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Triangulene-based diradicals as a blueprint for molecular quantum platforms with optical addressability and long spin coherence times

T0 review · 2 major / 7 minor · reviewed 2026-07-10 · glm-5.2

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Pith's one-line read Triangulene diradicals predicted as molecular analogs of NV centers

desk verdict First ab initio spin-resolved ISC rates in organic diradicals; ODMR selectivity is geometry-sensitive and not fully resolved read the letter →

arxiv 2607.08634 v1 pith:WRUBVL4L submitted 2026-07-09 quant-ph cond-mat.mtrl-sci

Arup Sarkar , Cathal Hogan , Conor Ryan , Lorenzo A. Mariano , Alessandro Lunghi This is my paper · ORCID
classification quant-phcond-mat.mtrl-sci
keywords triangulenediradicalNVcenteranalogspincoherenceintersystemcrossingODMRmolecularqubitspin-phononrelaxation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that triangulene and its aza-cation derivative — small, open-shell organic molecules with triplet ground states — replicate the key electronic architecture of nitrogen-vacancy (NV) centers in diamond. Using multireference quantum chemistry and first-principles spin-vibronic dynamics, the authors compute that these diradicals have a triplet ground state separated from the first singlet by roughly 0.5 eV, optically accessible excited triplets, and spin-selective intersystem crossing (ISC) at room temperature. The spin-selective ISC is the crucial feature: it means different spin states fluoresce at different rates, enabling optical readout of the spin state (ODMR) and optical spin initialization, just as in NV centers. The authors predict spin-lattice relaxation times T₁ as long as 27 ms at 300 K for the aza-cation core, and coherence times T₂ of 0.21 ms at 10 K for a deuterated, magnetically diluted crystal derivative. They also identify the specific molecular vibrations of bulky substituent groups as the primary decoherence bottleneck in realistic solid-state environments, and show that the spin selectivity of ISC can be tuned by engineering the energy gaps between singlet and triplet states.

What carries the argument

The computational machinery couples three layers: (1) multireference electronic structure (CASSCF/NEVPT2) to obtain spin-free states, followed by diagonalization of spin-orbit and spin-spin coupling to get spin-mixed wavefunctions; (2) vibronic coupling computed as numerical derivatives of the electronic Hamiltonian with respect to nuclear displacements, decomposed into a spin-free contribution (J, from Coulomb/relativistic state mixing) and a relativistic contribution (K, from direct modulation of spin-orbit/spin-spin interactions by nuclear motion); (3) quantum master equations for one- and two-phonon transition rates among spin sublevels, plus cluster-correlation expansion (CCE) for spin-

What would settle it

Synthesize a deuterated, magnetically diluted crystal of a triangulene derivative with rigid substituents and measure: (a) whether ODMR contrast is observed at room temperature, (b) whether T₂ exceeds 0.1 ms below 20 K, and (c) whether the direction of spin selectivity (which Ms state is brighter) matches the ab initio prediction. If no ODMR is observed, or if T₂ is orders of magnitude shorter, the core claim that these molecules replicate NV-center functionality would be undermined. If the spin selectivity direction is opposite to prediction, the methodology's treatment of excited-state reorg

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Extended reading notes

Core claim

The central discovery is that triangulene-based organic diradicals possess an electronic structure that mirrors NV centers — a well-isolated triplet ground state, optically accessible excited triplets, and spin-selective intersystem crossing — while simultaneously supporting exceptionally long spin relaxation times (T₁ up to 27 ms at room temperature for the bare molecular core). The paper also provides the first fully ab initio computation of spin-resolved ISC rates in molecules, revealing that the spin selectivity of ISC is governed by the interplay between in-plane and out-of-plane molecular vibrations and their distinct effects on orbital angular momentum, creating an energy-resolved and

Load-bearing premise

The spin selectivity of intersystem crossing — the feature that would make optical spin readout and initialization possible — is computed using a harmonic phonon approximation where all electronic states share the same potential energy surface, and the paper itself shows that a modest 400 cm⁻¹ shift in energy levels reverses which spin state is favored. This means the predicted ODMR contrast direction depends sensitively on energy-level alignment that the current methodology

