Spin-spin and spin-orbit interactions in nanographene fragments: a quantum chemistry approach

The relativistic behavior of graphene structures, starting from the fundamental building blocks--the poly-aromatic hydrocarbons (PAHs) along with other PAH nanographenes--is studied to quantify any associated intrinsic magnetism in the triplet (T) state and subsequently in the ground singlet (S) state with account of possible S-T mixture induced by spin-orbit coupling (SOC). We employ a first principle quantum chemical-based approach and density functional theory (DFT) for a systematic treatment of the spin-Hamiltonian by considering both the spin-orbit and spin-spin interactions as dependent on different numbers of benzene rings. We assess these relativistic spin-coupling phenomena in terms of splitting parameters which cause magnetic anisotropy in absence of external perturbations. Possible routes for changes in the couplings in terms of doping and defects are also simulated and discussed. Accounting for the artificial character of the broken-symmetry solutions for strong spin polarization of the so-called "singlet open-shell" ground state in zigzag graphene nanoribbons predicted by spin-unrestricted DFT approaches, we interpolate results from more sophisticated methods for the S-T gaps and spin-orbit coupling (SOC) integrals and find that these spin interactions become weak as function of size and increasing decoupling of electrons at the edges. This leads to reduced electron spin-spin interaction and hence almost negligible intrinsic magnetism in the carbon-based PAHs and carbon nanographene fragments. Our results are in agreement with the fact that direct experimental evidence of edge magnetism in pristine graphene has been reported so far. We support the notion that magnetism in graphene only can be ascribed to structural defects or impurities.     

A Peri‐tetracene Diradicaloid: Synthesis and Properties

Peri‐acenes are good model compounds for zigzag graphene nanoribbons, but their synthesis is extremely challenging owing to their intrinsic open‐shell diradical character. Now, the successful synthesis and isolation of a stable peri‐tetracene derivative PT‐2ClPh is reported; four 2,6‐dichlorophenyl groups are attached onto the most reactive sites along the zigzag edges. The structure was confirmed by X‐ray crystallographic analysis and its electronic properties were systematically investigated by both experiments and theoretical calculations. It exhibits an open‐shell singlet ground state with a moderate diradical character (y₀=51.5 % by calculation) and a small singlet–triplet gap (ΔE_S‐T=?2.5 kcal mol^?1 by SQUID measurement). It displays global aromatic character, which is different from the smaller‐size bisanthene analogue BA‐CF3 .     

Length-Dependent Magnetic Evolution of Anthenes on Au(111)

Nanographenes with zigzag edges, for example, anthenes, exhibit a unique nonbonding π-electron state, which can be described as a spin-polarized edge state that yields specific magnetic ground state. However, prior researches on the magnetism of anthenes with varying lengths on a surface is lacking. This study systematically fabricated anthenes with inherent zigzag carbon atoms of different lengths ranging from bisanthene to hexanthene. Their magnetic evolution on the Au(111) surface was analyzed through bond-resolved scanning probe techniques and density functional theory calculations. The analyses revealed a transition in magnetic properties associated with the length of the anthenes, arising from the imbalance between hybridization energy and the Coulomb repulsion between valence electrons. With the increasing length of the anthenes, the ground state transforms gradually from a closed-shell to an antiferromagnetic open-shell singlet, exhibiting a weak exchange coupling of 4 meV and a charge transfer-induced doublet. Therefore, this study formulated a chemically tunable platform to explore size-dependent π magnetism at the atomic scale, providing a framework for research in organic spintronics.     

A comparison of singlet and triplet states for one- and two-dimensional graphene nanoribbons using multireference theory

This study examines the radical nature and spin symmetry of the ground state of the quasi-linear acene and two-dimensional periacene series. For this purpose, high-level ab initio calculations have been performed using the multireference averaged quadratic coupled cluster theory and the COLUMBUS program package. A reference space consisting of restricted and complete active spaces is taken for the π-conjugated space, correlating 16 electrons with 16 orbitals with the most pronounced open-shell character for the acenes and a complete active-space reference approach with eight electrons in eight orbitals for the periacenes. This reference space is used to construct the total configuration space by means of single and double excitations. By comparison with more extended calculations, it is shown that a focus on the π space with a 6-31G basis set is sufficient to describe the major features of the electronic character of these compounds. The present findings suggest that the ground state is a singlet for the smaller members of these series, but that for the larger ones, singlet and triplet states are quasi-degenerate. Both the acenes and periacenes exhibit significant polyradical character beyond the traditional diradical.     

