Open-Shell Graphene Fragments

Abstract

Materials based on carbon allotropes such as amorphous carbon, graphite, and diamond play an important role in our daily life. Applications in the fields of electronics, photonics, spintronics, and quantum information technology are sought after. Recently, particularly magnetically active carbons have emerged as a new type of materials because of their unique magnetic properties and promising applications for room-temperature magnets, spintronics, and quantum devices. Bottom-up synthesis of well-defined magnetic carbons thus became crucial, and systematic discussion of the fundamental design principles of various open-shell graphene fragments and their syntheses, as well as highlighting the importance of the zigzag edge structure and local aromaticity is enabling further development of this area of research. The electronic properties of finite-sized graphene fragments are strongly dependent on their topological structures. The existence of two or more extended zigzag edges could lead to unique open-shell character and magnetic activity. In this review, various types of well-defined graphene nanoribbons, nanographenes, and graphene-like molecules with open-shell character are summarized. Particularly, chemistry and electronic properties of graphene fragments with one, two, and three pairs of parallel zigzag edges, zethrenes with quinoidal structures, and [n]triangulenes with three zigzag edges are discussed in detail. Synthesis of this kind of open-shell molecules is very challenging, and both solution-phase and on-surface chemistry have been used. Their radical characters can be simply predicted in terms of Clar’s sextets and quantitatively analyzed by spin-unrestricted density functional theory or multireference quantum mechanical calculations. Their unique magnetic activity and quantum properties would render them promising materials for all carbon-based spintronic and quantum devices. The electronic properties of finite-sized graphene fragments are strongly dependent on their topological structures. The existence of two or more extended zigzag edges could lead to unique open-shell character and magnetic activity. In this review, various types of well-defined graphene nanoribbons, nanographenes, and graphene-like molecules with open-shell character are summarized. Particularly, chemistry and electronic properties of graphene fragments with one, two, and three pairs of parallel zigzag edges, zethrenes with quinoidal structures, and [n]triangulenes with three zigzag edges are discussed in detail. Synthesis of this kind of open-shell molecules is very challenging, and both solution-phase and on-surface chemistry have been used. Their radical characters can be simply predicted in terms of Clar’s sextets and quantitatively analyzed by spin-unrestricted density functional theory or multireference quantum mechanical calculations. Their unique magnetic activity and quantum properties would render them promising materials for all carbon-based spintronic and quantum devices. So far, most reported π-conjugated molecules with an even number of π-electrons have a closed-shell ground electronic states; that means, all the frontier π-electrons are strongly bonded and paired. However, recent studies demonstrated that a number of pro-aromatic and anti-aromatic molecules and polycyclic aromatic hydrocarbons (PAHs) with extended zigzag edges could display a unique open-shell radical character.1Abe M. Diradicals.Chem. Rev. 2013; 113: 7011-7088Crossref PubMed Scopus (708) Google Scholar, 2Sun Z. Zeng Z. Wu J. Zethrenes, extended p-quinodimethanes, and periacenes with a singlet biradical ground state.Acc. Chem. Res. 2014; 47: 2582-2591Crossref PubMed Scopus (255) Google Scholar, 3Nakano M. Excitation Energies and Properties of Open-Shell Singlet Molecules. Springer, 2014Crossref Google Scholar, 4Zeng Z. Shi X. Chi C. López Navarrete J.T. Casado J. Wu J. Pro-aromatic and anti-aromatic π-conjugated molecules: an irresistible wish to be diradicals.Chem. Soc. Rev. 2015; 44: 6578-6596Crossref PubMed Google Scholar, 5Kubo T. Recent progress in quinoidal singlet biradical molecules.Chem. Lett. 2015; 44: 111-122Crossref Scopus (164) Google Scholar, 6Nakano M. Electronic structure of open-shell singlet molecules: diradical character viewpoint.Top. Curr. Chem. 2017; 375: 47Crossref Scopus (19) Google Scholar, 7Gopalakrishna T.Y. Zeng W. Lu X. Wu J. From open-shell singlet diradicaloids to polyradicaloids.Chem. Commun. (Camb). 