Editorial extensions

If this is right

  • If triangulene derivatives can be synthesized with rigid substituents that suppress low-energy vibrations while preserving the core electronic structure, they could become the first organic molecules with NV-center-like optical spin control at room temperature.
  • The finding that ISC spin selectivity reverses with modest (400 cm⁻¹) energy-level shifts provides a concrete design rule: chemically tuning singlet-triplet gaps could switch which spin state is 'dark,' enabling either Ms=0 or Ms=±1 initialization depending on application.
  • The ab initio framework for spin-resolved ISC rates, once validated experimentally, could replace empirical models currently used to screen molecular qubit candidates, accelerating discovery.
  • Integration of triangulene cores into rigid covalent organic frameworks (COFs) — already demonstrated for related systems — could simultaneously solve the vibrational decoherence problem and enable device-level integration.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The extreme sensitivity of ISC spin selectivity to energy-level alignment (a 400 cm⁻¹ shift reverses the selectivity) suggests that the predicted ODMR contrast direction is not robust to the approximations made. Experimental validation of which spin state is actually brighter will be a critical test of whether the harmonic-phonon, shared-PES methodology captures the relevant physics.
  • The predicted T₁ for the bare core (27 ms) versus the functionalized crystal (0.1 µs) — a five-order-of-magnitude drop — implies that the core electronic structure is not the limiting factor; rather, the entire decoherence budget is consumed by peripheral group vibrations. This means the design problem is primarily vibrational engineering, not electronic engineering.
  • If the general principle holds that in-plane vibrations couple ΔMs=0 transitions while out-of-plane vibrations couple ΔMs=±1 transitions in planar π-conjugated systems, this could be a universal design rule extending beyond triangulene to any planar organic diradical or radical, including larger nanographene fragments.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 7 minor

Summary. This manuscript presents a first-principles study of triangulene-based diradicals (compounds 1-3) as candidates for optically addressable molecular qubits. Using CASSCF/NEVPT2 electronic structure calculations, relativistic vibronic coupling theory, and cluster correlation expansion (CCE) methods, the authors predict that these organic diradicals possess an NV-center-like electronic structure: a triplet ground state separated from the first singlet by ~0.5 eV, optically accessible excited triplets, and spin-selective intersystem crossing (ISC). The predicted spin-phonon relaxation times for the bare molecular cores (T1 ~ 1-27 ms at 300 K) and spin-spin decoherence times (T2 = 0.21 ms at 10 K for deuterated 3 in a spin-free environment) are presented as evidence that these systems could serve as molecular quantum platforms. The work represents the first application of ab initio spin-phonon relaxation theory to organic diradicals and the first attempt to quantitatively simulate spin-resolved ISC rates within a fully ab initio framework.

Significance. The manuscript makes several contributions that advance the field of molecular quantum information. First, the electronic structure characterization of triangulene and its aza-cation derivative via multireference methods (NEVPT2 with ICE-CI, CAS(10,10)) is thorough and validated against experimental absorption bands. Second, the spin-phonon T1 calculations are parameter-free and follow established formalism from the authors' prior work (refs 39-43), providing falsifiable predictions. Third, the CCE decoherence simulations for the realistic crystal of compound 3 provide the first comprehensive ab initio characterization of spin decoherence in a solid-state molecular environment, including both spin relaxation and nuclear-spin dephasing. The identification of specific low-energy vibrations from tBu and mesityl groups as the bottleneck for T1 in the functionalized crystal is a concrete, actionable design rule. The spin-resolved ISC rate calculations, while approximate, represent a methodological advance and produce predictions that can be tested experimentally via ODMR.

