Dimerization of Polycyclic Aromatic Hydrocarbons in Soot Nucleation

Feb 3, 2014 - Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua University, Beijing 100084, China. § Depart...
1 downloads 6 Views 3MB Size
Download PDF
Article pubs.acs.org/JPCA

Dimerization of Polycyclic Aromatic Hydrocarbons in Soot Nucleation Hong-Bo Zhang,†,‡ Xiaoqing You,*,†,‡ Hongmiao Wang,†,‡ and Chung K. Law†,§ †

Center for Combustion Energy, Tsinghua University, Beijing 100084, China Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua University, Beijing 100084, China § Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United States ‡

S Supporting Information *

ABSTRACT: A possible pathway of soot nucleation, in which localized π electrons play an important role in binding the polycyclic aromatic hydrocarbon (PAH) molecules having multiradical characteristics to form stable polymer molecules through covalent bonds, is studied using density functional and semiempirical methods. Results show that the number of covalent bonds formed in the dimerization of two identical PAHs is determined by the radical character, and the sites to form bonds are related to the aromaticity of individual six-membered ring structure. It is further shown that the binding energy of dimerization increases linearly with the diradical character in the range relevant to soot nucleation.

1. INTRODUCTION Formation of condensed phase carbon materials from reacting gases is of interest to a wide range of scientific, technological, and societal problems, including air quality, global climate, human health, and materials synthesis.1 In the past several decades, substantial understanding has been gained on the mechanism of soot formation, showing that starting from the gas-phase molecules with size of a few angstroms, polycyclic aromatic hydrocarbon (PAH) molecules are first formed,2,3 followed by nucleation,4,5 coagulation,6,7 surface growth and oxidization,8−10 and finally aggregation into mature soot with the size of a few micrometers.6,7 The time scale of the entire process is on the order of milliseconds.1 Although there are still many unknowns in the soot formation processes mentioned above, we shall focus on soot nucleation in this work. In this regard we note that three conceptual paths of nucleation1 have been suggested. In the first path, a single PAH grows along its edge to eventually attain a curved, fullerene-like structure via the formation of fivemembered carbon rings.11 The predicted reaction rate of this path is, however, much slower than that given by experiments.12−14 In the second path, PAHs and PAH radicals react with the aryl radicals, form cross-link and turn into threedimensional structures.15−19 Although this path can explain the nucleation process well in regions rich of H atoms, it cannot explain the fact that soot nucleation also occurs in the postflame region where H atoms are scarce.20,21 In the third path, PAHs with moderate size interact with other PAHs through intermolecular forces such as the electrostatic force and dispersion force, and stack together.13,14,22,23 These stacked PAHs are, however, thermodynamically unstable at above 1600K.1 In summary, though all these three conceptual © 2014 American Chemical Society

pathways of nucleation are viable and important, additional pathways are needed for a comprehensive description. Koley et al.24 recently proposed a new pathway of nucleation in which several types of PAH molecules may bind together via covalent bonding, but without much exposition on how and why the bonding takes place. In this regard we note that many recent studies on theoretical material science and nonlinear optics1 have shown that due to localized π electrons, some PAHs have diradical or even multiradical properties, which can be described by the radical character yi (i = 0, 1, 2, ...) having twice the weight of a doubly excited configuration in multiconfigurational self-consistent field theory, ranging from 0 to 1 and y0 ≥ y1 ≥ y2 ≥ y3 ...25 From the above definition, PAHs are closed-shell if y0 = 0, and are pure diradical if y0 = 1 and yi = 0 (i > 0). Nonzero values of yi with i > 0 indicate that the PAHs have multiradical character. For example, y0 = y1 = 1 and yi = 0 (i > 1) means the molecule has a pure tetraradical character.25 Considering the multiradical property of PAH mentioned above, Wang1 proposed that the localized π electrons in PAHs may play an important role in soot nucleation, in that PAHs may be bound together by the covalent-like interaction of π electrons. Indeed, there have been substantial bimodality experiments showing that soot nucleation starts from the dimerization of PAHs.1,20 As such, we shall study the role of π electrons in the dimerization of PAHs, together with identifying possible new paths of nucleation induced by it. We shall focus Received: December 2, 2013 Revised: January 22, 2014 Published: February 3, 2014 1287

