pubs.acs.org/JACS Article Emergent Spin Frustration in Neutral Mixed-Valence 2D Conjugated Polymers: A Potential Quantum Materials Platform Isaac Alcón,* Jordi Ribas-Ariño, Ibério de P.R. Moreira, and Stefan T. Bromley* Cite This: J. Am. Chem. Soc. 2023, 145, 5674−5683 Read Online ACCESS Metrics & More Article Recommendations * sı Supporting Information ABSTRACT: Two-dimensional conjugated polymers (2DCPs)� organic 2D materials composed of arrays of carbon sp2 centers connected by π-conjugated linkers�are attracting increasing attention due to their potential applications in device technologies. This interest stems from the ability of 2DCPs to host a range of correlated electronic and magnetic states (e.g., Mott insulators). Substitution of all carbon sp2 centers in 2DCPs by nitrogen or boron results in diamagnetic insulating states. Partial substitution of C sp2 centers by B or N atoms has not yet been considered for extended 2DCPs but has been extensively studied in the analogous neutral mixed-valence molecular systems. Here, we employ accurate first-principles calculations to predict the electronic and magnetic properties of a new class of hexagonally connected neutral mixed-valence 2DCPs in which every other C sp2 nodal center is substituted by either a N or B atom. We show that these neutral mixed-valence 2DCPs significantly energetically favor a state with emergent superexchange-mediated antiferromagnetic (AFM) interactions between C-based spin-1/2 centers on a triangular sublattice. These AFM interactions are surprisingly strong and comparable to those in the parent compounds of cuprate superconductors. The rigid and covalently linked symmetric triangular AFM lattice in these materials thus provides a highly promising and robust basis for 2D spin frustration. As such, extended mixed- valence 2DCPs are a highly attractive platform for the future bottom-up realization of a new class of all-organic quantum materials, which could host exotic correlated electronic states (e.g., unusual magnetic ordering, quantum spin liquids). ■ INTRODUCTION Two-dimensional conjugated polymers (2DCPs) are based on The emergence of AFM states in hexagonal 2DCPs based on carbon sp2 centers (C-2DCPs) can be rationalized by planar networks of trigonal sp2 nodes and are an emerging class considering these materials as lattices of singly occupied π- of organic materials with a wide range of potential device conjugated orbitals. Formally, the Hubbard effective Hamil- applications.1−8 Graphene,9 a 2D hexagonal array of carbon sp2 tonian predicts such half-filled 2D systems to exhibit a Mott nodes, is the most celebrated 2DCP largely due to its insulating AFM solution if the unpaired electrons on each node semimetallic band structure with Dirac-like linear band are sufficiently localized.21 Apart from very highly delocalized crossings at the Fermi level (EF), and concomitant high systems such as graphene, Mott-like AFM states are predicted electron mobilities.10 However, as graphene does not display a to be typical for the more expanded, and thus more band gap, it is not a suitable platform for switchable electronic electronically localized, sp2 nodal networks of C-2DCPs.12−16 devices. Theoretically proposed hexagonal 2DCPs based on Chemical substitution of every carbon sp2 node in a C-2DCP modifying and extending the links between graphene’s sp2 with boron (B-2DCP) or nitrogen (N-2DCP) atoms removes nodes (e.g., 2D covalent organic radical frameworks (2D- or adds one electron per sp2 node, respectively. This either fills CORFs), graphynes) were initially also predicted to be Dirac (N) or empties (B) the π-conjugated orbitals of the substituted materials with corresponding graphenic electronic transport 2DCPs networks such that the half-filling requirement for a properties.3,11,12 Subsequently, however, a careful theoretical Mott AFM insulating phase is not fulfilled. Consequently, as analysis of such 2DCPs showed that the semimetallic solution is metastable with respect to antiferromagnetic (AFM) Received: October 22, 2022 multiradical or closed-shell quinoidal states.13−17 Synthesized Published: March 6, 2023 2DCPs have since been confirmed to exhibit AFM states.18−20 The associated finite band gaps of these states make 2DCPs potentially more attractive than graphene for electronic applications. © 2023 The Authors. Published by American Chemical Society https://doi.org/10.1021/jacs.2c11185 5674 J. Am. Chem. Soc. 2023, 145, 5674−5683 Journal of the American Chemical Society pubs.acs.org/JACS Article Figure 1. (a) Periodic structure of a series of chemically substituted 2DCPs. Note that hydrogen atoms are omitted in all structures for simplicity. The neutral mixed-valence 2DCPs (mv-2DCPs) considered in this work are highlighted. (b) Dependence of the electronic structure of 2DCPs on chemical substitution. Continuous and dashed lines represent occupied and conduction bands, respectively. EF denotes the Fermi level for conductors and an arbitrary energy level inside the gap for insulators. While both the nonsubstituted C-2DCPs and fully substituted situations (B- and N-2DCPs) have received much attention, the electronic structures of the partially substituted systems (i.e., B-mv-2DCP and N-mv-2DCP) are still unknown. See also Figure S1. schematically illustrated in Figure 1, B-2DCPs and N-2DCPs suggest that extended sp2-based mv-2DCPs could exhibit new are insulators that have been shown to recover the linear band exotic electronic and magnetic phenomena. crossings (i.e., Dirac cones) above and below EF, respectively.22 Herein, we investigate the electronic properties that emerge This behavior is in line with theoretical predictions3 and has when expanding the concept of neutral mixed-valence also been experimentally demonstrated.4 molecules to extended mv-2DCP materials. Specifically, we Although there have been significant efforts to understand use first-principles density functional theory (DFT)-based fully substituted B-, N-, and C-2DCPs, to the best of our calculations to study N-mv-2DCP and B-mv-2DCPs (see knowledge, there are no reports on the electronic and magnetic Figure 1a). Our study reveals that mv-2DCPs display well- properties of the corresponding neutral mixed-valence 2DCPs localized spin centers on their carbon sp2 nodes, in full (mv-2DCPs). Such materials could be formed by periodically agreement with their molecular analogues.29 The magnetic combining carbon nodes with either nitrogen or boron nodes, interactions between spins on the radical carbon atoms are as depicted in Figure 1a. For C-2DCPs, the low-energy AFM found to have an AFM character. However, the triangular and dimerized electronic solutions have strong analogies with symmetry of the carbon sublattice prevents extended 2D AFM known valence bond forms of molecular systems such as ordering due to spin frustration. By modeling the analogous Thiele’s hydrocarbon,23,24 which may be thought of as a mv-diradical, mv-triradical, and mv-cyclo-triradical molecules, triarylmethyl25 (TAM) dimer. Similarly, insights into the likely we find that such AFM interactions have a local character and electronic properties of mv-2DCPs systems