All-Sites

Letter pubs.acs.org/JPCL

Pancake π−π Bonding Goes Double: Unexpected 4e/All-Sites Bonding in Boron- and Nitrogen-Doped Phenalenyls Yong-Hui Tian,*,† Bobby G. Sumpter,‡ Shiyu Du,§ and Jingsong Huang*,‡ †

College of Life Science, Research Center of Analytical Instrumentation, Key Laboratory of Bio-resource and Eco-environment of Ministry of Education, Sichuan University, Chengdu, Sichuan 610064, People’s Republic of China ‡ Center for Nanophase Materials Sciences and Computer Science & Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States § Division of Functional Materials and Nanodevices, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Science, Ningbo, Zhejiang 315201, People’s Republic of China S Supporting Information *

ABSTRACT: Chemical bonding interactions are the main driving force for the formation of molecules and materials from atoms. The two-electron/multicenter pancake π−π bonding found in phenalenyl (PLY, 1) radical π-dimers is intriguing due to its unconventional nature of covalent bonding for molecular aggregations and its propensity to induce unique optical, electronic, and magnetic properties. By using highlevel quantum chemistry calculations, we show that the B- or N-doped PLYs (2 and 4), usually considered closed-shell and therefore trifling, can be rendered open-shell singlet by proper edge substitutions (3 and 5). The resulting two unpaired valence electrons on each molecular unit contribute to the formation of a genuine pancake-shaped 4e/all-sites double π−π bonding upon intermolecular π-dimerization, in contrast to the 2e/half-sites single π−π bonding in the parent PLY π-dimers. The unusual double π−π bonding motif discovered in these PLY analogues may broaden the landscape of, and find new applications for, intermolecular covalent bonding interactions. In addition to forming σ-dimers between two parent PLY radicals, PLY derivatives such as 2,5,8-tri-tert-butyl-PLY radical are found to form π-dimers through the so-called two-electron/ multicenter (2e/mc) covalent π−π bonding, as qualitatively depicted by the SOMO−SOMO interactions in the π-dimer 12 (Figure 1b).4,5 The concept of 2e/mc bonding can be traced back to Pauling’s fractional bonding model.6 The intermolecular separations (D) in the pancake-shaped π-dimers are much longer than conventional chemical bonds but meanwhile evidently shorter than van der Waals (vdW) distances. Despite the long D, theoretical progress has recently been made on rationalizing the unusual nature of the 2e/mc π−π bonding, suggesting a covalent character instead of only vdW interactions.7−10 Such a π-dimer structural motif has been found to exist ubiquitously in a variety of organic materials,11−15 which has been comprehensively reviewed.16,17 On top of that, organic materials featuring pancake πaggregations often exhibit fascinating optical, conducting, and magnetic properties,18−21 which are closely pertinent to the nature of the 2e/mc π−π bonding.22−24 Therefore, intensive studies of PLY and its various derivatives are emerging at the forefront of interdisciplinary science where the fundamental

P

henalenyl (PLY, 1) is a neutral odd alternate hydrocarbon radical species with its π-electron spin densities evenly distributed on the six α-carbon sites, as dictated by its singly occupied molecular orbital (SOMO) (Figure 1a). The PLY radical can be viewed as the most fundamental triangular unit among the various open-shell graphene fragments that are recognized as promising spin-based magnetic materials.1 Also, it has long been proposed that PLY is a good candidate for building intrinsic organic metals without metallic elements.2,3

Figure 1. Monomer and dimers of PLY. (a) The structure of the parent PLY and its SOMO diagram. (b) The steric views of σ- and πdimers, where the latter shows a pancake π−π bonding due to the SOMO−SOMO overlap. © XXXX American Chemical Society

Received: April 25, 2015 Accepted: June 3, 2015

2318

DOI: 10.1021/acs.jpclett.5b00857 J. Phys. Chem. Lett. 2015, 6, 2318−2325

Letter

The Journal of Physical Chemistry Letters concept of chemical bonding and potential applications of new functional materials intersect. It is known that doping with B or N is an important approach to tune the electronic and magnetic properties of graphene materials.25,26 Herein, we inspect the effects of graphitic B- and N-doping on the electronic properties of PLY derivatives and their π-aggregates. Figure 2 shows the B-doped

Figure 3. Hückel-level examination of the B- and N-doping effect. (a) A schematic illustration of the energy levels for the three frontier orbitals (FO) of the parent and the doped PLYs 1, 2, and 4. The β term refers to the bond integral of Hückel calculations. (b) FO diagrams at the Hückel level. The central atoms are C, B, and N for 1, 2, and 4, respectively.

