistent free radicals exist in carbonaceous materials with little to no oxygenates. Electron spin resonance (EPR) spectra of anthracite, a coal containing little to no oxygenated compounds, show a measurable concentration of free radicals.38 Furthermore, soot formed from the pyrolysis of ethylene, acetylene, and various jet fuel surrogates also shows measurable concentrations of radicals likely associated with carbon atoms.39 The reported Lande´ g-factors for such soot samples suggest that the radicals are of π nature, most of which are associated with aromatic compounds. For free radicals to persist on the surface of or within the structure of soot, they must have certain thermodynamic stablility; yet, to bind with water or a hydrocarbon species, they must be active enough to form hydrogen or covalent bonds. There are certainly many possibilities for stable radical types and classes. Examples are given in a review by Hicks.40

10.1021/jp909662m  2010 American Chemical Society Published on Web 12/29/2009

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Figure 1. Structures of selected model compounds (1-14) and the molecule accidentally synthesized by Gomberg,44,45 15.

Additionally, singlet diradical ground states have been shown to exist in polyacenes with eight or more rings.41 These radicals are known to be of π nature. Localized unpaired electrons in their ground states have also been detected in the EPR spectra of 4,4′-polymethylenebistriphenylmethyl, (1,4-phenylene) bisdiarylmethyl, and (4,4′-biphenylene) bisdiarylmethyl in suspensions of benzene.42 By using electronic structure calculations, this paper explores molecular analogues to possible aromatic diradical systems existing in young and mature soot. We explore a class of persistent free radicals that can be dynamically generated from aromatics with extremely weak bonds, namely, the hybrid derivatives of acenaphthene and hexaphenylethane (HPE, 1),

as depicted in Figure 1. These compounds were chosen from the consideration that HPE-like molecules, including pyracenes, are known to have weak central C-C bonds with lengths around or greater than 1.7 Å due to steric repulsion.43 The acenaphthene derivatives with increasing numbers of substituted phenyl groups are conceptual tools for probing the question of how carbonaceous aromatic radicals may persist in soot. For example, tetraphenylacenaphthene, 14, represents a hybrid structure between acenaphthene and HPE. Its molecular structure is similar to HPE but with two of the phenyl groups replaced by acenaphthene. HPE has long-standing history as a molecule with an extremely weak central carbon-carbon bond. It is generally recognized

C-C Bonds in Acenaphthene Derivatives

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TABLE 1: Summary of Calculated Electronic Energies (E0) and Zero-Point Energies (ZPE) in Hartrees, Sensible Enthalpy at 298 K (H°(298) - H°(0)) in cal/mol, and Literature Values of Enthalpy of Formation (∆fH°298) of Reference Species in kcal/mol B3LYP/6-31G(d) species

E0

M06-2X/6-31+G(d,p)

ZPEa

E0

H°298 - H°0

∆fH°298

ref

52.1 -17.8 ( 0.1 -20.0 ( 0.1 11.0 ( 0.7 20.0 ( 0.2 12.1 ( 0.1 49.5 ( 1.0 -54.0 ( 0.5 35.9 ( 0.4 37.3 ( 0.7

56 57 57 58 59 59 58

b

target species -1465.55335 -733.39873 -732.76509 -1619.13520 -1772.73444 -886.35608 -694.11356 -694.01692 -925.08636 -924.98093 -1156.05306 -1155.95174 -1387.01039 -1386.96031

1 (C38H30, HPE) 2 (C19H16, TPM) 3 (C19H15, TPM•) 4 (C42H32) 5 (C46H34) 6 (C23H17, DPNM•) 7 (C18H14) 8 (C18H14:) 9 (C24H18) 10 (C24H18:) 11 (C30H22) 12 (C30H22:) 13 (C36H26) 14 (C36H26:)

-1466.02914 -733.65829 -733.03119 -1619.67351 -1773.31634 -886.67866 -694.36209 -694.28015 -925.41206 -925.34145 -1156.44158 -1156.38703 -1387.46578 -1387.43668

0.54054 0.27987 0.26781 0.58353 0.62980 0.31214 0.25373 0.24861 0.33190 0.32777 0.40947 0.40517 0.48669 0.48380

H• CH4 C 2H 6 tert-C4H9• (tert-butyl) C6H6 (benzene) C7H8 (toluene) C7H7• (benzyl) C8H18 (hexamethylethane) C10H8 (naphthalene) C12H10 (acenaphthene)

-0.50027 -40.51826 -79.83016 -157.79778 -232.24777 -271.56563 -270.91516 -315.70006 -385.89144 -463.31311

reference species -0.49667 0.04352 -40.48874 0.07228 -79.78293 0.11278 -157.71592 0.09670 -232.15393 0.12322 -271.45391 0.11028 -270.79480 0.23680 -315.56185 0.14194 -385.89144 0.17567 -463.13309

a

33.38 17.28 16.60 35.19 39.16 19.59 14.77 15.78 20.25 20.62 25.15 25.16 30.11 30.47 0.89 3.49 4.65 7.48 5.87 7.68 7.05 13.20 8.60 10.37

c

59 59

Multiplied by 0.96 to account for anharmonicity. b See Figure 1 for structures. c Average of the values reported in refs 60 and 61.

