Chapter 1
Open-Shell Benzenoid Polycyclic Hydrocarbons

Soumyajit Das and Jishan Wu

1.1 Introduction

Graphene has been found to be an attractive material since its discovery in 2004 and has drawn enormous interest among researchers owing to its intrinsic electronic and magnetic properties. An indefinitely large graphene sheet, if cut along the two edge directions, can generate two distinct, well-defined small graphene nanoribbons (GNRs), which may be classified into "zigzag" edge (1, trans-polyacetylene) and "armchair" edge (2, cis-polyacetylene) structures (Figure 1.1). If graphene is cut in an all-zigzag fashion or in a triangular shape, the smallest unit that would come out is a phenalene unit (3) with one unpaired electron. The larger frameworks when cut in a zigzag shape will indefinitely lead to a series of non-Kekulé (i.e., open-shell) polycyclic hydrocarbons (PHs, 4-6) possessing one or more unpaired electrons, which can be termed as "open-shell graphene fragments" and are very interesting in terms of academic research. The number of unpaired electrons, or radicals, increases with the size of the framework, starting from phenalenyl monoradical to high-spin polyradical systems (3-6, Figure 1.1). If a graphene sheet is cut in an all-armchair fashion, it would lead to "all-benzenoid PHs," as their structures can be represented as fully aromatic sextet rings (the six-membered rings highlighted in blue background) without additional double bonds (7). Even though the PHs of such category are larger in size with extended conjugation, they generally show high stability due to the stabilization through the existence of more number of Clar's aromatic sextets (8). The studies on hexa-peri-hexabenzocoronene and other extended all-benzenoid PHs have provided information on armchair-edged GNRs at the molecular level [1].

Figure 1.1 Molecular graphenes by fusion of benzene rings in different modes.

Another intriguing class of PHs would be rectangular-shaped GNRs, which are characterized by existence of both zigzag and armchair edges (9, Figure 1.1) with a typical Kekulé (i.e., closed-shell) structure. Their structures can be formulated by cycles in a monocyclic system symbolizing benzenoid aromatic sextet rings according to Clar's aromatic sextet rule [2]. Therefore, the more Clar's sextets the molecule can have, the more stable the system will be. Interestingly, recent theoretical and experimental work indicate that for rectangular PHs with extended zigzag edges, such as anthenes and periacenes, a remarkable open-shell diradical character will emerge when the conjugation is extended to a certain point (n > 0 for anthenes and m > 2 for periacenes), which originates from a narrowed bandgap and stabilization through more Clar's sextet rings in the diradical form (10, Figure 1.1). The molecule possesses more aromatic sextet rings in the diradical or poly-radical resonance forms and, if the recovered resonance energy can compensate the energy required to break a double bond, an open-shell singlet diradical or polyradical ground state could appear. Two very nice examples to validate such a statement are the teranthene and quarteranthene derivatives reported by Kubo et al., which will be discussed in following sections.

Most benzenoid PHs actually can be characterized by a closed-shell electronic configuration accommodating their p electrons only in bonding orbitals. However, researchers faced difficulties for certain types of PHs due to their high reactivity. An important work by Bendikov et al. came into spotlight in 2004 when their computational study on oligoacenes supported that the longer acenes possessed a nonzero bandgap with a singlet open-shell ground state followed by a higher energy triplet state [3]. The open-shell electronic configuration refers to the existence of one or more unpaired electrons, or radicals, in the molecular structure [4]. The electronic states of the open-shell systems with two unpaired electrons can be further divided into open-shell singlet, when the unpaired electrons adopt antiparallel spin, or open-shell triplet, when the unpaired electrons adopt parallel spin. Among all of the electronic states, the one with the lowest energy defines the ground state of p-conjugated systems. The high reactivity derived from open-shell nature of these systems in the ground state largely impedes their synthesis and isolation, but still continuous efforts have been made to synthesize and stabilize them due to the passion to understand the interplay of the unpaired electrons and delocalized p-electron systems and charge fluctuation, as well as the possibility of using them as molecule-based functional materials [5]. Therefore, the ground state can now be systematically studied by various spectroscopic techniques including nuclear magnetic resonance (NMR), electron spin resonance (ESR), ultraviolet-visible-near infrared spectroscopy (UV-vis-NIR), Raman spectroscopy, X-ray crystallographic analysis, and superconducting quantum interfering device (SQUID) measurements, assisted by density functional theory (DFT) calculations.