LUMO gap in PLY 1. Similarly, upon B-doping in 2, the deficiency of one electron leads to an empty FO-b. Meanwhile, the FO-a orbital is lifted up toward the FO-b orbital, also giving a reduced HOMO−LUMO gap. For both 2 and 4, the near degeneracy of the HOMO and LUMO indicate the possibility of a static (or nondynamic) electron correlation,29 which may lead to diradicaloid ground states. It is further noteworthy that the nonbonding MO of FO-b is confined to a disjointed set of atoms30 compared to FO-a for 2 and FO-c for 4, and thereby, the B- or N-doping will likely lead to open-shell singlet ground states. The reduced HOMO−LUMO gap and the disjoint feature revealed above from the Hückel-level examination only indicate the tendency of diradicaloid ground states. If the HOMO− LUMO gaps for 2 and 4 are still too large to ensure diradicaloid ground states, appropriate edge substitutions may render them so, as will be demonstrated below for 3 and 5. To fine-tune the HOMO−LUMO gaps in 3 and 5, we adopt amino groups and dithio bridges with lone pairs on N and S for edge substitutions. Similar electron-donating groups have been experimentally used for PLY 1 but have not yet been considered for B- or Ndoped PLYs 2 or 4.31,32 Unlike the primary effect of B- or Ndoping, the effect of edge substitutions in 3 and 5 is only secondary, and therefore, we do not rely on the qualitative orbital analysis. Assuming open-shell ground states, FO-a and FO-b for 3 and FO-b and FO-c for 5 would be all singly occupied. Under such circumstance, it is possible for these doped and edge-functionalized molecules to form a novel double π−π bonding upon intermolecular π−π stacking due to the presence of two unpaired π-electrons in the diradicaloids. The beauty of such double π−π bonding is that the bonding electron densities are expected to distribute on all atomic sites of the molecular plane, giving a 4e/all-sites or 4-electron/26center (4e/26c) bonding, in contrast to the half-sites bonding (only on 12 α-carbons) characteristic of the parent π-dimer 12. This may be seen from the different sites for the orbital lobes in FO-a and FO-b for 2 and in FO-b and FO-c for 4 (Figure 3b; cf. Figure 4 at a higher level of theory showing that the two sets of sites are complementary to one another). High-Level Quantum Chemistry Calculations. The semiempirical Hückel theory applied to the monomers shown above does not take into consideration the static electron correlation as implied from the near degeneracy of the

Figure 2. PLY derivatives studied in this work. (a) B-doped 2 without and 3 with edge-substitutions by amino groups at the β-C atoms. (b) N-doped 4 without and 5 with edge-substitutions by dithio-bridges at the α-C atoms.

PLYs (2 and 3) and N-doped PLYs (4 and 5), which have 12 and 14 π-electrons corresponding to p- or n-type doping, respectively. B- or N-doped PLYs have been generally regarded as closed-shell systems and are hence unimportant compared to the parent PLY radical because certain derivatives of PLY are prone to the formation of pancake π−π bonding. For instance, previous theoretical studies only considered the vdW dimers of B- and N-doped PLYs in light of their anticipated closed-shell electronic structures.7,27,28 In the present study, we are intrigued by the following fundamental questions: (1) Although the doped PLYs 2 and 4 are closed-shell, can π−π bonding still occur upon intermolecular π−π stacking? (2) Can proper substitutions make the doped PLYs 3 and 5 open-shell diradicaloids? (3) Upon dimerization, how does the bonding nature in these closed-shell or open-shell PLY analogues differ from that of the parent 12 π-dimer? In the following, we address these questions and issues with state-of-art quantum chemistry calculations. We illustrate strategies to design doped PLY molecules featuring diradicaloid character in the singlet state and explore their electronic structures and the possibility of πdimerizations. As new members of the neutral PLY radical’s family, these doped species 2−5 and their π-aggregates possess great potential for making new materials with properties and applications that would be distinct from those based on the parent PLY radical. Qualitative Orbital Analysis. Within the simple Hückel scheme (Figure 3a), the three frontier orbitals, that is, FO-a, -b, and -c, are directly relevant to the effect of B- and N-doping. In the parent PLY 1, the radical π-electron is populated on the SOMO, which corresponds to a nonbonding FO-b. Upon Ndoping in 4, one extra electron fills into FO-b, leading to a closed-shell molecule. Another noteworthy outcome upon Ndoping is that the LUMO of FO-c is significantly lowered in energy with respect to the HOMO due to the higher electronegativity of N than that of C. Accordingly, the HOMO−LUMO gap is reduced compared to the SOMO− 2319