2018; 54: 2186-2199Crossref PubMed Google Scholar, 8Liu C. Ni Y. Lu X. Li G. Wu J. Global aromaticity in macrocyclic polyradicaloids: Hückel’s rule or Baird’s rule?.Acc. Chem. Res. 2019; 52: 2309-2321Crossref PubMed Scopus (0) Google Scholar, 9Stuyver T. Chen B. Zeng T. Geerlings P. De Proft F. Hoffmann R. Do diradicals behave like radicals?.Chem. Rev. 2019; 119: 11291-11351Crossref PubMed Scopus (62) Google Scholar In spin-unrestricted calculations of these molecules, the solution of the open-shell singlet lies below the closed-shell singlet in energy, thus defining the open-shell singlet ground state. This type of molecules displays diradical-like behavior and thus is called as the open-shell singlet diradicaloid. The history of diradicaloids can be dated back to 1907 when Tschitschibabin reported a quinoidal hydrocarbon which is now named as Tschitschibabin’s hydrocarbon (1, Figure 1).10Tschitschibabin A.E. Über einige phenylierte derivate des p, p-ditolyls.Ber. Dtsch. Chem. Ges. 1907; 40: 1810-1819Crossref Scopus (0) Google Scholar,11Montgomery L.K. Huffman J.C. Jurczak E.A. Grendze M.P. The molecular structures of Thiele's and Chichibabin's hydrocarbons.J. Am. Chem. 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On the biradicaloid nature of long quinoidal oligothiophenes: experimental evidence guided by theoretical studies.Angew. Chem. Int. Ed. Engl. 2007; 46: 9057-9061Crossref PubMed Scopus (105) Google Scholar were found to show similar open-shell radical character (see a historical introduction in Gopalakrishna et al.7Gopalakrishna T.Y. Zeng W. Lu X. Wu J. From open-shell singlet diradicaloids to polyradicaloids.Chem. Commun. (Camb). 2018; 54: 2186-2199Crossref PubMed Google Scholar). The past 20 years witnessed a rapid growth of the relatively stable open-shell singlet molecules, which allowed systematic investigation of their unique optical, electronic, and magnetic properties.1Abe M. Diradicals.Chem. Rev. 2013; 113: 7011-7088Crossref PubMed Scopus (708) Google Scholar, 2Sun Z. Zeng Z. Wu J. Zethrenes, extended p-quinodimethanes, and periacenes with a singlet biradical ground state.Acc. Chem. Res. 2014; 47: 2582-2591Crossref PubMed Scopus (255) Google Scholar, 3Nakano M. Excitation Energies and Properties of Open-Shell Singlet Molecules. Springer, 2014Crossref Google Scholar, 4Zeng Z. Shi X. Chi C. López Navarrete J.T. Casado J. Wu J. Pro-aromatic and anti-aromatic π-conjugated molecules: an irresistible wish to be diradicals.Chem. Soc. Rev. 2015; 44: 6578-6596Crossref PubMed Google Scholar, 5Kubo T. Recent progress in quinoidal singlet biradical molecules.Chem. Lett. 2015; 44: 111-122Crossref Scopus (164) Google Scholar, 6Nakano M. Electronic structure of open-shell singlet molecules: diradical character viewpoint.Top. Curr. Chem. 2017; 375: 47Crossref Scopus (19) Google Scholar, 7Gopalakrishna T.Y. Zeng W. Lu X. Wu J. From open-shell singlet diradicaloids to polyradicaloids.Chem. Commun. (Camb). 