Synthesis and characterization of triangulene

Pt-based graphene quantum dots for water dissociation

It is widely recognized that Pt nanostructures exhibit favorable catalytic properties for several important technological reactions. Furthermore, selecting an appropriate support has the potential to enhance the catalytic activity of these materials. In this study, we investigate Pt nanoparticles deposited on quantum dots using quantum chemical calculations. We explore the utilization of low-dimensional carbonaceous support by employing graphene quantum dots (GQDs), which offer abundant active sites, such as edges, and diverse conformations. This provides excellent tuning possibilities for both chemical and physical properties. Our goal is to gather information on the alterations in electronic properties, charge redistribution and reactivity of platinum particles on GQD, also analyzing their potential role as catalysts in the water dissociation reaction. Based on thermodynamic and kinetic considerations, our calculations suggest that a Pt3nanoparticle adsorbed on the edge of the GQD exhibits favorable energetics, leading to a promising catalytic material.

Observation of SOMO-HOMO Inversion in a Neutral Polycyclic Conjugated Hydrocarbon

We report the generation of a nonbenzenoid polycyclic conjugated hydrocarbon, which consists of a biphenyl moiety substituted by indenyl units at the 4,4' positions, on ultrathin sodium chloride films by tip-induced chemistry. Single-molecule characterization by scanning tunneling and atomic force microscopy reveals an open-shell biradical ground state with a peculiar electronic configuration wherein the singly occupied molecular orbitals (SOMOs) are lower in energy than the highest occupied molecular orbital (HOMO).

Regioselective On-Surface Synthesis of [3]Triangulene Graphene Nanoribbons

The integration of low-energy states into bottom-up engineered graphene nanoribbons (GNRs) is a robust strategy for realizing materials with tailored electronic band structure for nanoelectronics. Low-energy zero-modes (ZMs) can be introduced into nanographenes (NGs) by creating an imbalance between the two sublattices of graphene. This phenomenon is exemplified by the family of [n]triangulenes (n ∈ N ). Here, we demonstrate the synthesis of [3]triangulene-GNRs, a regioregular one-dimensional (1D) chain of [3]triangulenes linked by five-membered rings. Hybridization between ZMs on adjacent [3]triangulenes leads to the emergence of a narrow band gap, Eg,exp ∼ 0.7 eV, and topological end states that are experimentally verified using scanning tunneling spectroscopy. Tight-binding and first-principles density functional theory calculations within the local density approximation corroborate our experimental observations. Our synthetic design takes advantage of a selective on-surface head-to-tail coupling of monomer building blocks enabling the regioselective synthesis of [3]triangulene-GNRs. Detailed ab initio theory provides insights into the mechanism of on-surface radical polymerization, revealing the pivotal role of Au-C bond formation/breakage in driving selectivity.

On-Surface Covalent Synthesis of Carbon Nanomaterials by Harnessing Carbon gem-Polyhalides

The design of innovative carbon-based nanostructures stands at the forefront of both chemistry and materials science. In this context, π-conjugated compounds are of great interest due to their impact in a variety of fields, including optoelectronics, spintronics, energy storage, sensing and catalysis. Despite extensive research efforts, substantial knowledge gaps persist in the synthesis and characterization of new π-conjugated compounds with potential implications for science and technology. On-surface synthesis has emerged as a powerful discipline to overcome limitations associated with conventional solution chemistry methods, offering advanced tools to characterize the resulting nanomaterials. This review specifically highlights recent achievements in the utilization of molecular precursors incorporating carbon geminal (gem)-polyhalides as functional groups to guide the formation of π-conjugated 0D species, as well as 1D, quasi-1D π-conjugated polymers, and 2D nanoarchitectures. By delving into reaction pathways, novel structural designs, and the electronic, magnetic, and topological features of the resulting products, the review provides fundamental insights for a new generation of π-conjugated materials.

Superexchange Mechanism in Coupled Triangulenes Forming Spin-1 Chains

We show that the origin of the antiferromagnetic coupling in spin-1 triangulene chains, which were recently synthesized and measured by Mishra et al. ( Nature 2021, 598, 287-292), originates from a superexchange mechanism. This process, mediated by intertriangulene states, opens the possibility to control parameters in the effective bilinear-biquadratic spin model. We start from the derivation of an effective tight-binding model for triangulene chains using a combination of tight-binding and Hartree-Fock methods fitted to hybrid density functional theory results. Next, correlation effects are investigated within the configuration interaction method. Our low-energy many-body spectrum for NTr = 2 and NTr = 4 triangulene chains agree well with the bilinear-biquadratic spin-1 chain antiferromagnetic model when indirect coupling processes and superexchange coupling between triangulene spins are taken into account.

Highly entangled polyradical nanographene with coexisting strong correlation and topological frustration

Open-shell nanographenes exhibit unconventional π-magnetism arising from topological frustration or strong electron-electron interaction. However, conventional design approaches are typically limited to a single magnetic origin, which can restrict the number of correlated spins or the type of magnetic ordering in open-shell nanographenes. Here we present a design strategy that combines topological frustration and electron-electron interactions to fabricate a large fully fused 'butterfly'-shaped tetraradical nanographene on Au(111). We employ bond-resolved scanning tunnelling microscopy and spin-excitation spectroscopy to resolve the molecular backbone and reveal the strongly correlated open-shell character, respectively. This nanographene contains four unpaired electrons with both ferromagnetic and anti-ferromagnetic interactions, harbouring a many-body singlet ground state and strong multi-spin entanglement, which is well described by many-body calculations. Furthermore, we study the magnetic properties and spin states in the nanographene using a nickelocene magnetic probe. The ability to imprint and characterize many-body strongly correlated spins in polyradical nanographenes paves the way for future advancements in quantum information technologies.

Aromatic Rules of C22H122+/2•/2-: Flexibility in Electronic Structures of 2D Superatomic Molecules

Triangulene (C22H122•), a nonclassic non-Kekulé polycyclic aromatic hydrocarbon, is identified to be aromatic by structural and magnetic criteria. However, its aromatic origin remains confusing. Herein, the aromatic rules of C22H122• and its two charged counterparts C22H122+/2- were investigated on the basis of a recently developed two-dimensional (2D) superatomic-molecule theory. [C22H12]2+/2•/2- exhibit obvious local aromatic characters and can be regarded as [◊N3◊O3]+, [◊N3◊O3]-, and ◊N3◊F3 superatomic molecules, respectively, where ◊N, ◊O, and ◊F denote 2D superatoms bearing 3π, 4π, and 5π electrons. [C22H12]2+/2- realize electronic shell closure via superatomic lone pairs and covalent bonds, mimicking simple molecules, whereas the α-π and β-π electrons in C22H122• follow the superatomic bonding patterns of C22H122- and C22H122+, respectively. Furthermore, based on the local character in 2D superatomic molecules, a doped nanoporous graphene, namely, C9N12B monolayer, was predicted. The material possesses excellent dynamical and thermodynamical stability, as well as a wide band gap of 2.77 eV, positioning it as a promising 2D material for future electronic applications.