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The Journal of Physical Chemistry Letters

Electronic Structures of Monomers 2−5. As can be seen from Table 1, the high-level calculations indicate that B-PLY 2 has a Table 1. Singlet−Triplet Energy Differences (ΔEST) and the NOONs for the Monomers 2−5 monomer

notation

ΔESTa

NOONb

2 3 4 5

B-PLY B-PLY-NH2 N-PLY N-PLY-SS

−12.56 −5.94 −13.90 −1.91

2.00,0.00c 1.12,0.88c 2.00,0.00d 1.00,1.00d

ΔEST in kcal·mol−1, defined as ΔEST = Esinglet − Etriplet, is calculated by XMCQDPT/CAS(2,2) based on the respective geometries optimized by unrestricted B3LYP-D3/6-31G(d,p). The difference is between the closed-shell ground state and the triplet for 2 and 4 or between the open-shell singlet and the triplet for 3 and 5. bOccupancies are from natural orbital analysis following CAS(2,2) calculations. cOccupancies in 2 and 3 are for FO-a and FO-b, respectively (Figure 4a). d Occupancies in 4 and 5 are for FO-b and FO-c, respectively (Figure 4b). a

Figure 4. FO visualizations for monomers 2−5. (a) FO-a and FO-b for the B-doped 2 without and 3 with edge substitutions by amino groups at the β-C atoms. (b) FO-b and FO-c for the N-doped 4 without and 5 with edge substitutions by dithio bridges at the α-C atoms. The blue arrows indicate the orbital nodes between the substituting groups and the PLY core.

monomer’s frontier orbitals. Additionally, electron correlations could also play a significant role in dimers. As will be shown below, the intermolecular separations in the π−π-bonded dimers are much longer than conventional chemical bonds but meanwhile can be up to ∼0.4 Å shorter than the vdW distances. For these systems with stretched π−π bonding, one should consider two important ingredients in the intermolecular interactions, that is, the nonlocal dynamic electron correlation (the long-range dispersion) and the static electron correlation that is associated with the weakened intermolecular bonding interaction.33 Therefore, it is indispensable to go beyond the qualitative orbital analysis and resort to higher levels of theory that entertain these important effects to describe the electronic structures more precisely. The geometries of monomers 1−5 and dimers 12−52 were first fully optimized by using density functional theory (DFT) with unrestricted B3LYP-D3/6-31G(d,p), unless otherwise noted. Long-range dispersion corrections were accounted for by the D3 version of Grimme’s empirical dispersion potential, as indicated by “-D3”.34 Diffuse functions in the basis set on carbon centers were found to have negligible effect on the intermolecular separations for selected dimer structures (Table S1, Supporting Information). Single-point energies were then calculated with the extended multiconfiguration quasi-degenerate perturbation theory (XMCQDPT)35 applied at the second order in combination with Dunning’s cc-pVTZ basis set. Basis set superposition errors (BSSEs) were corrected for dimer binding energies by the counterpoise method.36 Orbitals relevant to the π−π bondings were included in the complete active space self-consistent field (CASSCF) calculations. Specifically, XMCQDPT/CAS(2,2) was applied for the doped monomers 2−5 and for the parent PLY’s π-dimers 12 of different configurations and multiplicities, whereas XMCQDPT/CAS(4,4) was adopted for B-PLY and N-PLY’s dimers 22−52 with and without edge substitutions. The highlevel theories applied are capable of entertaining all of the electron correlation effects mentioned above. Note that secondorder multireference perturbation methods are usually found to overestimate dispersion interactions in the PLY π-dimers.7,27 However, the trend predicted at the XMCQDPT level should be correct due to the similarity of π−π bonding nature for the π-dimers of PLY and its derivatives (with a difference only in the single versus double π−π bonding). Additional computational details are provided in the Supporting Information.