2018; 54: 2186-2199Crossref PubMed Google Scholar, 8Liu C. Ni Y. Lu X. Li G. Wu J. Global aromaticity in macrocyclic polyradicaloids: Hückel’s rule or Baird’s rule?.Acc. Chem. Res. 2019; 52: 2309-2321Crossref PubMed Scopus (0) Google Scholar, 9Stuyver T. Chen B. Zeng T. Geerlings P. De Proft F. Hoffmann R. Do diradicals behave like radicals?.Chem. Rev. 2019; 119: 11291-11351Crossref PubMed Scopus (62) Google Scholar Although the open-shell radical character can be qualitatively estimated based on the resonance structures with Clar’s sextet rule and aromaticity, a quantitative measure is necessary for a better understanding of the electronic structures and physical properties of open-shell singlet molecules. The theoretical treatments of diradicaloids were reported as early as in the 1970s and the weight of double excitation was proposed as the measure of diradical character.20Hayes E.F. Siu A.K.Q. Electronic structure of the open forms of three-membered rings.J. Am. Chem. Soc. 1971; 93: 2090-2091Crossref Scopus (143) Google Scholar, 21Salem L. Rowland C. The electronic properties of diradicals.Angew. Chem. Int. Ed. Engl. 1972; 11: 92-111Crossref Scopus (928) Google Scholar, 22Flynn C.R. 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Chem. 2017; 375: 47Crossref Scopus (19) Google Scholar Herein, we give a brief introduction to the electronic structure of open-shell singlet diradicaloids and the relationships between the diradical character and physical properties. For more detailed computational analysis, interested readers are referred to the related reviews.3Nakano M. Excitation Energies and Properties of Open-Shell Singlet Molecules. Springer, 2014Crossref Google Scholar,6Nakano M. Electronic structure of open-shell singlet molecules: diradical character viewpoint.Top. Curr. Chem. 2017; 375: 47Crossref Scopus (19) Google Scholar,9Stuyver T. Chen B. Zeng T. Geerlings P. De Proft F. Hoffmann R. Do diradicals behave like radicals?.Chem. Rev. 2019; 119: 11291-11351Crossref PubMed Scopus (62) Google Scholar In a simple two-site model with two electrons in two atomic orbitals, the diradical character can be regarded as an index to describe the effect bond order. In a pure diradical, the coupling between the two radicals is very weak; while in a closed-shell molecule, the bonding is strong. Therefore, the diradicaloid refers to an intermediate bonding state. In the spin-unrestricted calculations, the ground-state broken-symmetry (BS) wavefunction ΨBS can be expressed in three terms, the singlet ground-state determinant (ψG), the triplet determinant (ψT), and the singlet double excited determinant (ψD). Yamaguchi applied the perfect-pairing type spin-projection scheme to the BS solution and developed an easy evaluation method of diradical character y0, which is defined as twice the weight of the double-excitation configuration and is equal to the occupation number of the lowest unoccupied natural orbital (LUNO) of the spin-projected wavefunction.23Yamaguchi K. The electronic structures of biradicals in the unrestricted Hartree-Fock approximation.Chem. Phys. Lett. 1975; 33: 330-335Crossref Scopus (298) Google Scholar,24Yamaguchi K. Instability in chemical bonds: SCF, APUMP, APUCC, MR-CI AND MR-CC approaches.in: Carbo R. Klobukowski M. Self-Consistent Field: Theory and Applications. Elsevier, 1990: 727-828Google Scholar The expression can be extended to a 2n-radical system (Figure 2A), and the multiple diradical characters yi can be formally expressed in Equation 1:yi=nLUNO+i=1−2Ti1+Ti2(Equation 1) where Ti is the orbital overlap between the corresponding orbital pairs (i.e., HONO-i and LUNO+i, i = 0,1,2,…). The ground and excited states of open-shell singlet diradicaloids can be analyzed by the valence configuration interaction (VCI) method.25Nakano M. Champagne B. Theoretical design of open-shell singlet molecular systems for nonlinear optics.J. Phys. Chem. Lett. 2015; 6: 3236-3256Crossref Scopus (110) Google Scholar, 26Nakano M. Champagne B. Nonlinear optical properties in open-shell molecular systems.Wiley Interdiscip Rev Comput Mol Sci. 2016; 6: 198-210Crossref PubMed Scopus (39) Google Scholar, 27Nakano M. Open-shell-character-based molecular design principles: applications to nonlinear optics and singlet fission.Chem. Rec. 2017; 17: 27-62Crossref PubMed Scopus (81) Google Scholar For a symmetric two-site diradical system, diagonalizing the CI matrix gave four solutions: a neutral triplet state with u symmetry and pure