dx.doi.org/10.1021/jp411806q | J. Phys. Chem. A 2014, 118, 1287−1292

The Journal of Physical Chemistry A

Article

Density functional (U)M06-2X26 with basis set 6-31+G(d,p) was used to optimize geometries and calculate frequencies using Gaussian09.27 It is noted that M06-2X is suitable because it takes long-range noncovalent interaction into account. As shown in the upper part of Figure 2a, each R51 monomer in the dimer is no longer planar and two bonds form between two monomers, one bond at each zigzag side. To study the nature of the two bonds formed, natural bond orbital (NBO) analysis was conducted. The result shows that there are two sp3.2− sp3.2 σ bonds between the two monomers. Because the Wiberg bond index of each bond is 0.92, the bonds formed are covalent bonds instead of van der Waals bonds. The length of the chemical bond connecting the monomers and the angle between the two monomers are listed in Table 1. This result

on the dimerization of two identical PAHs with extension to the nonidentical case briefly. This paper is organized as follows. In section 2, we state the quantum chemistry method used to optimize the geometries and calculate the vibrational frequencies. In section 3, we show and discuss the results from geometry optimization, including the relation between the diradical character y0 and the binding energy of dimerization of identical PAHs, the number of covalent bonds formed, the possible sites where covalent bonds form in dimerization, and finally the thermodynamic stability of the dimer.

2. METHOD We select the rectangular PAHs as an example to study dimerization. The definition of Rxy is shown in Figure 1. Here

Table 1. Binding Energy and Geometry Parameters of the Optimized R51, R33, R53, and R47 Dimers

R51

R33 R53 R47

BE,a kcal/ mol length,b Å angle,b deg BE, kcal/mol length,b Å BE, kcal/mol length,b Å BE, kcal/mol length,b Å

(U)M06-2X/631G(d)

(U)M06-2X/631+G(d,p)

(U) PM6

39.1

38.0

41.1

1.60 51.0 24.8 1.66 41.2 1.70 22.7 1.73

1.61 50.8 25.5 1.66 41.2 1.70

1.57 50.6 23.2 1.59 46.8 1.61 53.5 1.59

a

BE is short for binding energy. bThe meaning of geometry parameters can be viewed graphically in the bottom part of Figure 2a.

Figure 1. Definition of Rxy.

indicates that in addition to the intermolecular force, PAHs can also interact with each other via covalent bonds in dimerization because of their diradical character. Because it is computationally demanding to compute the electronic structures by M06-2X, to facilitate our study, we took the semiempirical method PM6 as well,28 which is about 50 times faster than M06-2X. The geometries of all the optimized PAH dimers by both PM6 and M06-2X are plotted in the Supporting Information. As an example, the optimized

R stands for rectangular, and x and y respectively represent the number of 6-C rings at the zigzag and armchair edges. The radical characters y0 and y1 of the PAHs can be found in Nagai et al.,25 and we list those of interest in the Supporting Information. It is noted that the larger the y, the larger the yi for the PAHs that have the same x, and the same holds for x for the PAHs that have the same y.