COMPAS-3: a dataset of peri-condensed polybenzenoid hydrocarbons

We introduce the third installment of the COMPAS Project - a COMputational database of Polycyclic Aromatic Systems, focused on peri-condensed polybenzenoid hydrocarbons. In this installment, we develop two datasets containing the optimized ground-state structures and a selection of molecular properties of ∼39k and ∼9k peri-condensed polybenzenoid hydrocarbons (at the GFN2-xTB and CAM-B3LYP-D3BJ/cc-pvdz//CAM-B3LYP-D3BJ/def2-SVP levels, respectively). The manuscript details the enumeration and data generation processes and describes the information available within the datasets. An in-depth comparison between the two types of computation is performed, and it is found that the geometrical disagreement is maximal for slightly-distorted molecules. In addition, a data-driven analysis of the structure-property trends of peri-condensed PBHs is performed, highlighting the effect of the size of peri-condensed islands and linearly annulated rings on the HOMO-LUMO gap. The insights described herein are important for rational design of novel functional aromatic molecules for use in, e.g., organic electronics. The generated datasets provide a basis for additional data-driven machine- and deep-learning studies in chemistry.

A high density nanopore 3-triangulene kagome lattice

Nanopore-containing two-dimensional materials have been explored for a wide range of applications including filtration, sensing, catalysis, energy storage and conversion. Triangulenes have recently been experimentally synthesized in a variety of sizes. In this regard, using these systems as building blocks, we theoretically examined 3-triangulene kagome crystals with inherent holes of ∼12 Å diameter and a greater density array of nanopores (≥1013 cm-2) compared to conventional 2D systems. The energetic, electronic, and transport properties of pristine and B/N-doped 3-triangulene kagome crystals were evaluated through a combination of density functional theory and non-equilibrium Green's function method. The simulated scanning tunneling microscopy images clearly capture electronic perturbation around the doped sites, which can be used to distinguish the pristine system from the doped systems. The viability of precisely controlling the band structure and transport properties by changing the type and concentration of doping atoms is demonstrated. The findings presented herein can potentially widen the applicability of these systems that combine unique electronic properties and intrinsically high-density pores, which can pave the way for the next generation of nanopore-based devices.

N-Heterocyclic Carbene-Derived 1,3,5-Trimethylenebenzene: On-Surface Synthesis and Electronic Structure

1,3,5-Trimethylenebenzene (1,3,5-TMB), a 3-fold-symmetric triradical with a high-spin ground state, is an attractive platform for investigating the unique spin properties of π-conjugated triangular triradicals. Here, we report the on-surface synthesis of N-heterocyclic carbene (NHC)-derived 1,3,5-TMB (N-TMB) via surface-assisted C-C and C-N coupling reactions on Au(111). The chemical and electronic structures of N-TMB on the Au(111) surface are revealed with atomic precision using scanning tunneling microscopy and noncontact atomic force microscopy, combined with density functional theory (DFT) calculations. It is demonstrated that there is substantial charge transfer between N-TMB and the substrate, resulting in a positively charged N-TMB on Au(111). DFT calculations at the UB3LYP/def2-TZVP level of theory and multireference method, e.g., CASSCF/NEVPT2, indicate that N-TMB possesses a doublet ground state with reduced Cs symmetry in the gas phase, contrasting the quartet ground state of 1,3,5-TMB with D3h symmetry, and exhibits a doublet-quartet energy gap of -0.80 eV. The incorporation of NHC structures and the extended π-conjugation promote the spin-orbital overlaps in N-TMB, leading to Jahn-Teller distortion and the formation of a robust doublet state. Our results not only demonstrate the fabrication of polyradicals based on NHC but also shed light on the effect of NHC and π-conjugation on the electronic structure and spin coupling, which opens up new possibilities for precisely regulating the spin-spin exchange coupling of organic polyradicals.

Bistability between π-diradical open-shell and closed-shell states in indeno[1,2-a]fluorene

Indenofluorenes are non-benzenoid conjugated hydrocarbons that have received great interest owing to their unusual electronic structure and potential applications in nonlinear optics and photovoltaics. Here we report the generation of unsubstituted indeno[1,2-a]fluorene on various surfaces by the cleavage of two C-H bonds in 7,12-dihydroindeno[1,2-a]fluorene through voltage pulses applied by the tip of a combined scanning tunnelling microscope and atomic force microscope. On bilayer NaCl on Au(111), indeno[1,2-a]fluorene is in the neutral charge state, but it exhibits charge bistability between neutral and anionic states on the lower-workfunction surfaces of bilayer NaCl on Ag(111) and Cu(111). In the neutral state, indeno[1,2-a]fluorene exhibits one of two ground states: an open-shell π-diradical state, predicted to be a triplet by density functional and multireference many-body perturbation theory calculations, or a closed-shell state with a para-quinodimethane moiety in the as-indacene core. We observe switching between open- and closed-shell states of a single molecule by changing its adsorption site on NaCl.

Automated Structure Discovery for Scanning Tunneling Microscopy

Scanning tunneling microscopy (STM) with a functionalized tip apex reveals the geometric and electronic structures of a sample within the same experiment. However, the complex nature of the signal makes images difficult to interpret and has so far limited most research to planar samples with a known chemical composition. Here, we present automated structure discovery for STM (ASD-STM), a machine learning tool for predicting the atomic structure directly from an STM image, by building upon successful methods for structure discovery in noncontact atomic force microscopy (nc-AFM). We apply the method on various organic molecules and achieve good accuracy on structure predictions and chemical identification on a qualitative level while highlighting future development requirements for ASD-STM. This method is directly applicable to experimental STM images of organic molecules, making structure discovery available for a wider scanning probe microscopy audience outside of nc-AFM. This work also allows more advanced machine learning methods to be developed for STM structure discovery.

