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Local Electronic Structure and Stability of Pentacene Oxyradicals† Dmitry Yu. Zubarev,‡ Neil Robertson,| Dominik Domin,‡,§ Jarrod McClean,‡ Jinhua Wang,‡,∇ William A. Lester, Jr.,*,‡,§ Russell Whitesides,|,⊥ Xiaoqing You,| and Michael Frenklach|,⊥ Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, UniVersity of California at Berkeley, Berkeley, California 94720-1460, Chemical Sciences DiVision, Lawrence Berkeley National Laboratory, Berkeley, California 94720, EnVironmental Energy Technologies DiVision, Lawrence Berkeley National Laboratory, Berkeley, California 94720, Department of Mechanical Engineering, UniVersity of California at Berkeley, Berkeley, California 94720-1740, and State Key Laboratory of Superhard Materials, Jilin UniVersity, Changchun 130012, People’s Republic of China ReceiVed: June 22, 2009; ReVised Manuscript ReceiVed: October 12, 2009
A series of pentacene oxyradicals is studied as a model of an oxidized graphene edge. The relative stability of the oxyradical species formed is rationalized on the basis of the concept of local aromaticity. It is found that qualitative and quantitative measures of delocalized bonding show consistently that formation of the π-aromatic fragments associated with different reference π-aromatic systems explain trends in Gibbs free energies and relative energies. As a result, a chemically intuitive model based on aromaticity can explain the relative stability of the oxyradicals in a way that uniquely appeals to chemists’ knowledge of structure and reactivity. Introduction Notwithstanding the current push for advances in alternative energy sources, it is an unavoidable reality that combustion will in the near term continue to play a major role in applications ranging from internal combustion engines to industrial processes. As such, an understanding of associated hazards and potential byproducts is crucial to the safe optimization of combustion processes and mitigation of negative consequences. One byproduct, soot, is known to be particularly hazardous and quite detrimental to both the health of biological systems and the environment. As a result, the oxidative destruction and resistance to oxidation of this material, especially at high temperatures, are of practical interest, as these are primary pathways through which soot production is alleviated. However, experimental data are scarce and when available are typically collected on a composition of soot which is not well determined and dependent on many experimental factors1-5 making extrapolation to new systems challenging. Therefore, theoretical methods are ideal as they provide control over modeling conditions and facilitate extension to larger and more complex systems. Past theoretical studies of soot oxidation have focused on the model cases of oxidation reactions of one-ring aromatics6-9 and oxygen chemisorption at selective sites of two- and threering aromatics.10-13 Polycyclic aromatic molecular systems also constitute fundamental structural moieties of many other carbonaceous materials such as graphite, char, carbon black, fullerenes, carbon nanotubes, and most recently, graphene sheets. †
Part of the “Barbara J. Garrison Festschrift”. * To whom correspondence should be addressed. E-mail:
[email protected]. ‡ Kenneth S. Pitzer Center for Theoretical Chemistry, University of California at Berkeley. § Chemical Sciences Division, Lawrence Berkeley National Laboratory. | Department of Mechanical Engineering, University of California at Berkeley. ⊥ Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory. ∇ State Key Laboratory of Superhard Materials, Jilin University.
