Aza-[3]Triangulene Nodes: Tunable Quantum Building Blocks

Updated 23 October 2025

Aza-[3]Triangulene nodes are nitrogen-doped triangular nanographene molecules characterized by robust open-shell configurations and symmetry-adapted frontier orbitals.
Their electronic and magnetic properties are modulated via nitrogen substitution, substrate-induced charge transfer, and controlled Jahn–Teller distortions.
These nodes serve as programmable building blocks for molecular spintronics, quantum simulation, and the design of topologically correlated covalent organic frameworks.

Aza-[3]Triangulene (A[3]T) nodes are nitrogen-doped, triangular nanographene molecules derived from the [3]triangulene parent—a prototypical open-shell graphene quantum dot. The introduction of a nitrogen atom profoundly modulates the electronic, magnetic, and topological properties of the system, enabling designer quantum functionalities for molecular electronics, spintronics, and covalent organic frameworks (COFs). A[3]T nodes are characterized by their robust open-shell configurations, symmetry-adapted frontier orbitals, and their ability to undergo controlled intermolecular hybridizations, making them foundational building blocks for programmable correlated quantum nanomaterials.

1. Electronic Structure and Ground State Spin

A[3]Triangulene nodes inherit the unique open-shell behavior from [3]triangulene, itself defined by a triangular topology of fused benzene rings in which full electron pairing is precluded by the underlying sublattice imbalance. At the single-molecule level, [3]triangulene hosts two half-filled zero-energy modes and has a many-body ground state with $S=1$ (Ortiz et al., 2022). In A[3]T, replacement of a carbon by nitrogen alters the electron count and spatial distribution, introducing strong local perturbations in the zero-mode shell yet retaining open-shell character (Wang et al., 2021).

Density functional theory (DFT) and tight-binding (TB) calculations show that:

The frontier molecular orbitals (HOMO/SOMOs and LUMO/SUMOs) are highly sensitive to N-doping, allowing for pronounced tunability in chemical hardness $(\eta)$ and electronegativity $(\chi)$ via

$\chi = -\frac{1}{2}\left(E_{\text{HOMO}} + E_{\text{LUMO}}\right), \qquad \eta = \frac{1}{2}\left(E_{\text{LUMO}} - E_{\text{HOMO}}\right)$

(Sharma et al., 2017).

Charge transfer between A[3]T and substrates (Au(111), Ag(111)) can switch the ground state between open-shell (S = 1) and closed-shell (S = 0), offering external control over its magnetic state (Wang et al., 2021).
The degeneracy and character of zero modes can be probed/analyzed through local impurity substitutions (e.g., localized N atoms), as described by the impurity Hamiltonian:

$H^{\text{aza}} = H + V_{\text{imp}} \,, \quad V_{\text{imp}} = \delta \, c_{\text{imp}}^\dagger c_{\text{imp}}$

which lifts the zero-mode degeneracy proportionally to the local wave function amplitude at the impurity site, $\Delta = \delta |b'_{\text{imp}}|^2$ (Rodrigues et al., 4 Jun 2024).

A[3]T nodes typically retain two degenerate (or nearly degenerate) singly-occupied orbitals in the absence of symmetry-breaking perturbations, resulting in high-spin triplet or higher-spin (S = 3/2 in extended/aggregated forms) ground states.

2. Symmetry, Jahn–Teller Distortions, and Frontier Orbitals

The symmetry of A[3]T nodes is a critical factor in their electronic and magnetic structure. Pristine triangulene adopts $D_{3h}$ symmetry, yielding well-defined frontier orbitals that transform with characteristic $C_3$ phase factors (Lawrence et al., 2023). Upon introduction of nitrogen, two distinct symmetry classes emerge:

Centrally doped A[3]T: Nitrogen at the minority sublattice (central site) can induce Jahn–Teller distortions, lowering molecular symmetry from $D_{3h}$ to $C_{2v}$ and reducing the total spin via a quenching of radical character (e.g., S ideally drops from 3/2 to 1/2) (Lawrence et al., 2023).
Edge/stabilized A[3]T in frameworks or fused arrays: Covalent coupling (e.g., via cumulene/ethynylene linkers in COFs) can restore/stabilize $D_{3h}$ symmetry, preserve three degenerate single-occupied frontier orbitals, and suppress Jahn–Teller distortions even in nitrogen-doped cores (Yan et al., 17 Oct 2025).