closed-shell ground state, with the first exited triplet lying 12.56 kcal·mol−1 above it. The relatively small singlet−triplet energy difference (ΔEST) is in line with the aforementioned qualitative orbital analysis, showing a reduced HOMO−LUMO gap (Figure 3). In comparison, by simple substitutions at the βsites, as illustrated in Figure 2, B-PLY-NH2 3 turns out to have an open-shell singlet ground state as manifested by the two nearly singly occupied frontier orbitals according to the natural orbital occupation numbers (NOONs). The two active orbitals (FO-a-2 and FO-b-2 for 2 or FO-a-3 and FO-b-3 for 3) involved in the multireference calculations are presented in Figure 4a. The preference of 3 for a diradicaloid singlet ground state can be qualitatively attributed to the fact that in addition to the elevated FO-a-3 level by B-doping (Figure 3), the electron-donating amino groups further raise the FO-a-3 level to reduce the HOMO−LUMO gap, as can be seen from the orbital nodes present between the amino groups and the β-C atoms (Figure 4a). Similar to B-PLY 2, N-PLY 4 has a closedshell ground state. However, by introducing electron-donating dithio bridges at the α-sites, the ground state of N-PLY-SS 5 becomes an open-shell singlet, as indicated by the calculated NOONs. The two active orbitals (FO-b-4 and FO-c-4 for 4 or FO-b-5 and FO-c-5 for 5) involved in the multireference calculations are presented in Figure 4b. The reason for the open-shell singlet of 5 is that on top of the stabilization of FOc-5 due to N-doping (Figure 3), the HOMO−LUMO gap is further reduced by the dithio bridge substitutions, which raises the FO-b-5 level, as can be seen from the orbital nodes present between the dithio bridges and the α-C atoms (Figure 4b). Thus, a diradicaloid singlet ground state is favored for both 3 and 5 by means of appropriate edge substitutions although 2 and 4 prefer closed-shell ground state. B-Doped Dimers 22 and 32. For 22 dimers, three types of configurations were identified, including two π-dimers with eclipsed and staggered configurations and a vdW dimer (Table 2). In the eclipsed 22 π-dimer (22-eclipsed), the two monomeric units stack face to face, giving D3h symmetry (Figure 5a). In comparison, 22-staggered has D3d symmetry (Figures 5a and S1, Supporting Information). In contrast to the π-dimers, the vdW dimer 22-vdW is characterized by the long distance between two stacked monomers that are rotated with respect to one another (Figure S2, Supporting Information). At first sight, the observation of 22-eclipsed and 22-staggered π2320


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Table 2. Calculated Interaction Energies Eint (in kcal·mol−1) and the Optimized Bonding Distances D and ΔD (in Å) for the Ground Electronic State of 12−52 Dimers with Three Types of Configurationsa eclipsedb dimer

Eintc

Dd

12 22 32 42 52

−17.47 −22.52h −33.25h −15.22h −46.12h f

3.27(3.34) 3.05(2.82)i 3.08(2.85) 3.04(2.99)j,k 3.22(2.80)