covalent character (T1u), an ionic singlet state with u symmetry (S1u), a lower singlet state with g symmetry (S1g), and a higher singlet state with g symmetry (S2g) (Figure 2B). The state S1g has a larger weight of neutral determinant than that of ionic one, while state S2g has a larger weight of ionic determinant than that of a neutral one. The diradical character y0 can be expressed by Equation 2:y0=1−11+(U4tab)2(Equation 2) where U represents the difference between on- and neighbor-site Coulomb repulsions and tab is transferred integral. As increasing |U/tab|, y0 value is shown to increase from 0 to 1, which corresponds to |U/tab| ≤ ~1 and |U/tab| → ∞, respectively. From the physical meaning of the transfer integral tab and the effective Coulomb repulsion U, y0 → 1 at |U/tab| → ∞ implies the localization of electrons on each site, i.e., a pure diradical state, while y0 → 0 at |U/tab| ≤ ~1 implies the delocalization of electrons over two sites, i.e., a closed-shell stable bond state. The diradical character y0 can be also correlated to the excitation energies according to Equation 3:y0=1−1−(E1u1−E1u3E2g1−E1g1)2=1−1−(ES1u,S1g−ET1u,S1gES2g,S1g)2(Equation 3) where ES2g,S1g, ES1u,S1g, and ET1u,S1g represent the excitation energies of higher singlet state with g symmetry (two-photon allowed excited state), of lower singlet state with u symmetry (one-photon allowed excited state), and of triplet state with u symmetry, respectively. ES1u,S1g and ES2g,S1g can be estimated from the lowest-energy peaks of the one- and two-photon absorption spectra, respectively, while ET1u,S1g can be obtained from phosphorescence, or electron spin resonance (ESR), or superconducting quantum interference device (SQUID) measurements. Therefore, this relationship enables us to estimate the diradical character experimentally. Spin-unrestricted density functional theory (UDFT) as a mono-reference method in principle is not suitable for handling strongly correlated electrons. On the other hand, the complete active-space self-consistent field (CASSCF) method is too expensive to deal with large-size molecules. Recently, the restricted active-space spin-flip method (RAS-SF) as a multi-configurational method turned out to be a good approach to calculate the radical characters and excitation energies of open-shell singlet diradicaloids.28Casanova D. Head-Gordon M. 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As to OPA, one common observation for many open-shell singlet diradicaloids is the appearance of a weak low-energy shoulder in the measured absorption spectra, which was explained by the presence of a low-lying double exciton state.30Di Motta S.D. Negri F. Fazzi D. Castiglioni C. Canesi E.V. Biradicaloid and polyenic character of quinoidal oligothiophenes revealed by the presence of a low-lying double-exciton state.J. Phys. Chem. Lett. 2010; 1: 3334-3339Crossref Scopus (106) Google Scholar This feature almost becomes a fingerprint of open-shell singlet molecules. As to TPA, Nakano et al. first predicted that the third-order NLO properties would be drastically enhanced in symmetric open-shell diradical systems with intermediate diradical character,31Nakano M. Nagao H. Yamaguchi K. Many-electron hyperpolarizability density analysis: application to the dissociation processof one-dimensional H2S.Phys. Rev. A. 1997; 55: 1503-1513Crossref Scopus (73) Google Scholar, 32Nakano M. Kishi R. 