A recent study examined energetics of a series of aromatic molecules, focusing on the chemical nature of the graphene edge.14 The latter subject, the chemical nature of pure graphene edges, has been the subject of ongoing interest.15-17 Oxidative breakup of a graphene sheet has been also recently proposed.18 Our objective here is two-fold. The first is to report findings of an investigation of the thermodynamic stability of graphene oxyradicals that showed a systematic trend with position of the chemisorbed oxygen atom on the graphene edge. Our second objective is to explain the observed trend, and to this end, we employ the theory of aromaticity. We chose the linear pentacene polyaromatic hydrocarbon (PAH) as the model of the graphene edge. Because the present focus is on processes that involve only the exterior of a graphene sheet, this model should be adequate. It contains the essential structural element involved in the key processes, i.e., the zigzag edge which can be systematically extended by both increasing the length of the polycyclic chain and by adding extra layers. We undertake a systematic investigation into the thermodynamic stability of pentacene oxyradicals as a model for the critical intermediate in graphene oxidation. The result of this investigation is an intuitive chemical model based on aromaticity and localization that explains the observed trends. Additionally, it is the authors’ hope that this model will appeal to the chemists’ structural intuition, so that fundamental concepts of reactivity may be readily applied to better understand these and related systems. Computational Details The latest study of acenes19 showed that pentacene in its ground state is a singlet with a 23.4 kcal/mol singlet-triplet gap and does not possess noticeable polyradical character. As such, it can be safely treated as a singlet by single-configuration quantum chemical approaches. The geometries of the pentacene molecule and pentacene oxyradicals (systems I-V, Figure 1, left panel) were optimized using unrestricted hybrid density functional UB3LYP/6-311G(d,p) level of theory20-23 as implemented in the Gaussian 03 software package.24 The expectation
10.1021/jp9058615 2010 American Chemical Society Published on Web 11/17/2009
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Figure 1. (Left) Structures of the pentacene molecule (I) and pentacene oxyradicals with the oxygen atom in different positions (II-V). Connections between atoms are drawn on the basis of the interatomic distances. Upper case Roman numerals designate oxyradicals with different O atom positions; lower case italic Roman numerals designate six-atom rings; Arabic numerals enumerate C atoms. (Right) Schematic representation of chemical bonding in systems I-V. For open-shell systems II-V the bonds found simultaneously in R- and β-spaces are depicted as regular nc-2e bonds. Noncoinciding nc-1e bonds from R- and β-spaces are superimposed (R are dashed lines on the interior, β on the exterior). Oxygen lone-pairs and 2c-2e CH σ-bonds are omitted.
of the S2 operator after projection is 0.75 for oxyradicals II-V. On the basis of a normal-mode analysis, all structures are minima on the potential energy surface. Vibrational frequencies and zero-point energies (ZPEs) were scaled by a factor of 0.967.25 The relative energies of systems II-V were also obtained at the restricted open-shell resolution-of-identity scaledopposite-spin second order Moller-Plesset perturbation theory RO-RI-SOS-MP2/6-311G(d,p) level26 as implemented in the Q-Chem software package27 at B3LYP/6-311G(d,p) geometries. Relative and ZPEs, expectation values of the S2 operator for unrestricted open-shell calculations, vibrational frequencies, rotational constants, and Cartesian coordinates are reported in the Supporting Information (Tables S1 and S2). MOLEKEL 5.3 graphical software28 was used for visualization of results. A primary focus of the present study is the assessment of the local electronic structure of the parent pentacene molecule and its oxyradicals in terms of global/local aromaticity.29 In order to gain insight on aromaticity of these systems, we relied on the tools that provide qualitative and quantitative characteristics of delocalized bonding.27-34 We aimed qualitatively at revealing the systems possessing a π-bonding pattern similar to the prototypical organic aromatic systems of benzene and naphthalene. The analysis of chemical bonding was carried out using the adaptive natural density partitioning (AdNDP) method30,31 extended to open-shell systems. This approach represents charge density using objects with the highest degree of localization of electron pairs, n centertwo electron (nc-2e) bonds, which include core electrons, lonepairs (LPs), 2c-2e bonds, etc. For aromatic systems, e.g., benzene, completely delocalized objects similar to canonical
MOs emerge in the course of the present analysis that naturally incorporate the idea of completely delocalized bonding. The schematic representation of chemical bonding in systems I-V is shown in the right panel of Figure 1. For the open-shell pentacene oxyradicals II-V, the chemical bonding analysis was performed separately for R- and β-components of the electron density leading to nc-1e bonds. The bonds found in both Rand β-spaces were considered regular nc-2e bonds. The nc-1e bonds that were found only in R- or β-spaces, i.e., noncoinciding bonds, were superimposed in the schematic formulas and characterize the rearrangement of bonding pattern between two nearest closed-shell structures (a singly charged cation and a singly charged anion). It was shown previously31 that AdNDP results for PAHs agree with Clar’s sextet32 assignment only if a single Clar structure can be used to describe the electronic structure of the system. If a resonance involving several Clar structures is necessary, there is no direct correspondence between these two approaches because AdNDP localization was designed with a specific goal of avoiding a resonance description. It is easy to see that the pentacene molecule and all the related oxyradicals admit multiple Clar structures and therefore require resonance of Clar’s sextets. Aromaticity as a concept associated with delocalized bonding does not have a unique definition. Numerous approaches have been used to establish and characterize aromatic/antiaromatic character on the basis of various properties of a molecule.33-35 Energy-based approaches estimating resonance stabilization in aromatic systems are rigorous but require excessive computational efforts and, therefore, were not used in the present study.