Unlocking Ultrafast Spin Transfer in Single-Magnetic-Center-Decorated Triangulene Systems

Triangulene, as a typical open-shell graphene fragment, has attracted widespread attention for nanospintronics, promising to serve as building blocks in spin-logic units. Here, using ab initio calculations, we systematically study the laser-induced ultrafast spin-dynamic processes on triangulene nanoflakes, decorated with a transition-metal atom. The results reveal a competition between the induced magnetic center and the carbon edge of the triangulene, resulting in the coexistence of dual spin-density-distribution patterns on such single-magnetic-center systems, thus opening up possibilities of complex spin-dynamic scenarios beyond the spin flip. Interestingly, no matter what direction the spin points to, it is possible to achieve reversible spin-transfer processes using the same laser pulse. Increasing the pool of elementary processes to contain not only spin-direction-dependent but also spin-direction-independent scenarios allows for more versatile spin-logic operations, including classical handling of information and quantum computing. In the present work, we suggest downscaling nanospintronic devices by integrating triangulene-based nanostructures.

π-Radical Cascade to a Chiral Saddle-Shaped Peropyrene

Reactions of open-shell molecular graphene fragments are typically thought of as undesired decomposition processes because they lead to the loss of desired features like π-magnetism. Oxidative dimerization of phenalenyl to peropyrene shows, however, that these transformations hold promise as a synthetic tool for making complex structures via formation of multiple bonds and rings in a single step. Here, we explore the feasibility of using this "undesired" reaction of phenalenyl to build up strain and provide access to non-planar polycyclic aromatic hydrocarbons. To this end, we designed and synthesized a biradical system with two phenalenyl units linked via a biphenylene backbone. The design facilitates an intramolecular cascade reaction to a helically twisted saddle-shaped product, where the key transformations-ring-closure and ring-fusion-occur within one reaction. The negative curvature of the final peropyrene product, induced by the formed eight-membered ring, was confirmed by single-crystal X-ray diffraction analysis and the helical twist was validated via resolution of the product's enantiomers that display circularly polarized luminescence and high configurational stability.

Topological Structure Realized in Cove-Edged Graphene Nanoribbons via Incorporation of Periodic Pentagon Rings

Cove-edged zigzag graphene nanoribbons are predicted to show metallic, topological, or trivial semiconducting band structures, which are precisely determined by their cove offset positions at both edges as well as the ribbon width. However, due to the challenge of introducing coves into zigzag-edged graphene nanoribbons, only a few cove-edged graphene nanoribbons with trivial semiconducting bandgaps have been realized experimentally. Here, we report that the topological band structure can be realized in cove-edged graphene nanoribbons by embedding periodic pentagon rings on the cove edges through on-surface synthesis. Upon noncontact atomic force microscopy and scanning tunneling spectroscopy measurements, the chemical and electronic structures of cove-edged graphene nanoribbons with periodic pentagon rings have been characterized for different lengths. Combined with theoretical calculations, we find that upon inducing periodic pentagon rings the cove-edged graphene nanoribbons exhibit nontrivial topological structures. Our results provide insights for the design and understanding of the topological character in cove-edged graphene nanoribbons.

Atomic-Limit Mott Insulator in [4]Triangulene Frameworks

Triangulene, one unique class of zigzag-edged triangular graphene molecules, has attracted tremendous research interest. In this work, as an ultimate phase of the Mott insulator, we present the realization of the atomic-limit Mott insulator in experimentally synthesized [4]triangulene frameworks ([4]-TGFs) from first-principles calculations. The frontier molecular orbitals of the nonmagnetic [4]triangulene consist of three coupled corner modes. After the isolated [4]triangulene is assembled into [4]-TGF, one special enantiomorphic flat band is created through the coupling of these corner modes, which is identified to be a second-order topological insulator with half-filled topological corner states at the Fermi level. Moreover, [4]-TGF prefers an antiferromagnetic ground state under Hubbard interactions, which further splits these metallic zero-energy states into an atomic-limit Mott insulator with spin-polarized corners. Since the fractional filling of topological corner states is a smoking-gun signature of higher-order topology, our results demonstrate a universal approach to explore the atomic-limit Mott insulators in higher-order topological materials.

On-Surface Synthesis and Determination of the Open-Shell Singlet Ground State of Tridecacene

The character of the electronic structure of acenes has been the subject of longstanding discussion. However, convincing experimental evidence of their open-shell character has so far been missing. Here, we present the on-surface synthesis of tridecacene molecules by thermal annealing of octahydrotridecacene on a Au(111) surface. We characterized the electronic structure of the tridecacene by scanning probe microscopy, which reveals the presence of an inelastic signal at 126 meV. We attribute the inelastic signal to spin excitation from the singlet diradical ground state to the triplet excited state. To rationalize the experimental findings, we carried out many-body ab initio calculations as well as model Hamiltonians to take into account the effect of the metallic substrate. Moreover, we provide a detailed analysis of how the dynamic electron correlation and virtual charge fluctuation between the molecule and metallic surface reduces the singlet-triplet band gap. Thus, this work provides the first experimental confirmation of the magnetic character of tridecacene.

On-Surface Synthesis of a Radical 2D Supramolecular Organic Framework

The design of supramolecular organic radical cages and frameworks is one of the main challenges in supramolecular chemistry. Their interesting material properties and wide applications make them very promising for (photo)redox catalysis, sensors, or host-guest spin-spin interactions. However, the high reactivity of radical organic systems makes the design of such supramolecular radical assemblies challenging. Here, we report the on-surface synthesis of a purely organic supramolecular radical framework on Au(111), by combining supramolecular and on-surface chemistry. We employ a tripodal precursor, functionalized with 7-azaindole groups that, catalyzed by a single gold atom on the surface, forms a radical molecular product constituted by a π-extended fluoradene-based radical core. The radical products self-assemble through hydrogen bonding, leading to extended 2D domains ordered in a Kagome-honeycomb lattice. This approach demonstrates the potential of on-surface synthesis for developing 2D supramolecular radical organic chemistry.

Tailoring Magnetism of Graphene Nanoflakes via Tip-Controlled Dehydrogenation

Atomically precise graphene nanoflakes called nanographenes have emerged as a promising platform to realize carbon magnetism. Their ground state spin configuration can be anticipated by Ovchinnikov-Lieb rules based on the mismatch of π electrons from two sublattices. While rational geometrical design achieves specific spin configurations, further direct control over the π electrons offers a desirable extension for efficient spin manipulations and potential quantum device operations. To this end, we apply a site-specific dehydrogenation using a scanning tunneling microscope tip to nanographenes deposited on a Au(111) substrate, which shows the capability of precisely tailoring the underlying π-electron system and therefore efficiently manipulating their magnetism. Through first-principles calculations and tight-binding mean-field-Hubbard modeling, we demonstrate that the dehydrogenation-induced Au-C bond formation along with the resulting hybridization between frontier π orbitals and Au substrate states effectively eliminate the unpaired π electron. Our results establish an efficient technique for controlling the magnetism of nanographenes.