that the first literature occurrence of this molecule coincides with a failed attempt to synthesize it by Gomberg.44,45 On the other hand, acenaphthene, the base molecule for the target species studied here, which may be formed through the hydrogenation of acenaphthylene, has direct relevance to the evolution of soot precursors and soot formation itself.33,46-48 The likelihood that structures 7, 9, 11, and 13 would form in the gas phase of a flame is extremely small. However, similar moieties containing very weak C-C bonds are likely to exist in many types of soot, especially near graphitic edges at the interfaces of condensed polycyclic aromatic hydrocarbons (PAHs) and the neck regions of aggregates of primary particles. Sites on and within soot, possibly represented as boundaries between PAH conglomerates and/or graphitic edges, may facilitate the existence of these types of C-C bonds. Such bonds may freely open and close with photoexcitation, attack of a polar molecule, or even due to effects of molecular strain and thermal fluctuations. Thus, the purpose of this study is not to illustrate formation pathways of the model compounds in soot structures but to demonstrate how high levels of steric strain can substantially reduce specific C-C bond strengths. 2. Methodology Electronic structure calculations were performed on an inhouse cluster using the computational chemistry package QChem 3.1.49 Geometries were optimized using the B3LYP50,51 and M06-2X52 density functionals. For the B3LYP calculations, we used the 6-31G(d) basis set. For M06-2X, the 6-31+G(d,p) basis set was used to account for long-range interactions for which diffuse and polarization functions are expected to be important.52 The M06-2X functional was used in this study because it was specifically designed to take into account long-range noncovalent interactions typical of large

PAHs and includes roughly twice the amount of Hartree-Fock exchange (54%) compared to the B3LYP functional. The M06-2X functional has been validated and tested against a wide range of molecules.52 For purposes of comparison, calculations were performed at two other levels of theory to determine the bond dissociation energy (BDE) of the C-H bond in triphenylmethane. These are B3LYP/6-31+G(d) and B3LYP/6-311+G(d,p) . Local minima were confirmed by the lack of imaginary frequencies, while transition-state structures were confirmed by the presence of one, and only one, imaginary frequency. In most cases, the default direct inversion of the iterative subspace (DIIS)53 convergence algorithm was used; in cases where convergence failed, the algorithm was switched to either geometric direct minimization (GDM54 or DIIS_GDM, in which the first SCF cycle employs DIIS and subsequent cycles utilize GDM). All frequency calculations were performed at the B3LYP/6-31G(d) level of theory and multiplied by a factor of 0.96 to account for vibrational anharmonicity.55 Because of the large computational demand of force analyses at the M06-2X/ 6-31+G(d,p) level of theory, all enthalpy values were calculated utilizing frequencies taken from B3LYP/6-31G(d) calculations. In any case, the zero-point energy differences between B3LYP and M06-2X amounted to less than 1% for several closed and open shell systems tested here. Calculations involving acenaphthene derivatives in their diradical forms were performed in their triplet states (the eigenvalue of the S2 operator was confirmed to be within a few percent of the theoretical value, 2); reasoning for this is discussed later. Symmetry was not enforced in any calculations; in most cases, the symmetry of optimized structures belonged to the C1 point group.

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Figure 3. Central C-C bond lengths computed for selected molecules.

Figure 2. Schematic structures of selected molecules illustrating several key geometric properties. Left: central C-C bond length and C-C-C bond angles. Right: values of dihedral angles between adjacent substituents calculated with M06-2X/6-31+G(d,p). Values in parentheses are those calculated with B3LYP/6-31G(d).

Isodesmic reactions were used to estimate the enthalpies of formation for derivatives of HPE (1) and the triphenylmethyl radical. We note that, in most cases, reaction schemes were homodesmicsnot only was bond type conserved, but so was aromaticity. Most experimental standard enthalpies of formation of the reference species are well-documented,56-61 as shown in Table 1. Standard-state BDE values were determined directly from zero-point corrected electronic energies and sensible enthalpies at 298 K and indirectly from the enthalpy of formation of a parent molecule and its dissociated products or diradicals. 3. Results and Discussion Figure 2 depicts HPE and two similar molecules, in which one or more phenyl groups are replaced by the naphthyl groups. These geometries were optimized at the M06-2X/6-31+G(d,p) level of theory. They represent the lowest energy conformations and illustrate the uniqueness of this class of molecules. Not only are central bond lengths longer than a typical single C-C bond by ∼0.2 Å, their most stable conformations are opposite of what is conventionally expected. The Newmann projections of Figure 2 depict the lowest energy states of these conformations, a nearly eclipsed position. The stability of the eclipsed conformers is a manifestation of the attractive dispersion forces of the aromatic groups across the C-C axis. These dispersion forces counteract the steric repulsion among the same aromatic groups, which cause the central C-C bond to elongate. As expected, elongated C-C bonds are also prevalent in acenaphthene derivatives. Beginning with the central C-C bond in acenaphthene (1.57 Å), Figure 3 illustrates a clear trend between the number of phenyl group additions and bond length. In general, the central C-C bond length increases with additions of phenyl groups. For tetraphenylacenaphthene 13, the central C-C bond increases to 1.7 Å, as determined by the M06-2X/ 6-31+G(d,p) calculation. As expected, both M06-2X/6-31+G(d,p)