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The following considerations were essential for choosing measures of aromaticity in the present study. The measure of aromaticity should be widely used, making it possible to compare the present results with those previously reported for related systems. It should be readily available from standard quantum chemistry packages and be computationally inexpensive. It should be applicable to the systems of essentially any size without significant increase of computational resources. Finally, it is necessary to consider several aromaticity measures on the basis of different molecular properties to ensure consistency of analysis because all existing criteria have certain limitations. As a first step in identification of a quantitative measure of the local aromatic character of the individual six-atom carbon rings, we examined the nuclear-independent chemical shift index (NICS) proposed by Schleyer et al.36,37 NICS is a magneticproperty-based criterion of aromaticity that characterizes magnetic shielding within a ring structure. It is usually calculated at the geometric center of the ring, NICS(0), and at 0.5 and 1.0 Å above the ring, yielding NICS(0.5) and NICS(1), respectively. Negative NICS values are signatures of aromaticity, positive values correspond to antiaromaticity, and NICS values close to zero are typical for nonaromatic systems. NICS is used as a measure of aromaticity in both closed- and open-shell systems.38 In our work we relied on the out-of-plane components of the NICS tensor (NICSzz) as a measure of aromaticity because of its better performance for planar rings.39 Recent studies of small aromatic, antiaromatic, and nonaromatic organic molecules demonstrated that NICSzz is equal to the z-component of the induced magnetic field,40 and the latter was shown to be consistent with Pople’s model on the basis of first principles calculations.41 Performance of NICS and related techniques in the assessment of aromaticity has been recently reviewed.42 We also investigated the harmonic oscillator model of aromaticity (HOMA) as a measure of both local and global aromaticity. HOMA is a geometry-based criterion43 that relates energetic descriptions of aromaticity to the geometry of the system. At the moment, it is the fastest approach for assessing aromaticity that does not become prohibitively expensive with system size. The HOMA model focuses on the carbon-carbon bond lengths of the rings contained in the molecule, and is defined by
TABLE 1: Enthalpies of Formation and Entropies of Pentacene Oxyradicals at 298.15 K Relative to Those of Pentacene Oxyradical II at the B3LYP/6-311G(d,p) Level of Theory; Relative Energies of Pentacene Oxyradicals at 0 K at B3LYP/6-311G(d,p) and MP2/6-311G(d,p)//B3LYP/ 6-311G(d,p) (in parentheses) Levels of Theory pentacene oxyradical enthalpy (kcal/mol) relative to II entropy (cal/(mol K)) relative to II Erel (kcal/mol)
II
III
IV
V
0
2.8
13.6
16.5
0
3.0
3.2
3.7
0 (0)
2.9 (3.5)
14.1 (14.6)
17.1 (17.7)
bonded to exterior rings in the temperature range of interest. The enthalpies of formation and entropies of the four pentacene oxyradicals at 298.15 K relative to oxyradical II are shown in Table 1. The enthalpy of formation of oxyradical II is the smallest, while that of oxyradical V is the largest among the four. Compared with the change in enthalpy of formation from oxyradicals II to III, and IV to V, the change from oxyradicals III to IV is much larger. To assess thermodynamic stability, we calculated the standard Gibbs free energies of the four pentacene oxyradicals relative to oxyradical II with results shown in Figure 2. Inspection of the data displayed in Figure 2 indicates that below 1000 K the stability of the four oxyradicals follows the trend of the relative energies at both B3LYP and MP2 levels of theory, i.e., is in the order II > III > IV > V, while above 1000 K oxyradical III becomes more stable than II. The latter switch in the order is because the entropy of pentacene oxyradical III is larger than that of II, and the entropy contribution to the Gibbs free energy change increases with temperature. Details of entropies, heat capacities, and thermal enthalpies of the pentacene oxyradicals can be found in the Supporting Information (Table S3). The electronic structure rearrangements between pentacene and its oxyradicals with different positions of O atoms hold the key to the understanding relative stability of the latter. Pentacene. We first discuss chemical bonding in the pentacene molecule (Figure 1, I) to establish a reference point for analysis of the oxyradicals. The framework of σ-bonds includes the appropriate number of 2c-2e CC and CH bonds. For
n
HOMA ) 1 -
∑
a (r - rcc-ideal)2 n i)1 cc
(1)
where a was chosen to be 257.7 so that HOMA ) 0 for a Kekule´ form of benzene and HOMA ) 1 for the aromatic form of benzene, n is the number of bond lengths in the ring, rcc is the computed carbon-carbon bond length, and rcc-ideal is set to the experimental carbon-carbon bond length of benzene. Deviation of HOMA from 1 means deviation of aromatic character of the ring from that of benzene. It is possible to use the sum of the HOMA indices for individual rings in the PAH (cumulative HOMA) to characterize global aromaticity of a molecule.44-46 Studies of the global and local aromaticity of polyacenes show that HOMA and NICS have similar trends with the size of the system, but NICS generally overestimates local aromaticity, which is especially true in the case of the aromaticity of the central rings.47,48 Results and Discussion Thermodynamic Stability. Oxyradicals with O bonded to interior rings were found to be more stable than those with O
Figure 2. Standard Gibbs free energy of pentacene oxyradicals relative to that of pentacene oxyradical II as a function of temperature at B3LYP/6-311G(d,p) level of theory.
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Figure 3. (a) Structure of the pentacene molecule; (b) results of AdNDP localization. Eight 2c-2e CC π-bonds are superimposed on the molecular frame; 2c-2e CH σ-bonds and 2c-2e CC σ-bonds are omitted; (c) 2c-2e and 6c-2e CC π-bonds superimposed on the molecular frame; (d) schematic representation of the localization pattern in pentacene. 2c-2e CH bonds are omitted.
pentacene and all the oxyradicals, the former are shown on the right panel of Figure 1 to outline the framework of carbon atoms. As σ-bonding remains trivial for the systems studied, it is not discussed further. We found eight 2c-2e and three 6c-2e CC π-bonds, with the occupation numbers (ON) ranging from 1.59 to 1.97 |e|. Out of the five fused six-atom rings in the pentacene molecule, the central one is identified as having π-electronic structure similar to the prototypical aromatic benzene molecule (Figure 3b and c). We designate this particular type of π-bonding involving six electrons delocalized over a six-atom ring by a circle inscribed in a hexagon. Each of the remaining rings has two 2c-2e π-bonds that are conjugated with each other and with the aromatic π-system of the central ring. The conjugation of the π-bonds is manifested in the deviations of the occupation numbers from the exact value 2.00 |e|. This finding is in agreement with earlier results of Dixon et al.49 In that work Boys localization was performed for all electrons and for π-electrons only. In both cases, one found a resonance between two Kekule structures associated with the central ring of the pentacene molecule. These Kekule structures have three double bent bonds in case of allelectron localization and three three-center two-electron (3c2e) π-bonds in case of π-only localization suggesting presence of a sextet of π-electrons in the central pentacene ring. Quantitative