Figure 2. Demonstration of five optimized Rxy dimers of identical PAHs. 1288

dx.doi.org/10.1021/jp411806q | J. Phys. Chem. A 2014, 118, 1287−1292

The Journal of Physical Chemistry A

Article

geometry of the R51 dimer by (U)PM6 is shown in the bottom of Figure 2a. Furthermore, to validate our choice of (U)PM6, we list the binding energies and geometry parameters of R51, R33, R53, and R47 dimers optimized by (U)M06-2X and the semiempirical (U)PM6 in Table 1. We shall compare the molecule properties obtained by PM6 and M06-2X. The differences in the binding energies between these two methods are less than 10 kcal/mol for the PAHs with a small size; and for the large ones, the differences in binding energy become larger. As in the case of R47, the binding energy obtained by M06-2X is much smaller than that obtained by PM6, and the length of the bonds formed in the dimer from the M06-2X calculation is slightly longer than that from the PM6 calculation. At first glance, one may suspect whether there are covalent bonds formed between the two R47 monomers in the M06-2X calculation, because the results show a smaller binding energy and a larger bond length. To confirm this possibility, we conducted an NBO analysis of R47 at the (U)M06-2X/631G(d) level. The result indicates that there are four sp4.3− sp4.3 σ bonds between the two R47 monomers, and the Wiberg bond index of each bond is 0.78. Therefore, four single bonds indeed are formed in dimerization of two R47 monomers from the M06-2X calculation. For the PM6 calculation of the R47 dimer, we show the optimized geometry in the middle part of Figure 2b. One can see that there are four covalent bonds formed in the figure, and the length of each bond is typical of the C−C single bond. Therefore although the binding energies obtained by these two methods are quite different in the R47 case, the nature of the bonds such as the bond order, the number of bonds and the bonding sites obtained by PM6 and M06-2X agree with each other well.

Figure 4. Binding energy versus y0 (at the PM6 level). Blue dot, purple square, green triangle, and yellow diamond represent Rx1, Rx3, Rx5, and Rx7, respectively. The solid line is the best fitting curve of all the points in the linear zone.

results from the two methods show very similar dependence of the binding energy on the diradical charcter. In the region y0 ≤ 0.22, the PAH such as R11, R31, R23, and R17 cannot form a stable dimer via covalent bonds. For example, the binding energy of R31 is 4.2 kcal/mol at the (U)M06-2X/6-31+G(d,p) level if R31 dimerizes via covalent bonds, which is much smaller than if R31 dimerizes via dispersion force to form a crossed structure.29 Consequently, the PAHs will dimerize via intermolecular interaction in this region instead of forming covalent bonds. We have therefore designated this region as the “dispersion and electrostatic zone”. In the region 0.22 ≤ y0 ≤ 0.9, the binding energy increases linearly with y0. A best fitting curve of all the data in this region is also plotted in Figure 4. We designate this region as the “linear zone” and note that the PAHs in this region are relevant to soot nucleation. Further noting that the data in this region scatter slightly, we use different symbols to show the PAHs with different y’s, which is the number of 6-C rings at the armchair edge. It is seen that the binding energies of the PAHs with the same y have a stronger linear relation with y0, whereas those with different values of y scatter slightly. Therefore the geometry effect is the main reason for the scattering in the linear zone, and the binding energy of the PAHs also depends on their respective shapes. In the region y0 ≥ 0.9, the linear relation disappears, as shown in Figure 4 for the PM6 method and Figure S2 (Supporting Information) for the M06-2X method. As the multiradical characters y1, y2, ... become larger in this region, the binding energy also depends on y1, y2, ... instead of y0 only. Therefore, we designate this region as the “multidimension zone”. 3.3. Number of Bonds and Bonding Sites. As we have mentioned in section 2, the bonding nature, such as the bond order, the number of bonds, and the bonding sites obtained by PM6 and M06-2X, agree with each other well. Therefore, we shall use the results by the PM6 method to analyze the number of bonds and the bonding sites in dimerization. Our results show that the radical character is related not only to the binding energy but also to the number of bonds formed in dimerization. As displayed in Figure 2b, two, four, or six bonds may form between two monomers. For some PAHs such as the R43, there are more than one way to dimerize as shown in Figure 2c. Our results indicate that the number of bonds

3. RESULTS AND DISCUSSION 3.1. PAH Dimers. Many Rxy dimers of identical PAHs have been optimized, with five of them shown in Figure 2 as examples. Because the dimerization of two nonidentical PAHs is more likely to occur in flame environment, several dimers of two nonidentical PAHs are optimized by the (U)PM6 method and shown in Figure 3. It is seen that it is very common to form