can be gained by have a strength that should ensure that the magnetic considering the analogous neutral mixed-valence molecular systems. For instance, linking a TAM and a triarylamine interactions are robust at room temperature. By comparing (TAA) via a π-conjugated linker results in neutral C−N mixed- the mv-cyclo-triradical molecules with an isoelectronic valence compounds,26−28 which host a localized unpaired electron-doped carbon-based hexamer, we find that spin electron on the sp2 carbon center.29 These types of compounds frustration cannot be obtained in the parent C-2DCPs by, have been shown to act as donor−acceptor systems that may for instance, electrochemical reduction. This highlights the be optically excited to undergo N-to-C charge transfer unique spin-electronic nature of our proposed mv-2DCPs. By processes.27 Mixed-valence diradicals, triradicals, and even ab initio molecular dynamics (AIMD) simulations, we also find polymers made of alternating TAMs and TAAs displaying that the spin-polarized nature of these materials is persistent to similar excitations have also been synthesized.30,31 Similarly, in thermally induced structural fluctuations, contrary to C- diradicals or triradicals where the TAM centers are bridged by 2DCPs, where the spin-electronic structure is more sensitive triarylborane (TAB) centers, optical excitation results in C-to- to structural conformation.15,16 The magnetic interactions in B charge transfer processes.30 All of these characteristics, which our materials depends on the sterically determined twist angles are not exhibited in the corresponding unmixed molecular of the linking aryl rings in these mv-2DCPs networks.32 These systems (i.e., pure TAM, TAA, or TAB dimers), strongly twist angles can, however, be modified by chemical 5675 https://doi.org/10.1021/jacs.2c11185 J. Am. Chem. Soc. 2023, 145, 5674−5683 Journal of the American Chemical Society pubs.acs.org/JACS Article functionalization and/or external strain/pressure15,16,33,34 to 2DCPs could provide a promising all-organic 2D quantum tune the AFM interaction strength. materials platform for exploring exotic magnetically ordered The fact that we find robust AFM interactions between sites phases and even superconducting or QSL-based states. on an emergent triangular network in mv-2DCPs could be of particular interest due to their potential for hosting exotic quantum states due to the frustrated spin−spin interactions ■ RESULTS AND DISCUSSION We evaluate the structure and properties of our mv-2DCPs nature of such systems. The covalent skeleton of mv-2DCPs with periodic DFT calculations using the hybrid PBE0 provides a rigid and highly symmetric 2D system in which functional,41 which has been shown to properly capture the structural distortions to remove spin frustration thus are electronic structure of this type of 2D material13 and their strongly inhibited. The quantum states of materials in which molecular analogues.15,16,42 Closed-shell states were obtained localized S = 1/2 spins on a fixed lattice interact by isotropic via spin-restricted calculations, whereas the open-shell spin exchange coupling are often analyzed in terms of the solutions were generated via spin-unrestricted electronic Heisenberg Hamiltonian. On the frustrated 2D triangular configurations, using spin-polarized initial guesses for each lattice, this model is predicted to have an ordered AFM-like particular case (see the Methods Section). Here, we consider insulating ground state.35 Generally, such frustrated magnetic mv-2DCPs based on sp2 nodes, which are connected via single systems can host a wide variety of unusual ordered phases with benzene rings in the hexagonal lattice making up their periodic complex dynamics upon increases in temperature.36 Predic- structure (see Figure 1a). We note that macro cycles tions of the pure Heisenberg model may also be affected by composed of six sp2 nodes with such type of ring-sharing spin−orbit coupling, which can lead to spin canting competing connectivity have been synthesized based on C,42 N,43 and B− with frustration via Dzyaloshinskii−Moriya interactions.37 The N44,45 and C−N46 combinations but not, as far as we are lack of significant spin−orbit coupling in organic sp2-based aware, on C−B combinations. systems would tend to rule out noncollinear canted spin states Figure 2a,b shows the optimized structures of our in our mv-2DCPs. Specifically, we note that electron considered mv-2DCPs, namely, the N- and B-mv-2DCPs. paramagnetic resonance measurements on the molecular We note that in each case, the a and b parameters are equal analogues of both B-mv-2DCP and N-mv-2DCP can be well with an angle of almost exactly 60° indicating that the B and N fitted using the Bleaney−Bowers equation, which is purely substitutions negligibly affect the original hexagonal symmetry based on a two-body Heisenberg model (i.e., isotropic spin of the parent C-2DCP. In a spin-restricted configuration, exchange coupling).30 Moreover, the g-factors in triphenyl- partial filling (emptying) of the conduction (valence) bands methyl radicals have very similar values to that of the free occurs and N- and B-mv-2DCPs are predicted to be metallic electron, again confirming the almost total absence of any and diamagnetic. However, allowing the system to break the spin−orbit coupling effect.38 spin degeneracy using a spin-unrestricted setup, one obtains a Formally, the Heisenberg model also corresponds to the spin-polarized solution (i.e., paramagnetic) emerging from the Hubbard model in the limit of a large U/t ratio, where U is the C sp2 nodes for both mv-2DCPs as shown with the associated onsite Coulomb repulsion term and t is the intersite hopping spin density maps for N- (Figure 2e) and B-mv-2DCP (Figure integral (i.e., the Mott insulating regime). The parent S2a in the Supporting Information, SI). In this situation, the nonsubstituted C-2DCP material is a Mott insulator with previously partially filled bands split into a fully filled spin-up AFM spin ordering on the hexagonal 2D lattice. However, it channel and an empty spin-down channel (see Figure 2c,d for can be tuned toward a semimetal−insulator transition (i.e., N- and B-mv-2DCP). These spin-polarized gapped solutions lowering the U/t ratio) by chemical functionalization and out- are 167 meV and 287 meV per fu more stable than the spin- of-plane compression.15 In the case of our proposed mv- restricted diamagnetic metallic solutions for N- and B-mv- 2DCPs, as a Mott insulator they could likely host various spin- 2DCP, respectively. This implies that the metallic solutions are ordered phases on the frustrated 2D triangular lattice. Around energetically well above kBT at room temperature, and so the metal−insulator transition, quantum spin liquid (QSL)- almost inaccessible. based states have been formally predicted to emerge on 2D To assess the magnetic structure of our mv-2DCPs, we triangular lattices of S = 1/2 spins.39,40 Mechanically and/or constructed a 2 × 2 in-plane supercell including four radical C chemically tuning the U/t ratio toward the (semi)metal− sp2 centers for each case. Figure 2e shows a spin density map insulator