Designer spin order in diradical nanographenes

Tunable Magnetic Coupling in Graphene Nanoribbon Quantum Dots

Carbon-based quantum dots (QDs) enable flexible manipulation of electronic behavior at the nanoscale, but controlling their magnetic properties requires atomically precise structural control. While magnetism is observed in organic molecules and graphene nanoribbons (GNRs), GNR precursors enabling bottom-up fabrication of QDs with various spin ground states have not yet been reported. Here the development of a new GNR precursor that results in magnetic QD structures embedded in semiconducting GNRs is reported. Inserting one such molecule into the GNR backbone and graphitizing it results in a QD region hosting one unpaired electron. QDs composed of two precursor molecules exhibit nonmagnetic, antiferromagnetic, or antiferromagnetic ground states, depending on the structural details that determine the coupling behavior of the spins originating from each molecule. The synthesis of these QDs and the emergence of localized states are demonstrated through high-resolution atomic force microscopy (HR-AFM), scanning tunneling microscopy (STM) imaging, and spectroscopy, and the relationship between QD atomic structure and magnetic properties is uncovered. GNR QDs provide a useful platform for controlling the spin-degree of freedom in carbon-based nanostructures.

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.

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.

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.

Stiffer Bonding of Armchair Edge in Single-Layer Molybdenum Disulfide Nanoribbons

The physical and chemical properties of nanoribbon edges are important for characterizing nanoribbons and applying them in electronic devices, sensors, and catalysts. The mechanical response of molybdenum disulfide nanoribbons, which is an important issue for their application in thin resonators, is expected to be affected by the edge structure, albeit this result is not yet being reported. In this work, the width-dependent Young's modulus is precisely measured in single-layer molybdenum disulfide nanoribbons with armchair edges using the developed nanomechanical measurement based on a transmission electron microscope. The Young's modulus remains constant at ≈166 GPa above 3 nm width, but is inversely proportional to the width below 3 nm, suggesting a higher bond stiffness for the armchair edges. Supporting the experimental results, the density functional theory calculations show that buckling causes electron transfer from the Mo atoms at the edges to the S atoms on both sides to increase the Coulomb attraction.

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.

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.

Strong ferromagnetism of g-C3N4 achieved by atomic manipulation

Two-dimensional (2D) metal-free ferromagnetic materials are ideal candidates to fabricate next-generation memory and logic devices, but optimization of their ferromagnetism at atomic-scale remains challenging. Theoretically, optimization of ferromagnetism could be achieved by inducing long-range magnetic sequence, which requires short-range exchange interactions. In this work, we propose a strategy to enhance the ferromagnetism of 2D graphite carbon nitride (g-C₃N₄), which is facilitating the short-range exchange interaction by introducing in-planar boron bridges. As expected, the ferromagnetism of g-C₃N₄ was significantly enhanced after the introduction of boron bridges, consistent with theoretical calculations. Overall, boosting ferromagnetism of 2D materials by introducing bridging groups is emphasized, which could be applied to manipulate the magnetism of other materials.

Triangle Counting Rule: An Approach to Forecast the Magnetic Properties of Benzenoid Polycyclic Hydrocarbons

Open-shell benzenoid polycyclic hydrocarbons (BPHs) are promising materials for future quantum applications. However, the search for and realization of open-shell BPHs with desired properties is a challenging task due to the gigantic chemical space of BPHs, requiring new strategies for both theoretical understanding and experimental advancement. In this work, by building a structure database of BPHs through graphical enumeration, performing data-driven analysis, and combining tight-binding and mean-field Hubbard calculations, we discovered that the number of the internal vertices of the BPH graphs is closely correlated to their open-shell characters. We further established a simple rule, the triangle counting rule, to predict the magnetic ground states of BPHs. These findings not only provide a database of open-shell BPHs, but also extend the well-known Lieb's theorem and Ovchinnikov's rule and provide a straightforward method for designing open-shell carbon nanostructures. These insights may aid in the exploration of emerging quantum phases and the development of magnetic carbon materials for technology applications.

Steering Large Magnetic Exchange Coupling in Nanographenes near the Closed-Shell to Open-Shell Transition

The design of open-shell carbon-based nanomaterials is at the vanguard of materials science, steered by their beneficial magnetic properties like weaker spin-orbit coupling than that of transition metal atoms and larger spin delocalization, which are of potential relevance for future spintronics and quantum technologies. A key parameter in magnetic materials is the magnetic exchange coupling (MEC) between unpaired spins, which should be large enough to allow device operation at practical temperatures. In this work, we theoretically and experimentally explore three distinct families of nanographenes (NGs) (A, B, and C) featuring majority zigzag peripheries. Through many-body calculations, we identify a transition from a closed-shell ground state to an open-shell ground state upon an increase of the molecular size. Our predictions indicate that the largest MEC for open-shell NGs occurs in proximity to the transition between closed-shell and open-shell states. Such predictions are corroborated by the on-surface syntheses and structural, electronic, and magnetic characterizations of three NGs (A[3,5], B[4,5], and C[4,3]), which are the smallest open-shell systems in their respective chemical families and are thus located the closest to the transition boundary. Notably, two of the NGs (B[4,5] and C[4,3]) feature record values of MEC (close to 200 meV) measured on the Au(111) surface. Our strategy for maximizing the MEC provides perspectives for designing carbon nanomaterials with robust magnetic ground states.