Theoretically, the diradical character (y) (0 < y < 1, where 0 = closed-shell, 1 = open-shell) can be estimated by the extent of the mixing of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) in the ground state [6]. The occupation number of the LUMO is used as an index of the diradical character, which can be estimated by a complete active space self-consistent field (CASSCF) calculation using the restricted Hartree-Fock (RHF) and two-configuration self-consistent field (SCF) calculations considering the Coulombic interaction between two unpaired electrons permitted to occupy the different parts is space. Another approach [7] is the broken-symmetry (BS) formalism based on the unrestricted Hartree-Fock (UHF) wave function, which defines the occupation number of the lowest unoccupied natural orbital (LUNO) as the extent of the diradical character [8]. This method was further revised by applying a spin-projection method to discard the spin contamination problem [9]. The diradical character can be also evaluated experimentally using the following formula [10], recently proposed by Kamada et al.:

where ES1u,S1g and ES2g,S1g correspond to the energy of the lowest energy peaks in the one- and two-photon absorption (TPA) spectra, and ET1u,S1g corresponds to the energy gap between the triplet and the singlet ground state.

The synthesis and study of open-shell PHs have become a rising hot topic nowadays, so we aim to provide a brief overview on recent advancements including theoretical studies and experimental characterizations of a series of benzenoid PH-based diradicaloids comprising higher order acenes, bis(phenalenyl)s, zethrenes, anthenes, and periacenes, p-extended p-quinodimethane, and triangulene-based triplet biradicals.

1.2 Higher Order Acenes

Acenes can be regarded as one-dimensional fragments of graphene and belong to a class of PHs consisting of linearly fused benzene rings. The small acenes, namely naphthalene and anthracene, are among the most widely studied organic molecules, while the fascinating electronic properties of pentacene and higher order acenes larger than pentacene [11] have received considerable attention [12]. Pentacene has a closed-shell singlet (CS) ground state and has been the center of attention among the materials scientists as an effective organic semiconducting material in organic field-effect transistors (OFETs) because of its potentially high charge-carrier mobility. Synthesis of acenes larger than pentacene is, however, hampered by their increased reactivity as the number of rings increases [13]. Significant efforts had been devoted to the development of appropriate methods, albeit tedious, for the synthesis of larger stable acenes, which was quite challenging because of their very low solubility, poor light and oxygen stability, and their tendency to dimerize [14]. Despite of challenges, noteworthy progress has been made in the synthesis of larger acenes in recent years. The electronic properties, aromaticity, and HOMO-LUMO gaps of larger acenes have been examined extensively using computational techniques [12a], but we will be highlighting their "open-shell" characteristics.

The open-shell feature of acenes can be symbolized by the chemical structure of acenes (as exemplified by pentacene 11 in Figure 1.2) in either a closed-shell Kekulé form (11) with only one aromatic sextet ring, or a diradical (17a)/tetraradical (17b) form with two or three aromatic sextet rings. The extra aromatic rings can help to compensate the energy loss from p-bond cleavage and enhance the open-shell contribution to the ground state. Studies have revealed that linear oligoacenes possess the CS ground state, and only those larger than hexacene are expected to have open-shell diradical character in their ground states but these are still not completely understood and a large controversy was raised from the ground-state multiplicities of larger oligoacenes. Calculations on the ground state of higher order...