transition could also open up the possibility of QSLs for N-mv-2DCP in the ferromagnetic (FM) configuration (see in our materials. Figure S2 for B-mv-2DCP). Here, as the spin polarization We note that ground-state predictions of model Hamil- emerges from the C sp2 centers, we obtain a regular triangular tonians are formally only valid at 0 K for a static unperturbed lattice of spin-1/2 centers, resulting from the N (B) chemical lattice and may not reflect the actual macroscopic observed substitution in these networks. Figure 2f provides the state in materials at finite temperatures. The thermal stability analogous spin density map for an AFM configuration which, of any spin-ordered or QSL-based state also depends on the as shown in Figure S2, may also be obtained for B-mv-2DCP. strength of AFM coupling. In mv-2DCPs strong superexchange Importantly, the AFM solution lies below the FM solution by AFM interactions evolve between nearest-neighbor sp2 carbon 0.186 and 0.048 eV per fu for N- and B-mv-2DCP, centers forming a covalent triangular lattice of formally spin-1/2 respectively. This means that these mv-2DCPs significantly centers. We find that the magnitude of the coupling strength energetically favor emergent AFM solutions in which (J) of the AFM interactions for our mv-2DCPs is comparable interactions between spin-1/2 centers create a regular triangular and even higher than those in well-known organometallic magnetic sublattice. This, in turn, inherently leads to magnetic materials exhibiting a QSL character. Overall, our study frustration (i.e., where each C sp2 center cannot be provides a general design recipe to realize spin frustration in antiferromagnetically coupled with all its nearest-neighbor C carbon-based 2D materials by embedding a triangular lattice of sp2 centers simultaneously). This spin frustration also gives rise spin-1/2 centers in mv-2DCPs. We thus suggest that mv- to the possibility of many distinct but energetically degenerate 5676 https://doi.org/10.1021/jacs.2c11185 J. Am. Chem. Soc. 2023, 145, 5674−5683 Journal of the American Chemical Society pubs.acs.org/JACS Article [−250,−220] K = [−22,−19] meV) depending on the susceptibility fitting47,48 and κ-(ET)2Ag2(CN)3 (with J = −220, −270, and −310 K, for P = 0.5, 0.75, and 0.95 GPa).49 To better understand the type of magnetic interactions in these mv-2DCPs, we now consider their molecular analogues. We note that the synthesis of molecular neutral mixed-valence systems of the type we consider below has been shown to be feasible and to provide a good platform for studying magnetic interactions.30 In Figure 3a, we consider CN-based nanoring molecular analogue of our extended N-mv-2DCP where we can obtain both the FM and AFM solutions. This is also the case for the CB-based nanoring molecular analogue of the B- mv-2DCP (see Figure S4). As in the corresponding mv- 2DCPs, the spin-frustrated AFM configuration is the ground state for these molecular systems, being 53 meV (16 meV) per Figure 2. (a) Structure (top) and electronic band structure (bottom) for N-mv-2DCP and the same for (b) B-mv-2DCP, both from spin- restricted DFT calculations (i.e., diamagnetic solution). The respective unit cells contain one formula unit (fu). Atom color key: C�gray, H�white, B�mauve, N�blue. (c) Band structures for the ferromagnetic (FM) solution for the unit cell of N-mv-2DCP and for (d) B-mv-2DCP obtained from spin-unrestricted DFT calculations (spin-up: blue lines; spin-down: red lines). EF has been set as the top of valence bands in (c,d). (e) Spin density map for the 2 × 2 supercell of N-mv-2DCP in the FM configuration and (f) an AFM configuration (spin-up: blue; spin-down: red). Note that the AFM alignment in (f) is not possible in the primitive cells shown in (a, b). Significant spin densities are only found on C sp2 nodes which form a highly symmetric triangular sublattice (dashed lines). (g) Representa- tion of different near-degenerate AFM frustrated spin configurations in our mv-2DCPs. AFM-aligned spin configurations (see examples in Figure 2g). The associated density of states for the AFM and FM solution for N-mv-2DCP are shown in Figure S3. The corresponding nearest-neighbor magnetic coupling constants between C sp2 centers of a standard Heisenberg− Dirac−Van Vleck spin Hamiltonian (with −JijŜ i·Ŝ j two-body Figure 3. Spin density maps for (a) the CN-nanoring, (b) the CN interactions and Jij < 0 denoting AFM interactions) have been model with three magnetic centers and (c) the CN model with two evaluated by means of a mapping between the spin eigenstates magnetic centers. FM spin configurations are shown on the left and of this spin model and the relevant electronic solutions with AFM spin configurations are shown on the right. In (a−c), blue corresponds to spin-up and red corresponds to spin-down. (d) Singly different spin arrangements (see the SI for full details). The occupied natural orbitals (SONO) for the singlet ground state of the calculated magnetic coupling constants are: J = −46 meV for CN model with two magnetic centers. These orbitals were obtained N-mv-2DCP and J = −12 meV for B-mv-2DCP (see SI for full from unrestricted DFT calculations carried out with the Gaussian 09 details). We note that the AFM interaction strength in N-mv- program50 using the PBE0 functional and an Ahlrichs TZVP basis 2DCP is predicted to be significantly larger than that found for set.51 The electron occupation is 1.181 and 0.819 for the the possible QSL candidates EtMe3Sb[Pd(dmit)2]2 (J = antisymmetric (left) and symmetric (right) SONOs, respectively. 5677 https://doi.org/10.1021/jacs.2c11185 J. Am. Chem. Soc. 2023, 145, 5674−5683 Journal of the American Chemical Society pubs.acs.org/JACS Article Figure 4. (a) Spin populations on each αC center (see (b)) in N-mv-2DCP (μαCi) during a 3 ps AIMDS at 300 K. (b) Spin density maps for an N- d mv-2DCP taken from a snapshot during the AIMD calculations at the time indicated with vertical dashed line in (a). (c) Spin density maps for the fully optimized ox-N-mv-2DCP and for (d) Cl-N-mv-2DCP structures in an AFM spin configuration (see the Methods Section for details). (e) Average of the absolute value of spin population on the αCs (⟨|μαC|⟩) against ⟨cos φi2⟩ for the three different considered N-mv-2DCPs in (b−d). ⟨cos φi2⟩ = ∑ cos φi2 / n and ϕi are the twist angle of each aryl ring i with respect to the 2D material plane. (f) Energy difference between the AFM and FM configurations against ⟨cos φi2⟩ for the same three 2DCPs. fu below the FM solution for the CN-based (CB-based) not obtained when the analogous full-carbon nanoring (as nanorings. This strongly suggests that the magnetic inter- recently synthesized42) is triply reduced, as shown in Figure actions in both molecular and extended systems arise at the S5, despite the fact it is isoelectronic with the CN-based local scale. This is further corroborated by considering even nanoring. This highlights the need for chemical substitution, as smaller molecular analogues, including two or three magnetic herein proposed, to induce spin frustration either in the centers, also displaying an AFM ground state (see Figures 3b,c molecular