major comments (2)
  1. Table II and surrounding text: The central ODMR claim rests on spin-selective ISC, but the computed ISC selectivity reverses sign depending on geometry choice. At the ground-state geometry, T1→S2 ISC favors Ms=0 (rate 1.0×10^5 s^-1 vs ~10^2 for Ms=±1), while at the T1-optimized geometry it favors Ms=±1 (rate ~3.7×10^6 vs 7.4×10^4 for Ms=0). The authors acknowledge this sensitivity, noting that a 400 cm^-1 energy shift would flip selectivity. The deeper methodological issue is that the shared-PES approximation (V_aa=0, stated in Theoretical Methods) forces all electronic states onto one harmonic surface, precluding the thermal averaging or displaced-oscillator treatment that would determine which selectivity actually governs the optical cycle. By computing ISC at three separate optimized geometries and obtaining qualitatively different answers, the paper inadvertently demonstrates that a单
  2. Discussion and Conclusions, paragraph on condition 3: The claim that 'engineering of specific low-energy vibrations could significantly improve T2' is supported by computation only for the bare cores (1, 2), where T1 is already long. For the practically relevant functionalized crystal (3a), T1 degrades to 0.1 µs at 300 K, and the assertion that rigid substituents or COF integration would recover long T2 is stated without computation in the functionalized case. The paper would be strengthened by either (a) a model calculation demonstrating that removing specific low-energy modes of 3a recovers T1 closer to the bare-core limit, or (b) a more cautious framing that explicitly labels this as a hypothesis rather than a demonstrated result.
minor comments (7)
  1. Fig. 2a: The degeneracies of triplets/singlets are 'artificially lifted to aid visualization' but the caption does not state the magnitude of the lifting, making it difficult to distinguish real near-degeneracies (S0/S1) from visual artifacts.
  2. Theoretical Methods, Eq. 12: The numerical differentiation step size δ is listed as a free parameter in the axiom ledger but its value is not stated in the main text. This should be specified, along with convergence tests (referenced as Figs. S21-S23 but only for T1, not for the differentiation itself).
  3. Table I: The entry '1-D' with T2 = ∞ is physically misleading. While deuterium's weaker gyromagnetic ratio reduces decoherence, 'no decoherence over 1 s' would be more precise than the symbol ∞.
  4. The magnetic field B = 0.33 T is introduced in the Vibronic Coupling section without justification. Since this is a free parameter, the choice should be motivated or at least stated earlier.
  5. Fig. 3: The atom IDs 1-22 (C) and 23-34 (H) are referenced but the figure does not label individual atoms, making it difficult to connect the histograms to specific molecular positions.
  6. The abbreviation 'ss-ISC' for spin-selective ISC is used before its first explicit definition (Introduction, paragraph 3).
  7. Reference [42] (Lunghi, 2026) appears to be a very recent or in-press publication; if this is a self-citation to unpublished work, this should be noted.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; self-citations are to parameter-free ab initio methodological frameworks, not to fitted results or definitions.

full rationale

The paper applies first-principles quantum chemistry (CASSCF/NEVPT2 for electronic structure, ab initio vibronic coupling via numerical differentiation of the electronic Hamiltonian, and CCE for nuclear-spin decoherence) to triangulene-based diradicals. The spin-phonon relaxation theory (Eqs. 1–18) and the CCE decoherence framework (Eqs. 19–25) are drawn from the authors' own prior methodological work (refs 39–43, 46–47), but these are parameter-free ab initio frameworks: they take electronic structure and vibrational modes as input and produce relaxation rates as output without fitting to experimental T1, T2, or ISC data. The T1 = 27 ms (compound 2, 300 K), T2 = 0.21 ms (deuterated 3, 10 K), and ISC rates (Table II) are genuine computational predictions, not renamed fits. The electronic structure is validated against experimental absorption bands (~17500 cm⁻¹ vs experimental 533/580 nm) and experimental D-tensor values, but these are consistency checks, not fitted inputs. The shared-PES approximation (V_aa = 0) and the geometry-dependence of ISC spin selectivity are acknowledged limitations, not circular constructions. The CCE method itself (ref 46 by Yang & Liu, ref 47 by Onizhuk & Galli) is from external authors. No step in the derivation chain reduces to its own inputs by construction. The only minor concern is that the methodological framework is self-cited rather than independently re-derived, but since it is parameter-free and externally falsifiable, this does not constitute circularity. Score 1 reflects the presence of self-citation to methodological work that is not load-bearing in the circular sense.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