and B3LYP/6-31G(d) predict the same C-C length for acenaphthene, a molecule with comparatively minimal long-range interactions. With phenyl substitution however, M06-2X/631+G(d,p) calculations exhibit consistently shorter C-C bond lengths than their B3LYP/6-31G(d) counterparts, resulting from an enhanced stability through dispersion forces. All calculated electronic and zero-point energies are reported in Table 1. Although the results shown in Table 1 allow us to estimate the central C-C bond energies readily, there is a cause for concern with regard to the accuracy of these estimates, simply because the errors in the electronic energies calculated for the closed-shell parent molecule and its open-shell diradical generally do not cancel out. For this reason, we also employed the approach of isodesmic reactions to obtain estimates for BDE through enthalpies of formation estimated for the parent molecule and its diradical resulting from central C-C bond fission. We note that, for molecules considered in the current study, the use of isodesmic reactions can also lead to some errors. Because these systems generally have large sizes, compounding errors may result from the need to use a large number of small reference species whose enthalpies of formation are uncertain to an extent. Conversely, large species may be used as reference species, but their enthalpies of formation are usually associated with even larger uncertainties. In addition, it is not trivial to write reactions that preserve the amount and type of electron correlation present in large target species. Hence, our interest here is not to provide accurate estimates for the enthalpy of formation but rather to explore the bond energies using two separate approaches. Results from the isodesmic reactions at the B3LYP/6-31G(d) and M06-2X/6-31+G(d,p) levels of theory are presented in Table 2. One isodesmic reaction was written for each target species. With regards to the acenaphthene derivatives M, isodesmic reactions use CH4, acenaphthene (C12H10), and toluene (C7H8) as the reference species and are written as follows:

M + nCH4 f C12H10 + mC7H8 For their diradical counterparts (R•), we utilized the enthalpy of formation estimated for the parent molecule M and isodesmic reactions given by

R · + 2C2H6 f 2C7H7 · + 2CH4 + M where C7H7• is the benzyl radical. The coefficients n and m are given in Table 2. In all cases, the values of enthalpy of formation determined from M06-2X/6-31+G(d,p) are smaller than those from B3LYP/6-31G(d), by as much as 30 kcal/mol. In general, the M06-2X/6-31+G(d,p) values are expected to be more

C-C Bonds in Acenaphthene Derivatives

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TABLE 2: Isodesmic Reactions and Enthalpies of Formation at the Standard State ∆fH°298 (kcal/mol)

a

species

isodesmic reaction

1

a

B3LYP/6-31G(d)

M06-2X/6-31+G(d,p)

+6CH4 f 6C6H6 + C8H18

199

169

2

+2CH4 f 3C7H8

73

62

3

+3CH4 f 3C6H6 + tert-C4H9 ·

96

90

4

+6CH4 f 5C6H6 + C8H18 + C10H8

212

185

5

+6CH4 f 4C6H6 + C8H18 + 2C10H8

231

195

6

+C6H6 f 3 + C10H8

107

102

7

+CH4 f C12H10 + C7H8

65

57

8

+2C7H8 + C2H6 f 7 + 2C7H7 · + 2CH4

121

112

9

+2CH4 f C12H10 + 2C7H8

94

82

10

+2C7H8 + C2H6 f 9 + 2C7H7 · + 2CH4

143

135

11

+3CH4 f C12H10 + 3C7H8

135

111

12

+2C7H8 + C2H6 f 11 + 2C7H7 · + 2CH4

174

161

13

+4CH4 f C12H10 + 4C7H8

178

145

14

+2C7H8 + C2H6 f 13 + 2C7H7 · + 2CH4

203

165

See Table 1 for species nomenclatures.