staggeredb ΔDe

Eintc

+0.07 −0.23 −0.23 −0.05 −0.42

−24.71 −17.78h −35.56h n/am −47.00h

Dd f

3.08(3.16) 3.03(2.62)j,k 3.01(2.75) n/am 3.16(3.07)j

vdwb ΔDe

Eintc

Dd

+0.08 −0.41 −0.26 n/am −0.09

g

n/ag (3.31)l n/ag (3.30)l n/ag

n/a −13.91h n/ag −17.76h n/ag

Configurations: eclipsed π-dimer, staggered π-dimer, and vdW dimer. bGeometries were optimized by unrestricted B3LYP-D3/6-31G(d,p) unless otherwise noted. cThe interaction energy is defined as Eint = Edimer − 2 × Emonomer. dThe numbers outside and inside of the parentheses correspond to the peripheral Cα−Cα and the central XCntr−XCntr bonding distances, respectively, where X is C for 12, B for 22 and 32, and N for 42 and 52. e Difference between the central XCntr−XCntr and the Cα−Cα distances; positive and negative values indicate convex and concave π-dimer geometries, respectively. fSingle-point calculations by XMCQDPT/CAS(2,2). gvdW dimers do not exist due to the radical nature of their monomers (cf. Table 1). hSingle-point calculations by XMCQDPT/CAS(4,4). iThe π-dimer structures were verified with the optB88-vdW functional. jGeometries were optimized by restricted B3LYP-D3/6-31G(d,p) because the π-dimer structures cannot be located with unrestricted B3LYP-D3/6-31G(d,p). kThe πdimer structure cannot be verified with the optB88-vdW functional. lNo direct intermolecular contact is available between peripheral α-C atoms due to the relative rotations of two monomers in the vdW dimers (see Figures S2 and S4, Supporting Information). mThe π-dimer structure cannot be located with either restricted or unrestricted B3LYP-D3/6-31G(d,p). a

Frontier orbital visualizations and corresponding NOONs as shown in Figures 5b and S1 (Supporting Information) indicate that both 22-eclipsed and 22-staggered have open-shell singlet ground states, even though their monomers have a closed-shell ground state. As can be also seen from Figure 5b, for 22eclipsed (and Figure S1 (Supporting Information) for 22staggered), the doubly occupied orbital corresponds to the bonding combination of two fragmental FO-a-2 orbitals. For the next two singly occupied orbitals, the first one takes a bonding character, while the other is antibonding. On the basis of this orbital ordering, the formation of π-dimers can be ascribed to the level crossing between the middle two dimer orbitals (see the qualitative level diagram provided in the Supporting Information). On the other hand, the calculated NOONs indicate that the full bonding effect of FO-a-2-bond is partially canceled by the antibonding. Consequently, an overall 2e double π−π bonding, with 1e for each bonding orbital of FO-a-2 and FO-b-2 and therefore a formal bond order of 1, is present in both 22-eclipsed and 22-staggered. Note that the π−π bonding of 22-eclipsed is distributed on all of the atomic sites, giving a 2e/all-sites double π−π bonding, in contrast to the 2e/ half-sites single π−π bonding in the parent PLY π-dimers. These observations are in sharp contrast with the general observation that only vdW dimers can be formed between the B-doped closed-shell molecules 2. The dimerization energies calculated at the high-level theory are summarized in Table 2. For the two π-dimers of 12, 12staggered is energetically preferred over 12-eclipsed, as found previously.27,28 For both 22-eclipsed and 22-staggered, the πdimers are significantly more stable than the vdW dimer, indicating the pancake π−π bonding formation. In addition, the bonding energies are comparable to those for the parent PLY’s π-dimers 12, which feature a 2e single π−π bonding. This is reasonable due to the contribution of the same number of two bonding electrons in 12 and 22. However, 22-eclipsed is energetically preferred over 22-staggered, in contrast to the parent PLY’s π-dimers favoring 12-staggered. This difference can be attributed to the π−π bonding formation, as revealed by the frontier orbitals in Figures 5b and S1 (Supporting Information). For 22-eclipsed, the FO-a-2-bond orbital displays in-phase overlaps on 14 sites (cf. Figure 4a), whereas direct orbital overlap is only available at the central B sites for 22staggered. This analysis is corroborated by the optimized

Figure 5. Structures and frontier orbitals of the π-dimers 22 and 32. (a) Top views of the π-dimers with eclipsed and staggered configurations. (b) Frontier orbitals of 22-eclipsed (for 22-staggered, see Figure S1, Supporting Information). (c) Frontier orbitals of 32-eclipsed (for 32staggered, see Figure S3, Supporting Information). The terms “bond” and “anti” indicate bonding and antibonding overlaps. The NOONs are obtained from the natural orbital analysis following CAS(4,4) calculations.