Cycl[2,2,4]azine-embedded non-alternant nanographenes containing fused antiaromatic azepine ring

The development of non-alternant nanographenes has attracted considerable attention due to their unique photophysical properties. Herein, we reported a novel aza-doped, non-alternant nanographene (NG) 1 by embedding the cycl[2,2,4]azine unit into the benzenoid NG framework. Single-crystal X-ray diffractometry suggests saddle or twisted nonplanar geometry of the entire backbone of 1 and coplanar conformation of the cycl[2,2,4]azine unit. DFT calculation together with solid structure indicates that NG 1 possesses significant local antiaromaticity in the azepine ring. By oxidative process or trifluoroacetic acid treatment, this nanographene can transform into a mono-radical cation, which was confirmed by UV/Vis absorption, 1H NMR, and electron paramagnetic resonance (EPR) spectroscopy. The antiaromaticity/aromaticity switching of the azepine ring on 1˙+ from 1 enables the high stability of this radical cation, which remained intact for over 1 day. Due to the electron-donating nature of the nitrogen and the unique electronic structure, NG 1 exhibits strong electron-donating properties, as proved by the intermolecular charge transfer towards C60 with a high association constant. Furthermore, selective modification of NG 1 was accomplished by Vilsmeier reaction, and the derivatives 7 and 8 with substituted benzophenone were obtained. The photophysical and electronic properties can be tuned by the introduction of different electronic groups in benzophenone.

Highly Selective On-Surface Ring-Opening of Aromatic Azulene Moiety

Controllable ring-opening of polycyclic aromatic hydrocarbons plays a crucial role in various chemical and biological processes. However, breaking down aromatic covalent C-C bonds is exceptionally challenging due to their high stability and strong aromaticity. This study presents a seminal report on the precise and highly selective on-surface ring-opening of the seven-membered ring within the aromatic azulene moieties under mild conditions. The chemical structures of the resulting products were identified using bond-resolved scanning probe microscopy. Furthermore, through density functional theory calculations, we uncovered the mechanism behind the ring-opening process and elucidated its chemical driving force. The key to achieving this ring-opening process lies in manipulating the local aromaticity of the aromatic azulene moiety through strain-induced internal ring rearrangement and cyclodehydrogenation. By precisely controlling these factors, we successfully triggered the desired ring-opening reaction. Our findings not only provide valuable insights into the ring-opening process of polycyclic aromatic hydrocarbons but also open up new possibilities for the manipulation and reconstruction of these important chemical structures.

The role of aromaticity in the cyclization and polymerization of alkyne-substituted porphyrins on Au(111)

Aromaticity is an established and widely used concept for the prediction of the reactivity of organic molecules. However, its role remains largely unexplored in on-surface chemistry, where the interaction with the substrate can alter the electronic and geometric structure of the adsorbates. Here we investigate how aromaticity affects the reactivity of alkyne-substituted porphyrin molecules in cyclization and coupling reactions on a Au(111) surface. We examine and quantify the regioselectivity in the reactions by scanning tunnelling microscopy and bond-resolved atomic force microscopy at the single-molecule level. Our experiments show a substantially lower reactivity of carbon atoms that are stabilized by the aromatic diaza[18]annulene pathway of free-base porphyrins. The results are corroborated by density functional theory calculations, which show a direct correlation between aromaticity and thermodynamic stability of the reaction products. These insights are helpful to understand, and in turn design, reactions with aromatic species in on-surface chemistry and heterogeneous catalysis.

Direct Observation of Twin van der Waals Molecular Chains

The van der Waals (vdW) assemblies are the most common structures of materials. However, direct mapping of intermolecular electron clouds of a vdW assembly has never been obtained, even though the intramolecular electron clouds were visualized by atomic-resolution techniques. In this report, we unprecedentedly mapped the intermolecular electron cloud of the assemblies of ethanol molecules via ethyl groups with high-resolution atomic force microscopy and scanning tunneling microscopy at 5 K, leading to the first visualization of vdW molecular chains, in which ethanol molecules assemble into twin vdW molecular chains in a reverse parallel configuration on the Ag(111) plane. Furthermore, spontaneous order-disorder transitions in the chain were dynamically observed, suggesting its unusual properties different from those of 2D vdW materials. These findings provide an "eye" to see the atomic world of vdW materials.

Local probe-induced structural isomerization in a one-dimensional molecular array

Synthesis of one-dimensional molecular arrays with tailored stereoisomers is challenging yet has great potential for application in molecular opto-, electronic- and magnetic-devices, where the local array structure plays a decisive role in the functional properties. Here, we demonstrate the construction and characterization of dehydroazulene isomer and diradical units in three-dimensional organometallic compounds on Ag(111) with a combination of low-temperature scanning tunneling microscopy and density functional theory calculations. Tip-induced voltage pulses firstly result in the formation of a diradical species via successive homolytic fission of two C-Br bonds in the naphthyl groups, which are subsequently transformed into chiral dehydroazulene moieties. The delicate balance of the reaction rates among the diradical and two stereoisomers, arising from an in-line configuration of tip and molecular unit, allows directional azulene-to-azulene and azulene-to-diradical local probe structural isomerization in a controlled manner. Furthermore, our theoretical calculations suggest that the diradical moiety hosts an open-shell singlet with antiferromagnetic coupling between the unpaired electrons, which can undergo an inelastic spin transition of 91 meV to the ferromagnetically coupled triplet state.

Sequential On-Surface Cyclodehydrogenation in a Nonplanar Nanographene

On-surface synthesis has emerged as an attractive method for the atomically precise synthesis of new molecular nanostructures, being complementary to the widespread approach based on solution chemistry. It has been particularly successful in the synthesis of graphene nanoribbons and nanographenes. In both cases, the target compound is often generated through cyclodehydrogenation reactions, leading to planarization and the formation of hexagonal rings. To improve the flexibility and tunability of molecular units, however, the incorporation of other, nonbenzenoid, subunits is highly desirable. In this letter, we thoroughly analyze sequential cyclodehydrogenation reactions with a custom-designed molecular precursor. We demonstrate the step-by-step formation of hexagonal and pentagonal rings from the nonplanar precursor within fjord and cove regions, respectively. Computer models comprehensively support the experimental observations, revealing that both reactions imply an initial hydrogen abstraction and a final [1,2] hydrogen shift, but the formation of a pentagonal ring proceeds through a radical mechanism.

Molecular Carbons: How Far Can We Go?