systems or in the corresponding 2D materials. and S4 for the corresponding ΔEAFM‑FM values). These results The nature of the magnetic interactions in mv-2DCPs can are also consistent with those reported elsewhere.30 We note be further understood by close inspection of the frontier that the magnitude of the J coupling constants of our orbitals of the corresponding molecular models including two considered molecular systems is larger than those in ref 30 magnetic centers. The singly occupied natural orbitals due to (i) the more planar conformation of aryl rings in our (SONOs) of the CN and CB models with two magnetic systems compared to those based on perchlorotriarylmethyls, centers show that the unpaired electrons are mainly localized and (ii) the fact that our sp2 nodes are separated only by a on the TAM moieties (i.e., the carbon sp2 nodes). Specifically, single aryl ring, as opposed to two aryl rings. We also note that the SONOs result from the symmetric and antisymmetric a triangular arrangement of AFM coupled spin-1/2 centers is combinations of the singly occupied molecular orbitals 5678 https://doi.org/10.1021/jacs.2c11185 J. Am. Chem. Soc. 2023, 145, 5674−5683 Journal of the American Chemical Society pubs.acs.org/JACS Article (SOMOs) of the TAMs and a small contribution of the p resulting 2D frameworks with a persistent multiradical orbitals of the bridging B/N atom (see Figures 3d and S6). character which is undisturbed by thermally induced structural Both the CN (Figures 3d) and CB models (Figure S6) with fluctuations. two magnetic centers have a SONO with an occupation Finally, we considered the effect of chemical functionaliza- significantly larger than 1.0 and a SONO with an occupation tion of the aryl rings in our mv-2DCPs. The localization of spin significantly smaller than 1.0. In the case of the CN model with density depends on the dihedral angle of the aryl rings34 which, two magnetic centers, the SONO with a larger occupation in turn, affects the magnetic interactions between spin-1/2 Figure 3d, left) does not involve any contribution of the p radical centers in the 2D frameworks.32 Here, we consider two orbital of the N atom. However, for the SONO with a smaller additional N-mv-2DCPs built from the molecular oxygen- occupation (Figure 3d, right) , the p orbital of N combines in functionalized triarylmethyl (oxTAM)54 and perchlorotriar- an antibonding fashion with the p orbitals of its neighboring ylmethyl (PTM).55 These molecular functionalizations lead, atoms (see Figure 3d). In the case of the CB models with two respectively, to fully planarized aryl rings within the ox-N-mv- magnetic centers, the SONO with a larger occupation features 2DCP, ⟨φ⟩ = 0.02°, and to highly out-of-plane twisted aryl a bonding combination of the p orbital of B with the p orbitals rings for the Cl-N-mv-2DCP, ⟨φ⟩ = 48.5° deg., compared with of its neighboring atoms, whereas the SONO with a smaller the hydrogenated N-mv-2DCP, ⟨φ⟩ = 36.8° (see Figure S8). occupation does not involve any contribution of the p orbital As shown in Figure 4, both the ox-N-mv-2DCP (4c) and Cl-N- of the B atom (see Figure S6). The differences in the atomic mv-2DCP (4d) also display an AFM ground state, being −276 contributions of the SONOs of the CN and CB models can be and −47 meV per fu below the respective FM solution. The rationalized by means of a simple molecular orbital diagram, as corresponding magnetic coupling constants between nearest- shown in the SI (Figure S12). The shape of the SONOs neighbor sp2 centers are calculated to be: J = −68 meV (ox-N- suggests that complex electronic interactions between the mv-2DCP) and J = −13 meV (Cl-N-mv-2DCP). localized unpaired electrons through the bridging π-system in These results demonstrate that the AFM interactions are N- and B-mv-2DCP is similar to a superexchange mechanism inherently correlated with the alternating distribution of C and where the π-orbitals (and electrons) of the central N or B N (B) sp2 nodes within N-mv-2DCPs (B-mv-2DCPs). The atoms play the role of the closed-shell ligand in Anderson chemical functionalization of aryl rings, though, has a model.52,53 This helps to rationalize the large AFM interactions significant effect on the strength of such magnetic interactions. found in these systems and its dependence on structural In Figure 4e, we plot ⟨|μαC|⟩, which gives a measure of spin deformations (see below). localization, against the average of the cosine squared of all aryl As previously shown for the parent C-2DCPs, the rings twist angles (⟨cos φi2⟩). As we may see, there is a linear conformation of the 2D framework (e.g., dihedral angles of correlation between the two quantities, which is in line with aryl rings) can determine its electronic configuration.15,16 For previous studies,32,34 and highlights the principal role of aryl instance, the effect of thermal fluctuations may lead to ring twist angles to determine spin localization in this type of significant variations in the total absolute spin population of 2DCPs. Since spin localization has a direct impact on magnetic the networks, due to electron pairing.16 On the other hand, the interactions, we also obtain a correlation between ΔEAFM‑FM chemical functionalization of aryl rings also affects the and ⟨cos φi2⟩ (see Figure 4f). These results highlight the role multiradical character of C-2DCPs, as it affects the π- of the chemical functionalization of aryl rings to tune the conjugation via the dihedral twist angles of the aryl strength of the spin-frustrated magnetic phase in mv-2DCPs. rings.33,34 To evaluate the impact of these different parameters, The highly twisted aryl rings in Cl-N-mv-2DCP (see Figure we first used ab initio molecular dynamics (AIMD) at 300 K S8) leads to strong spin localization (Figure 4d), which entails for N-mv-2DCP (see the Methodology Section for details). a smaller AFM coupling (see above). However, the fully planarized ox-N-mv-2DCP has significant spin delocalization Here, we set the initial spin polarization to zero to avoid any and we obtain a larger AFM coupling (see above), which bias towards an AFM solution, thus allowing the system to should be robust even at room temperature (Figure 4c). These spontaneously evolve with temperature. As shown in Figure 4a, trends can be understood in terms of the Anderson model a rapid spontaneous spin population appears for each of the since a larger planarity increases orbital delocalization through four αCs within the unit cell which couple via local AFM the bridging aromatic rings which, in turn, increases the interactions (i.e., two μαCi > 0 and two μαCi < 0). We can see d d superexchange contribution to the magnetic coupling to the resulting AFM configuration more clearly by examining the further stabilize the low spin states with respect to the high spin density map shown in Figure 4b for a random snapshot spin state. during the dynamics. We can also see that this AFM As mentioned above, a 2D triangular lattice of strongly AFM configuration remains stable for the full 3 ps of our AIMD interacting spin-1/2 centers can be described by the Heisenberg run, with no significant drops in the average of the