dimers is surprising because only the 22-vdW is expected based on its closed-shell singlet ground state (Table 1). It is possible that the π-dimerizations may have resulted from the use of an empirical dispersion correction term in B3LYP-D3 that lacks the flexibility to readjust the charge density distributions with the intermolecular separations. To rule out this possibility, we further adopted a fully self-consistent vdW-DF method that uses specifically the nonlocal optB88-vdW correlation functional37,38 for the geometry optimizations. However, the πdimer structure was verified for 2 2 -eclipsed, showing intermolecular distances close to those obtained at the B3LYP-D3 level (see the computational details, Supporting Information). Although the 22-staggered could not be verified with this nonlocal functional, under the high-level theory, its πdimer structure found by B3LYP-D3 has a lower energy than 22-vdW, suggesting the existence of 22-staggered (see below). 2321


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Figure 6. Structures and frontier orbitals of the π-dimers 42 and 52. (a) Top views of the π-dimers with eclipsed configurations. (b) Frontier orbitals of 42-eclipsed. (c) Frontier orbitals of 52-eclipsed (for 52-staggered, see Figure S5, Supporting Information). The terms “bond” and “anti” indicate bonding and antibonding overlaps. The NOONs are from the natural orbital analysis following CAS(4,4) calculations.

geometric parameters as tabulated in Table 2. Unlike the 12 πdimers, which are convex for both the eclipsed and staggered singlets, the 22 π-dimers have concave shapes, where the central intermolecular distance (BCntr−BCntr) is remarkably shorter than the peripheral distances (Cα−Cα), clearly indicative of the π−π bonding formation between the central B atoms in addition to that between the peripheral α-C atoms. Unlike the 22 π-dimers with diradicaloid characters, the 32 πdimers functionalized by amino groups at β-positions take essentially closed-shell ground states, as suggested by the natural orbital occupancy analysis shown in Figure 5c for 32eclipsed (for 3 2 -staggered, see Figure S3, Supporting Information). This observation is as expected due to the diradicaloid singlet ground state of 3 (B-PLY-NH2) (cf. Table 1). Figure 5c also shows that the two doubly occupied frontier orbitals of the dimer 32 are comprised of bonding overlap of two FO-a-3 and two FO-b-3 fragmental orbitals, respectively (cf. Figure 4a). Furthermore, the intermolecular orbital overlaps for the two bonding orbitals are located on different sites, and therefore, an overall 4e/26c double π−π bonding is formed covering all of the atomic sites on the PLY rings, leading to a genuine pancake-shaped π-dimer. As a result of the 4e bonding and, accordingly, a formal bond order of 2, the 32 π-dimers have significantly larger dimerization energies than 12 and 22 πdimers, which are bound only by 2e (Table 2). This evidence further supports the 4e double π−π bonding formation in 32 πdimers. N-Doped Dimers 42 and 52. The geometry optimization for 42-staggered at both of the restricted and unrestricted B3LYPD3 level automatically led to 42-vdW with long N−N distances (Table 2 and Figure S4, Supporting Information). In comparison, a π-dimer of 42-eclipsed was obtained at the restricted B3LYP-D3 level (Figure 6a), despite the closed-shell electronic structure of the monomer. According to the natural orbital analysis shown in Figure 6b, 42-eclipsed is an open-shell singlet with diradicaloid character. Overall, 42-eclipsed features a 2e/all-sites double π−π bonding, similar to the 22-eclipsed shown above. However, unlike the B-doping 22-eclipsed, the πdimer structure of 42-eclipsed cannot be located when the nonlocal optB88-vdW functional is used for the geometry optimization. In addition, as shown in Table 2, the π-dimer 42eclipsed is slightly less stable than the vdW dimer 42-vdW. Combining these two observations, we conclude that the πdimer 42-eclipsed optimized by the restricted B3LYP-D3 method could be an artifact and that the π-dimerization between two closed-shell monomers 4 does not happen.