reliable because they more accurately describe the dispersion forces in these systems. For molecular structures without significant dispersion interactions (e.g., triphenylmethane 2), both levels of theory are reasonably accurate in predicting BDE, that is, within 5 kcal/ mol from the corresponding experimental values. This accuracy is adequate for the purpose of the current study. Table 3 illustrates BDE values estimated for the quaternary C-H bond dissociation in 2, forming the hydrogen and triphenylmethyl 3 radicals. The available experimental BDE values of (Ph)3C-H are 75 ( 2 and 80.8 ( 3.0 kcal/mol.62,63 The latter value was determined in a dimethyl sulfoxide solution from equilibrium acidity and electrochemical data, while the former value was obtained through a pyrolytic and photochemical process,

TABLE 3: Standard, (Ph)3C-H Bond Dissociation Energy (kcal/mol) B3LYP/6-31G(d) B3LYP/6-31+G(d) B3LYP/6-31G(d) isodesmic B3LYP/6-311+G(d,p) M06-2X/6-31+G(d,p) M06-2X/6-31+G(d,p) isodesmic ONIOM64 expt62 expt63 b a

71.5 72.6 74.9a 73.2 77.9 79.8a 75.9 75 ( 2 80.8 ( 3.0

See Table 2. b In aqueous Me2SO solution.

whereby the author measured the activation energy associated with the unimolecular dissociation of a parent molecule in a

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TABLE 4: Standard, Central C-C Bond Dissociation Energy (kcal/mol) of HPE (1) B3LYP/6-31G(d) B3LYP/6-31G(d) isodesmica M06-2X/6-31+G(d,p) M06-2X/6-31+G(d,p) isodesmica ONIOM64 expt62

-23.8 -8.1 ( 1.4 11.6 11.3 ( 1.4 16.6 11 ( 2

a See Table 2. The uncertainty values are determined from the uncertainties in the enthalpies of formation of the reference species. They do not indicate the accuracy of the computational method.

toluene bath gas. Also available is the BDE value determined with the ONIOM method (75.9 kcal/mol).62 The BDE values estimated from different approaches, including the use of isodesmic reactions and M06-2X/6-31+G(d,p), all fall in the range of current experimental and theoretical uncertainties with small effects arising from the basis set sizes. From the M06-2X/6-31+G(d,p) isodesmic calculations, we estimate the central C-C BDE of HPE (1) to be 11.3 ( 1.4 kcal/mol (Table 4). The uncertainty value was determined from the uncertainties in the enthalpies of formation of the reference species; they do not indicate the accuracy of the computational method. The BDE was also calculated directly from the electronic energies with zero-point and sensible enthalpy corrections. The value determined in this manner is 11.6 kcal/ mol, in close agreement with the results obtained from isodesmic reactions. The only available gaseous phase experimental value for the BDE of HPE comes from Szwarc.62 They reported a BDE value of 11 ( 2 kcal/mol, which is in close agreement with the M06-2X/6-31+G(d,p) results. Admittedly, the value reported by Szwarc62 is close to that of the intradimer C-C BDE in 15, the molecule Gomberg originally and accidentally synthesized. That C-C BDE is incidentally also around 11 kcal/ mol.65 A theoretical study performed by Vreven and Morokuma,64 for which they calibrate a three-layer hybrid quantum mechanical scheme known as the ONIOM method, predicted the BDE of the central C-C bond of HPE (1) to be 16.6 kcal/mol, somewhat larger than our M06-2X/6-31+G(d,p) results. The discrepancy may be attributed, at least in part, to the use of the B3LYP functional for geometry optimizations in the ONIOM calculation. In comparison to the results obtained for triphenylmethane, the B3LYP/6-31G(d) calculations fail miserably when predicting the central C-C BDE in HPE, as shown in Table 4. The BDE values are underestimated by as much as 30 kcal/ mol. Use of isodesmic reaction improves the prediction only slightly. Overall, this reflects the inability of B3LYP to accurately account for long-range dispersion interactions. In essence, the difference in the BDE values predicted by B3LYP/ 6-31G(d) and M06-2X/6-31+G(d,p) reflects the overall stabilization energy gained from the long-range interactions of the phenyl groups. In what follows, we shall use the M06-2X/631+G(d,p) results exclusively in our discussion of central C-C BDE. Figure 4 shows the variation of standard, central C-C BDE values for the acenaphthene and hexaphenylethane series of compounds. For comparison, the plot also shows the BDE values estimated from taking the difference of the electronic energies of the diradical and its parent molecule, both corrected for zeropoint energy and sensible enthalpy. It is seen that the BDE values of acenaphthene derivatives generally decrease with an increase in phenyl substitution. For example, the BDE value is 55-60 kcal/mol for phenylacenaphthene 7 and decreases to about 20 kcal/mol in tetraphenylacenaphthene 13.

Figure 4. Standard-state, central C-C BDEs for the class of acenaphthene derivatives studied, HPE and its derivatives. *Open circles represent BDE values estimated directly by subtracting the electronic energy of the diradical from that of the parent molecule, both with zero-point energy and sensible enthalpy corrections.