Figure 3. Demonstration of two optimized dimers of nonidentical PAHs.

bonds in the dimerization of PAHs, which implies a new possible pathway of nucleation. For the sake of simplicity, we shall focus on the dimerization of two identical PAHs and explore how the multiradical character affects the binding. 3.2. Binding Energy. We now study the relation between the diradical character y0 and the binding energy of dimerization, as shown in Figure 4. All the data here were obtained by the (U)PM6 method. The data obtained by M062X are not shown because most of them overlap with the PM6 data and as such cannot be readily distinguished. All the PM6 and M06-2X data are given in the Supporting Information. The 1289

dx.doi.org/10.1021/jp411806q | J. Phys. Chem. A 2014, 118, 1287−1292

The Journal of Physical Chemistry A

Article

Figure 5. Schematic showing that the number of bonds formed is determined by yi, and the sites of bonding are determined by HOMA. The numbers in the fold-shaped figure represent the number of bonds formed in the corresponding parameter space. The numbers in hexagons show the HOMA value of the 6-C ring, and a, a′, a″, a‴, (a), and (a′) represent the bonding sites.

the π electrons concentrated there, it is the easiest to form bonds. In fact, from Figure 2a we can see that the bonds indeed form at the center ring in the R51 dimer. We next consider other examples. In the left-top of Figure 5, we show the HOMA value of each ring in R47 and the sites of the four bonds formed, a, a′, a″, a‴. Indeed, four bonds form at the rings with the largest HOMA value of 0.69. In the rightbottom of Figure 5, we show the HOMA values of R43 and the possible sites of forming the bonds a, a′ and (a), (a′). There are four rings with the largest HOMA value of 0.68. However, y1 of R43 is small, being 0.14, so only two bonds are allowed to form. As a result, Figure 2c shows that there are two isomers of the R43 dimer. For one isomer, the bonds form at a, a′ of one monomer and a, a′ of the other; for the other isomer, the bonds form at a, a′ of one monomer and (a), (a′) of the other. Each of the isomers satisfies the condition that the bonds form at the ring with the largest HOMA value. This example shows that not all the rings with the largest HOMA value form bonds, and they are only candidates of sites for bonding. From the discussion above, we conclude that the yi of a PAH monomer determines the possibility of forming bonds whereas the number of bonds formed in the dimer, and the HOMA values of a PAH, are related to the sites to form bonds. The rings with the largest HOMA are candidates for bonding. The above conclusion on HOMA and the sites of bonding, however, may be oversimplified, noting that there is an anomaly among our calculations, namely R53. The HOMA and the bonding sites of R53, shown in Figure 6 indicate that four bonds form between two R53 monomers because of the large y1 of R53, and the bonding site is not at the ring with the largest HOMA

formed between two monomers depends on yi: if y0 ≤ 0.22, no bond forms between the two monomers; if y0 ≥ 0.22 and y1 ≤ 0.22, two bonds form; if y1 ≥ 0.22 and y2 is small, four bonds form; and so on (noting that although the specific value 0.22 is obtained from extensive calculations, it only has qualitative instead of quantitative significance). The relation between yi and the number of bonds is shown in Figure 5 schematically. It is easy to understand that because yi describes the multiradical character, the PAHs show the property of a di (tetra, ...) radical when the corresponding yi is large enough and form 2 (4, ...) bonds. We note in passing the nonidentical case here. From the R11-R71 case in Figure 3, it is seen that the PAH with small y0, which is considered to be stable in the identical case, as discussed in the previous paragraph, can form bonds with another PAH whose y0 is large enough. Though we know the number of bonds depends on yi, the specific sites at which the bonds form remain to be explored. To answer this question, we calculate the HOMA (harmonic oscillator model of aromaticity) of each 6-C ring in all the PAHs. HOMA describes the similarity between the 6-C ring and benzene,30,31 with a value between 0 and 1. The larger the HOMA, the more similar is the 6-C ring with benzene, and the larger the aromaticity. In Figure 5, the HOMAs of several PAHs are shown and discussed next. Take R51 as an example. In the left-bottom of Figure 5, we plot the HOMA of R51 and the sites of forming bonds a, a′. It is seen that the five 6-C rings of R51 are aligned in a line, with the center ring having the largest HOMA value of 0.73. This means that the center ring is most similar to benzene, and with 1290