No new physical entities are postulated. The framework uses standard quantum chemistry (CASSCF, NEVPT2) and established open quantum system theory. The molecules studied (triangulene, aza-triangulene cation, and compound 3) are all experimentally known. The axioms are standard approximations in computational chemistry, with two ad-hoc simplifications (neglecting FC/HT factors and peripheral quadratic coupling) made for computational tractability.

free parameters (3)
  • Magnetic field B = 0.33 T = 0.33 T
    Chosen to resemble X-band EPR; affects Zeeman splitting and spin level ordering but not fitted to data.
  • Numerical differentiation step size δ = Not specified
    Used in Eq. 12 for vibronic coupling derivatives; affects accuracy but is a convergence parameter, not a physical fit.
  • Active space CAS(10,10) = 10 electrons, 10 orbitals
    Selected based on convergence tests (Tables S1-S2) as minimal active space; not fitted to target results.
assumptions (5)
  • standard math Born-Oppenheimer approximation: electrons and nuclei are separable, with vibronic coupling treated perturbatively.
    Standard assumption underlying Eqs. 1-4; invoked throughout the Theoretical Methods section.
  • domain assumption Harmonic approximation for nuclear dynamics: each electronic state shares the same set of phonons (ground-state normal modes).
    Stated explicitly in Theoretical Methods: 'we assume that every electronic state shares the same set of phonons, usually of the ground state.' Diagonal vibronic coupling set to zero (V_aa = 0).
  • domain assumption Markovian bath approximation for phonons: phonons are treated as an equilibrium thermal bath with no memory.
    Invoked in the Vibronic dynamics section: 'we treat the phonons as an equilibrium thermal Markovian bath.'
  • ad hoc to paper Franck-Condon and Herzberg-Teller factors neglected for ISC rate calculations.
    Stated in Excited states relaxation section: 'Franck-Condon and Herzberg-Teller factors arising from molecular geometry reorganization are neglected.' This is a simplification that affects ISC rate magnitudes.
  • ad hoc to paper Quadratic vibronic coupling neglected for peripheral atoms of compound 3.
    Stated near Fig. 6: 'been neglected for the atoms belonging to the peripheral groups of 3 to reduce the number of DFT calculations needed from 290,322 to 20,808.'

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Pith. "Pith review of Triangulene-based diradicals as a blueprint for molecular quantum platforms with optical addressability and long spin coherence times." pith.science (2026). https://pith.science/paper/WRUBVL4L

@misc{pith2026260708634,
  author       = {Pith},
  title        = {Pith review of: Triangulene-based diradicals as a blueprint for molecular quantum platforms with optical addressability and long spin coherence times},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WRUBVL4L}},
  note         = {Machine review of arXiv:2607.08634}
}
abstract

The identification of molecules that combine long spin coherence times and efficient spin-optical interfaces, ideally at room temperature, is pivotal towards the development of molecular quantum technology. By means of advanced first-principles methods, we here unravel the electronic structure for triangulene (1), its aza-cation derivative (2), and the crystal of 2,6,10-tri-tert-butyl-4,8,12-trimesityl-triangulene (3), and show that these organic diradicals possess a triplet ground state well separated from the first singlet excited state approaching 0.5 eV, closely resembling solid-state defects like nitrogen vacancy centers. In addition, we compute spin decoherence times due to the interaction with phonons and surrounding nuclear spins, showing that a deuterated molecule of 3 in a nuclear spin-free environment would support $T_2 = 0.21$ ms at 10 K. Importantly, we show that the engineering of specific low-energy vibrations could significantly improve $T_2$ toward the limit imposed by the molecular core spin relaxation, here estimated to be as long as $T_1=27$ ms at 300 K for 2. Finally, we compute two-phonon contributions to inter-system crossing at 300 K for2 as a luminescent prototype, and find that it is highly spin-selective, supporting the possibility to engineer optical read out and spin initialization. These results advance a unified first-principles theoretical foundation of spin decoherence and spin-selective excited-state processes and point to novel chemical design strategies for optically addressable, highly coherent molecular qubits.