measures of aromaticity, NICSzz and HOMA, both confirm the enhanced aromaticity of the central ring (Table 2). Also, they show noticeable aromatic character of the other four rings, leading to the conclusion that the significant conjugation of the π-bonds leads to a single strongly delocalized π-bonding system. Oxyradicals. Substitution of H by O at position 1 of the central ring of pentacene I leads to oxyradical II (Figure 1, II). The results of localization are shown in Figure 4. Components of O lone-pairs, 2c-1e CO σ- and π-bonds, 2c-1e CH and 2c1e CC σ-bonds, and nc-1e CC π-bonds are identified in both R- and β-spaces and should be considered as regular lone pairs and 2c-2e bonds, respectively. The localization patterns for CC
π-bonds are not identical. Ring iii has one 3c-1e π-bond in R-space that is not present in β-space. It can be seen that the localization pattern over rings i, ii, and iV, V is similar to the localization pattern of the prototypical naphthalene molecule (see ref 31). Closer examination of the 4c-1e π-bonds in R-space and 6c-1e π-bonds in β-space shows that these bonds have a somewhat higher contribution from rings ii and iV. Therefore, we associate rings ii and iV with benzene-like π-electronic structure (three 6c-1e π-bonds in R- and three 6c-1e π-bonds in β-spaces) which corresponds to a distorted benzene ring (Figure 4b and c). The oxygen atom forms a double bond with C that leads to major rearrangement of the π-bonds of the C framework of the oxyradical. The single strongly conjugated π-electron system of pentacene now splits into two fragments. Each of these fragments is a benzene-like π-aromatic system (rings ii and iV) conjugated with two 2c-2e π-bonds (rings i and V) (Figure 4d). Assessment of the AdNDP localization pattern leads to the conclusion that each of these fragments is related to the prototypical aromatic naphthalene molecule. The unpaired electron gives rise to a 3c-1e π-bond between the naphthalenelike aromatic fragments mentioned above (Figure 1, II, right panel). NICSzz and HOMA provide quantitative confirmation of the aromatic character of the fragments i, ii, and iV, V (Table 2). These results are consistent with the assignment of fragments i, ii and iV, V as related to the prototypical naphthalene molecule (Table 2), which has undergone structural distortions and can be represented as a benzene ring conjugated with two 2c-2e π-bonds. For oxyradical II, both NICSzz and HOMA show that fragments i and V are more aromatic than fragments ii and iV, while AdNDP results suggest the opposite. It is emphasized that AdNDP reveals aromatic regions by identifying patterns of delocalized bonding and does not provide a quantitative measure of aromaticity. If the substitution of H by O occurs at position 7 (oxyradical III, Figure 1), the AdNDP localization gives the results shown in Figure 5. Considering the π-framework, one can see that the
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TABLE 2: Assessment of Local Aromaticity: Values of HOMA and NICSzz Indices for Structures I-V and Prototypical Aromatic Benzene and Naphthalene Molecules ring i
ring ii
HOMA
NICSzza
I
0.49
II
0.77
III
0.89
IV
0.10
V
0.03
benzene
0.99
naphthalene
0.79
-4 -13 -21 -7 -16 -24 -3 -12 -24 19 12 0 16 8 -3 -14 -23 -29 -13 -22 -29
structure
a
HOMA 0.57 0.71 -0.12
0.51 0.43 na 0.79
ring iii
NICSzza -17 -27 -33 -1 -11 -20 24 16 3 2 -7 -17 10 1 -10 na -13 -22
ring V
ring iV
NICSzza
HOMA
NICSzza
HOMA
NICSzza
0.57
na
-17 -27 -33 -1 -11 -20 -10 -19 -27 -15 -24 -31 -11 -21 -28 na
0.49
na
-22 -31 -37 25 17 4 2 -7 -17 -9 -19 -27 -3 -12 -21 na
na
-4 -13 -21 -7 -16 -24 -7 -16 -24 -6 -15 -23 -7 -15 -23 na
na
na
na
na
na
na
HOMA 0.59 -0.17
0.57 0.60 0.58
0.71 0.69 0.65 0.67
0.77 0.67 0.59 0.63
-29
Three NICSzz values are calculated at 0.0, 0.5, and 1.0 Å above the ring, yielding NICS(0.0), NICS(0.5), and NICS(1), respectively.