Recent Advances in the Spintronic Application of Carbon-Based Nanomaterials

The term "carbon-based spintronics" mostly refers to the spin applications in carbon materials such as graphene, fullerene, carbon nitride, and carbon nanotubes. Carbon-based spintronics and their devices have undergone extraordinary development recently. The causes of spin relaxation and the characteristics of spin transport in carbon materials, namely for graphene and carbon nanotubes, have been the subject of several theoretical and experimental studies. This article gives a summary of the present state of research and technological advancements for spintronic applications in carbon-based materials. We discuss the benefits and challenges of several spin-enabled, carbon-based applications. The advantages include the fact that they are significantly less volatile than charge-based electronics. The challenge is in being able to scale up to mass production.

Quantum nanomagnets in on-surface metal-free porphyrin chains

Unlike classic spins, quantum magnets are spin systems that interact via the exchange interaction and exhibit collective quantum behaviours, such as fractional excitations. Molecular magnetism often stems from d/f-transition metals, but their spin-orbit coupling and crystal field induce a significant magnetic anisotropy, breaking the rotation symmetry of quantum spins. Thus, it is of great importance to build quantum nanomagnets in metal-free systems. Here we have synthesized individual quantum nanomagnets based on metal-free multi-porphyrin systems. Covalent chains of two to five porphyrins were first prepared on Au(111) under ultrahigh vacuum, and hydrogen atoms were then removed from selected carbons using the tip of a scanning tunnelling microscope. The conversion of specific porphyrin units to their radical or biradical state enabled the tuning of intra- and inter-porphyrin magnetic coupling. Characterization of the collective magnetic properties of the resulting chains showed that the constructed S = 1/2 antiferromagnets display a gapped excitation, whereas the S = 1 antiferromagnets exhibit distinct end states between even- and odd-numbered spin chains, consistent with Heisenberg model calculations.

Synthesis of Dendronized Polymers on the Au(111) Surface

Dendronized polymers (DPs) consist of a linear polymeric backbone with dendritic side chains. Fine-tuning of the functional groups in the side chains enriches the structural versatility of the DPs and imparts a variety of novel physical properties. Herein, the first on-surface synthesis of DPs is achieved via the postfunctionalization of polymers on Au(111), in which the surface-confinement-induced planar conformation and chiral configurations were unambiguously characterized. While the dendronized monomer was synthesized in situ on Au(111), the subsequent polymerization afforded only short, cross-linked DP chains owing to multiple side reactions. The postfunctionalization approach selectively produced brominated polyphenylene backbone moieties by the deiodination polymerization of 4-bromo-4″-iodo-5'-(4-iodophenyl)-1,1':3',1″-terphenyl on Au(111), which smoothly underwent divergent cross-coupling reactions with two different isocyanides to form two types of DPs as individual long chains.

Addressing Electron Spins Embedded in Metallic Graphene Nanoribbons

Spin-hosting graphene nanostructures are promising metal-free systems for elementary quantum spintronic devices. Conventionally, spins are protected from quenching by electronic band gaps, which also hinder electronic access to their quantum state. Here, we present a narrow graphene nanoribbon substitutionally doped with boron heteroatoms that combines a metallic character with the presence of localized spin 1/2 states in its interior. The ribbon was fabricated by on-surface synthesis on a Au(111) substrate. Transport measurements through ribbons suspended between the tip and the sample of a scanning tunneling microscope revealed their ballistic behavior, characteristic of metallic nanowires. Conductance spectra show fingerprints of localized spin states in the form of Kondo resonances and inelastic tunneling excitations. Density functional theory rationalizes the metallic character of the graphene nanoribbon due to the partial depopulation of the valence band induced by the boron atoms. The transferred charge builds localized magnetic moments around the boron atoms. The orthogonal symmetry of the spin-hosting state's and the valence band's wave functions protects them from mixing, maintaining the spin states localized. The combination of ballistic transport and spin localization into a single graphene nanoribbon offers the perspective of electronically addressing and controlling carbon spins in real device architectures.