dx.doi.org/10.1021/jp411806q | J. Phys. Chem. A 2014, 118, 1287−1292

The Journal of Physical Chemistry A

Article

tion, which shows the dimers are thermodynamically unstable at combustion temperatures. Considering that the lifetime of dimers may be longer than the time scale of collision, they still could be a source of soot nucleation once they are formed.

■

ASSOCIATED CONTENT

S Supporting Information *

Binding energies, y0, and y1 obtained by PM6, UM06-2X/631G(d), and UM06-2X/6-31+G(d,p) in this work, optimized geometric structures of Rxy, and plots of binding energy versus y0 in UM06-2X/6-31G(d) calculation are available free of charge via the Internet at http://pubs.acs.org.

Figure 6. HOMA values and sites of bonding of R53, showing that the site of bonding is not the 6-C ring with largest HOMA, but rather the 6-C ring with the largest possible HOMA under the condition that these bonds distribute at the zigzag edges of PAH symmetrically.

■

AUTHOR INFORMATION

Corresponding Author

*X. You: e-mail, [email protected].

value. So in the case with large yi (i > 0) in the multidimension zone, the bonds form at the ring with the largest HOMA value under the condition that these bonds distribute at the zigzag edges of the PAH symmetrically. This rule can be generalized to the case without large yi (i > 0) in the linear zone. This exception, however, does not affect our conclusion that π electrons play an important role in the dimerization of PAHs, and a bond tends to be formed at the ring where the π electrons concentrate. 3.4. Thermochemistry. So far, we have discussed our findings on the dimerization of PAHs at zero temperature. However, we are more interested in the dimerization of PAHs in the flame environment at combustion temperatures. Therefore, the thermochemistry of dimerization of identical PAHs was also studied. The results show that due to the large entropy decrease the difference in the Gibbs free energy of R51 dimerization becomes positive above room temperature, for example, 4 kcal/mol at room temperature (300 K) and 165 kcal/mol at 1500 K. This result agrees with that of Koley et al.,24 which shows dimerization is unstable thermodynamically at the temperatures interested. However, the Gibbs free energy at high temperatures using static quantum mechanics methods is not very reliable because several approximations leading to thermal corrections will deviate drastically at high temperatures.32 Moreover, the 10 ps quantum molecular dynamics simulations by Koley et al. reveal the stability of R51 dimer24 and show the lifetime of the dimer is at least 10 ps, which is longer than the collision time scale.33 As a result, dimers could be a source of soot nucleation once they are formed.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Science Foundation of China (51206090), the National Basic Research Program (2013CB228502), the 111 project (B13001), and Tsinghua National Laboratory for Information Science and Technology. We thank Prof. Hai Wang and Dr. Z. F. Kou for helpful discussions.