The symmetry-adapted zero mode basis is mathematically constructed to diagonalize symmetry operators (e.g., $C_3$ rotation, reflection), ensuring that interaction matrix elements (density-assisted hopping $t_{12}$ , pair hopping $\Delta$ ) respect invariance constraints (Ortiz et al., 2019).

3. Synthesis, Substrate Effects, and On-Surface Chemistry

A[3]Triangulene nodes are synthesized via regioselective on-surface strategies, including the deposition of ketone- or aryl-functionalized precursors onto clean metal substrates, followed by radical activation by atomic hydrogen and thermal annealing (Wang et al., 2021, Daugherty et al., 24 Feb 2024). Key steps include:

Hydrogen reduction and annealing: Remove edge or core functional groups, allowing for cyclodehydrogenation and planarization.
Tip-induced manipulation: STM tips can selectively dehydrogenate reactive sites, enabling precise control over radical formation and charge state (Turco et al., 2022).
Substrate control: On Au(111), A[3]T nodes donate electrons and yield open-shell triplets (e.g., Kondo resonance width $\sim$ 13 mV indicating $S=1$ ); on Ag(111), substrate electron donation leads to closed-shell configurations (no magnetic fingerprints, fully paired orbitals) (Wang et al., 2021, Calupitan et al., 2023).

Substrate-induced charge transfer thus allows toggling between magnetic and non-magnetic states, and fusion pathways (e.g., dimer formation) are strongly symmetry/stereochemically controlled—only asymmetric dimers on Au(111) reveal open-shell signatures and Kondo effects due to localized spin density arising from disrupted $\pi$ -conjugation (Calupitan et al., 2023).

4. Magnetic Properties, Exchange Coupling, and Many-Body Effects

A[3]T nodes, when isolated or in molecular ensembles, manifest robust $\pi$ -paramagnetism and complex magnetic couplings:

Exchange Hamiltonians:
- For dimers/rings, the effective Heisenberg model:
$H = J \sum_{i=1}^N \vec{S}_i \cdot \vec{S}_{i+1}$

describes antiferromagnetic coupling between local $S = 1$ spins (e.g., $J \sim 18$ meV in a triangulene nanostar ring) (Hieulle et al., 2021). - For triple radicals (e.g., N-doped triangulene trimer TTAT), symmetric ferromagnetic coupling yields $S = 3/2$ ground state with:

$\hat{H} = J \left(\vec{S}_1 \cdot \vec{S}_2 + \vec{S}_1 \cdot \vec{S}_3 + \vec{S}_2 \cdot \vec{S}_3 \right), \quad J \sim 10\,\text{meV}$

(Vegliante et al., 14 May 2025).
Zero-mode occupation and spin counting: The total spin obeys

$S = \frac{1}{2}|N_A - N_B|$

with $N_A, N_B$ counting sublattice sites (including N substitutions modifying $N_A$ ) (Li et al., 2019, Ortiz et al., 2019).

Band structure in periodic arrays: Hybridization between zero modes yields narrow bands, Mott-insulating behavior at half filling, and topological end states or collective magnetic excitations (e.g., Haldane gap, symmetry-protected edge states) (Ortiz et al., 2022, Catarina et al., 2023).
Spin wave spectrum: Calculated using random phase approximation (RPA) and corroborated by STM/STS, showing degenerate Goldstone modes and magnon excitations in AF-ordered COFs (Catarina et al., 2023).