Carbon-based nanostructures as a versatile platform for tunableπ-magnetism

Emergence ofπ-magnetism in open-shell nanographenes has been theoretically predicted decades ago but their experimental characterization was elusive due to the strong chemical reactivity that makes their synthesis and stabilization difficult. In recent years, on-surface synthesis under vacuum conditions has provided unprecedented opportunities for atomically precise engineering of nanographenes, which in combination with scanning probe techniques have led to a substantial progress in our capabilities to realize localized electron spin states and to control electron spin interactions at the atomic scale. Here we review the essential concepts and the remarkable advances in the last few years, and outline the versatility of carbon-basedπ-magnetic materials as an interesting platform for applications in spintronics and quantum technologies.

Manipulation of Spin Polarization in Boron-Substituted Graphene Nanoribbons

The design of magnetic topological states due to spin polarization in an extended π carbon system has great potential in spintronics application. Although magnetic zigzag edges in graphene nanoribbons (GNRs) have been investigated earlier, real-space observation and manipulation of spin polarization in a heteroatom substituted system remains challenging. Here, we investigate a zero-bias peak at a boron site embedded at the center of an armchair-type GNR on a AuSi_X/Au(111) surface with a combination of low-temperature scanning tunneling microscopy/spectroscopy and density functional theory calculations. After the tip-induced removal of a Si atom connected to two adjacent boron atoms, a clear Kondo resonance peak appeared and was further split by an applied magnetic field of 12 T. This magnetic state can be relayed along the longitudinal axis of the GNR by sequential removal of Si atoms.

Elucidating the molecular orbital dependence of the total electronic energy in multireference problems

The accurate resolution of the chemical properties of strongly correlated systems, such as biradicals, requires the use of electronic structure theories that account for both multi-reference and dynamic correlation effects. A variety of methods exist that aim to resolve the dynamic correlation in multi-reference problems, commonly relying on an exponentially scaling complete-active-space self-consistent-field (CASSCF) calculation to generate reference molecular orbitals (MOs). However, while CASSCF orbitals provide the optimal solution for a selected set of correlated (active) orbitals, their suitability in the quest for the resolution of the total correlation energy has not been thoroughly investigated. Recent research has shown the ability of Kohn-Shan density functional theory to provide improved orbitals for coupled cluster (CC) and Møller-Plesset perturbation theory (MP) calculations. Here, we extend the search for optimal and more cost effective MOs to post-configuration-interaction [post-(CI)] methods, surveying the ability of the MOs obtained with various density functional theory (DFT) functionals, as well as Hartree-Fock and CC and MP calculations to accurately capture the total electronic correlation energy. Applying the anti-Hermitian contracted Schrödinger equation to the dissociation of N₂, the calculation of biradical singlet-triplet gaps, and the transition states of bicylobutane isomerization, we demonstrate that DFT provides a cost-effective alternative to CASSCF in providing reference orbitals for post-CI dynamic correlation calculations.

On-surface synthesis of triangulene trimers via dehydration reaction

Triangulene and its homologues are of considerable interest for molecular spintronics due to their high-spin ground states as well as the potential for constructing high spin frameworks. Realizing triangulene-based high-spin system on surface is challenging but of particular importance for understanding π-electron magnetism. Here, we report two approaches to generate triangulene trimers on Au(111) by using surface-assisted dehydration and alkyne trimerization, respectively. We find that the developed dehydration reaction shows much higher chemoselectivity thus resulting in significant promotion of product yield compared to that using alkyne trimerization approach, through cutting the side reaction path. Combined with spin-polarized density functional theory calculations, scanning tunneling spectroscopy measurements identify the septuple (S = 3) high-spin ground state and quantify the collective ferromagnetic interaction among three triangulene units. Our results demonstrate the approaches to fabricate high-quality triangulene-based high spin systems and understand their magnetic interactions, which are essential for realizing carbon-based spintronic devices.

Magnetic Interactions Between Radical Pairs in Chiral Graphene Nanoribbons

Open-shell graphene nanoribbons have become promising candidates for future applications, including quantum technologies. Here, we characterize magnetic states hosted by chiral graphene nanoribbons (chGNRs). The substitution of a hydrogen atom at the chGNR edge by a ketone effectively adds one p_z electron to the π-electron network, producing an unpaired π-radical. A similar scenario occurs for regular ketone-functionalized chGNRs in which one ketone is missing. Two such radical states can interact via exchange coupling, and we study those interactions as a function of their relative position, which includes a remarkable dependence on the chirality, as well as on the nature of the surrounding ribbon, that is, with or without ketone functionalization. Besides, we determine the parameters whereby this type of system with oxygen heteroatoms can be adequately described within the widely used mean-field Hubbard model. Altogether, we provide insight to both theoretically model and devise GNR-based nanostructures with tunable magnetic properties.