absolute model for highly localized spins (i.e., for a Mott insulator with value of the αC spin populations (⟨|μαC|⟩; see Figure S7). This high onsite Coulomb repulsion, U). With increasing electron result also highlights the different nature of N-mv-2DCP (and delocalization the hopping integral between sites (t) becomes B-mv-2DCP) compared to the analogous C-2DCP, where more significant and tends to disrupt magnetically ordered ⟨|μαC|⟩ is significantly lower in magnitude and varies strongly states. The situation arising from U/t values corresponding to during an AIMD run. In fact, in C-2DCP, ⟨|μαC|⟩ can the metal−insulator transition is thought to be ideal for sometimes completely vanish due to the possibility of electron creating a QSL ground state where the system fluctuates pairing of radical centers forming a quinoidal configuration.16 between degenerate frustrated AFM spin configurations, even Such a pairing mechanism is not observed for N-mv-2DCP and without thermal energy.56−58 For the Hubbard model on the B-mv-2DCP, as the N and B substitutions inhibit direct 2D triangular lattice, the QSL regime has been predicted to interactions between C centers. Consequently, all αC centers occur for approximately 8 ≤ U/t ≤ 11.39,40 Following the exhibit a robust associated spin-1/2, thus equipping the approach in ref 59, we use the FM band structures of the three 5679 https://doi.org/10.1021/jacs.2c11185 J. Am. Chem. Soc. 2023, 145, 5674−5683 Journal of the American Chemical Society pubs.acs.org/JACS Article materials in Figure 4 to estimate their respective U and t.59 In Perhaps the most spectacular example of electrostatic doping line with the increasing delocalization with increasing planarity of a 2D material based on sp2 centers is realized in magic angle of the linkers going through the series: Cl-N-mv-2DCP, N-mv- bilayer graphene, in which a transition between a Mott 2DCP, ox-N-mv-2DCP, we also find a concomitant increase in insulator and a superconducting phase was achieved.68 We t and decrease in U. For Cl-N-mv-2DCP, the U/t value is further note that the redox properties (i.e., ease of doping) of estimated to be 35.5 which is deep inside the Mott insulating our materials would also be tunable by chemical design.30,69 regime. However, for N-mv-2DCP and ox-N-mv-2DCP, the We thus envisage that electrostatic doping would be a feasible corresponding U/t values significantly decrease to 19.2 and way to introduce additional spins in the triangular “2D 16.1 respectively (see Figure S10 in the SI). These extracted Heisenberg sea” of mv-2DCPs in which the strong AFM estimates of U and t are from all-electron calculations of interactions of mv-2DCPs would tend to induce large spin realistic chemical structures and cannot thus be directly fluctuations. This scenario is much like that observed in the compared with the parameters used to define the approximate cuprates, for which the RVB theory of high-Tc super- single-band Hubbard model. Nevertheless, they indicate that conductivity provides the most complete description of the N-mv-2DCP and ox-N-mv-2DCP may be weak Mott pairing mechanism.70 We note that the magnitude of the insulators, i.e., close to the metal−insulator transition. Weak magnetic coupling constants in our mv-2DCPs is comparable Mott insulators are thought to be particularly good candidates to those found in the parent compounds of superconducting for hosting a QSL state.56 The chemically induced variability of cuprates (J ∼−125 meV = −1450 K) for La2CuO4,71 U/t in our mv-2DCPs clearly demonstrates that modification Nd2CuO4,72,73 and YBa2Cu3O6.74 In this sense, our proposed of the spin-bearing units can be used to tune their electronic family of mv-2DCPs may provide the essential structural and properties toward the QSL regime. The application of electronic features necessary to develop a plausible chemical moderate out-of-plane pressure could also be used to tune basis for a superconducting phase upon doping. In summary, the U/t ratio of these materials towards the metal−insulator we suggest that the properties of mv-2DCPs could have great transition.15 This is also in line with recent experiments carried potential for providing a well-defined, robust, and tunable out on a hybrid organic−inorganic molecule-based material general platform for developing a new class of all-organic sp2- showing that pressure can induce the emergence of a QSL based 2D quantum materials. state.60 Taken together, our results show that partially B- or N- substituted mv-2DCPs can host symmetric triangular lattices of ■ CONCLUSIONS We have studied the electronic and magnetic properties of a AFM interacting spins for which the magnetic interaction new class of 2DCPs by means of first-principles hybrid DFT strength can be tuned by chemical functionalization. If suitably calculations. Our proposed materials can be envisaged as tuned materials of this type were synthesized, the resulting chemically substituted versions of previously well-known frustration between different AFM configurations in mv- hexagonal networks of sp2 carbon centers, here referred to as 2DCPs could lead to the emergence of unusual spin-ordered C-2DCPs (also known as 2D-CORFs). From another states and potentially to elusive QSL-based states. The current perspective, our materials can be conceptually viewed as most widely accepted candidate QSL-host materials are 2D proposed 2D extended versions of neutral mixed-valence organic salts such as κ-(ET)2Cu2(CN)349 and EtMe3Sb[Pd- molecules. The resulting N- and B-mv-2DCPs display a (dmit)2]2,47,48 which form arrays of discrete molecules in a semiconducting multiradical ground state, which, contrary to triangular lattice. These materials tend to have fairly low the parent material (C-2DCP), is not in competition with strength AFM interactions (J ∼−250 K = −21.5 meV) and closed-shell quinoidal configurations. This makes the spin- their nonbonded arrays of molecular spin-carrying nodes are polarized multiradical state very robust against thermal susceptible to thermal disruption due to the weak cohesive fluctuations. Consequently, N- and B-mv-2DCPs may be intermolecular forces taking place. In contrast, mv-2DCPs are regarded as 2D arrays of persistent spin-1/2 centers. We further based on robust and highly symmetric covalently linked sp2- find that the radical carbon nodes interact through significant based 2D lattice which can host significantly stronger AFM AFM coupling in both N- and B-mv-2DCPs. These AFM interactions. The low spin−orbit coupling in our sp2-based interactions appear to be of a local character, as they also magnetic states also inhibits spin canting, which can lead to emerge for the corresponding molecular systems. Because of competing nonfrustrated spin orderings.37 the extended triangular arrangement of spin-1/2 centers in Several experimental realizations of 2D spin lattice systems these 2DCPs, such AFM coupling would lead to magnetic (e.g., square lattice in cuprates, the honeycomb lattice, or the frustration, due to the impossibility of having all spin centers frustrated triangular or kagomé lattices) have shown interesting antiferromagnetically coupled