Structures 4 and 5 were studied to explore the effect of naphthyl substitution in HPE. The M06-2X/6-31+G(d,p) derived BDEs of both are very low, at 7.7 and 10.5 kcal/mol, respectively. Not surprisingly, the central C-C bond lengths of 4 and 5 (1.71 and 1.745 Å, respectively) are larger than that of HPE. As can be deduced from the BDE values, no simple correlation can be made between the number of phenyl groups added to the parent HPE molecule and its corresponding BDE value. The addition of larger aromatic groups to HPE does not necessarily lead to lower BDEs. The central C-C bond strength is a result of competition between steric repulsion and dispersive attraction. Comparing tetraphenylacenaphthene 13 with HPE, we found that, although the central bond lengths are approximately equal, the BDE in 13 is substantially higher than that in HPE, by roughly 10 kcal/mol. This difference is related to the naphthalene group in 13 that enhances central C-C bonding strength through resonance. Compared to the typical C-C bond strength of 90 kcal/mol66 found in many hydrocarbons, a bond strength of 20 kcal/mol still illustrates the significance of steric repulsions in 13. For acenaphthene derivatives with fewer phenyl groups than in 13, our results show that the central BDEs are about 50-60 kcal/mol. As was mentioned earlier, the reported BDEs for acenaphthene derivatives are based on calculations for their triplet diradicals. Recent CASSCF and CBSQB3 calculations for some smaller hydrocarbon diradicals show that triplet energy levels lie above their singlet counterparts.67 In the current work, attempts to perform geometry optimizations for diradical acenaphthene derivatives in the open-shell singlet states failed in all but one case, because the geometries converged toward those of closed-shell, parent molecules. We therefore carried out single-point B3LYP/6-31G(d) calculations for diradical acenaphthene derivatives, comparing the energies of closed-shell singlet, open-shell singlet and triplet. These calculations used the geometries optimized at the M062X/6-31+G(d,p) level of theory. To obtain the correct atomic spin densities for open-shell singlet systems, spin symmetry was broken in the initial guess of the wave function by mixing 50% of the lowest unoccupied molecular orbital (LUMO) with the highest occupied molecular orbital (HOMO). In each case, the eigenvalues of the S2 operator were confirmed to be within a few percent of their respective, expected values, as shown in Table 5. A value close to unity suggests a substantial amount of triplet-state contamination and a small singlet-triplet gap. In all cases, the triplet state lies 10 kcal/ mol). The tests performed above suggest that, with proper geometry optimization, the open-shell singlets would probably

C-C Bonds in Acenaphthene Derivatives

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TABLE 5: Single-Point, Relative B3LYP/6-31G(d) Electronic Energies Erel (kcal/mol) and Eigenvalues of the S2 Operator Calculated for Triplet Diradical Acenaphthene Derivatives Optimized at the M06-2X/6-31+G(d,p) Level of Theory speciesa

stateb

Erel



14

CSS OSS T CSS OSS T CSS OSS T CSS OSS T

10.7 0.0 0.0 16.6 1.4 0.0 13.9 1.6 0.0 22.1 2.7 0.0

0.00 1.01 2.05 0.00 1.05 2.07 0.00 1.01 2.08 0.00 1.05 2.08

12 10 8

b

CCS: closed-shell singlet; OSS: open-shell singlet; T: triplet.

lie lower in energy than the triplets, and hence, the BDEs reported here for acenaphthene derivatives should be considered as upper limit values. Equilibrium constants for central C-C fission were calculated as a function of temperature using the values of the enthalpy of formation from isodesmic reactions, in addition to the molecular parameters calculated at the B3LYP/6-31G(d) level of theory. At 1000 K, 13 f 14 has an equilibrium constant on the order of 10-4. Within the realm of radical concentrations, this is rather high. Near room temperature, however, the equilibrium constant of 13 f 14 reduces to ∼10-15. These results are not interpreted as discouraging because, in any soot-like system, it is likely that molecular analogues to the systems here will experience enhanced steric interactions due to the presence of larger aromatic structures than phenyl, resulting in even longer bond lengths, and possibly in smaller bond strengths than that found in HPE. Absolute correlations between bond length and dissociation energy can be applied to the types of molecules studied here but only semiquantitatively. Glockler has made such correlations using the heat of sublimination of carbon and C-C distances for various molecules obtained through Raman spectroscopy.68 More recently, Zavitsas69 used both experimental and theoretical bond lengths, including results of the HPE BDE from the ONIOM calculation, to define a linear relationship between BDE and C-C bond length. Figure 5 presents his data, along with our M06-2X/6-31+G(d,p) isodesmic results. As seen, the straight-line correlation proposed by Zavitsas is qualitatively correct. At the quantitative level and especially above 1.65 Å, however, the scatter in the plot suggests that second order factors do influence this correlation. Zavitsas admittedly left out certain large molecules such as dicumyl and 3,3,4,4-tetramethylhexane because they do not fit the linear correlation well. Additionally, X-ray analyses of isolated HPE derivatives by Suzuki et al.43 show bond lengths up to 1.77 Å, greater than the theoretical 1.75 Å maximum projected by Zavitsas. Indeed, an ab initio study on many forms of highly crowded alkanes performed by Zhu et al.70 illustrate a correlation between BDE and C-C length that quickly loses strength as the C-C bond length approaches 1.65 Å, and hence, the correlation weakens above this bond length. Lastly, we note that the current theoretical results underscore the importance of competition between steric repulsion and dispersive attraction in influencing the strength of aliphatic C-C bonds that join several small aromatic units together (e.g., phenyl