Triplet states of zigzag edged hexagonal graphene molecules C(6m∗∗2)H(6m) (m = 1, 2, 3, ..., 10) and carbon based magnetism

The geometry and magnetization (spin distribution) of the series of flat hexagonal zigzag edged molecules C(6m??2)H(6m) (m = 1,2, ..., 10) in their lowest triplet state (S(z) = 1) has been calculated using density functional theory and a connection established from the known benzene (m = 1) triplets to the triplets and singlet ground state of the largest molecules (m = 9, 10). The triplet state potential energy surface has two minima corresponding to distortions from the ground state geometry, such that CC bonds bisected by a C(2)" rotation axis are either longer or shorter. For both geometries, the spin on the carbon atoms forms a pattern that peaks at the middle of an edge and for large index (m) values is the same (apart from sign) as the edge pattern of the hexagonally sectored singlet radical ground state of the largest member C(600)H(60). This similarity suggests that the singlet ground state of the larger (m = 9, 10) zigzag edged hexangulenes is possibly a hex-radical, in some ways analogous to the di- and higher multiradical ground state of the linear acenes C(4m + 2)H(2m + 4) starting around m ≥ 8 and 9. The spin patterns provide guidance in interpreting the multiradical nature of ground and low lying excited states of large hexangulenes and how magnetism evolves with size in molecules with graphene cores.     

First principles study of magnetism in nanographenes

Magnetism in nanographenes [also known as polycyclic aromatic hydrocarbons (PAHs)] is studied with first principles density functional calculations. We find that an antiferromagnetic (AFM) phase appears as the PAH reaches a certain size. This AFM phase in PAHs has the same origin as the one in infinitely long zigzag-edged graphene nanoribbons, namely, from the localized electronic state at the zigzag edge. The smallest PAH still having an AFM ground state is identified. With increased length of the zigzag edge, PAHs approach an infinitely long ribbon in terms of (1) the energetic ordering and difference among the AFM, ferromagnetic, and nonmagnetic phases and (2) the average local magnetic moment at the zigzag edges. These PAHs serve as ideal targets for chemical synthesis of nanographenes that possess magnetic properties. Moreover, our calculations support the interpretation that experimentally observed magnetism in activated carbon fibers originates from the zigzag edges of the nanographenes.     

The radical character of the acenes: a density matrix renormalization group study

We present a detailed investigation of the acene series using high-level wave function theory. Our ab initio density matrix renormalization group algorithm has enabled us to carry out complete active space calculations on the acenes from napthalene to dodecacene correlating the full pi-valence space. While we find that the ground state is a singlet for all chain lengths, examination of several measures of radical character, including the natural orbitals, effective number of unpaired electrons, and various correlation functions, suggests that the longer acene ground states are polyradical in nature.     

Oligoacenes: theoretical prediction of open-shell singlet diradical ground states

A series of oligoacenes from benzene to decacene were studied computationally with DFT and CASSCF methods. In contrast to the common view that acenes are closed-shell systems or may have a triplet ground state, these results offer the first theoretical predictions for the singlet ground state and diradical character for oligoacenes. The nature of the ground states of these molecules arises from the disjoint nature of the NBMOs that are singly occupied in the diradical.     

Polyacene and cyclacene geometries and electronic structures: bond equalization, vanishing band gaps, and triplet ground states contrast with polyacetylene

The ground-state geometries and excited singlet and lowest triplet energies of polyacenes from benzene through nonacene are predicted with B3LYP/6-31G* calculations and compared to experimental data where available. The results are compared to these data for cyclacenes and polyenes. The polyacenes and cyclacenes have geometries consisting of two fully delocalized nonalternating ribbons joined by relatively long bonds. Polyacenes are predicted to have smaller band gaps than the corresponding polyenes and triplet ground states for nine or more benzene rings. The fully delocalized nonalternating nature of polyacenes differs from the bond alternation resulting from Peierls distortion in polyenes. The differences are rationalized in terms of a simple MO model, and the results are compared to extensive prior theoretical work in the literature. Predictions about the electronic structure of analogues containing polyacene units are made.     