Figures

Figures reproduced from arXiv: 2607.08634 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
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Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
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Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
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Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
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Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
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Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]

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Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    highly spin selective intersystem crossing dimming a single spin channel and funneling population from ex- cited states into a singleM S component of the ground state. While condition 1 allows to preserve and manipu- late quantum information, conditions 2 enables efficient optical addressing on timescales shorter than decoher- ence, and condition 3 provid...

    work page 2024

  2. [2]

    Ardavan, A.et al.Will Spin-Relaxation Times in Molec- ular Magnets Permit Quantum Information Processing? Phys. Rev. Lett.98, 57201 (2007)

    work page 2007

  3. [3]

    J., Von Kugelgen, S., Laorenza, D

    Yu, C. J., Von Kugelgen, S., Laorenza, D. W. & Freed- man, D. E. A Molecular Approach to Quantum Sensing. ACS Cent. Sci.7, 712–723 (2021)

    work page 2021

  4. [4]

    & Car- retta, S

    Chiesa, A., Santini, P., Garlatti, E., Luis, F. & Car- retta, S. Molecular nanomagnets: a viable path toward quantum information processing?Rep. Prog. Phys.87, 034501 (2024)

    work page 2024

  5. [5]

    & Sessoli, R

    Atzori, M. & Sessoli, R. The Second Quantum Revolu- tion: Role and Challenges of Molecular Chemistry.J. Am. Chem. Soc.141, 11339–11352 (2019)

    work page 2019

  6. [6]

    R.et al.Exploiting chemistry and molecular systems for quantum information science.Nat

    Wasielewski, M. R.et al.Exploiting chemistry and molecular systems for quantum information science.Nat. Rev. Chem.4, 490–504 (2020)

    work page 2020

  7. [7]

    M., Niklas, J., Poluektov, O

    Zadrozny, J. M., Niklas, J., Poluektov, O. G. & Freed- man, D. E. Millisecond coherence time in a tunable molecular electronic spin qubit.ACS Cent. Sci.1, 488– 492 (2015)

    work page 2015

  8. [8]

    Atzori, M.et al.Quantum Coherence Times En- hancement in Vanadium(IV)-based Potential Molecular Qubits: The Key Role of the Vanadyl Moiety.J. Am. Chem. Soc.138, 11234–11244 (2016)

    work page 2016

Show all 62 references
  1. [9]

    Shiddiq, M.et al.Enhancing coherence in molecular spin qubits via atomic clock transitions.Nature531, 348–351 (2016)

    2016

  2. [10]

    & Yanai, N

    Ishiwata, H., Song, J., Shigeno, Y., Nishimura, K. & Yanai, N. Molecular quantum nanosensors functioning in living cells.Sci. Adv.12, eaeb5422 (2026)

    2026

  3. [11]

    & Blank, A

    Artzi, Y., Twig, Y. & Blank, A. Induction-detection electron spin resonance with spin sensitivity of a few tens of spins.Appl. Phys. Lett.106, 84104 (2015)

    2015

  4. [12]

    & Balestro, F

    Vincent, R., Klyatskaya, S., Ruben, M., Wernsdorfer, W. & Balestro, F. Electronic read-out of a single nuclear spin using a molecular spin transistor.Nature488, 357–360 (2012)

    2012

  5. [13]

    Baumann, S.et al.Electron paramagnetic resonance of individual atoms on a surface.Science350, 417–420 (2015)

    2015

  6. [14]

    Godfrin, C.et al.Operating Quantum States in Single Magnetic Molecules: Implementation of Grover’s Quan- tum Algorithm.Phys. Rev. Lett.119, 187702 (2017)

    2017

  7. [15]

    Reale, S.et al.Electrically driven spin resonance of 4f electrons in a single atom on a surface.Nat. Commun. 15, 5289 (2024)

    2024

  8. [16]

    Kwiram, A. L. Optical detection of paramagnetic reso- nance in phosphorescent triplet states.Chem. Phys. Lett. 1, 272–275 (1967)