Figure 5. M06-2X/6-31+G(d,p) results and literature values for BDE vs central C-C bond length. The line represents a least-squares fit of the data reviewed by Zavitsas,69 excluding the ONIOM result of Vreven and Morokuma for HPE.64

and naphthyl). This competition dictates the actual strength of these bonds. Extrapolation of this findings to soot with constituent molecules bound to the edges of adjacent graphene sheets or at the interfaces of condensed PAHs suggests that extremely weak C-C bonds could indeed exist in otherwise strongly bound systems. Stronger dispersive forces in soot structure, coupled with the facts that aromatic ring sizes are generally larger than phenyl36 and that additional steric strain may result from imperfectly annealed graphetic structures, all point toward the possible existence of persistent free radicals formed dynamically through repetitive cleavage and formation of unique aliphatic C-C bonds holding aromatic structures together. This dynamical process is of course molecular vibrational and thermal fluctuational in nature. 4. Conclusions Analogues representing a class of possible molecular scenarios in young and mature soot are presented as an explanation for the existence of persistent free radicals found in products of combustion. These molecules are probably diradical in nature. Computational results show that increasing the number of phenyl groups in acenaphthene results in increased central bond length and a decrease in bond dissociation energy. This is due to the overall increase in steric repulsion that accompanies phenyl group additions. Ab initio calculations involving these structures illustrate that, with increased levels of long-range interactions, the B3LYP density functional fails to accurately predict bond dissociation enthalpies. Finally, we propose that structures similar to 13 and HPE may exist within the turbostratic framework of soot particles thus facilitating the existence of indefinitely persistent free radicals formed dynamically through repetitive bond cleavage and formation. Acknowledgment. This work was supported by the National Science Foundation (CBET 0651990). Supporting Information Available: Optimized geometries and vibrational frequencies at the B3LYP/6-31G(d) level of theory for all reference and target species. Optimized geometries and vibrational frequencies at the B3LYP/6-31G(d) and M062X/6-31+G(d,p) levels of theory for all reference species used in isodesmic reactions. Optimized geometries for all target