The creation and development of carbon nanomaterials promoted material science significantly. Bottom-up synthesis has emerged as an efficient strategy to synthesize atomically precise carbon nanomaterials, namely, molecular carbons, with various sizes and topologies. Different from the properties of the feasibly obtained mixture of carbon nanomaterials, numerous properties of single-component molecular carbons have been discovered owing to their well-defined structures as well as potential applications in various fields. This Perspective introduces recent advances in molecular carbons derived from fullerene, graphene, carbon nanotube, carbyne, graphyne, and Schwarzite carbon acquired with different synthesis strategies. By selecting a variety of representative examples, we elaborate on the relationship between molecular carbons and carbon nanomaterials. We hope these multiple points of view presented may facilitate further advancement in this field.

On-Surface Synthesis and Real-Space Visualization of Aromatic P3 N3

On-surface synthesis is at the verge of emerging as the method of choice for the generation and visualization of unstable or unconventional molecules, which could not be obtained via traditional synthetic methods. A case in point is the on-surface synthesis of the structurally elusive cyclotriphosphazene (P3 N3 ), an inorganic aromatic analogue of benzene. Here, we report the preparation of this fleetingly existing species on Cu(111) and Au(111) surfaces at 5.2 K through molecular manipulation with unprecedented precision, i.e., voltage pulse-induced sextuple dechlorination of an ultra-small (about 6 Å) hexachlorophosphazene P3 N3 Cl6 precursor by the tip of a scanning probe microscope. Real-space atomic-level imaging of cyclotriphosphazene reveals its planar D3h -symmetric ring structure. Furthermore, this demasking strategy has been expanded to generate cyclotriphosphazene from a hexaazide precursor P3 N21 via a different stimulation method (photolysis) for complementary measurements by matrix isolation infrared and ultraviolet spectroscopy.

Emergence of π-Magnetism in Fused Aza-Triangulenes: Symmetry and Charge Transfer Effects

On-surface synthesis has paved the way toward the fabrication and characterization of conjugated carbon-based molecular materials that exhibit π-magnetism such as triangulenes. Aza-triangulene, a nitrogen-substituted derivative, was recently shown to display rich on-surface chemistry, offering an ideal platform to investigate structure-property relations regarding spin-selective charge transfer and magnetic fingerprints. Herein, we study electronic changes upon fusion of single molecules into larger dimeric derivatives. We show that the closed-shell structure of aza-triangulene on Ag(111) leads to closed-shell dimers covalently coupled through sterically accessible carbon atoms. Meanwhile, its open-shell structure on Au(111) leads to coupling via atoms displaying a high spin density, resulting in symmetric or asymmetric products. Interestingly, whereas all dimers on Au(111) exhibit similar charge transfer properties, only asymmetric ones show magnetic fingerprints due to spin-selective charge transfer. These results expose clear relationships among molecular symmetry, charge transfer, and spin states of π-conjugated carbon-based nanostructures.

Quantum Phase Transition in Magnetic Nanographenes on a Lead Superconductor

Quantum spins, also known as spin operators that preserve SU(2) symmetry, lack a specific orientation in space and are hypothesized to display unique interactions with superconductivity. However, spin-orbit coupling and crystal field typically cause a significant magnetic anisotropy in d/f shell spins on surfaces. Here, we fabricate atomically precise S = 1/2 magnetic nanographenes on Pb(111) through engineering sublattice imbalance in the graphene honeycomb lattice. Through tuning the magnetic exchange strength between the unpaired spin and Cooper pairs, a quantum phase transition from the singlet to the doublet state has been observed, consistent with the quantum spin models. From our calculations, the particle-hole asymmetry is induced by the Coulomb scattering potential and gives a transition point about kBTk ≈ 1.6Δ. Our work demonstrates that delocalized π electron magnetism hosts highly tunable magnetic bound states, which can be further developed to study the Majorana bound states and other rich quantum phases of low-dimensional quantum spins on superconductors.

Bis-Olefin Based Crystalline Schlenk Hydrocarbon Diradicals with a Triplet Ground State

A modular approach for the synthesis of isolable crystalline Schlenk hydrocarbon diradicals from m-phenylene bridged electron-rich bis-triazaalkenes as synthons is reported. EPR spectroscopy confirms their diradical nature and triplet electronic structure by revealing a half-field signal. A computational analysis confirms the triplet state to be the ground state. As a proof-of-principle for the modular methodology, the 4,6-dimethyl-m-phenylene was further utilized as a coupling unit between two alkene motifs. The steric conjunction of the 4,6-dimethyl groups substantially twists the substituents at the nonbonding electron bearing centers relative to the central coupling m-phenylene motif. As a result, the spin delocalization is decreased and the exchange coupling between the two unpaired spins, hence, significantly reduced. Notably, 108 years after Schlenk's m-phenylene-bis(diphenylmethyl) synthesis as a diradical, for the first time we were able to isolate its derivative with the same spacer, i.e. m-phenylene, between two radical centers in a crystalline form.

Exchange Interactions and Intermolecular Hybridization in a Spin-1/2 Nanographene Dimer

Phenalenyl is a radical nanographene with a triangular shape hosting an unpaired electron with spin S = 1/2. The open-shell nature of the phenalenyl is expected to be retained in covalently bonded networks. As a first step, we report synthesis of the phenalenyl dimer by combining in-solution synthesis and on-surface activation and its characterization on Au(111) and on a NaCl decoupling layer by means of inelastic electron tunneling spectroscopy (IETS). IETS shows inelastic steps that are identified as singlet-triplet excitation arising from interphenalenyl exchange. Spin excitation energies with and without the NaCl decoupling layer are 48 and 41 meV, respectively, indicating significant renormalization due to exchange with Au(111) electrons. Furthermore, third-neighbor hopping-induced interphenalenyl hybridization is fundamental to explaining the position-dependent bias asymmetry of the inelastic steps and activation of kinetic interphenalenyl exchange. Our results pave the way for bottom-up synthesis of S = 1/2 spin-lattices with large exchange interactions.

From Stable Radicals to Thermally Robust High-Spin Diradicals and Triradicals

Stable radicals and thermally robust high-spin di- and triradicals have emerged as important organic materials due to their promising applications in diverse fields. New fundamental properties, such as SOMO/HOMO inversion of orbital energies, are explored for the design of new stable radicals, including highly luminescent ones with good photostability. A relation with the singlet-triplet energy gap in the corresponding diradicals is proposed. Thermally robust high-spin di- and triradicals, with energy gaps that are comparable to or greater than a thermal energy at room temperature, are more challenging to synthesize but more rewarding. We summarize a number of high-spin di- and triradicals, based on nitronyl nitroxides that provide a relation between the experimental pairwise exchange coupling constant J/k in the high-spin species vs experimental hyperfine coupling constants in the corresponding monoradicals. This relation allows us to identify outliers, which may correspond to radicals where J/k is not measured with sufficient accuracy. Double helical high-spin diradicals, in which spin density is delocalized over the chiral π-system, have been barely explored, with the sole example of such high-spin diradical possessing alternant π-system with Kekulé resonance form. Finally, we discuss a high-spin diradical with electrical conductivity and derivatives of triangulene diradicals.