with their nearest neighbors. quantum phases at low temperatures, such as superconductiv- Such a frustrated situation makes our proposed 2DCPs purely ity, QSL-based phases, or topological quantum states.56,61−65 organic candidates to host unusual magnetically ordered Often the focus in these studies is on materials with lattices of states36 and, potentially, QSL-based states.56−58,75 We note antiferromagnetically interacting spins in which states exhibit- that our strategy could also be applicable to other 2DCPs ing the conventional Néel order are thought to compete with based on open-shell organic molecular building blocks e.g., resonating valence bond (RVB)-like states. It has been triangulenes.76 Considering different chemical functionaliza- suggested that doped Mott insulators that are close to the tions of the aryl rings for N-mv-2DCP, we find that the (semi)metal−AFM−insulator transition could be good candi- strength of such (frustrated) AFM interactions may be tuned dates to host such novel quantum phases. In relation to this, from ca. −50 to −300 meV, due to the effect of flattening aryl we note that our proposed B/N-substituted C-2DCPs could ring twist angles on spin localization. At the same time, the also be electrostatically doped by supporting them on an Au- increase in delocalization leads to the estimated U/t ratio based electrode. Such a setup has been shown to promote becoming progressively closer to the metal−Mott insulator oxidation of N and C sites in 1D sp2-based systems.66,67 transition, where QSL states are more likely to emerge. Due to 5680 https://doi.org/10.1021/jacs.2c11185 J. Am. Chem. Soc. 2023, 145, 5674−5683 Journal of the American Chemical Society pubs.acs.org/JACS Article the strong AFM coupling in some of our proposed materials 2DCP, N-mv-2DCP, and Cl-N-mv-2DCP; species- (well above kBT at room temperature), it is likely that the projected density of states for ox-N-mv-2DCP, N-mv- magnetic frustration would be persistent at temperatures well 2DCP, and Cl-N-mv-2DCP; U/t estimation for ox-N- above nitrogen liquid. Generally, our proposed mv-2DCPs are mv-2DCP, N-mv-2DCP, and Cl-N-mv-2DCP; magnetic attractive synthetic targets for realizing a robust tunable all- coupling constant calculations; and molecular orbital organic quantum materials platform for bottom-up design and diagrams for N- and B-based systems (PDF) generation of exotic phases (e.g., QSL states, spin crystals, RVB states, superconductivity). ■ METHODOLOGY ■ AUTHOR INFORMATION Corresponding Authors The atomic and electronic structure of our 2DCPs was Isaac Alcón − Catalan Institute of Nanoscience and modeled by first-principles density functional theory (DFT)- Nanotechnology (ICN2), CSIC and BIST, Bellaterra 08193 based calculations using periodic boundary conditions and the Barcelona, Spain; orcid.org/0000-0002-7569-2000; hybrid PBE0 functional.41 The PBE0 functional was found in Email: isaac.alcon@icn2.cat prior studies to reproduce experimentally measured magnetic Stefan T. Bromley − Departament de Ciència de Materials i coupling coefficients of this type of systems.16,42 The closed- Química Física & Institut de Química Teòrica i shell metallic solutions for N-mv-2DCP and B-mv-2DCP were Computacional (IQTC), Universitat de Barcelona, 08028 obtained from spin-restricted DFT calculations. The two Barcelona, Spain; Institució Catalana de Recerca i Estudis magnetic configurations (FM and AFM) were separately Avançats (ICREA), 08010 Barcelona, Spain; orcid.org/ obtained by appropriately initializing the spin moment on αC 0000-0002-7037-0475; Email: s.bromley@ub.edu radical centers in spin-unrestricted DFT calculations. Atomic coordinates and in-plane unit cell parameters were preopti- Authors mized using the PBE77 functional and a Tier-1 light numerical Jordi Ribas-Ariño − Departament de Ciència de Materials i atom-centered orbital (NAO) basis set,78 as implemented in Química Física & Institut de Química Teòrica i the Fritz Haber Institute ab initio molecular simulations Computacional (IQTC), Universitat de Barcelona, 08028 package (FHI-AIMS).79,80 Subsequent full optimizations were Barcelona, Spain; orcid.org/0000-0003-4088-6187 performed with the PBE0 hybrid functional41 and the same Ibério de P.R. Moreira − Departament de Ciència de NAO basis set. Optimizations of the unit cells (supercells) Materials i Química Física & Institut de Química Teòrica i were performed using 18 × 18 × 1 (6 × 6 × 1) Γ-centered Computacional (IQTC), Universitat de Barcelona, 08028 Monkhorst−Pack (MP) sampled k-grids. Convergence criteria Barcelona, Spain; orcid.org/0000-0002-2684-6982 of 1 × 10−5 eV and 1 × 10−2 eV/Å were used for the total Complete contact information is available at: energy and for the maximum atomic force component, https://pubs.acs.org/10.1021/jacs.2c11185 respectively. The same functional, basis set, and convergence criteria were used for the studied molecular systems. Band Notes structures, total energies, and atomically partitioned spin The authors declare no competing financial interest. populations and spin densities were then extracted from single- point calculations using the fully optimized structures. These final SCF runs were performed using the PBE0 functional and the same MP k-grid and NAO basis set previously indicated for ■ ACKNOWLEDGMENTS I.A. is grateful for a Juan de la Cierva postdoctoral grant each periodic cell type. Atomically partitioned spin populations (FJC2019-038971-I) from the Ministerio de Ciencia e (μi) were calculated using the Hirshfeld scheme.81 Finally, the Innovación. ICN2 is funded by the CERCA Programme effect of thermal fluctuations was modeled via ab initio from Generalitat de Catalunya and is supported by the Severo molecular dynamics (AIMD) calculations at 300 K for 3 ps, Ochoa program from Spanish MINECO (Grant No. SEV- using the Bussi−Donadio−Parrinello thermostat,82 the PBE0 2017-0706). S.T.B acknowledges support from the MICINN- functional, a 2 × 2 × 1 MP k-grid, and a Tier-1 light NAO funded project grants: PID2021-127957NB-I00 and basis set. TED2021-132550B-C21. I.P.R.M acknowledges support from the MICINN-funded project grant: PID2019-109518GB-I00. ■ * ASSOCIATED CONTENT sı Supporting Information J.R.A. acknowledges support from the MICINN-funded project grant: PID2020-117803GB-I00. S.T.B., I.P.R.M., and J.R.A. also acknowledge support from project grant The Supporting Information is available free of charge at 2021SGR00354 funded by the Generalitat de Catalunya. The https://pubs.acs.org/doi/10.1021/jacs.2c11185. IQTC-UB is funded by the María de Maeztu program for Electronic band structures for the B-, C- and N-2DCPs; Spanish Structures of Excellence (CEX2021-001202-M). The atom-resolved spin population maps for FM and AFM authors also acknowledge access to supercomputer resources configurations in the B-mv-2DCP; spin-resolved density as provided through grants from the Red Española de of states for 2 × 2 supercells in N-mv-2DCP in FM and Supercomputación (RES). AFM configurations; atom-resolved spin population maps for FM and AFM configurations in all N- and B- based molecular systems; atom-resolved spin population maps for cyclo-para-phenylmethine; singly occupied ■ REFERENCES (1) Liu, K.; Wang, L.; Dong, R. Two-dimensional conjugated polymer films: Via liquid-interface-assisted synthesis toward organic natural orbitals for the B-based diradical molecule; electronic devices. J. Mater. Chem. C 2020, 8, 10696−10718. time-resolved average of the αC spin population for N- (2) Wei, X.; Wang, M. Two dimensional semiconducting polymers. mv-2DCP at 300 K; periodic structures of ox-N-mv- Mater. Chem. Front. 