Figure 4. (a) Structure of pentacene oxyradical II; (b) results of AdNDP localization for R- and β- densities; (c) nc-1e CC π-bonds superimposed on the molecular frame separately for R- and β-spaces; (d) schematic representation of bonding in R- and β-spaces. Components of O lone-pairs and 2c-1e CH bonds are omitted. A circle inscribed inside a ring represents the R (β) component of a benzene-like π-electron structure.
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Figure 5. (a) Structure of pentacene oxyradical III; (b) results of the AdNDP localization for R- and β-densities; (c) nc-1e CC π-bonds superimposed on the molecular frame separately for R- and β-spaces; (d) schematic representation of bonding in R- and β-spaces. Components of O lone-pairs and 2c-1e CH bonds are omitted. A circle inscribed inside a ring represents the R (β) component of a benzene-like π-electron structure.
localization pattern over rings i and iV is similar to that of the prototypical benzene molecule under structural distortion. Therefore, we associate rings i and iV with benzene-like π-electron structure (three 6c-1e π-bonds in R and three 6c-1e π-bonds in β systems) which corresponds to a distorted benzene ring (Figure 5b and 5c). Nonidentical π-bonds in R- and β-spaces are associated with rings ii and iii (Figure 5d). Summarizing, for the oxyradical III delocalized π-system, one again finds a split into two nonidentical fragments. Fragment i is an isolated benzene-like ring, and fragment iV, V is a benzene-like π-system conjugated with two 2c-2e π-bonds (Figure 5d). The aromaticity indices (Table 2) confirm the enhanced aromaticity of these fragments. Comparison of NICSzz and HOMA with the reference systems shows that the aromatic character of fragment iV, V is in fact closer to that of naphthalene than benzene. The open-shell character of oxyradical III leads to the emergence of nonidentical R- and β-bonding patterns (Figure 1, III, right panel). Superimposing the bonding patterns results in a structure that can be seen as a three-electron bond over centers 2, 4, 6, and 8 (rings ii and iii). This bond is conjugated with the 2c-2e π-bond in fragment iii and with the π-aromatic system of fragment iV, V, which results in an increase of aromatic character of fragment iii (Table 2). Oxyradicals IV and V have O in positions 15 and 19, respectively. These positions of H substitution lead to a different type of rearrangement of the delocalized π-system of pentacene
according to AdNDP localization findings (Figures 6 and 7, respectively). In the case of oxyradical IV, it can be seen that the localization pattern over rings iii and iV is similar to that of the prototypical naphthalene molecule (see ref 31). Closer examination of the 4c-1e π-bonds in R- and β-spaces shows that these bonds have somewhat higher contributions from ring iV. Therefore, we associate ring iV with benzene-like π-electron structure (three 6c-1e π-bonds in R- and three 6c-1e π-bonds in β- spaces) which can be localized due to the distortions of the geometry of the ring (Figure 6b and c). The nonidentical CC π-bonds in R- and β-spaces are associated with rings ii and iii (Figure 6d). For oxyradical V it can be seen that the localization pattern over ring iV is similar to that of the prototypical benzene molecule under structural distortion. Therefore, we associate ring iV with benzene-like π-electron structures (three 6c-1e π-bonds in R- and three 6c-1e π-bonds in β-systems) that can be localized due to the distortions of the geometry of the rings (Figure 7b and c). Again, nonidentical CC π-bonds in R- and β-spaces are associated with rings ii and iii (Figure 7d). In both oxyradicals IV and V, fragment iV is the only one associated with benzene-like π-electron structure and is conjugated with two 2c-2e π-bonds of fragment V (Figure 1, IV and V, right panel). NICSzz and HOMA show that fragment iV of oxyradicals IV and V has the highest degree of aromaticity (Table 2). In both cases, patterns of R- and β-one-electron bonds
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Figure 6. (a) Structure of pentacene oxyradical IV; (b) results of AdNDP localization for R- and β-densities; (c) nc-1e CC π-bonds superimposed on the molecular frame separately for R- and β-spaces; (d) schematic representation of bonding in R- and β-spaces. Components of O lone-pairs and 2c-1e CH bonds are omitted. A circle inscribed inside a ring represents the R (β) component of a benzene-like π-electron structure.