    1967

  9. [17]

    K¨ ohler, J.et al.Magnetic resonance of a single molecular spin.Nature363, 242–244 (1993)

    1993

  10. [18]

    K.et al.Chemically Tuning Room Temperature Pulsed Optically Detected Magnetic Resonance.Jour- nal of the American Chemical Society147, 22911–22918 (2025)

    Mann, S. K.et al.Chemically Tuning Room Temperature Pulsed Optically Detected Magnetic Resonance.Jour- nal of the American Chemical Society147, 22911–22918 (2025)

    2025

  11. [19]

    L.et al.Optically addressable molecular spins for quantum information processing.Science370, 1309– 1312 (2020)

    Bayliss, S. L.et al.Optically addressable molecular spins for quantum information processing.Science370, 1309– 1312 (2020)

    2020

  12. [20]

    Sutcliffe, E., Kazmierczak, N. P. & Hadt, R. G. Ultra- fast all-optical coherence of molecular electron spins in room-temperature water solution.Science386, 888–892 (2024)

    2024

  13. [21]

    & Lunghi, A

    Atzori, M. & Lunghi, A. Optical control of spin states in magnetic molecules.Trends Chem.7, 413–416 (2025)

    2025

  14. [22]

    Wolfowicz, G.et al.Quantum guidelines for solid-state spin defects.Nat. Rev. Mater.6, 906–925 (2021)

    2021

  15. [23]

    Ab initio theory of the nitrogen-vacancy center in diamond.Nanophotonics8, 1907–1943 (2019)

    Gali, A. Ab initio theory of the nitrogen-vacancy center in diamond.Nanophotonics8, 1907–1943 (2019)

    1907

  16. [24]

    R.et al.Alternant Hydrocarbon Diradicals as Optically Addressable Molecular Qubits.J

    Poh, Y. R.et al.Alternant Hydrocarbon Diradicals as Optically Addressable Molecular Qubits.J. Am. Chem. Soc.146, 15549–15561 (2024)

    2024

  17. [25]

    M.et al.Luminescent Organic Triplet Diradi- cals as Optically Addressable Molecular Qubits.J

    Kopp, S. M.et al.Luminescent Organic Triplet Diradi- cals as Optically Addressable Molecular Qubits.J. Am. Chem. Soc.146, 27935–27945 (2024)

    2024

  18. [26]

    Chem.17, 1410–1417 (2025)

    Chowdhury, R.et al.Bright triplet and bright charge- separated singlet excitons in organic diradicals enable op- tical read-out and writing of spin states.Nat. Chem.17, 1410–1417 (2025)

    2025

  19. [27]

    Poh, Y. R. & Yuen-Zhou, J. Enhancing the Optically De- tected Magnetic Resonance Signal of Organic Molecular Qubits.ACS Cent. Sci.11, 116–126 (2025)

    2025

  20. [28]

    M.et al.Optically Detected Coherent Spin Control of Organic Molecular Color Center Qubits.J

    Kopp, S. M.et al.Optically Detected Coherent Spin Control of Organic Molecular Color Center Qubits.J. Am. Chem. Soc.147, 22951–22960 (2025)

    2025

  21. [29]

    Chowdhury, R.et al.Room temperature optical control of spin states in organic diradicals.arXiv:2510.094401– 18 (2025)

    2025

  22. [30]

    M.et al.Molecular Diradical Spin Qubits in a Crystalline Host as a Platform for Quantum Sensing

    Kopp, S. M.et al.Molecular Diradical Spin Qubits in a Crystalline Host as a Platform for Quantum Sensing. ACS Cent. Sci.(2026)

    2026

  23. [31]

    R., Chen, X., Cheng, H.-P

    Poh, Y. R., Chen, X., Cheng, H.-P. & Yuen-Zhou, J. Electron Sextets as Optically Addressable Molecu- lar Qubits: Triplet Carbenes.J. Am. Chem. Soc.147, 22529–22541 (2025)

    2025

  24. [32]