2020, 4, 3472−3486. 5681 https://doi.org/10.1021/jacs.2c11185 J. Am. Chem. Soc. 2023, 145, 5674−5683 Journal of the American Chemical Society pubs.acs.org/JACS Article (3) Adjizian, J.-J.; Briddon, P.; Humbert, B.; et al. Dirac Cones in pounds; Hicks, R. G., Ed.; John Wiley & Sons, Ltd: Chichester, UK., two-dimensional conjugated polymer networks. Nat. Commun. 2014, 2010; pp 1−31. 5, No. 5842. (26) Heckmann, A.; Lambert, C.; Goebel, M.; Wortmann, R. (4) Galeotti, G.; De Marchi, F.; Hamzehpoor, E.; et al. Synthesis of Synthesis and Photophysics of a Neutral Organic Mixed-Valence mesoscale ordered two-dimensional π-conjugated polymers with Compound. Angew. Chem., Int. Ed. 2004, 43, 5851−5856. semiconducting properties. Nat. Mater. 2020, 19, 874−880. (27) Heckmann, A.; Lambert, C. Neutral Organic Mixed-Valence (5) Li, C.; Wang, Y.; Zou, Y.; et al. Two-Dimensional Conjugated Compounds: Synthesis and All-Optical Evaluation of Electron- Polymer Synthesized by Interfacial Suzuki Reaction: Towards Transfer Parameters. J. Am. Chem. Soc. 2007, 129, 5515−5527. Electronic Device Applications. Angew. Chem., Int. Ed. 2020, 59, (28) Wu, X.; Kim, J. O.; Medina, S.; et al. Push-Pull-Type 9403−9407. Polychlorotriphenylmethyl Radicals: New Two-Photon Absorbers (6) Bian, G.; Yin, J.; Zhu, J. Recent Advances on Conductive 2D and Dyes for Generation of Photo-Charges. Chem. - Eur. J. 2017, 23, Covalent Organic Frameworks. Small 2021, 17, No. 2006043. 7698−7702. (7) Wang, C.; Zhang, Z.; Zhu, Y.; et al. 2D Covalent Organic (29) Kaupp, M.; Renz, M.; Parthey, M.; et al. Computational and Frameworks: From Synthetic Strategies to Advanced Optical- spectroscopic studies of organic mixed-valence compounds: where is Electrical-Magnetic Functionalities. Adv. Mater. 2022, 34, the charge? Phys. Chem. Chem. Phys. 2011, 13, 16973−16986. No. 2102290. (30) Hattori, Y.; Michail, E.; Schmiedel, A.; et al. Luminescent (8) Souto, M.; Perepichka, D. F. Electrically conductive covalent Mono-, Di-, and Triradicals: Bridging Polychlorinated Triarylmethyl organic frameworks: Bridging the fields of organic metals and 2D Radicals by Triarylamines and Triarylboranes. Chem. - Eur. J. 2019, materials. J. Mater. Chem. C 2021, 9, 10668−10676. 25, 15463−15471. (9) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; et al. Electric (31) Reitzenstein, D.; Quast, T.; Kanal, F.; et al. Synthesis and Field Effect in Atomically Thin Carbon Films. Science 2004, 306, electron transfer characteristics of a neutral, low-band-gap, mixed- 666−669. valence polyradical. Chem. Mater. 2010, 22, 6641−6655. (10) Geim, A. K.; Novoselov, K. S. The rise of graphene. Nat. Mater. (32) Alcón, I.; Reta, D.; Moreira, I. de P. R.; Bromley, S. T. Design 2007, 6, 183−191. of multi-functional 2D open-shell organic networks with mechanically (11) Adjizian, J.-J.; Lherbier, A.; Dubois S, M.-M.; Botello-Méndez, controllable properties. Chem. Sci. 2017, 8, 1027−1039. A. R.; Charlier, J.-C. The electronic and transport properties of two- (33) Alcón, I.; Bromley, S. T. Triarylmethyl-based 2D covalent dimensional conjugated polymer networks including disorder. Nano- networks: virtual screening of chemical functionalisation for scale 2016, 8, 1642−1651. optimising strain-induced property control. Phys. Chem. Chem. Phys. (12) Kim, B. G.; Choi, H. J. Graphyne: Hexagonal network of 2018, 20, 5028−5035. carbon with versatile Dirac cones. Phys. Rev. B 2012, 86, No. 115435. (34) Alcón, I.; Bromley, S. T. Structural Control over Spin (13) Alcón, I.; Viñes, F.; Moreira, I. de P. R.; Bromley, S. T. Localization in Triarylmethyls. RSC Adv. 2015, 5, 98593−98599. Existence of multi-radical and closed-shell semiconducting states in (35) Bernu, B.; Lecheminant, P.; Lhuillier, C.; Pierre, L. Exact post-graphene organic Dirac materials. Nat. Commun. 2017, 8, spectra, spin susceptibilities, and order parameter of the quantum No. 1957. Heisenberg antiferromagnet on the triangular lattice. Phys. Rev. B (14) Thomas, S.; Li, H.; Bredas, J.-L. Emergence of an 1994, 50, 10048−10062. Antiferromagnetic Mott Insulating Phase in Hexagonal π-Conjugated (36) Starykh, O. A. Unusual ordered phases of highly frustrated Covalent Organic Frameworks. Adv. Mater. 2019, 31, No. 1900355. magnets: A review. Rep. Prog. Phys. 2015, 78, No. 052502. (15) Santiago, R.; Alcón, I.; Ribas-Arino, J.; et al. 2D Hexagonal (37) Gîrţu, M. A.; Wynn, C. M.; Fujita, W.; Awaga, K. Glassiness Covalent Organic Radical Frameworks as Tunable Correlated and canted antiferromagnetism in three geometrically frustrated Electron Systems. Adv. Funct. Mater. 2020, 31, No. 2004584. triangular quantum Heisenberg antiferromagnets with additional (16) Alcón, I.; Santiago, R.; Ribas-Arino, J.; et al. Controlling pairing Dzyaloshinskii-Moriya interaction. Phys. Rev. B 2000, 61, 4117−4130. of π-conjugated electrons in 2D covalent organic radical frameworks (38) Dai, Y.-Z.; Dong, B. W.; Kao, Y.; et al. Chemical Modification via in-plane strain. Nat. Commun. 2021, 12, No. 1705. toward Long Spin Lifetimes in Organic Conjugated Radicals. (17) Lleopart, G.; Lopez-Suarez, M.; Moreira, I. de P. R.; Bromley, ChemPhysChem 2018, 19, 2972−2977. S. T. How graphenic are graphynes? Evidence for low-lying correlated (39) Szasz, A.; Motruk, J.; Zaletel, M. P.; Moore, J. E. Chiral Spin gapped states in graphynes. J. Chem. Phys. 2022, 157, No. 214704. Liquid Phase of the Triangular Lattice Hubbard Model: A Density (18) Yang, Y.; Liu, C.; Xu, X.; et al. Antiferromagnetism in two- Matrix Renormalization Group Study. Phys. Rev. X 2020, 10, dimensional polyradical nanosheets. Polym. Chem. 2018, 9, 5499− No. 021042. 5503. (40) Chen, B.-B.; Chen, Z.; Gong, S.-S.; et al. Quantum spin liquid (19) Wu, J.; Li, M.; Phan, H.; et al. Toward π-Conjugated 2D with emergent chiral order in the triangular-lattice Hubbard model. Covalent Organic Radical Frameworks. Angew. Chem., Int. Ed. 2018, Phys. Rev. B 2022, 106, No. 094420. 57, 8007−8011. (41) Adamo, C.; Barone, V. Toward reliable density functional (20) Jiang, Y.; Oh, I.; Joo, S. H.; et al. Organic Radical-Linked methods without adjustable parameters: The PBE0 model. J. Chem. Covalent Triazine Framework with Paramagnetic Behavior. ACS Nano Phys. 1999, 110, 6158−6170. 2019, 13, 5251−5258. (42) Li, Z.; Gopalakrishna, T. Y.; Han, Y.; et al. Cyclo-para- (21) Meng, Z. Y.; Lang, T. C.; Wessel, S.; Assaad, F. F.; Muramatsu, phenylmethine: An Analog of Benzene Showing Global Aromaticity A. Quantum spin liquid emerging in two-dimensional correlated Dirac and Open-shell Diradical Character. J. Am. Chem. Soc. 2019, 141, fermions. Nature 2010, 464, 847−851. 