Topological Design and Synthesis of High-Spin Aza-triangulenes without Jahn-Teller Distortions

The atomic doping of open-shell nanographenes enables precise tuning of their electronic and magnetic states, which is crucial for their promising potential applications in optoelectronics and spintronics. Among this intriguing class of molecules, triangulenes stand out with their size-dependent electronic properties and spin states, which can also be influenced by the presence of dopant atoms and functional groups. However, the occurrence of Jahn-Teller distortions in such systems can have a crucial impact on their total spin and requires further theoretical and experimental investigation. In this study, we examine the nitrogen-doped aza-triangulene series via a combination of density functional theory and on-surface synthesis. We identify a general trend in the calculated spin states of aza-[n]triangulenes of various sizes, separating them into two symmetry classes, one of which features molecules that are predicted to undergo Jahn-Teller distortions that reduce their symmetry and thus their total spin. We link this behavior to the location of the central nitrogen atom relative to the two underlying carbon sublattices of the molecules. Consequently, our findings reveal that neutral centrally doped aza-triangulenes have one less radical than their undoped counterparts, irrespective of their predicted symmetry. We follow this by demonstrating the on-surface synthesis of π-extended aza-[5]triangulene, a large member of the higher symmetry class without Jahn-Teller distortions, via a simple one-step annealing process on Cu(111) and Au(111). Using scanning probe microscopy and spectroscopy combined with theoretical calculations, we prove that the molecule is positively charged on the Au(111) substrate, with a high-spin quintet state of S = 2, the same total spin as undoped neutral [5]triangulene. Our study uncovers the correlation between the dopant position and the radical nature of high-spin nanographenes, providing a strategy for the design and development of these nanographenes for various applications.

Detecting the spin-polarization of edge states in graphene nanoribbons

Low dimensional carbon-based materials can show intrinsic magnetism associated to p-electrons in open-shell π-conjugated systems. Chemical design provides atomically precise control of the π-electron cloud, which makes them promising for nanoscale magnetic devices. However, direct verification of their spatially resolved spin-moment remains elusive. Here, we report the spin-polarization of chiral graphene nanoribbons (one-dimensional strips of graphene with alternating zig-zag and arm-chair boundaries), obtained by means of spin-polarized scanning tunnelling microscopy. We extract the energy-dependent spin-moment distribution of spatially extended edge states with π-orbital character, thus beyond localized magnetic moments at radical or defective carbon sites. Guided by mean-field Hubbard calculations, we demonstrate that electron correlations are responsible for the spin-splitting of the electronic structure. Our versatile platform utilizes a ferromagnetic substrate that stabilizes the organic magnetic moments against thermal and quantum fluctuations, while being fully compatible with on-surface synthesis of the rapidly growing class of nanographenes.

On-Surface Synthesis and Characterization of a High-Spin Aza-[5]-Triangulene

Triangulenes are a class of open-shell triangular graphene flakes with total spin increasing with their size. In the last years, on-surface-synthesis strategies have permitted fabricating and engineering triangulenes of various sizes and structures with atomic precision. However, direct proof of the increasing total spin with their size remains elusive. In this work, we report the combined in-solution and on-surface synthesis of a large nitrogen-doped triangulene (aza-[5]-triangulene) on a Au(111) surface, and the detection of its high-spin ground state. Bond-resolved scanning tunneling microscopy images uncovered radical states distributed along the zigzag edges, which were detected as weak zero-bias resonances in scanning tunneling spectra. These spectral features reveal the partial Kondo screening of a high-spin state. Through a combination of several simulation tools, we find that the observed distribution of radical states is explained by a quintet ground state (S=2), instead of the quartet state (S=3/2) expected for the neutral species. This confirms that electron transfer to the metal substrate raises the spin of the ground state. We further provide a qualitative description of the change of (anti)aromaticity introduced by N-substitution, and its role in the charge stabilization on a surface, resulting in an S=2 aza-triangulene on Au(111).

On-Surface Synthesis of Graphene Nanoribbons with Atomically Precise Structural Heterogeneities and On-Site Characterizations

Graphene nanoribbons (GNRs) are strips of graphene, with widths of a few nanometers, that are promising candidates for future applications in nanodevices and quantum information processing due to their highly tunable structure-dependent electronic, spintronic, topological, and optical properties. Implantation of periodic structural heterogeneities, such as heteroatoms, nanopores, and non-hexagonal rings, has become a powerful manner for tailoring the designer properties of GNRs. The bottom-up synthesis approach, by combining on-surface chemical reactions based on rationally designed molecular precursors and in situ tip-based microscopic and spectroscopic techniques, promotes the construction of atomically precise GNRs with periodic structural modulations. However, there are still obstacles and challenges lying on the way toward the understanding of the intrinsic structure-property relations, such as the strong screening and Fermi level pinning effect of the normally used transition metal substrates and the lack of collective tip-based techniques that can cover multi-internal degrees of freedom of the GNRs. In this Perspective, we briefly review the recent progress in the on-surface synthesis of GNRs with diverse structural heterogeneities and highlight the structure-property relations as characterized by the noncontact atomic force microscopy and scanning tunneling microscopy/spectroscopy. We furthermore motivate to deliver the need for developing strategies to achieve quasi-freestanding GNRs and for exploiting multifunctional tip-based techniques to collectively probe the intrinsic properties.

Structural Expansion of Cyclohepta[def]fluorene towards Azulene-Embedded Non-Benzenoid Nanographenes

Non-benzenoid non-alternant nanographenes (NGs) have attracted increasing attention on account of their distinct electronic and structural features in comparison to their isomeric benzenoid counterparts. In this work, we present a series of unprecedented azulene-embedded NGs on Au(111) during the attempted synthesis of cyclohepta[def]fluorene-based high-spin non-Kekulé structure. Comprehensive scanning tunneling microscopy (STM) and non-contact atomic force microscopy (nc-AFM) evidence the structures and conformations of these unexpected products. The dynamics of the precursor bearing 9-(2,6-dimethylphenyl)anthracene and dihydro-dibenzo-cyclohepta[def]fluorene units and its reaction products on the surface are analyzed by density functional theory (DFT) and molecular dynamics (MD) simulations. Our study sheds light on the fundamental understanding of precursor design for the fabrication of π-extended non-benzenoid NGs on a metal surface.