do not coincide (Figure 1, IV and V, right panel). There are essentially five electrons forming the conjugated one-electron π-bonds in fragments i, ii, and iii. Strong conjugation of π-bonds between fragments ii, iii, and V and the benzene-like fragment iV leads to significant aromatic character of the former (Table 2). The pattern of conjugation of 2c- and 3c-1e π-bonds in fragments i, ii, and iii of oxyradicals IV and V is different (Figure 1, IV and V, right panel). These bonds are conjugated both along the edges and inside the rings in oxyradical IV leading to an orthobenzoquinone-like structures. They are conjugated only along the edges in oxyradical V leading to a parabenzoquinone-like structures. This difference is presumed to account for the somewhat higher aromaticity of rings i, ii, and iii of oxyradical IV and overall higher stability of oxyradical IV in comparison to oxyradical V. All three local measures of aromaticity utilized in the present study, AdNDP localization, HOMA, and NICSzz, consistently show that the relative stability of the pentacene oxyradicals is explained by their local π-aromaticity. For the four oxyradicals, binding of O to a particular ring via a double bond destroys delocalization in the ring and makes it nonaromatic (Table 2), i.e., excludes the ring from globally delocalized π-bonding. Consequently, oxyradicals II and III each have two separated locally π-aromatic fragments and systems IV and V both have
only one locally π-aromatic fragment. It is the total number of nonconjugate π-aromatic fragments that determines the more significant stabilization of systems II and III compared to IV and V. Also, the nature of the locally π-aromatic fragments (i.e., their relation to the reference aromatic systems of benzene and naphthalene) is important. AdNDP localization patterns (Figure 3-7) suggest that a naphthalene-like fragment is more stabilizing than a benzene-like fragment (e.g., oxyradical II vs III). The patterns of conjugation in the rings with neighboring aromatic islands also influence relative stability, with the orthobenzoquinone-like pattern of oxyradical IV yielding more stability than the parabenzoquinone-pattern of oxyradical V. Another interesting issue is the behavior of the unpaired electron and its delocalization over the fragments of pentacene oxyradicals. While detailed consideration of this topic is beyond the scope of the present research, it suffices to say that emergence of 3c-1e bonds can be attributed to formation of allyl-like systems. The relationship between local π-aromaticity in the pentacene oxyradicals and their relative energies can be clearly seen from the nearly linear dependence of the latter and the cumulative HOMA calculated as a sum of HOMA indices for each sixatom fragment of a given molecule (Figure 8). In this way, the contributions from C-C bonds shared by conjugated rings are counted twice. This is not a problem, however, because the
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Figure 7. (a) Structure of pentacene oxyradical V; (b) results of AdNDP localization for R- and β-densities; (c) nc-1e CC π-bonds superimposed on the molecular frame separately for R- and β-spaces; (d) schematic representation of bonding in R- and β-spaces. Components of O lone-pairs and 2c-1e CH bonds are omitted. A circle inscribed inside a ring represents the R (β) component of a benzene-like π-electron structure.
from the locally aromatic fragments. This is the reason for the simple correlation between relative energies and cumulative HOMA. Fragmentation of globally aromatic pentacene into independent locally aromatic subsystems upon oxidation is expected to be typical for linear one-dimensional PAHs. In systems with several layers of fused six-atom rings (twodimensional) there is a possibility of rearrangement of the globally delocalized π-electronic system without fragmentation. Conclusions
Figure 8. ZPE-corrected relative energies of oxyradicals II-V (at the UB3LYP/6-311G(d,p) level of theory) plotted against cumulative HOMA. The straight line reflects nearly linear dependence.