Topological analysis of the electron density and of the electron localization function of pyrene and its radicals

The topological properties of the charge distribution of pyrene and the three derived monoradicals in their ground state and of didehydrogenated pyrenes in the lowest singlet and triplet electronic states are discussed in detail by means of the quantum theory of atoms in molecules (TAIM) and by the electron localization function (ELF). The non-equivalence of the fused aromatic rings of pyrene prevents one from anticipating the stability and reactivity of these species from the chemistry of didehydrogenated species derived from benzene only. Whereas some of these didehydrogenated molecules were found to display a diradical character in the singlet ground state, the topological analysis reveals that others correspond to normal closed shells. Using these theoretical tools, the energetic and geometric details of o-, m- and p-benzyne-like pyrene derivatives are explained.     

A Unified Mechanism on the Formation of Acenes,Helicenes, and Phenacenes in the Gas Phase

A unified low-temperature reaction mechanism on the formation of acenes, phenacenes, and helicenes—polycyclic aromatic hydrocarbons (PAHs) that are distinct via the linear, zigzag, and ortho-condensed arrangements of fused benzene rings—is revealed. This mechanism is mediated through a barrierless, vinylacetylene mediated gas-phase chemistry utilizing tetracene, [4]phenacene, and [4]helicene as benchmarks contesting established ideas that molecular mass growth processes to PAHs transpire at elevated temperatures. This mechanism opens up an isomer-selective route to aromatic structures involving submerged reaction barriers, resonantly stabilized free-radical intermediates, and systematic ring annulation potentially yielding molecular wires along with racemic mixtures of helicenes in deep space. Connecting helicene templates to the Origins of Life ultimately changes our hypothesis on interstellar carbon chemistry.     

Quenching of local magnetic moment in oxygen adsorbed graphene nanoribbons

The electronic and magnetic properties of oxidized zigzag and armchair graphene nanoribbons, with hydrogen passivated edges, have been investigated from ab initio pseudopotential calculations within the density functional scheme. The oxygen molecule in its triplet state is adsorbed most stably at the edge of a zigzag nanoribbon. The Stoner metallic behavior of the ferromagnetic nanoribbons and the Slater insulating (ground state) behavior of the antiferromagnetic nanoribbons remain intact upon oxygen adsorption. The formation of a spin-paired C-O bond drastically reduces the local atomic magnetic moment of carbon at the edge of the ferromagnetic zigzag ribbon.     

Kekulé versus Lewis: When Aromaticity Prevents Electron Pairing and Imposes Polyradical Character

Some conjugated alternant hydrocarbons, of singlet ground state according to Ovchinnikov’s rule, may exhibit strong polyradical character, despite admitting complete pairing of electrons in bond orbitals between adjacent atoms. Typical organizations of this kind are encountered in polycyclic frames supporting two or more extracyclic methylene groups. Lewis bond pairing would require quinonization of six‐membered rings, whereas safeguarding aromaticity proves sufficient to impose ground‐state open‐shell character, that is, the existence of unpaired electrons, providing the number of benzene rings to be quinonized is larger than two. Several examples built as variations around para‐polyphenylene frames are examined through unrestricted DFT (UDFT) calculations, using various methods for spin decontamination of wavefunctions, geometries, and singlet–triplet energy gaps. They all illustrate how it is possible to conceive architectures that can be written with a closed‐shell bond pairing, although they exhibit a large number of unpaired electrons. The same analyses also apply to systems in which quinonization would not kill but only reduce the number of unpaired electrons.     

Pushing the Limits of Acene Chemistry: The Recent Surge of Large Acenes

Acenes, consisting of linearly fused benzene rings, are an important fundamental class of organic compounds with various applications. Hexacene is the largest acene that was synthesized and isolated in the 20th century. The next largest member of the acene family, heptacene, was observed in 2007 and since then significant progress in preparing acenes has been reported. Significantly larger acenes, up to undecacene, could be studied by means of low-temperature matrix isolation spectroscopy with in situ photolytic generation, and up to dodecacene by means of on-surface synthesis employing innovative precursors and highly defined crystalline metal surfaces under ultrahigh vacuum conditions. The review summarizes recent experimental and theoretical advances in the area of acenes that give a significantly deeper insight into the fundamental properties and nature of the electronic structure of this fascinating class of organic compounds.     

Magnetic Properties of Acenes and Their <Emphasis Type="Italic">o</Emphasis>-Quinone Derivatives: Computer Simulation

Quantum chemical study (DFT UB3LYP/6-311++G(d,p)) of the structure and properties of acenes functionalized with two o-benzoquinone groups and their complexes with sodium cations has been performed. An increase in the number of fused rings has been shown to result in the stabilization of biradicaloid state of acenes and the switching of the character of exchange interactions between redox-active moieties from antiferromagnetic to ferromagnetic. The obtained results allow one to consider o-quinone acene derivatives as a basis for designing magnetoactive compounds.     