    & Casanova, D

    Ricci, G., Tonnel´ e, C. & Casanova, D. Optical Address- ability of the Arylnitrene Spin Triplet.J. Phys. Chem. Lett.16, 5659–5665 (2025)

    2025

  25. [33]

    Roggors, S.et al.Optically Detected Magnetic Reso- nance on Carbene Molecular Qubits.J. Am. Chem. Soc. 147, 36383–36392 (2025)

    2025

  26. [34]

    Roggors, S.et al.A Single-Molecule Spin-Photon Inter- face.arXiv:2605.100771–54 (2026)

    2026 arXiv

  27. [35]

    Inoue, J.et al.The first detection of a Clar’s hydro- carbon, 2,6,10-tri-tert-butyltriangulene: A ground-state 17 triplet of non-kekul´ e polynuclear benzenoid hydrocarbon. J. Am. Chem. Soc.123, 12702–12703 (2001)

    2001

  28. [36]

    Nanotechnol.12, 308–311 (2017)

    Pavliˇ cek, N.et al.Synthesis and characterization of tri- angulene.Nat. Nanotechnol.12, 308–311 (2017)

    2017

  29. [37]

    & Takui, T

    Morita, Y., Suzuki, S., Sato, K. & Takui, T. Synthetic organic spin chemistry for structurally well-defined open- shell graphene fragments.Nat. Chem.3, 197–204 (2011)

    2011

  30. [38]

    & Shin- tani, R

    Arikawa, S., Shimizu, A., Shiomi, D., Sato, K. & Shin- tani, R. Synthesis and Isolation of a Kinetically Stabi- lized Crystalline Triangulene.J. Am. Chem. Soc.143, 19599–19605 (2021)

    2021

  31. [39]

    Arikawa, S.et al.A Kinetically Stabilized Nitrogen- Doped Triangulene Cation: Stable and NIR Fluorescent Diradical Cation with Triplet Ground State.Angew. Chem. Int. Ed.62, e202302714 (2023)

    2023

  32. [40]

    A., Mondal, S

    Mariano, L. A., Mondal, S. & Lunghi, A. Spin-Vibronic Dynamics in Open-Shell Systems beyond the Spin Hamil- tonian Formalism.J. Chem. Theory Comput.20, 323– 332 (2024)

    2024

  33. [41]

    A.et al.The role of electronic excited states in the spin-lattice relaxation of spin-1/2 molecules.Sci

    Mariano, L. A.et al.The role of electronic excited states in the spin-lattice relaxation of spin-1/2 molecules.Sci. Adv.11, eadr0168 (2025)

    2025

  34. [42]

    & Lunghi, A

    Ryan, C., Briganti, V., Hogan, C., O’Neill, M. & Lunghi, A. Spin decoherence in molecular crystals: Nuclear vs electronic spin baths.J. Chem. Phys.163, 134104 (2025)

    2025

  35. [43]

    A unified ab initio theory of spin-phonon relaxation and decoherence uncovers fast dephasing in magnetic molecules.Sci

    Lunghi, A. A unified ab initio theory of spin-phonon relaxation and decoherence uncovers fast dephasing in magnetic molecules.Sci. Adv.12, eaeb3868 (2026)

    2026

  36. [44]

    Toward exact predictions of spin-phonon relaxation times: An ab initio implementation of open quantum systems theory.Sci

    Lunghi, A. Toward exact predictions of spin-phonon relaxation times: An ab initio implementation of open quantum systems theory.Sci. Adv.8, eabn7880 (2022)

    2022

  37. [45]

    Plasser, F.et al.Efficient and Flexible Computation of Many-Electron Wave Function Overlaps.J. Chem. The- ory and Comput.12, 1207–1219 (2016)

    2016

  38. [46]

    & Liu, R.-B

    Zhao, N., Ho, S.-W. & Liu, R.-B. Decoherence and dy- namical decoupling control of nitrogen vacancy center electron spins in nuclear spin baths.Phys. Rev. B85, 115303 (2012)

    2012

  39. [47]

    & Liu, R.-B

    Yang, W. & Liu, R.-B. Quantum many-body theory of qubit decoherence in a finite-size spin bath.Phys. Rev. B78, 85315 (2008)