■

REFERENCES

(1) Wang, H. Formation of nascent soot and other condensed-phase materials in flames. Proc. Combust. Inst. 2011, 33 (1), 41−67. (2) Wang, H.; Frenklach, M. A detailed kinetic modeling study of aromatics formation in laminar premixed acetylene and ethylene flames. Combust. Flame 1997, 110 (1−2), 173−221. (3) Richter, H.; Howard, J. B. Formation of polycyclic aromatic hydrocarbons and their growth to soot - a review of chemical reaction pathways. Prog. Energy Combust. Sci. 2000, 26 (4−6), 565−608. (4) Giordana, A.; Maranzana, A.; Tonachini, G. Theoretical investigation of soot nanoparticle inception via polycyclic aromatic hydrocarbon coagulation (condensation): Energetic, structural, and electronic features. J. Phys. Chem. C 2011, 115 (5), 1732−1739. (5) D’Anna, A.; Sirignano, M.; Kent, J. A model of particle nucleation in premixed ethylene flames. Combust. Flame 2010, 157 (11), 2106− 2115. (6) Balthasar, M.; Frenklach, M. Monte-Carlo simulation of soot particle coagulation and aggregation: The effect of a realistic size distribution. Proc. Combust. Inst. 2005, 30, 1467−1475. (7) Kazakov, A.; Frenklach, M. Dynamic modeling of soot particle coagulation and aggregation: Implementation with the method of moments and application to high-pressure laminar premixed flames. Combust. Flame 1998, 114, 484−501. (8) Edwards, D. E.; You, X. Q.; Zubarev, D. Y.; Lester, W. A., Jr.; Frenklach, M. Thermal decomposition of graphene armchair oxyradicals. Proc. Combust. Inst. 2013, 34 (1), 1759−1766. (9) You, X. Q.; Zubarev, D. Y.; Lester, W. A.; Frenklach, M. Thermal decomposition of pentacene oxyradicals. J. Phys. Chem. A 2011, 115 (49), 14184−14190. (10) You, X. Q.; Whitesides, R.; Zubarev, D.; Lester, W. A.; Frenklach, M. Bay-capping reactions: Kinetics and influence on graphene-edge growth. Proc. Combust. Inst. 2011, 33, 685−692. (11) Homann, K.-H. Fullerenes and soot formation  new pathways to large particles in flames. Angew. Chem., Int. Ed. 1998, 37 (18), 2434−2451. (12) Frenklach, M. Reaction mechanism of soot formation in flames. Phys. Chem. Chem. Phys. 2002, 4 (11), 2028−2037. (13) Frenklach, M.; Wang, H. Detailed modeling of soot particle nucleation and growth. Proc. Combust. Inst. 1991, 23 (1), 1559−1566.

4. SUMMARY In this work, we studied a possible path of soot nucleation, in which the nucleation begins with the dimerization of identical or nonidentical PAHs by forming bonds of π electrons. We have found that the radical character yi determines the number of bonds formed in the dimerization of PAHs, and the sites of forming bonds are related to HOMA. The rings with the largest HOMA values are candidates of forming bonds. We have also studied the relation between the binding energy and the diradical character y0. Results show that, in the linear zone, the binding energy increases with y0 linearly. In the dispersion and electrostatic zone, the PAHs dimerize via the intermolecular force instead of forming covalent bonds. In the multidimension zone, because the multiradical characters yi (i > 0) are large and become important, the binding energy depends not only on the diradical character y0 but also on the yi (i > 0). All of these results show that the π electrons play an important role in soot nucleation. We also studied the thermochemistry of dimeriza1291