Defect-Induced π-Magnetism into Non-Benzenoid Nanographenes

The synthesis of nanographenes (NGs) with open-shell ground states have recently attained increasing attention in view of their interesting physicochemical properties and great prospects in manifold applications as suitable materials within the rising field of carbon-based magnetism. A potential route to induce magnetism in NGs is the introduction of structural defects, for instance non-benzenoid rings, in their honeycomb lattice. Here, we report the on-surface synthesis of three open-shell non-benzenoid NGs (A1, A2 and A3) on the Au(111) surface. A1 and A2 contain two five- and one seven-membered rings within their benzenoid backbone, while A3 incorporates one five-membered ring. Their structures and electronic properties have been investigated by means of scanning tunneling microscopy, noncontact atomic force microscopy and scanning tunneling spectroscopy complemented with theoretical calculations. Our results provide access to open-shell NGs with a combination of non-benzenoid topologies previously precluded by conventional synthetic procedures.

Pseudo-atomic orbital behavior in graphene nanoribbons with four-membered rings

The incorporation of nonhexagonal rings into graphene nanoribbons (GNRs) is an effective strategy for engineering localized electronic states, bandgaps, and magnetic properties. Here, we demonstrate the successful synthesis of nanoribbons having four-membered ring (cyclobutadienoid) linkages by using an on-surface synthesis approach involving direct contact transfer of coronene-type precursors followed by thermally assisted [2 + 2] cycloaddition. The resulting coronene-cyclobutadienoid nanoribbons feature a narrow 600-meV bandgap and novel electronic frontier states that can be interpreted as linear chains of effective p_x and p_y pseudo-atomic orbitals. We show that these states give rise to exceptional physical properties, such as a rigid indirect energy gap. This provides a previously unexplored strategy for constructing narrow gap GNRs via modification of precursor molecules whose function is to modulate the coupling between adjacent four-membered ring states.

Spin State Switching in Heptauthrene Nanostructure by Electric Field: Computational Study

Recent experimental studies proved the presence of the triplet spin state in atomically precise heptauthrene nanostructure of nanographene type (composed of two interconnected triangles with zigzag edge). In the paper, we report the computational study predicting the possibility of controlling this spin state with an external in-plane electric field by causing the spin switching. We construct and discuss the ground state magnetic phase diagram involving S=1 (triplet) state, S=0 antiferromagnetic state and non-magnetic state and predict the switching possibility with the critical electric field of the order of 0.1 V/Å. We discuss the spin distribution across the nanostructure, finding its concentration along the longest zigzag edge. To model our system of interest, we use the mean-field Hubbard Hamiltonian, taking into account the in-plane external electric field as well as the in-plane magnetic field (in a form of the exchange field from the substrate). We also assess the effect of uniaxial strain on the magnetic phase diagram.

Designing Two-Dimensional Versatile Room-Temperature Ferromagnets via Assembling Large-Scale Magnetic Quantum Dots

Two-dimensional (2D) ferromagnets possess astonishing potential in new-concept spintronics. However, most of the reported intrinsic 2D ferromagnets show a low Curie temperature far below room temperature. Here, we propose a series of 2D magnetic covalent and metal organic frameworks (COFs/MOFs) by assembling triangular zigzag graphene quantum dots (TZGDs) with various linkages, involving small-sized TZGDs, nonmetal atoms, magnetic metal atoms, and molecules. Upon first-principles calculations, we demonstrate 2D magnetic semiconductors with an enhanced Curie temperature of up to 472 K can be realized through the strong p(d)-p direct exchange interaction between TZGDs and linkages. Particularly, the TZGD size hardly affects the Curie temperature, whereas linkages can modulate the Curie temperature significantly. The TZGD size and linkages can regulate the electronic and magnetic properties of TZGD-based 2D ferromagnets. Our results confirm the possibility of designing 2D ferromagnets based on TZGDs and motivate the research of 2D ferromagnets on magnetic quantum dots and molecular magnets.

Visualizing designer quantum states in stable macrocycle quantum corrals

Creating atomically precise quantum architectures with high digital fidelity and desired quantum states is an important goal in a new era of quantum technology. The strategy of creating these quantum nanostructures mainly relies on atom-by-atom, molecule-by-molecule manipulation or molecular assembly through non-covalent interactions, which thus lack sufficient chemical robustness required for on-chip quantum device operation at elevated temperature. Here, we report a bottom-up synthesis of covalently linked organic quantum corrals (OQCs) with atomic precision to induce the formation of topology-controlled quantum resonance states, arising from a collective interference of scattered electron waves inside the quantum nanocavities. Individual OQCs host a series of atomic orbital-like resonance states whose orbital hybridization into artificial homo-diatomic and hetero-diatomic molecular-like resonance states can be constructed in Cassini oval-shaped OQCs with desired topologies corroborated by joint ab initio and analytic calculations. Our studies open up a new avenue to fabricate covalently linked large-sized OQCs with atomic precision to engineer desired quantum states with high chemical robustness and digital fidelity for future practical applications.