Five-Membered Rings Create Off-Zero Modes in Nanographene

The low-energy electronic structure of nanographenes can be tuned through zero-energy π-electron states, typically referred to as zero-modes. Customizable electronic and magnetic structures have been engineered by coupling zero-modes through exchange and hybridization interactions. Manipulation of the energy of such states, however, has not yet received significant attention. We find that attaching a five-membered ring to a zigzag edge hosting a zero-mode perturbs the energy of that mode and turns it into an off-zero mode: a localized state with a distinctive electron-accepting character. Whereas the end states of typical 7-atom-wide armchair graphene nanoribbons (7-AGNRs) lose their electrons when physisorbed on Au(111) (due to its high work function), converting them into off-zero modes by introducing cyclopentadienyl five-membered rings allows them to retain their single-electron occupation. This approach enables the magnetic properties of 7-AGNR end states to be explored using scanning tunneling microscopy (STM) on a gold substrate. We find a gradual decrease of the magnetic coupling between off-zero mode end states as a function of GNR length, and evolution from a more closed-shell to a more open-shell ground state.

−8 In recent years local sublattice imbalances, 9−14 the substitution of heteroatoms, 15−21 and the incorporation of four-, five-, seven-, and eight-membered rings 22−28 have been used to engineer low-energy electronic states in NGs.−34 Engineering localized lowenergy states thus provides a tool for bypassing the natural tendency of aromatic structures to exhibit a gapped, closedshell electronic structure and creating emergent low-energy electronic behavior instead.−48 Zero-modes also arise more generally whenever an open-shell (or spin-split) ground state is lower in energy than its closed-shell counterpart, and this can be caused by the open-shell resonance structure featuring greater aromatic stabilization. 32,487-atom wide armchair-type graphene nanoribbons (7-AGNRs) demonstrate this behavior by featuring an openshell biradical ground state with two characteristic endlocalized states. 49,50In short 7-AGNRs, however, end states may hybridize and thus introduce closed-shell character to the ground state.Anthracene and bisanthene, for example, exhibit primarily closed-shell ground states. 51The zero-energy nature of zero-modes typically implies that these localized states have magnetic moments, since at charge neutrality they are usually singly occupied. 49Hence, zero-modes in close proximity can couple through exchange interactions to impart magnetic behavior to NGs.For 7-AGNRs a length-dependent exchangecoupling strength J between spins has been predicted on top of the transition from a closed-shell to an open-shell ground state. 52,53Unfortunately the magnetic characteristics of 7-AGNRs cannot be studied on a gold surface (typically used for the synthesis of 7-AGNRs) because of p-doping by the surface which is known to extract electrons from the end states. 50In the absence of electron occupation the end states only interact through hybridization, which has recently been shown between empty 7-AGNR end states in teranthene (three repeating anthracenes) and hexanthene (six repeating anthracenes) on Au(111). 54ere we describe a strategy to create localized states, hereafter termed off-zero modes, that are energetically offset compared to their zero-mode counterparts.Off-zero modes can be thought of as basis states for generating designer quantum structures in NGs (see Supplementary Discussion 1).Our strategy leverages the intrinsic stabilizing effect imparted by electron-withdrawing cyclopentadienyl groups: the fivemembered rings in fluorenyl radicals.Fusion of cyclopentadienyl groups to the zigzag ends of 7-AGNRs prevents electron transfer from the 7-AGNR to the underlying gold that would otherwise leave these states unoccupied. 50−57 We identify singlet-to-triplet spin-flip excitations for 7-AGNRs (oligoanthenes) having three and four repeating anthracene units and a Kondo effect for five and six repeating units, reflecting a monotonically decreasing exchange-coupling interaction with increasing separation.Differential conductance maps suggest significant closed-shell character for shorter 7-AGNRs.Our study thus reveals an evolution from a more closed-shell to a more open-shell ground state in 7-AGNR segments with increasing length.