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species at the M06-2X/6-31+G(d,p) level of theory. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Dellinger, B.; Pryor, W. A.; Cueto, R.; Squadrito, G. L.; Hegde, V.; Deutsch, W. A. Chem. Res. Toxicol. 2001, 14, 1371. (2) Dellinger, B.; Loninicki, S.; Khachatryan, L.; Maskos, Z.; Hall, R. W.; Adounkpe, J.; McFerrin, C.; Truong, H. Proc. Combust. Inst. 2007, 31, 521. (3) Heinrich, U.; Fuhst, R.; Rittinghausen, S.; Creutzenberg, O.; Bellmann, B.; Koch, W.; Levsen, K. Inhal. Toxic. 1995, 7, 533. (4) Kulmala, M. Science 2003, 302, 1000. (5) Persiantseva, N. M.; Popovicheva, O. B.; Shonija, N. K. J. EnViron. Monit. 2004, 6, 939. (6) Karcher, B.; Peter, T.; Biermann, U. M.; Schumann, U. J. Atmos. Sci. 1996, 53, 3066. (7) Demirdjian, B.; Ferry, D.; Suzanne, J.; Popovicheva, O. B.; Persiantseva, N. M.; Shonija, N. K. J. Atmos. Chem. 2007, 56, 83. (8) Popovicheva, O.; Persiantseva, N. M.; Shonija, N. K.; DeMott, P.; Koehler, K.; Petters, M.; Kreidenweis, S.; Tishkova, V.; Demirdjian, B.; Suzanne, J. Phys. Chem. Chem. Phys. 2008, 10, 2332. (9) Popovicheva, O. B.; Persiantseva, N. M.; Kuznetsov, B. V.; Rakhmanova, T. A.; Shonija, N. K.; Suzanne, J.; Ferry, D. J. Phys. Chem. A 2003, 107, 10046. (10) Popovicheva, O. B.; Persiantseva, N. M.; Lukhovitskaya, E. E.; Shonija, N. K.; Zubareva, N. A.; Demirdjian, B.; Ferry, D.; Suzanne, J. Geophys. Res. Lett. 2004, 31. (11) Ferry, D.; Suzanne, J.; Nitsche, S.; Popovitcheva, O. B.; Shonija, N. K. J. Geophys. Res.-Atmos. 2002, 107, 10. (12) Smith, D. M.; Chughtai, A. R. Colloid. Surf. A. Physicochem. Eng. Asp. 1995, 105, 47. (13) Smith, D. M.; Chughtai, A. R. J. Atmos. Chem. 1997, 26, 77. (14) Chughtai, A. R.; Brooks, M. E.; Smith, D. M. J. Geophys. Res.Atmos. 1996, 101, 19505. (15) Chughtai, A. R.; Jassim, J. A.; Peterson, J. H.; Stedman, D. H.; Smith, D. M. Aerosol Sci. Technol. 1991, 15, 112. (16) Chughtai, A. R.; Williams, G. R.; Atteya, M. M. O.; Miller, N. J.; Smith, D. M. Atmos. EnViron. 1999, 33, 2679. (17) Lary, D. J.; Shallcross, D. E.; Toumi, R. J. Geophys. Res. 1999, 104, 15929. (18) Decesari, S.; Facchini, M. C.; Matta, E.; Mircea, M.; Fuzzi, S.; Chughtai, A. R.; Smith, D. M. Atmos. EnViron. 2002, 36, 1827. (19) Kotzick, R.; Niessner, R. Atmos. EnViron. 1999, 33, 2669. (20) Kotzick, R.; Panne, U.; Niessner, R. J. Aerosol. Sci. 1997, 28, 725. (21) Metts, T. A.; Batterman, S. A.; Fernandes, G. I.; Kalliokoski, P. Atmos. EnViron. 2005, 39, 3343. (22) Nienow, A. M.; Roberts, J. T. Annu. ReV. Phys. Chem. 2006, 57, 105. (23) Zuberi, B.; Johnson, K. S.; Aleks, G. K.; Molina, L. T.; Laskin, A. Geophys. Res. Lett. 2005, 32. (24) Bertram, A. K.; Ivanov, A. V.; Hunter, M.; Molina, L. T.; Molina, M. J. J. Phys. Chem. A 2001, 105, 9415. (25) Bedjanian, Y.; Lelievre, S.; Le Bras, G. Phys. Chem. Chem. Phys. 2005, 7, 334. (26) Esteve, W.; Budzinski, H.; Villenave, E. Atmos. EnViron. 2006, 40, 201. (27) Mak, J.; Gross, S.; Bertram, A. K. Geophys. Res. Lett. 2007, 34. (28) Park, J. H.; Ivanov, A. V.; Molina, M. J. J. Phys. Chem. A 2008, 112, 6968. (29) Crespo-Otero, R.; Sa´nchez-Garcı´a, E.; Suardı´az, R.; Montero, L. A.; Sander, W. Chem. Phys. 2008, 353, 193. (30) An, X. L.; Liu, H. P.; Li, Q. Z.; Gong, B. A.; Cheng, J. B. J. Phys. Chem. A 2008, 112, 5258. (31) Li, Q. Z.; Zhu, H. J.; An, X. L.; Gong, B. A.; Cheng, J. B. Int. J. Quantum Chem. 2009, 109, 605. (32) Chipman, D. M. J. Phys. Chem. A 2000, 104, 11816. (33) Frenklach, M.; Wang, H. Proc. Combust. Inst. 1990, 23, 1559. (34) Wang, H.; Frenklach, M. Combust. Flame 1997, 110, 173.