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Nakano et al. also theoretically correlated the multiple diradical character yi with the singlet fission process,38Minami T. Nakano M. Diradical character view of singlet fission.J. Phys. Chem. Lett. 2012; 3: 145-150Crossref Scopus (177) Google Scholar which was demonstrated by using a series of zethrene based diradicaloids.39Lukman S. Richter J.M. Yang L. Hu P. Wu J. Greenham N.C. Musser A.J. Efficient singlet fission and triplet-pair emission in a family of zethrene diradicaloids.J. Am. Chem. Soc. 2017; 139: 18376-18385Crossref PubMed Scopus (66) Google Scholar One common feature for most open-shell singlet diradicaloids is their low-lying triplet state, which allows experimental observation of the thermally populated triplet species. The singlet-triplet gap (ΔEST = ES − ET) can be experimentally estimated by variable temperature (VT) ESR and SQUID measurements. In many examples, the larger diradical character would lead to a small ΔEST value. However, it should be mentioned that the relationship between the y0 and ΔEST is not so simple, and other factors such as the HOMO-LUMO energy gap and spatial distribution of the frontier molecular orbitals play important roles.40Huang R. Phan H. Herng T.S. Hu P. Zeng W. Dong S.Q. Das S. Shen Y. Ding J. Casanova D. Wu J. Higher order π-conjugated polycyclic hydrocarbons with open-shell singlet ground state: nonazethrene versus nonacene.J. Am. Chem. Soc. 2016; 138: 10323-10330Crossref PubMed Scopus (73) Google Scholar,41Dressler J.J. Teraoka M. Espejo G.L. Kishi R. Takamuku S. Gómez-García C.J. Zakharov L.N. Nakano M. Casado J. Haley M.M. Thiophene and its sulfur inhibit indenoindenodibenzothiophene diradicals from low-energy lying thermal triplets.Nat. Chem. 2018; 10: 1134-1140Crossref PubMed Scopus (55) Google Scholar As a general design strategy, pro-aromatic (mainly quinoidal structures) and anti-aromatic molecules are studied in many cases due to their intrinsic tendency to become diradicals via aromatic stabilization.4Zeng Z. Shi X. Chi C. López Navarrete J.T. Casado J. Wu J. Pro-aromatic and anti-aromatic π-conjugated molecules: an irresistible wish to be diradicals.Chem. Soc. Rev. 2015; 44: 6578-6596Crossref PubMed Google Scholar In addition, steric repulsion can also serve as a driving force to push sterically crowded molecules into open-shell diradicals by releasing strain.42Zeng Z. Ishida M. Zafra J.L. Zhu X. Sung Y.M. Bao N. Webster R.D. Lee B.S. Li R.W. Zeng W. et al.Pushing extended p-quinodimethanes to the limit: stable tetracyano-oligo(N-annulated perylene)quinodimethanes with tunable ground states.J. Am. Chem. 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Electronic structure of open-shell singlet molecules: diradical character viewpoint.Top. Curr. Chem. 2017; 375: 47Crossref Scopus (19) Google Scholar, 7Gopalakrishna T.Y. Zeng W. Lu X. Wu J. From open-shell singlet diradicaloids to polyradicaloids.Chem. Commun. (Camb). 2018; 54: 2186-2199Crossref PubMed Google Scholar, 8Liu C. Ni Y. Lu X. Li G. Wu J. Global aromaticity in macrocyclic polyradicaloids: Hückel’s rule or Baird’s rule?.Acc. Chem. Res. 2019; 52: 2309-2321Crossref PubMed Scopus (0) Google Scholar, 9Stuyver T. Chen B. Zeng T. Geerlings P. De Proft F. Hoffmann R. Do diradicals behave like radicals?.Chem. Rev. 2019; 119: 11291-11351Crossref PubMed Scopus (62) Google Scholar the current review will mainly discuss a type of graphene fragments with open-shell radical character. Their electronic properties are found to be strongly dependent on their topological structures, namely, size and edge structure. This type of topological materials is particularly useful for spintronics, magnets, and quantum devices, and thus are highlighted in this review. Theoretical studies predict that the electronic states of finite-sized graphene fragments in a nanometer length are strongly dependent on the peripheral shape.43Fujita M. Wakabayashi K. Nakada K. Kusakabe K. Peculiar localized state at zigzag graphite edge.J. Phys. Soc. Jpn. 1996; 65: 1920-1923Crossref Scopus (2267) Google Scholar,44Nakada K. Fujita M. Dresselhaus G. Dresselhaus M.S. Edge state in graphene ribbons: nanometer size effect and edge shape dependence.Phys. Rev. B. 1996; 54: 17954-17961Crossref PubMed Google Scholar Zigzag graphene nanoribbons (ZGNRs) are always metallic or half-metallic, with peculiar localized edge states along the two trans-polyacetylene (PA) zigzag edges (Figure 3A).45Son Y.W. Cohen M.L. Louie S.G. 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