RESULTS/DISCUSSION
Five-Membered-Ring-Induced Off-Zero Modes.The design of our off-zero mode structures is guided by density functional theory (DFT) simulations of a finite 7-AGNR featuring one pristine zigzag end, while the second end is capped by a fluorenyl group (Figure 1a,b).Our calculations predict an open-shell ground state for this GNR, with a singly occupied molecular orbital (SOMO) localized on the capped end 0.45 eV lower in energy than the SOMO on the pristine zigzag end (Figure 1b).The electronic stabilization gained by introducing the cyclopentadienyl ring thus converts the endstate zero-mode to a lower-energy of f-zero mode.This behavior can be rationalized using the Frost circle heuristic wherein a planar, monocyclic, and conjugated ring of five C atoms exhibits an electron-accepting state at E < 0 (Figure 1c). 58The DFT-calculated density of states (DOS) of a semi-infinite 7-AGNR terminated by either a pristine zigzag end or a cyclopentadienyl ring shows similar behavior (Supplementary Discussion 2 and Figure S1).Interestingly, the Frost circle model also implies that the introduction of a 7-membered ring, i.e., a cycloheptatrienyl group, would give rise to the opposite effect: off-zero modes with E > 0 and thus electron-donating character.
The extremely low vapor pressure of oligoanthrylenes precludes thermal sublimation, and so we relied on a matrixassisted direct (MAD) transfer technique to deposit these molecules onto Au(111) substrates suitable for on-surface CDH and STM characterization. 63,64Figure 2a shows an STM image of a Au(111) surface after MAD transfer of 1b in a pyrene matrix, followed by gradual heating to T = 200 °C for t = 1 h to remove the bulk of the pyrene.Molecules of 1b are recognizable by the presence of four lobes that result from the dihedral angle between neighboring anthracenes (inset of Figure 2a) and are preferentially localized along the Au(111) step edges.Figure 2b shows the sample after further heating to the CDH temperature T CDH = 300 °C for t = 20 min.The molecules have fully cyclized, yielding the planar quateranthene 6b, while almost all the residual pyrene has sublimed from the surface.The fin-shaped ends observed for 6b suggest that the phenyl rings have fused with the zigzag end forming the expected terminal fluorenyl groups (Figure 2b).Since the phenyl rings can fuse with either peri position on the terminal anthracene unit, the surface shows a mixture of C 2v and C 2h symmetric molecules representing the cis and trans configurations, respectively.The three other capped oligoanthenes (6a, 6c, and 6d) were prepared in a similar fashion.Figure 2c shows a topographic image of a sample containing 6a and 6c on Au(111), generated from a mixture of 1a and 1c in pyrene.Figure 2d shows bond-resolved STM (BRSTM) images of the two configurational isomers of 6d, corroborating the structure of the sexianthene molecular core terminated on either end by fluorenyl groups. 65,66The five-membered rings of the fluorenyl groups exhibit high brightness in the BRSTM image, consistent with the localization of off-zero modes at the ends of the GNRs.
Confirmation of the electron occupation of the off-zero modes was obtained by scanning tunneling spectroscopy (STS).The longest oligoanthene examined here, cis/trans-6d, provides a useful platform to gauge electron occupation since the hybridization between the end states is expected to be negligibly small. 56STS recorded on the ends of 6d reveals a narrow zero-bias peak, indicative of a Kondo resonance (Figure 2e).Here the independent magnetic moments of the end-state electrons are screened by itinerant electrons of the gold. 29The SOMOs associated with the end state can be imaged by spatially mapping the differential conductance at zero bias (Figure 2f).The observation of a Kondo resonance contrasts with STS of pristine 7-AGNR end states on Au(111) where the zero-modes are observed at positive bias and the Kondo peak is absent, consistent with these states being vacant due to p-doping from the Au(111) substrate. 50xperimental Length Dependence of the Ground State.Using five-membered rings to retain the electron occupation of 7-AGNR end states in oligoanthenes 6a−d on Au(111), we can study the intramolecular coupling between end states as a function of molecular length.This was Scheme 1. Synthesis of Oligoanthenes 6a−d accomplished by characterizing the four oligoanthenes 6a−d by BRSTM, STS, and differential conductance mapping.