In comparison, upon substitutions with dithio bridges at the α-positions on the edges, a closed-shell π-dimer 52-eclipsed was obtained, as suggested by the frontier orbital diagrams and corresponding occupancies in Figure 6c. Similar to the 32eclipsed shown in Figure 5c, a 4e/all-sites double π−π bonding is formed in 52-eclipsed, in accordance with the diradicaloid singlet ground-state structure of molecule 5, as mentioned above (cf. Table 1). On the other hand, on the basis of the natural orbital analysis provided in Figure S5, Supporting Information, 52-staggered is an open-shell singlet. This electronic structure can be ascribed to inefficient FO-c-5 orbital overlap, which gives rise to a near degeneracy of all four frontier dimer orbitals. It can be seen from the dimerization energies in Table 2 that 52-eclipsed is slightly less stable than 52-staggered, similar to the 32 π-dimers. Nevertheless, 52eclipsed has a rather large dimerization energy, partly due to the 4e/all-sites double π−π bonding and partly due to the vdW interactions between the overlapping substituents. Unlike the first-row N atoms in the amino groups, the second-row S atoms in the dithio bridges are more prone to polarization and therefore may contribute to stronger vdW attractions. Comparison of Single and Double π−π Bondings. The key finding of the present work is that both the B-doped 3 and Ndoped 5 with appropriate edge substitutions can form unusual 4e/all-sites double π−π bonding. It is interesting to compare the current 4e/all-sites double π−π bonding in the π-dimers of 32 and 52 with the bonding interactions in the sulfur-containing dithiatriazines synthesized 3 decades ago.39 A “double pancake bonding” concept has recently been introduced for the latter.10 For the dithiatriazine π-dimers, it is clear from the X-ray structures that the SS pairs are more involved in the bonding formation than the NN pairs (2.529 versus 2.861 Å on average) due to the experimentally observed half-chair distortion of the constituent monomers. In comparison, the present double π−π bonding found in the π-dimers 32 and 52 is more evenly distributed on all 26 carbon sites on the PLY rings, leading to a genuine pancake-shaped double π−π bonding. Nevertheless, all of these molecular species bear a similarity in the number of frontier π-electrons. The dithiatriazine molecule contains 8 πelectrons, making it antiaromatic. The monomer 3 is also antiaromatic due to the presence of 12 π-electrons on the PLY core. Although 5 has 14 π-electrons on the PLY core, it should also be treated as antiaromatic due to the presence of 12 πelectrons in the cyclic conjugation along the periphery associated with the [12]annulene framework, which is perturbed by the central N atom. The commonality of 2322


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anticipated for the 52-eclipsed π-dimer as implied from its doubly occupied bonding orbitals shown in Figure 6c. In summary, we have found that proper chemical modifications of the B- and N-doped PLY molecules (3 and 5) lead to open-shell singlet diradicaloid molecules, which may undergo dimerizations giving essentially closed-shell π-dimers. These pancake π-dimers bound by genuine 4e/all-sites double π−π bonding are more stable than the prototypical π-dimers of 1. In recent years, a plethora of functional molecular materials based on PLY and its derivatives have been realized, displaying diverse fascinating optical, conducting, and magnetic properties.1,18−21,41,42 We note that the new molecular species introduced in this work may be equally exploited as building blocks of new functional materials for the realization of unique material properties. The double π−π bonding in fact consists of two separate single “bonds” of comparable strength as the single π−π-bonded PLY dimer. Therefore, breaking each individual bond would require essentially the same amount of energy (or temperature) as the parent PLY π-dimer. Furthermore, assuming that the double-bonded dimers form a 1D stack, the Peierls-distorted stack could be converted to a uniform stack by breaking one of the double bonds followed by forming alternating single bonds along the stack. This is expected to give rise to a conducting pathway along the π−π stacking and magnetic exchanges between partially unpaired spins. The coexistence of magnetic and conducting properties, together with the interplay between them, could be an indispensable ingredient for the development of molecule spin-electronic (or “spintronics”) devices.43 Therefore, we envision that the unusual double π−π bonding motif discovered in these PLY analogues may open a new avenue toward the rational design of molecular conductors, magnets, and spintronic devices. This work invites experimentalists to make these simple and yet fascinating molecules and materials.

