We examine the electronic ground state of acenes with different number of fused benzene rings (up to 40) by using first principles density functional theory. Their properties are compared with those of infinite polyacene. We find that the ground state of acenes that consist of more than seven fused benzene rings is an antiferromagnetic (in other words, open-shell singlet) state, and we show that this singlet is not necessarily a diradical, because the spatially separated magnetizations for the spin-up and spin-down electrons increase with the size of the acene. For example, our results indicate that there are about four spin-up electrons localized at one zigzag edge of 20-acene. The reason that both acenes and polyacene have the antiferromagnetic ground state is due to the zigzag-shaped boundaries, which cause pi-electrons to localize and form spin orders at the edges. Both wider graphene ribbons and large rectangular-shaped polycyclic aromatic hydrocarbons have been shown to share this antiferromagnetic ground state. Therefore, we demonstrate that the pi-electronic structure of higher acenes and ployacene are still dictated by the zigzag edges, and our results provide a consistent description of their electronic ground state.
Acenes have attracted great interest from a wide spectrum of researchers. [1][2][3][4][5][6] These linearly fused benzene rings (see Figure 1a) provide interesting electronic properties due to the conjugated π-electron system. Especially, pentacene has been widely used in molecular electronics. [7][8][9][10][11][12][13][14][15][16][17][18][19] Acenes belong to polycyclic aromatic hydrocarbons (PAH). Great progress has been made towards the synthesis of large PAHs 20 since the publication of Clar's two volumes on polycyclic hydrocarbons. 21 In the books, Clar pointed out heptacene's enormous reactivity that rendered it impossible to obtain heptacene in a pure form. Clar also described early unsuccessful efforts to synthesize octacene, nonacene, and undecacene. Only very recently was heptacene-containing single crystal obtained, 22 and higher acenes remain elusive. So does the corresponding polymer, polyacene. 23 Several theoretical studies have attempted to understand the electronic structures of higher acenes and explain their high reactivity. Houk and co-workers predicted a triplet ground state for acenes with n (the number of fused benzene rings) > 8, 24 using unrestricted B3LYP (UB3LYP) for the triplet but restricted B3LYP for the singlet (both with 6-31G* basis). Later, Bendikov et al. showed that the ground state is an open-shell singlet for n > 6, by using UB3LYP (with 6-31G* basis) also for the singlet, and claimed that this open-shell singlet represents a diradical. 25,26 Because a diradical is a molecule with two unpaired electrons, 27 their claim implies that there are one up and one down spins in acenes with n > 6.
In a recent study, dos Santos 28 reported a higher spin ground state, a quintet, for n=20-23, also based on UB3LYP/6-31G*. More recently, Chan and coworkers used a density matrix renormalization group algorithm and studied acenes with n=2-12. They found that the ground states for longer acenes are polyradical singlets. 29 In the meantime, there has been much interest in zigzag-edged graphene nanoribbons (ZGNR), [30][31][32][33][34][35][36][37][38][39] which can be viewed as parallel polyacetylene chains cross-linked together (the number of parallel polyacetylene chains is used as an index to characterize the width of a ZGNR). Acenes and polyacene also share this structural feature of zigzag edges. We and others 30,40 have predicted that infinitely long ZGNRs with a width index of four or higher have an antiferromagnetic (AFM) ground state and each edge carbon atom has a finite local magnetic moment. This result demands that the number of unpaired electrons in a finite-sized ribbon increase with the ribbon length as the properties of acenes approach those of polyacene. We have observed this trend in finite-sized ZGNRs with a width index higher than two. 41 Because polyacene can be viewed as a ZGNR with a width index of two, one would expect that acenes will also have an increasing number of unpaired electrons with the number of fused rings if polyacene has an AFM ground state as well, thereby indicating that the diradical concept would be inaccurate for higher acenes. To show that this is indeed the case, in this paper we employ a spinpolarized density functional theory (DFT) method, which is less prone to spin contamination, 42 to first address the electronic ground state of polyacene and then that of acenes.
DFT calculations using the Vienna Ab Initio Simulation Package were performed, 43,44 based on planewave bases and periodic boundary conditions and within the generalized-gradient approximation for electron exchange and correlation. 45 Projector-augmented wave method was used within the frozen core approximation to describe the electron-core interaction. 46,47 Supercell models were employed; i.e., an acene molecule was put in a large box. The flat molecule was placed in the xy-plane (see Figure 1a).
The y and z dimensions of the boxes were fixed at 15 and 10 Å, respectively, while the x dimension increased from 23 Å for pentacene to 116 Å for 40-acene. Only the Γ-point was used to sample the Brillouin zone for the molecules. For polyacene, the unit cell is shown in Figure 1b. The x-dimension (i.e., the repeating length of the polymer) was optimized to be 2.461 Å, and 49 irreducible k-points were used to sample the Brillouin zone.
A kinetic energy cutoff (450 eV) was used, and all atoms in the supercell were allowed to relax and the force tolerance was set at 0.025 eV/Å. Full relaxation of magnetization was performed for spinpolarized calculations.
We started our investigation with polyacene. Although synthesis of polyacene has not been reported, numeral theoretical examinations exist and conflicting conclusions have been reached. 27,[48][49][50][51][52][53][54] Detailed discussion of previous literature about polyacene is documented in Ref. 57. Because we will address the electronic structures of polyacene in comparison with other polymers in greater detail in a forthcoming pu
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