Representative spectroscopic data for the trans isomers of 6a−c are summarized in Figure 3. BRSTM images (Figure 3a−  c) confirm the molecular structures of 6a−c including the fluorenyl end groups (Figure 3a inset).dI/dV point spectroscopy of 6a shows two distinct step-like spectral features located symmetrically around zero bias at V = ±120 mV (Figure 3d).dI/dV maps at these energies reveal strikingly different orbital patterns (Figure 3g).The cis isomer of 6a shows identical behavior (Figure S4).
Similar electronic behavior is also observed for 6b, albeit with a markedly reduced spectral gap of ΔE = 40 meV (Figure 3e).dI/dV maps acquired at the peak energies (Figure 3h) reveal a horizontal nodal plane for the higher energy state that is absent in the lower energy state (dashed boxes).Similarly to 6a, the cis isomer of 6b behaves identically to its trans counterpart, with resonant features at the same energies and with similar orbital patterns at these energies (Figure S4).
6c is different in that it has no spectral gap but rather exhibits a single peak centered at zero bias (Figure 3f), similarly to 6d.This implies that 6c exists in an open-shell ground state where single electrons occupy each of the two end states, and the moments of these electrons are individually Kondo-screened by itinerant electrons in the gold surface.The interaction strength between the electrons in the two SOMOs is thus small compared to the Kondo binding energy k B T K .A Frota fit to the zero-bias resonance is shown by the blue dashed line in Figure 3f, and a peak width of Γ F = 14 meV is obtained (corresponding to T K ≈ 400 K). 67The differential conductance map recorded at zero bias for trans-6c is shown in Figure 3i.In addition to a zero-bias peak, 6c also exhibits a positive ion resonance (PIR) at V = −550 mV (Figure S5a).Differential conductance maps acquired at this bias reveal an orbital pattern similar to that of maps recorded at zero-bias (Figure S5b), implying that the same SOMOs are probed both at V = 0 mV and at V = −550 mV.The presence of distinct tunneling pathways into the same SOMOs (i.e., the Kondo peak at zero bias and the PIR at V = −550 mV) corroborates the open-shell nature of 6c.Similar electronic behavior is observed in the cis isomer (Figure S4).
Theoretical Length Dependence of the Ground State.Our experiments imply that the longer oligoanthenes (6c and 6d) exhibit open-shell character with the spins on either end of the molecules individually Kondo-screened.This is reasonably intuitive, since the coupling between end states (characterized by the hybridization interaction parameter t) should decrease with increasing separation between them.Analogously, the aromatic stabilization gained by the increased number of Clar sextets in the open-shell or biradical resonance structure exceeds the energy required to break one π-bond and generate two radicals (Figure 4a−c). 32For the shorter oligoanthenes (6a and 6b), the situation is more complicated.The symmetric spectral features around zero bias and step-like nature of these features in 6a are suggestive of spin-flip excitations for two exchange-coupled spins from a singlet ground state to a triplet excited state, similarly to the previously studied Clar goblet system. 46However, the different wave function patterns observed at the edges of the pseudogap (Figure 3g,h) suggest the quite different scenario of tunneling into the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of a closed-shell configuration resulting from strong hybridization between the two end states.