aromaticity assessment is provided for each individual ring and the goal here is to express global aromaticity in terms of local aromaticity. The cumulative HOMA is an additive quantity with respect to the contributions from the individual locally aromatic fragments by definition. As global aromaticity of the pentacene molecule is destroyed in oxyradicals, their relative energies remain additive with respect to the stabilization effects that arise
The relative stability of linear pentacene oxyradicals can be explained by fragmentation of the delocalized π-electron system of the precursor pentacene molecule. The relative energies of oxyradicals with different placement of O depend on the amount of locally π-aromatic fragments formed and their nature. The fragments formed can be readily related to the reference aromatic hydrocarbons of benzene (prototypical system with odd number of six-atom rings) and naphthalene (prototypical system with even number of six-atom rings). The relative stability of linear oxyradicals does not seem to be related to the delocalization of the unpaired electron in the open-shell oxyradical. Relative energies of linear oxyradicals show linear dependency of the cumulative HOMA aromaticity measure (Figure 8). This relation can be useful for quickly assessing the thermodynamic stability of oxyradicals for arbitrary-size graphene edges.
Bonding in Pentacene Oxyradicals Acknowledgment. R.W., D.D., W.A.L., and M.F. were supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division of the US Department of Energy, under Contract No. DE-AC03-76F00098. N.R., X.Y., and M.F. were supported by the US Army Corps of Engineers, Humphreys Engineering Center Support Activity, under Contract No. W912HQ-07-C-0044. D.Y.Z. was supported by the National Science Foundation under Grant No. NSF CHE-0809969. J.W. is a UC Berkeley visitor supported by a stipend from the China Scholarship Council. Supporting Information Available: Relative energies, zeropoint energies, expectation values of the S2 operator for the unrestricted open-shell calculations, vibrational frequencies, rotational constants and Cartesian coordinates of the species studied; details of entropies, heat capacities, and thermal enthalpies of the pentacene oxyradicals; full refs 24 and 27. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Nagle, J.; Strickland-Constable, R. F. Proc. Fifth Carbon Conf. 1962, 1, 154. (2) Kennedy, I. M. Prog. Energy Combust. Sci. 1997, 23, 95. (3) Stanmore, B. R.; Brilhac, J. F.; Gilot, P. Carbon 2001, 39, 2247. (4) Higgins, K. J.; Jung, H.; Kittelson, D. B.; Roberts, J. T.; Zachriah, M. R. J. Phys. Chem. A 2002, 106, 96. (5) Kim, C. H.; Xu, F.; Faeth, G. M. Combust. Flame 2008, 152, 301. (6) Brezinsky, K. Prog. Energy Combust. Sci. 1986, 12, 1. (7) Olivella, S.; Sole, A.; Garcia-Raso, A. J. Phys. Chem. 1995, 99, 10549. (8) Fadden, M.; Hadad, C. M. J. Phys. Chem. A 2000, 104, 3004. (9) Xu, Z. F.; Lin, M. C. J. Phys. Chem. A 2006, 110, 1672. (10) Montoya, A.; Mondragon, F.; Truong, T. N. Fuel Proc. Technol. 2002, 77-78, 125. (11) Sendt, K.; Haynes, B. S. Proc. Combust. Inst. 2005, 30, 2141. (12) Sendt, K.; Haynes, B. S. Combust. Flame 2005, 143, 629. (13) Sendt, K.; Haynes, B. S. J. Phys. Chem. A 2005, 109, 3438. (14) Radovic, L. R.; Bockrath, B. J. Am. Chem. Soc. 2005, 127, 5917. (15) Stein, S. E.; Brown, R. L. Carbon 1985, 23, 105. (16) Stein, S. E.; Brown, R. L. J. Am. Chem. Soc. 1987, 109, 3721. (17) Philpott, M. R.; Kawazoe, Y. Chem. Phys. 2009, 358, 85. (18) Li, Z. Y.; Zhang, W. H.; Luo, Y.; Yang, J. L.; Hou, J. G. J. Am. Chem. Soc. 2009, 131, 6320.
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