    2008

  40. [48]

    & Galli, G

    Onizhuk, M. & Galli, G. PyCCE: A Python Package for Cluster Correlation Expansion Simulations of Spin Qubit Dynamics.Adv.Theory Simul.4, 2100254 (2021)

    2021

  41. [49]

    & Malrieu, J.-P

    Angeli, C., Cimiraglia, R., Evangelisti, S., Leininger, T. & Malrieu, J.-P. Introduction of n-electron valence states for multireference perturbation theory.J. Chem. Phys. 114, 10252–10264 (2001)

    2001

  42. [50]

    Lang, L., Chilkuri, V. G. & Neese, F. Treating Spin–Orbit Coupling and Spin–Spin Coupling in the Framework of the Iterative Configuration Expansion Se- lected CI.J. Chem. Theory Comput.21, 6482–6504 (2025)

    2025

  43. [51]

    Haldar, S., Mitra, A., Hermes, M. R. & Gagliardi, L. Local Excitations of a Charged Nitrogen Vacancy in Di- amond with Multireference Density Matrix Embedding Theory.J. Phys. Chem. Lett.14, 4273–4280 (2023)

    2023

  44. [52]

    & Bar- cza, G

    Benedek, Z., Ganyecz, A., Pershin, A., Iv´ ady, V. & Bar- cza, G. Accurate and convergent energetics of color cen- ters by wavefunction theory.npj Comput. Mater.11, 346 (2025)

    2025

  45. [53]

    Allinson, G.et al.ESR Spectrum of a Stable Triplet- pi-biradical: Trioxytriangulene.J. Am. Chem. Soc.115, 2062–2064 (1993)

  46. [54]

    Garlatti, E.et al.The critical role of ultra-low-energy vi- brations in the relaxation dynamics of molecular qubits. Nat. Commun.14, 1653 (2023)

    2023

  47. [55]

    & Wigner, E

    Weisskopf, V. & Wigner, E. Berechnung der nat¨ urlichen Linienbreite auf Grund der Diracschen Lichttheorie. Zeitschrift f¨ ur Physik63, 54–73 (1930)

    1930

  48. [56]

    Hagai, M., Inai, N., Yasuda, T., Fujimoto, K. J. & Yanai, T. Extended theoretical modeling of reverse intersystem crossing for thermally activated delayed fluorescence ma- terials.Sci. Adv.10, eadk3219 (2026)

    2026

  49. [57]

    M., Jensen, K., Chemerisov, S

    Jarmola, A., Acosta, V. M., Jensen, K., Chemerisov, S. & Budker, D. Temperature- and Magnetic-Field- Dependent Longitudinal Spin Relaxation in Nitrogen- Vacancy Ensembles in Diamond.Phys. Rev. Lett.108, 197601 (2012)

    2012

  50. [58]

    Lakshmi, V.et al.A Two-Dimensional Poly(azatriangulene) Covalent Organic Framework with Semiconducting and Paramagnetic States.J. Am. Chem. Soc.142, 2155–2160 (2020)

    2020

  51. [59]

    & Yamashita, M

    Suzuki, Y., Sato, K., Wakizaka, M., Sakamoto, R. & Yamashita, M. Spin–lattice relaxation of copper and vanadyl porphyrins in extended molecular framework materials.Dalton Trans.55, 9218–9222 (2026)

    2026

  52. [60]

    Sun, Z.et al.Ultralong Room-Temperature Qubit Life- times of Covalent Organic Frameworks.J. Am. Chem. Soc.147, 31930–31939 (2025)

    2025

  53. [61]

    & Rajca, A

    Shu, C., Yang, Z. & Rajca, A. From Stable Radicals to Thermally Robust High-Spin Diradicals and Triradicals. Chem. Rev.123, 11954–12003 (2023)

    2023

  54. [62]

    Zeng, W. & Wu, J. Open-Shell Graphene Fragments. Chem7, 358–386 (2021)

    2021

Pith tools

Reviewed July 10, 2026 · model on record in the stance chip above.