16266−16270. (22) Jing, Y.; Heine, T. Two-Dimensional Kagome Lattices Made of (43) Ito, A.; Yokoyama, Y.; Aihara, R.; et al. Preparation and Hetero Triangulenes Are Dirac Semimetals or Single-Band Semi- Characterization of N-Anisyl-Substituted Hexaaza[16]- conductors. J. Am. Chem. Soc. 2019, 141, 743−747. paracyclophane. Angew. Chem., Int. Ed. 2010, 49, 8205−8208. (23) Montgomery, L. K.; Huffman, J. C.; Jurczak, E. A.; Grendze, M. (44) Chen, P.; Lalancette, R. A.; Jäkle, F. π-Expanded Borazine: An P. The molecular structures of Thiele’s and Chichibabin’s hydro- Ambipolar Conjugated B-π-N Macrocycle. Angew. Chem., Int. Ed. carbons. J. Am. Chem. Soc. 1986, 108, 6004−6011. 2012, 51, 7994−7998. (24) Zeng, Z.; Shi, X.; Chi, C.; et al. Pro-aromatic and anti-aromatic (45) Li, P.; Shimoyama, D.; Zhang, N.; Jia, Y.; Hu, G.; Li, C.; Yin, π-conjugated molecules: an irresistible wish to be diradicals. Chem. X.; Wang, N.; Jakle, F.; Chen, P.; et al. A New Platform of B/N- Soc. Rev. 2015, 44, 6578−6596. Doped Cyclophanes: Access to a π-Conjugated Block-Type B3N3 (25) Tidwell, T. T. Triarylmethyl and Related Radicals In Stable Macrocycle with Strong Dipole Moment and Unique Optoelectronic Radicals: Fundamentals and Applied Aspects of Odd-Electron Com- Properties. Angew. Chem., Int. Ed. 2022, 61, No. e202200612. 5682 https://doi.org/10.1021/jacs.2c11185 J. Am. Chem. Soc. 2023, 145, 5674−5683 Journal of the American Chemical Society pubs.acs.org/JACS Article (46) Dong, S.; Gopalakrishna, T. Y.; Han, Y.; Chi, C. Cyclobis(7,8- (70) O’Mahony, S. M.; Ren, W.; Chen, W.; et al. On the electron (para -quinodimethane)-4,4′-triphenylamine) and Its Cationic Spe- pairing mechanism of copper-oxide high temperature superconduc- cies Showing Annulene-Like Global (Anti)Aromaticity. Angew. Chem., tivity. Proc. Natl. Acad. Sci. U.S.A. 2022, 119, No. e2207449119. Int. Ed. 2019, 58, 11742−11746. (71) Keimer, B.; Belk, N.; Birgeneau, R. J.; et al. Magnetic excitations (47) Itou, T.; Oyamada, A.; Maegawa, S.; Tamura, M.; Kato, R. in pure, lightly doped, and weakly metallic La2CuO4. Phys. Rev. B Quantum spin liquid in the spin- 1 2 triangular antiferromagnet et 1992, 46, 14034−14053. Me3 Sb [Pd (dmit)2] 2. Phys. Rev. B 2008, 77, No. 104413. (72) Thurston, T. R.; Matsuda, M.; Kakurai, K.; et al. Anti- (48) Itou, T.; Oyamada, A.; Maegawa, S.; Kato, R. Instability of a ferromagnetic spin correlations in (Nd,Pr)2-xCexCuO4. Phys. Rev. quantum spin liquid in an organic triangular-lattice antiferromagnet. Lett. 1990, 65, 263−266. Nat. Phys. 2010, 6, 673−676. (73) Matsuda, M.; Yamada, K.; Kakurai, K.; et al. Three-dimensional (49) Shimizu, Y.; Hiramatsu, T.; Maesato, M.; et al. Pressure-Tuned magnetic structures and rare-earth magnetic ordering in Nd2CuO4 Exchange Coupling of a Quantum Spin Liquid in the Molecular and Pr2CuO4. Phys. Rev. B 1990, 42, 10098−10107. Triangular Lattice κ- (ET)2Ag2 (CN)3. Phys. Rev. Lett. 2016, 117, (74) Shamoto, S.; Sato, M.; Tranquada, J. M.; Sternlieb, B. J.; No. 107203. Shirane, G. Neutron-scattering study of antiferromagnetism in (50) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; YBa2Cu3O6.15. Phys. Rev. B 1993, 48, 13817−13825. Robb, M. A.et al. Gaussian 09, Revision D.01; Gaussian, Inc: (75) Szirmai, P.; Mézière, C.; Bastien, G.; et al. Quantum spin-liquid Wallingford CT, 2009. states in an organic magnetic layer and molecular rotor hybrid. Proc. (51) Schäfer, A.; Huber, C.; Ahlrichs, R. Fully optimized contracted Natl. Acad. Sci. U.S.A. 2020, 117, 29555−29560. (76) Anindya, K. N.; Rochefort, A. Controlling the magnetic Gaussian basis sets of triple zeta valence quality for atoms Li to Kr. J. properties of two-dimensional carbon-based Kagome polymers. Chem. Phys. 1994, 100, 5829−5835. Carbon Trends 2022, 7, 100170. (52) Anderson, P. W. Antiferromagnetism. Theory of superexchange (77) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient interaction. Phys. Rev. 1950, 79, 350−356. Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (53) Anderson, P. W. Theory of Magnetic Exchange Interaction- (78) Zhang, I. Y.; Ren, X.; Rinke, P.; Blum, V.; Scheffler, M. s:Exchange in Insulators and Semiconductors. Solid State Phys. 1963, Numeric atom-centered-orbital basis sets with valence-correlation 14, 99−214. consistency from H to Ar. New J. Phys. 2013, 15, No. 123033. (54) Sabacky, M. J.; Johnson, C. S.; Smith, R. G.; Gutowsky, H. S.; (79) Havu, V.; Blum, V.; Havu, P.; Scheffler, M. Efficient O(N) Martin, J. C. Triarylmethyl Radicals. Synthesis and Electron Spin integration for all-electron electronic structure calculation using Resonance Studies of Sesquixanthydryl Dimer and Related Com- numeric basis functions. J. Comput. Phys. 2009, 228, 8367−8379. pounds. J. Am. Chem. Soc. 1967, 89, 2054−2058. (80) Blum, V.; Gehrke, R.; Hanke, F.; et al. Ab initio molecular (55) Ballester, M.; Riera-Figueras, J.; et al. Inert Carbon Free simulations with numeric atom-centered orbitals. Comput. Phys. Radicals. I. Perchlorodiphenylmethyl and Perchlorotriphenylmethyl Commun. 2009, 180, 2175−2196. Radical Series. J. Am. Chem. Soc. 1971, 93, 2215−2225. (81) Hirshfeld, F. L. Bonded-atom fragments for describing (56) Balents, L. Spin liquids in frustrated magnets. Nature 2010, 464, molecular charge densities. Theor. Chim. Acta 1977, 44, 129−138. 199−208. (82) Bussi, G.; Donadio, D.; Parrinello, M. Canonical sampling (57) Imai, T.; Lee, Y. S. Do quantum spin liquids exist? Phys. Today through velocity rescaling. J. Chem. Phys. 2007, 126, No. 014101. 2016, 69, 30−36. (58) Broholm, C.; Cava, R. J.; Kivelson, S. A.; et al. Quantum spin liquids. Science 2020, 367, No. aay0668. (59) Xiang, H.; Lee, C.; Koo, H. J.; Gong, X.; Whangbo, M. H. Magnetic properties and energy-mapping analysis. Dalton Trans. 2013, 42, 823−853. (60) Hong, T.; Ying, T.; Huang, Q.; et al. Evidence for pressure induced unconventional quantum criticality in the coupled spin ladder antiferromagnet C9H18N2CuBr4. Nat. Commun. 2022, 13, No. 3073. (61) Anderson, P. W. Resonating valence bonds: A new kind of insulator? Mater. Res. Bull. 1973, 8, 153−160. (62) Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 1987, 235, 1196−1198. (63) Moore, J. E. The birth of topological insulators. Nature 2010, 464, 194−198. (64) Zhou, Y.; Kanoda, K.; Ng, T. K. Quantum spin liquid states. Rev. Mod. Phys. 2017, 89, No. 025003. (65) Smaha, R. W.; He, W.; Jiang, J. M.; et al. Materializing rival ground states in the barlowite family of kagome magnets: quantum spin liquid, spin ordered, and valence bond crystal states. npj Quantum Mater. 2020, 5, No. 23. (66) Friedrich, N.; Brandimarte, P.; Li, J.; et al. Magnetism of Topological Boundary States Induced by Boron Substitution in Graphene Nanoribbons. Phys. Rev. Lett. 2020, 125, No. 146801. (67) Sun, Q.; Yao, X.; Gröning, O.; et al. Coupled Spin States in Armchair Graphene Nanoribbons with Asymmetric Zigzag Edge Extensions. Nano Lett. 2020, 20, 6429−6436. (68) Cao, Y.; Fatemi, V.; Fang, S.; et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 2018, 556, 43−50. (69) Simão, C.; Mas-Torrent, M.; Crivillers, N.; et al. A Robust Molecular Platform for Non-Volatile Memory Devices with Optical and Magnetic Responses. Nat. Chem. 2011, 3, 359−364. 5683 https://doi.org/10.1021/jacs.2c11185 J. Am. Chem. Soc. 2023, 145, 5674−5683