antiaromaticity is in accordance with the previous suggestion that antiaromaticity is a prerequisite for the formation of pancake double π−π bonding.10,40 To highlight the difference between the 2e/half-sites single π−π bonding in the parent PLY π-dimers and the novel 4e/allsites double π−π bonding found in the PLY derivatives, we compare the covalent bonding characters and bond orders between the 12 and 32 π-dimers of both the eclipsed and staggered configurations. On the basis of the Heitler−London valence bond approximation, the covalent bonding components in the π-dimers can be roughly evaluated by8 1 K = (E LS − E HS) (1) 2 where K refers to the exchange term representing the covalent bonding strength arising from two-electron coupling, while ELS and EHS refer to the energies of low-spin (LS) bonding and high-spin (HS) nonbonding states. Note that HS states are triplets for 12 but quintets for 32. Meanwhile, the bond orders pNO for the π−π bondings can be calculated based on the NOONs of the frontier orbitals using the formula10 (NEBO − NEABO) (2) 2 where NEBO is the number of electrons in the bonding orbitals and NEABO is the number of electrons in the antibonding orbitals based on the natural orbital occupancies for the two and four frontier orbitals of 12 and 32, respectively. As displayed in Table 3, the covalent contribution for the two 12 π-dimers is pNO =

Table 3. Comparison of the Covalent Components (K, in kcal·mol−1) and the Formal Bond Orders (pNO) between Single π−π-Bonded 12 and Double π−π-bonded 32 of Two Configurations configuration

12-eclipsed

12-staggered

32-eclipsed

32-staggered

Ka pNOd

−7.11b 0.75e

−11.72b 0.84e

−23.88c 1.75f

−20.46c 1.74f

■

ASSOCIATED CONTENT

S Supporting Information *

Computational details; structural comparison for 12−5 2 optimized with the 6-31+G(d,p) basis set; visualizations of frontier orbitals and natural orbital occupancies for 22staggered, 32-staggered, and 52-staggerd; structures of 22-vdW and 42-vdW; schematic level correlation diagrams for 22 and 32; possible σ-dimerization of closed-shell 4; and full author list for ref 20. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.jpclett.5b00857.

a

K is defined by eq 1. bThe HS triplet state energy in eq 1 is from the single-point CAS(2,2) calculation using the singlet geometry of 12 optimized by unrestricted B3LYP-D3/6-31G(d,p). cThe HS quintet state energy in eq 1 is from the single-point CAS(4,4) calculation using the singlet geometry of 32 optimized by unrestricted B3LYP-D3/631G(d,p). dpNO is defined in eq 2. eThe NEBO and NEABO occupancies in eq 2 are from natural orbital analysis following CAS(2,2) calculations. fThe NEBO and NEABO occupancies in eq 2 are from natural orbital analysis following CAS(4,4) calculations.

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AUTHOR INFORMATION

Corresponding Authors

around −10 kcal·mol−1, while that for the two 32 π-dimers is twice as large at ∼−20 kcal·mol−1, in line with the difference in the bond orders pNO for the π−π bondings. The subtle difference of the K values between 12-eclipsed and 12-staggered simply comes from the different intermolecular separations; a longer D in 12-eclipsed corresponds to its smaller K (Table 2). Although the D is also longer for 32-eclipsed, its K is in fact slightly larger than that of 32-staggered as a result of the all-sites overlap in the eclipsed configuration, whereas direct orbital overlap is only available at the central B sites in the staggered configuration (compare the orbital FO-a-3 bond in Figures 5c and S3 (Supporting Information)). The factor of 2 for both K and pNO between 12 and 32 is consistent with the double π−π bonding character in the two 32 π-dimers. Similar behavior is

*E-mail: [email protected] (Y.-H.T.). *E-mail: [email protected] (J.H.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research is supported by the Faculty Startup Grant of Sichuan University, by the National Science Foundation of China (Grant No. 21443012), and by the Center for Nanophase Materials Sciences (CNMS), which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. Y.T. thanks the National Super2323


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computing Center in Shenzhen for providing the computational resources and Gaussian09 program (version of ES64LG09RevD.01). B.G.S. and J.H. are indebted to the computational resource of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DEAC02-05CH11231. This work also benefited from the insightful discussions with Prof. Miklos Kertesz at Georgetown University.

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