Magnetic Coupling Control in Triangulene Dimers

Metal-free magnetism remains an enigmatic field, offering prospects for unconventional magnetic and electronic devices. In the pursuit of such magnetism, triangulenes, endowed with inherent spin polarization, are promising candidates to serve as monomers to construct extended structures. However, controlling and enhancing the magnetic interactions between the monomers persist as a significant challenge in molecular spintronics, as so far only weak antiferromagnetic coupling through the linkage has been realized, hindering their room temperature utilization. Herein, we investigate 24 triangulene dimers using first-principles calculations and demonstrate their tunable magnetic coupling (J), achieving unprecedented strong J values of up to -144 meV in a non-Kekulé dimer. We further establish a positive correlation between bandgap, electronic coupling, and antiferromagnetic interaction, thereby providing molecular-level insights into enhancing magnetic interactions. By twisting the molecular fragments, we demonstrate an effective and feasible approach to control both the sign and strength of J by tuning the balance between potential and kinetic exchanges. We discover that J can be substantially boosted at planar configurations up to -198 meV. We realize ferromagnetic coupling in nitrogen-doped triangulene dimers at both planar and largely twisted configurations, representing the first example of ferromagnetic triangulene dimers that cannot be predicted by the Ovchinnikov rule. This work thus provides a practical strategy for augmenting magnetic coupling and open up new avenues for metal-free ferromagnetism.

Discovery and construction of surface kagome electronic states induced by p-d electronic hybridization in Co3Sn2S2

Kagome-lattice materials possess attractive properties for quantum computing applications, but their synthesis remains challenging. Herein, based on the compelling identification of the two cleavable surfaces of Co3Sn2S2, we show surface kagome electronic states (SKESs) on a Sn-terminated triangular Co3Sn2S2 surface. Such SKESs are imprinted by vertical p-d electronic hybridization between the surface Sn (subsurface S) atoms and the buried Co kagome-lattice network in the Co3Sn layer under the surface. Owing to the subsequent lateral hybridization of the Sn and S atoms in a corner-sharing manner, the kagome symmetry and topological electronic properties of the Co3Sn layer is proximate to the Sn surface. The SKESs and both hybridizations were verified via qPlus non-contact atomic force microscopy (nc-AFM) and density functional theory calculations. The construction of SKESs with tunable properties can be achieved by the atomic substitution of surface Sn (subsurface S) with other group III-V elements (Se or Te), which was demonstrated theoretically. This work exhibits the powerful capacity of nc-AFM in characterizing localized topological states and reveals the strategy for synthesis of large-area transition-metal-based kagome-lattice materials using conventional surface deposition techniques.

Role of π-Radical Localization on Thermally Stable Cross-Links Between Polycyclic Aromatic Hydrocarbons

The thermal stability of cross-links between polycyclic aromatic hydrocarbons (PAHs) is critical for understanding the formation of soot pollutants, graphite, and carbon blacks. Recently, a variety of different π-radicals have been directly imaged and suggested to enable thermally stable bonding; however, a systematic study of reactivity has been lacking. In this work, we use density functional theory to study the reactivity of PAH π-radicals. The Mulliken spin densities are initially used to categorize the different classes of localization, and the bond energy is computed to determine the degree of localization required for thermal stability. The results showed that the bond energies of PAHs are strongly correlated with the calculated spin densities, but bond energies do not exist with the bond lengths due to significant rearrangement and steric effects during bond formation. A threshold for π-radical localization is suggested that will be stable in combustion and pyrolysis environments of ρMα ≥ 0.5. Finally, the formation of multicenter bonds between localized and delocalized π-radicals was investigated using the nudge elastic band (NEB) scan, and it was found that only delocalized π-radicals provided local energy minima. These results show that the localization of π-radicals is critical for the formation of thermally stable single-center bonds between aromatic radicals.

Radical Single-Molecule Junctions

Radicals are unique molecular systems for applications in electronic devices due to their open-shell electronic structures. Radicals can function as good electrical conductors and switches in molecular circuits while also holding great promise in the field of molecular spintronics. However, it is both challenging to create stable, persistent radicals and to understand their properties in molecular junctions. The goal of this Perspective is to address this dual challenge by providing design principles for the synthesis of stable radicals relevant to molecular junctions, as well as offering current insight into the electronic properties of radicals in single-molecule devices. By exploring both the chemical and physical properties of established radical systems, we will facilitate increased exploration and development of radical-based molecular systems.

Predicting a New Δ-Proton Sponge-Base of 4,12-Dihydrogen-4,8,12-triazatriangulene through Proton Affinity, Aromatic Stabilization Energy, and Aromatic Magnetism

Herein, we report designing a new Δ (delta-shaped) proton sponge base of 4,12-dihydrogen-4,8,12-triazatriangulene (compound 1) and calculating its proton affinity (PA), aromatic stabilization, natural bond orbital (NBO), electron density ρ(r), Laplacian of electron density ∇2 ρ(r), (2D-3D) multidimensional off-nucleus magnetic shielding (σzz (r) and σiso (r)), and scanning nucleus-independent chemical shift (NICSzz and NICS). Density functional theory (DFT) at B3LYP/6-311+G(d,p), ωB97XD/6-311+G(d,p), and PW91/def2TZVP were used to compute the magnetic shielding variables. In addition, relevant bases like pyridine, quinoline, and acridine were also studied and compared. The protonation of compound 1 yields a highly symmetric carbocation of three Hückel benzenic rings. Comparing our findings of the studied molecules showed that compound 1 precedes others in PA, aromatic isomerization stabilization energy, and basicity. Therefore, the basicity may be enhanced when a conjugate acid gains higher aromatic features than its unprotonated base. Both multidimensional σzz (r) and σiso (r) off-nucleus magnetic shieldings outperformed electron-based techniques and can visually monitor changes in aromaticity that occur by protonation. The B3LYP/6-311+G(d,p), ωB97XD/6-311+G(d,p), and PW91/def2TZVP levels showed no significant differences in detailing isochemical shielding surfaces.