Dames et al. (35) Wang, H.; Du, D. X.; Sung, C. J.; Law, C. K. Proc. Combust. Inst. 1996, 26, 2359. (36) Oktem, B.; Tolocka, M. P.; Zhao, B.; Wang, H.; Johnston, M. V. Combust. Flame 2005, 142, 364. (37) Zhao, B.; Uchikawa, K.; Wang, H. Proc. Combust. Inst. 2007, 31, 851. (38) Retcofsk, H. l.; Stark, J. M.; Friedel, R. A. Anal. Chem. 1968, 40, 1699. (39) Pugmire, R.; Yan, S. H.; Jiang, Y. J.; Solum, M. S.; Preciado, I.; Eddings, E. G.; Sarofim, A. F. Abstr. Pap. Am. Chem. Soc. 2006, 231, 102. (40) Hicks, R. G. Org. Biomol. Chem. 2007, 5, 1321. (41) Bendikov, M.; Duong, H. M.; Starkey, K.; Houk, K. N.; Carter, E. A.; Wudl, F. J. Am. Chem. Soc. 2004, 126, 7416. (42) Jarrett, H. S.; Sloan, G. J.; Vaughan, W. R. J. Chem. Phys. 1956, 25, 697. (43) Suzuki, T.; Takeda, T.; Kawai, H.; Fujiwara, K. Pure Appl. Chem. 2008, 80, 547. (44) McBride, J. M. Tetrahedron 1974, 30, 2009. (45) Gomberg, M. Ber. Deut. Chem. Gesell. 1902, 35, 3914. (46) Wang, H.; Frenklach, M. J. Phys. Chem. 1994, 98, 11465. (47) Violi, A.; Kubota, A.; Truong, T. N.; Pitz, W. J.; Westbrook, C. K.; Sarofim, A. F. Proc. Combust. Inst. 2002, 29, 2343. (48) Wang, D.; Violi, A. J. Org. Chem. 2006, 71, 8365. (49) Shao, Y.; Molnar, L. F.; Jung, Y.; Kussmann, J.; Ochsenfeld, C.; Brown, S. T.; Gilbert, A. T. B.; Slipchenko, L. V.; Levchenko, S. V.; O’Neill, D. P.; DiStasio, R. A.; Lochan, R. C.; Wang, T.; Beran, G. J. O.; Besley, N. A.; Herbert, J. M.; Lin, C. Y.; Van Voorhis, T.; Chien, S. H.; Sodt, A.; Steele, R. P.; Rassolov, V. A.; Maslen, P. E.; Korambath, P. P.; Adamson, R. D.; Austin, B.; Baker, J.; Byrd, E. F. C.; Dachsel, H.; Doerksen, R. J.; Dreuw, A.; Dunietz, B. D.; Dutoi, A. D.; Furlani, T. R.; Gwaltney, S. R.; Heyden, A.; Hirata, S.; Hsu, C. P.; Kedziora, G.; Khalliulin, R. Z.; Klunzinger, P.; Lee, A. M.; Lee, M. S.; Liang, W.; Lotan, I.; Nair, N.; Peters, B.; Proynov, E. I.; Pieniazek, P. A.; Rhee, Y. M.; Ritchie, J.; Rosta, E.; Sherrill, C. D.; Simmonett, A. C.; Subotnik, J. E.; Woodcock, H. L.; Zhang, W.; Bell, A. T.; Chakraborty, A. K.; Chipman, D. M.; Keil, F. J.; Warshel, A.; Hehre, W. J.; Schaefer, H. F.; Kong, J.; Krylov, A. I.; Gill, P. M. W.; Head-Gordon, M. Phys. Chem. Chem. Phys. 2006, 8, 3172. (50) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (51) Lee, C. T.; Yang, W. T.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (52) Zhao, Y.; Truhlar, D. G. Theor. Chem. Acc. Theor. Comput. Model. 2008, 120, 215. (53) White, C. A.; HeadGordon, M. J. Chem. Phys. 1996, 104, 2620. (54) Van Voorhis, T.; Head-Gordon, M. Mol. Phys. 2002, 100, 1713. (55) Irikura, K. K.; Johnson, R. D.; Kacker, R. N. J. Phys. Chem. A 2005, 109, 8430. (56) Chase, M. W., Jr. NIST-JANAF Themochemical Tables, 4th ed.; 1998; Vol. 9, p 1. (57) Manion, J. A. J. Phys. Chem. Ref. Data 2002, 31, 123. (58) Tsang, W. Heats of Formation of Organic Free Radicals by Kinetic Methods. In Energetics of Organic Free Radicals; Martinho Simoes, J. A., Greenberg, A., Liebman, J. F., Eds.; Blackie Academic and Professional: London, 1996; p 22. (59) Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds; Chapman and Hall: London, 1986. (60) Good, W. D. J. Chem. Thermodyn. 1972, 4, 709. (61) Prosen, E. J.; Gilmont, R.; Rossini, F. D. J. Res. Nat. Bur. Stand. 1945, 34, 65. (62) Szwarc, M. Proc. Roy. Soc. (London) A Math. Phys. Sci. 1951, 207, 5. (63) Bordwell, F. G.; Cheng, J. P.; Harrelson, J. A. J. Am. Chem. Soc. 1988, 110, 1229. (64) Vreven, T.; Morokuma, K. J. Phys. Chem. A 2002, 106, 6167. (65) Neumann, W. P.; Uzick, W.; Zarkadis, A. K. J. Am. Chem. Soc. 1986, 108, 3762. (66) Blanksby, S. J.; Ellison, G. B. Acc. Chem. Res. 2003, 36, 255. (67) Sirjean, B.; Fournet, R.; Glaude, P. A.; Ruiz-Lopez, M. F. Chem. Phys. Lett. 2007, 435, 152. (68) Glockler, G. J. Chem. Phys. 1953, 21, 1242. (69) Zavitsas, A. A. J. Phys. Chem. A 2003, 107, 897. (70) Zhu, C.; Rui, L.; Fu, Y. Chin. J. Chem. 2008, 26, 1493.

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