A Unified Mechanism on the Formation of Acenes,Helicenes, and Phenacenes in the Gas Phase

A unified low‐temperature reaction mechanism on the formation of acenes, phenacenes, and helicenes—polycyclic aromatic hydrocarbons (PAHs) that are distinct via the linear, zigzag, and ortho‐condensed arrangements of fused benzene rings—is revealed. This mechanism is mediated through a barrierless, vinylacetylene mediated gas‐phase chemistry utilizing tetracene, [4]phenacene, and [4]helicene as benchmarks contesting established ideas that molecular mass growth processes to PAHs transpire at elevated temperatures. This mechanism opens up an isomer‐selective route to aromatic structures involving submerged reaction barriers, resonantly stabilized free‐radical intermediates, and systematic ring annulation potentially yielding molecular wires along with racemic mixtures of helicenes in deep space. Connecting helicene templates to the Origins of Life ultimately changes our hypothesis on interstellar carbon chemistry.     

The Antiferromagnetic Spin Coupling in Non‐Kekulé Acenes—Impressive Polyradical Character Revealed by High‐Level Multireference Methods

Complete active space (CASSCF) and multireference (MR‐CISD(Q) and MR‐AQCC) calculations were performed for non‐Kekulé analogues of acenes, dimethylenepolycyclobutadienes, with lengths of up to eight cyclobutadiene (CBD) units. Multireference calculations predict that the most stable energy state of the system is either triplet (if there is an odd number of CBD units) or singlet (if there is an even number of CBD units) due to antiferromagnetic spin coupling, which thus violates Hund's rule in larger molecules. We also show an impressive polyradical character in the system that increases with the size of the molecule, as witnessed by more than eleven unpaired electrons in the singlet state of the molecule with eight CBD units. Together with the small energy gap between singlet and higher multiplicity energy states even above the triplet state, this demonstrates the exceptional polyradical properties of these π‐conjugated oligomeric chains.     

石墨烯条带的电子结构与性质:电场及长度效应

在密度泛函理论(DFT)和含时密度泛函理论(TDDFT)的基础上对宽度上含有8个zigzag链的石墨烯条带(8-ZGNR)的基态和激发态的性质进行了理论研究,着重考察了条带长度及电场的影响.B3LYP杂化泛函的计算结果显示:在基态上,8-ZGNR的最低能量态并不具有磁性,随着长度的增加,才会显示出反铁磁的性质.静电场的加入使8-ZGNR显示出反铁磁性和半金属性.在激发态上,诱导电子会随着外激光脉冲的变化而发生移动和变化,但是相比而言,α自旋电子更容易被激发而产生较明显的诱导电子密度,而β自旋电子则更容易脱离外激光场的控制而产生非绝热现象.     

Energetics of dioxygen binding into graphene patches with various sizes and shapes

Density functional theory (DFT) calculations were employed to investigate the electronic properties of an H-atom terminated graphene patch (hydrographene) smaller than a rhombic C96H26 structure with zigzag edges. Depending on shapes and sizes of hydrographenes, some hydrographenes have the triplet ground state where unpaired electrons are localized on their zigzag edges. The stability of the triplet spin state is diminished, decreasing the hydrographene sizes. The existence of the localized spin densities allows triplet dioxgen to bind into a hydrographene. According to the DFT calculations, the energetics of the dioxygen bindings is negatively influenced by downsizing hydrographenes, as well as depends on their shapes. The size-and shape-dependences of the dioxygen bindings reflect from the stability of the triplet state of a hydrographene, because its localized unpaired electrons can be utilized to be attached to an unpaired electron of triplet dioxygen.     

Local aromaticity of the lowest-lying singlet States of [N]acenes (N = 6-9)

The local aromaticities of the six-membered rings in the two lowest-lying singlet states of [n]acenes (n = 6-9) have been assessed by means of three probes of local aromaticity based on structural, magnetic, and electron delocalization properties. Important differences between the local aromaticities of the closed-shell and diradical singlet electronic states are found. Thus, while the inner rings have the largest aromatic character in the closed-shell singlet states, the outer rings become the most aromatic for the diradical singlet states.