Orbital-symmetry effects on magnetic exchange in open-shell nanographenes

Open-shell nanographenes appear as promising candidates for future applications in spintronics and quantum technologies. A critical aspect to realize this potential is to design and control the magnetic exchange. Here, we reveal the effects of frontier orbital symmetries on the magnetic coupling in diradical nanographenes through scanning probe microscope measurements and different levels of theoretical calculations. In these open-shell nanographenes, the exchange energy exhibits a remarkable variation between 20 and 160 meV. Theoretical calculations reveal that frontier orbital symmetries play a key role in affecting the magnetic coupling on such a large scale. Moreover, a triradical nanographene is demonstrated for investigating the magnetic interaction among three unpaired electrons with unequal magnetic exchange, in agreement with Heisenberg spin model calculations. Our results provide insights into both theoretical design and experimental realization of nanographene materials with different exchange interactions through tuning the orbital symmetry, potentially useful for realizing magnetically operable graphene-based nanomaterials.

Autonomous Molecular Structure Imaging with High-Resolution Atomic Force Microscopy for Molecular Mixture Discovery

Due to its single-molecule sensitivity, high-resolution atomic force microscopy (HR-AFM) has proved to be a valuable and uniquely advantageous tool to study complex molecular mixtures, which hold promise for developing clean energy and achieving environmental sustainability. However, significant challenges remain to achieve the full potential of the sophisticated and time-consuming experiments. Automation combined with machine learning (ML) and artificial intelligence (AI) is key to overcoming these challenges. Here we present Auto-HR-AFM, an AI tool to automatically collect HR-AFM images of petroleum-based mixtures. We trained an instance segmentation model to teach Auto-HR-AFM how to recognize features in HR-AFM images. Auto-HR-AFM then uses that information to optimize the imaging by adjusting the probe-molecule distance for each molecule in the run. Auto-HR-AFM is the initial tool that will lead to fully automated scanning probe microscopy (SPM) experiments, from start to finish. This automation will allow SPM to become a mainstream characterization technique for complex mixtures, an otherwise unattainable target.

Portraits of Soot Molecules Reveal Pathways to Large Aromatics, Five-/Seven-Membered Rings, and Inception through π-Radical Localization

Incipient soot early in the flame was studied by high-resolution atomic force microscopy and scanning tunneling microscopy to resolve the atomic structure and orbital densities of single soot molecules prepared on bilayer NaCl on Cu(111). We resolved extended catacondensed and pentagonal-ring linked (pentalinked) species indicating how small aromatics cross-link and cyclodehydrogenate to form moderately sized aromatics. In addition, we resolved embedded pentagonal and heptagonal rings in flame aromatics. These nonhexagonal rings suggest simultaneous growth through aromatic cross-linking/cyclodehydrogenation and hydrogen abstraction acetylene addition. Moreover, we observed three classes of open-shell π-radical species. First, radicals with an unpaired π-electron delocalized along the molecule's perimeter. Second, molecules with partially localized π-electrons at zigzag edges of a π-radical. Third, molecules with strong localization of a π-electron at pentagonal- and methylene-type sites. The third class consists of π-radicals localized enough to enable thermally stable bonds, as well as multiradical species such as diradicals in the open-shell triplet state. These π-diradicals can rapidly cluster through barrierless chain reactions enhanced by van der Waals interactions. These results improve our understanding of soot formation and the products formed by combustion and could provide insights for cleaner combustion and the production of hydrogen without CO₂ emissions.

Quantum simulator to emulate lower-dimensional molecular structure

Bottom-up quantum simulators have been developed to quantify the role of various interactions, dimensionality, and structure in creating electronic states of matter. Here, we demonstrated a solid-state quantum simulator emulating molecular orbitals, based solely on positioning individual cesium atoms on an indium antimonide surface. Using scanning tunneling microscopy and spectroscopy, combined with ab initio calculations, we showed that artificial atoms could be made from localized states created from patterned cesium rings. These artificial atoms served as building blocks to realize artificial molecular structures with different orbital symmetries. These corresponding molecular orbitals allowed us to simulate two-dimensional structures reminiscent of well-known organic molecules. This platform could further be used to monitor the interplay between atomic structures and the resulting molecular orbital landscape with submolecular precision.

Organic Molecules as Origin of Visible-Range Single Photon Emission from Hexagonal Boron Nitride and Mica

The discovery of room-temperature single-photon emitters (SPEs) hosted by two-dimensional hexagonal boron nitride (2D hBN) has sparked intense research interest. Although emitters in the vicinity of 2 eV have been studied extensively, their microscopic identity has remained elusive. The discussion of this class of SPEs has centered on point defects in the hBN crystal lattice, but none of the candidate defect structures have been able to capture the great heterogeneity in emitter properties that is observed experimentally. Employing a widely used sample preparation protocol but disentangling several confounding factors, we demonstrate conclusively that heterogeneous single-photon emission at ∼2 eV associated with hBN originates from organic molecules, presumably aromatic fluorophores. The appearance of those SPEs depends critically on the presence of organic processing residues during sample preparation, and emitters formed during heat treatment are not located within the hBN crystal as previously thought, but at the hBN/substrate interface. We further demonstrate that the same class of SPEs can be observed in a different 2D insulator, fluorophlogopite mica.

Predicting Magnetic Coupling and Spin-Polarization Energy in Triangulene Analogues

Triangulene and its analogue metal-free magnetic systems have garnered increasing attention since their discovery. Predicting the magnetic coupling and spin-polarization energy with quantitative accuracy is beyond the predictive power of today's density functional theory (DFT) due to their intrinsic multireference character. Herein, we create a benchmark dataset of 25 magnetic systems with nonlocal spin densities, including the triangulene monomer, dimer, and their analogues. We calculate the magnetic coupling (J) and spin-polarization energy (ΔE_spin) of these systems using complete active space self-consistent field (CASSCF) and coupled-cluster methods as high-quality reference values. This reference data is then used to benchmark 22 DFT functionals commonly used in material science. Our results show that, while some functionals consistently correctly predict the qualitative character of the ground state, achieving quantitative accuracy with small relative errors is currently not feasible. PBE0, M06-2X, and MN15 are predicting the correct electronic ground state for all systems investigated here and also have the lowest mean absolute error for predicting both ΔE_spin (0.34, 0.32, and 0.31 eV) and J (11.74, 12.66, and 10.64 meV). They may therefore also serve as starting points for higher-level methods such as the GW or the random phase approximation. As other functionals fail for the prediction of the ground state, they cannot be recommended for metal-free magnetic systems.

Algebraic Method for Solving Multiple Degenerate Eigenvalues in [r]Triangulenes

An algebraic procedure for overcoming the multiple degeneracy problem in eigenvalue (root) determination of the characteristic polynomial of 3-fold symmetrical molecular graphs is given. This leads to the tabulation of Hückel molecular orbital binding energy (E_π) and eigenvalues (roots) for [2]triangulene to [9]trianguene for the first time. Triangulenes are the smallest possible condensed benzenoid polyradicals.