dx.doi.org/10.1021/jp411806q | J. Phys. Chem. A 2014, 118, 1287−1292

The Journal of Physical Chemistry A

Article

(14) Frenklach, M.; Wang, H. Detailed mechanism and modeling of soot particle formation. In Soot Formation in Combustion: Mechanisms and Models of Soot Formation; Bockhorn, H., Ed.; Springer-Verlag: Berlin, 1994; Vol. 59, pp 165−192. (15) Richter, H.; Benish, T. G.; Mazyar, O. A.; Green, W. H.; Howard, J. B. Formation of polycyclic aromatic hydrocarbons and their radicals in a nearly sooting premixed benzene flame. Proc. Combust. Inst. 2000, 28 (2), 2609−2618. (16) Ciajolo, A.; Tregrossi, A.; Barbella, R.; Ragucci, R.; Apicella, B.; de Joannon, M. The relation between ultraviolet-excited fluorescence spectroscopy and aromatic species formed in rich laminar ethylene flames. Combust. Flame 2001, 125 (4), 1225−1229. (17) Allouis, C.; Apicella, B.; Barbella, R.; Beretta, F.; Ciajolo, A.; Tregrossi, A. Monitoring of fuel consumption and aromatics formation in a kerosene spray flame as characterized by fluorescence spectroscopy. Chemosphere 2003, 51 (10), 1097−1102. (18) Violi, A.; Kubota, A.; Truong, T. N.; Pitz, W. J.; Westbrook, C. K.; Sarofim, A. F. A fully integrated kinetic Monte Carlo/molecular dynamics approach for the simulation of soot precursor growth. Proc. Combust. Inst. 2002, 29 (2), 2343−2349. (19) Violi, A.; Sarofim, A. F.; Voth, G. A. Kinetic Monte Carlo− molecular dynamics approach to model soot inception. Combust. Sci. Technol. 2004, 176 (5−6), 991−1005. (20) Zhao, B.; Yang, Z.; Johnston, M. V.; Wang, H.; Wexler, A. S. Balthasar, M.; Kraft, M., Measurement and numerical simulation of soot particle size distribution functions in a laminar premixed ethyleneoxygen-argon flame. Combust. Flame 2003, 133 (1−2), 173−188. (21) Zhao, B.; Yang, Z.; Li, Z.; Johnston, M. V.; Wang, H. Particle size distribution function of incipient soot in laminar premixed ethylene flames: effect of flame temperature. Proc. Combust. Inst. 2005, 30 (1), 1441−1448. (22) Miller, J. H. The Kinetics of polynuclear aromatic hydrocarbon agglomeration in flames. Proc. Combust. Inst. 1991, 23 (1), 91−98. (23) Herdman, J. D.; Miller, J. H. Intermolecular potential calculations for polynuclear aromatic Hydrocarbon clusters. J. Phys. Chem. A 2008, 112 (28), 6249−6256. (24) Koley, D.; Arunan, E.; Ramakrishnan, S. Computational investigations on covalent dimerization/oligomerization of polyacenes: Is it relevant to soot formation? J. Comput. Chem. 2012, 33 (21), 1762−1772. (25) Nagai, H.; Nakano, M.; Yoneda, K.; Kishi, R.; Takahashi, H.; Shimizu, A.; Kubo, T.; Kamada, K.; Ohta, K.; Botek, E.; Champagne, B. Signature of multiradical character in second hyperpolarizabilities of rectangular graphene nanoflakes. Chem. Phys. Lett. 2010, 489 (4−6), 212−218. (26) Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: Two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Acc. Theor. Comput. Model 2008, 120 (1−3), 215−241. (27) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J., Gaussian 09, Revision B.01. Wallingford CT, 2009.

(28) Stewart, J. P. Optimization of parameters for semiempirical methods V: modification of NDDO approximations and application to 70 elements. J. Mol. Model 2007, 13 (12), 1173−1213. (29) Gonzalez, C.; Lim, E. C. Evaluation of the Hartree-Fock dispersion (HFD) model as a practical tool for probing intermolecular potentials of small aromatic clusters: Comparison of the HFD and MP2 intermolecular potentials. J. Phys. Chem. A 2003, 107 (47), 10105−10110. (30) Zubarev, D. Y.; Robertson, N.; Domin, D.; McClean, J.; Wang, J.; Lester, W. A.; Whitesides, R.; You, X.; Frenklach, M. Local electronic structure and stability of pentacene oxyradicals. J. Phys. Chem. C 2009, 114 (12), 5429−5437. (31) Zubarev, D. Y.; You, X.; McClean, J.; Lester, J. W. A.; Frenklach, M. Patterns of local aromaticity in graphene oxyradicals. J. Mater. Chem. 2011, 21 (10), 3404−3409. (32) Kozuch, S.; Shaik, S. How to conceptualize catalytic cycles? The energetic span model. Acc. Chem. Res. 2010, 44 (2), 101−110. (33) Schuetz, C. A.; Frenklach, M. Nucleation of soot: molecular dynamics simulations of pyrene dimerization. Proc. Combust. Inst. 2002, 29 (2), 2307−2314.

1292

dx.doi.org/10.1021/jp411806q | J. Phys. Chem. A 2014, 118, 1287−1292