71 This explains the experimentally obtained spectral line shape with symmetrically distributed features around zero bias.However, depending on the polarity of the tunneling bias, different hybridized combinations of end states�bonding and antibonding�can also be probed.This is because the GNR exhibits partial open-and closed-shell character, and as a result, tunneling electrons have both an elastic channel (involving the HOMO and LUMO) and an inelastic channel (involving the SOMOs) available.STM spectroscopic signatures thus naturally contain a combination of both features.72 The mixed open-shell/closed-shell character of this system can be modeled using the Hubbard dimer model (HDM), similar to the procedure of Ortiz et al. 61 where the results from ab initio density functional theory (DFT) calculations are used as input parameters.Our DFT calculations are at the singledeterminant level (as opposed to explicit multireference models such as configuration-interaction (CI) or complete active space (CAS) calculations 68 ), and so we separately simulated the closed-shell, singlet open-shell, and triplet openshell configurations of the oligoanthenes in vacuo.Figure 4a−c shows the calculated energy difference ΔE = E C − E S between the closed-shell ground state energy E C and the singlet openshell ground state energy E S for trans oligoanthenes, as well as the exchange coupling J (equal to the energy difference between the singlet and triplet (E T ) open-shell configuration energies; J = E T − E S ) and the Coulomb gap U (equal to the energy difference between the SOMOs and SUMOs in the singlet open-shell configuration).The calculated J values (Figure 4a−c) agree reasonably well with the energies of the spectral features observed for 6a and 6b (Figure 3d,e), suggesting that spin-flip excitations play a role in the spectroscopic features that we observe for these oligomers. We also alculated the HOMO−LUMO gaps from closed-shell calculations (Figure 4d−f, blue), enabling us to parametrize the hybridization interaction between end states as ΔE HL = E LUMO − E HOMO = 2t.
We used our DFT results as input for a HDM calculation where the parameters t and J allow calculation of the biradical index y (the procedure is described in Supplementary Discussion 3).In the two-site Hubbard model, the ground state of each oligoanthene is a weighted sum of open-shell singlet and closed-shell singlet, and the first excited state is a triplet.We thus conclude that the observed spectral features in STS indeed include singlet-to-triplet spin-flip excitations.The HDM calculation suggests that the oligoanthenes exhibit a smooth evolution to increased open-shell character as the length is increased.This overall physical picture suggests that dI/dV maps should include both a fraction of closed-shell wave function and a fraction of open-shell wave function as determined by the HDM y parameter.If we follow this protocol and use the y-values obtained from our HDM calculation (75% ≤ y ≤ 99% for structures 6a−c) then we obtain a poor fit to our experimental dI/dV maps because the y-values are too high (see Supplementary Figure S6).We do, however, obtain reasonable fits to the data for reduced y-values of 59%−97% for structures 6a−c, as shown in Figure 4g− i. 51,69,73 This suggests that neglect of the substrate in our calculations leads to an overestimation of the open-shell proportion of the low-lying states.Au(111), and their open-shell character increases in a smooth evolution as the length is increased.6a has the highest closed-shell character, with 6b being more open-shell and 6c,d having end states that are so weakly hybridized that they are individually Kondo-screened by electrons in the gold surface. 18This progression is characterized by a decrease in the exchange-coupling strength J between spins on opposite ends of the 7-AGNR: J = 120 meV for 6a, J = 20 meV for 6b, and J < k B T K for 6c and 6d.The overall trend, including spin-flip excitations, is captured by combining DFT calculations with the HDM, but the proportion of open-shell character appears to be overestimated.We assume that the omission of the metallic substrate in the DFT calculations causes inaccuracies in the singlet−triplet energies because of the absence of both charge screening and magnetic (i.e., Kondo) screening. 71Additionally, DFT may underestimate HOMO−LUMO gaps, and this may also impact the value of the hybridization parameter t and, by extension, the value of the biradical index y.These inaccuracies may explain the underestimation of the degree of open-shell character in the DFT-HDM model.

7-AGNR segments appear to exhibit partial closed-shell and partial open-shell character on
Although we are unable to mitigate the effects of substrateinduced screening, we successfully countered the unwanted effect of surface-induced charge transfer (which quenches magnetism).This was made possible by fusing five-membered rings to GNR zigzag ends, which has the benefit of inducing a downward shift in the end state energy due to the electronaccepting character of the cyclopentadienyl ring, thereby counteracting the p-doping effect of the gold surface.Tuning local mode energy offsets is thus a useful tool for quantum engineering of NGs.