5. Flat Bands, Phase-Frustration, and Topological COFs

A[3]T nodes integrated within diatomic Kagome COFs form quantum lattices characterized by flat bands and orbital phase frustration (Yan et al., 17 Oct 2025):

Wannier function construction: Each A[3]T node contributes three edge-localized MLWFs; their alternating phase arrangements (arising from $D_{3h}$ symmetry and conjugated cumulene bridges) produce orthogonality and destructive interference, sharply reducing hopping and generating non-dispersive (flat) bands.
TB Hamiltonian (simplified):

$H = -t_1 \sum_{\langle i,j \rangle} c_i^\dagger c_j - t_2 \sum_{\langle\langle i,j \rangle\rangle} c_i^\dagger c_j + E_A \sum_i c_i^\dagger c_i$

Band features: Flat bands (CFB/VFB), Dirac dispersions, and Van Hove singularities observed via STM/STS and supported by DFT and FT-QPI analysis.

Flat bands in A[3]T-based Kagome lattices enhance electronic correlation, supporting correlated phases such as magnetism, superconductivity, and topologically protected quantum states.

6. Methodologies: Theoretical Models and Experimental Probes

The investigation of A[3]T node properties utilizes an integrated computational and experimental toolkit:

Computational:
- Tight-binding (TB), mean-field Hubbard, and extended Hubbard models for zero-mode analysis and many-body state ordering (Ortiz et al., 2019, Catarina et al., 2023).
- DFT (PBE, HSE06) for frontier orbital mapping, symmetry optimization, and hybridization energetics (Wang et al., 2021, Yan et al., 17 Oct 2025).
- CASCI/CASSCF for polyradical systems and multiconfigurational exchange interactions (Vegliante et al., 14 May 2025).
- Wannier function and QPI analysis for fine mapping of band structure and phase interplay (Yan et al., 17 Oct 2025).
Experimental:
- Scanning tunneling microscopy (STM), bond-resolved STM (BRSTM), and non-contact AFM (nc-AFM) for real-space lattice imaging and electronic structure determination.
- dI/dV spectroscopy for frontier orbital and Kondo resonance detection, probing zero-mode occupancy, and mapping topological end states (Wang et al., 2021, Daugherty et al., 24 Feb 2024).
- Manipulation techniques (atomic hydrogen reduction, STM tip-induced dehydrogenation) for precise synthesis and charge state control (Turco et al., 2022).

Substrate selection (Au(111), Ag(111), Cu(111)), annealing protocol, and precursor design are all critical in directing the magnetic and electronic configuration of A[3]T nodes.

7. Applications and Future Directions

A[3]Triangulene nodes serve as fundamental elements for emerging quantum nanotechnologies:

Spintronics: Tunable spin states (S = 1, S = 3/2) and robust $\pi$ -paramagnetism offer applications in spin logic, quantum bits, and molecular magnets (Vegliante et al., 14 May 2025, Li et al., 2019).
Quantum simulation: Networks of A[3]T nodes form Mott insulators, Haldane spin chains, and models for topological edge states, enabling simulation of correlated quantum phenomena (Ortiz et al., 2022, Catarina et al., 2023).
Nanoelectronics and optoelectronics: Narrow-gap semiconducting ribbons and designer band structures support molecular-scale switching, spin-filtering, and optoelectronic components (Daugherty et al., 24 Feb 2024, Lawrence et al., 2023).
Programmable COFs: Modular synthesis of phase-frustrated Kagome lattices with tailored band structure opens pathways toward correlated quantum materials, possibly hosting exotic magnetic and superconducting phases (Yan et al., 17 Oct 2025).

Future research will likely expand the chemical landscape of A[3]T nodes (via alternative heteroatom doping, linker engineering), investigate their dynamic spin interactions via ultrafast spectroscopy, and exploit their designer properties for molecular-scale quantum devices and hybrid classical-quantum interfaces.

Aza-[3]Triangulene nodes encapsulate the convergence of symmetry engineering, orbital hybridization, and open-shell chemistry in molecular graphenes, providing a uniquely tunable platform for next-generation functional materials and quantum nanotechnology.