METHODS/EXPERIMENTS
Synthetic Procedures.Unless otherwise stated, all manipulations of air-and/or moisture-sensitive compounds were carried out in ovendried glassware under an atmosphere of N 2 .All solvents and reagents were purchased from Alfa Aesar, Spectrum Chemicals, Acros Organics, TCI America, and Sigma-Aldrich and used as received unless otherwise noted.Organic solvents were dried by passing through a column of alumina and were degassed by vigorous bubbling of N 2 through the solvent for 20 min.Flash column chromatography was performed on SiliCycle silica gel (particle size 40−63 μm).Thinlayer chromatography was carried out using SiliCycle silica gel 60 Å F-254 precoated plates (0.25 mm thick) and visualized by UV absorption.All 1 H and 13 C NMR spectra were recorded on a Bruker AV-600 spectrometer and are referenced to residual solvent peaks (CDCl 3 , 1 H NMR = 7.26 ppm, 13 C NMR = 77.16ppm; CD 2 Cl 2 , 1 H NMR = 5.32 ppm, 13 C NMR = 53.84ppm).EI mass spectrometry was performed on an AutoSpec Premier (Waters) system in positive ionization mode.MALDI mass spectrometry was performed on a Voyager-DE PRO (Applied Biosystems Voyager System 6322) instrument in positive mode using a matrix of dithranol.10,10′-Dibromo-9,9′-bianthryl was synthesized following a reported procedure. 74reparation of MAD Transfer Samples.Samples of 1a−d were mixed with solid pyrene at T = 24 °C in a scintillation vial to make a 0.1 wt % mixture of sample in pyrene.The solid mixtures were placed into a preheated sand bath held at T = 200 °C until the pyrene completely melted (approximately 2 min).The melted mixtures were lightly swirled for 15 s in the sand bath to ensure homogeneous dispersion of the sample in the pyrene melt.The melted mixtures were immediately placed in an T = −78 °C acetone/dry ice bath to induce rapid crystallization.The solid was ground to a fine powder prior to deposition.
Sample Preparation.Clean Au(111) surfaces were prepared through iterative cycles of Ar + sputtering (p = 4 × 10 −6 Torr) and annealing (T = 400 °C).The fiberglass applicator of the MAD transfer setup was outgassed in high vacuum (p ≈ 5 × 10 −8 Torr) by resistive heating of a tungsten filament to approximately T = 500 °C for 20 min prior to use. 63After cooldown, the chamber was vented, and the applicator was removed and lightly pressed into the finely ground MAD transfer sample.The loaded fiberglass applicator was reintroduced to the chamber and pumped down to a high vacuum.After a high vacuum was reached, a cleaned Au(111) substrate was transferred into the chamber, and the fiberglass applicator was pressed against the Au(111) substrate to transfer the sample material.
STM Measurements.All STM experiments were performed using a commercial Createc LT-STM instrument operating at T = 4.5 K using chemically etched tungsten STM tips.dI/dV spectra were recorded using a lock-in amplifier with a modulation frequency of f = 533 Hz and a modulation amplitude of V ac = 2.0 mV.All STS experiments and differential conductance maps were acquired in constant height mode.Image processing of the STM scans was performed using WSxM software. 75Tip passivation with carbon monoxide or other surface absorbates was achieved using standard methods. 76alculations.First-principles calculations were performed at the density functional theory level as implemented in VASP. 77We adopted the hybrid HSE06 78 functional for both structure relaxations and accurate band gap evaluation.Electron−core interactions were described through the projector augmented wave (PAW) method. 79,80ohn−Sham wave functions were expanded in a plane wave basis set with a cutoff on kinetic energy of 400 eV.All structures were subject to periodic boundary conditions with a vacuum layer of 10 Å in all directions to prevent interaction between replica images.Atomic positions were optimized using the conjugate gradient method, where the total energy and atomic forces were minimized.The convergence criterion for energy was chosen to be 10 −6 eV, and the maximum force acting on each atom was less than 0.02 eV/Å.Open-shell configurations were obtained by setting appropriate initial magnetic moments and conducting spin-resolved calculations.
Additional DFT calculations involving semi-infinite leads as displayed in Supplementary Figure S1 were performed within the generalized gradient approximation to the exchange and correlation functional following Perdew, Burke, and Ernzerhof 81 as implemented in SIESTA. 82Core electrons were described by separable normconserving pseudopotentials, 83 whereas single-particle wave functions of valence electrons were expanded as linear combinations of atomic orbitals with double-ζ polarization quality.Real space integrations were performed with a 400 Ry mesh cutoff, and a k-point grid of 150 points in the semi-infinite directions was utilized.

* sı Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.3c06006.Discussion of the low-energy emergent physics in NGs, the molecular orbital perspective of off-zero modes and the Hubbard dimer model, synthetic procedures and schemes, 1 H and 13 C{ 1 H} NMR spectra, experimental results on the cis and trans isomers of oligoanthenes, experimental results on the identification of the PIR in 6c, and simulated dI/dV maps (PDF)

Figure 1 .
Figure 1.Off-zero modes.(a) Normal 7-AGNR zigzag end with a radical end state (left) and a fluorenyl-capped zigzag end (right) obtained by fusion of a pendant phenyl group (center).The fluorenyl moiety perturbs the state associated with the radical.(b) Result of a DFT calculation on a 7-AGNR with n = 7 repeating anthracene units that is capped with a fluorenyl on the right end only.The SOMOs and their respective energies are shown.(c) Frost circle for cyclopentadienyl.The frontier states lie below E = 0. (d) Chemical structure of precursors 1a−d.

Figure 2 .
Figure 2. Synthesis of fluorenyl-capped oligoanthenes.(a) STM topographic image (V = −1800 mV, I = 50 pA) of a sample of 1b on Au(111) after MAD transfer.The inset shows a single molecule of 1b.(b) STM topographic image (V = −300 mV, I = 50 pA) of a sample of 6b on Au(111) obtained after MAD transfer of 1b followed by heating to T = 300 °C for 20 min.(c) STM topographic image (V = −1600 mV, I = 50 pA) of a mixed sample of 6a and 6c on Au(111) obtained after MAD transfer of a mixture of 1a and 1c followed by heating to T = 300 °C for 20 min.(d) BRSTM images (V = −300 mV, V ac = 100 mV) of cis-6d and trans-6d obtained after MAD transfer of 1d followed by heating to T = 300 °C for 20 min.(e) dI/dV spectra (V ac = 2 mV) recorded at the end of trans-6d (black) and cis-6d (blue).(f) Differential conductance maps (V = 0, V ac = 10 mV, constant height) of the zero-bias resonance on trans-6d and cis-6d.All STM measurements were recorded at T = 4.5 K.

Figure 4 .
Figure 4. Theoretical analysis of oligoanthenes.(a−c) Kekuléstructures corresponding to closed-shell (left) and open-shell (right) configurations for (a) trans-6a, (b) trans-6b, and (c) trans-6c.Clar sextets are highlighted in red.Energy differences between the singlet and triplet open-shell configurations (J = E T − E S ) and between the closed-shell and singlet open-shell configurations (ΔE = E C − E S ) as obtained from DFT calculations.(d−f) DFT-calculated HOMO−LUMO gaps (ΔE HL = E L − E H ) for the closed-shell configurations of trans-6a−c and Coulomb gaps between SOMOs and SUMOs (U = E SUMO − E SOMO ) for the open-shell configurations of trans-6a−c indicated in blue and yellow, respectively.The energy levels are referenced to their midgap energy (set at E = 0).(g−i) Simulated dI/dV maps of the frontier states of (g) trans-6a, (h) trans-6b, and (i) trans-6c, using weighted superpositions of the HOMO and LUMO from the closed-shell configuration and SOMOs from the open-shell configuration using biradical indices y as indicated.