Bistability between π-diradical open-shell and closed-shell states in indeno[1,2-a]fluorene

Indenofluorenes are non-benzenoid conjugated hydrocarbons that have received great interest owing to their unusual electronic structure and potential applications in nonlinear optics and photovoltaics. Here we report the generation of unsubstituted indeno[1,2-a]fluorene on various surfaces by the cleavage of two C–H bonds in 7,12-dihydroindeno[1,2-a]fluorene through voltage pulses applied by the tip of a combined scanning tunnelling microscope and atomic force microscope. On bilayer NaCl on Au(111), indeno[1,2-a]fluorene is in the neutral charge state, but it exhibits charge bistability between neutral and anionic states on the lower-workfunction surfaces of bilayer NaCl on Ag(111) and Cu(111). In the neutral state, indeno[1,2-a]fluorene exhibits one of two ground states: an open-shell π-diradical state, predicted to be a triplet by density functional and multireference many-body perturbation theory calculations, or a closed-shell state with a para-quinodimethane moiety in the as-indacene core. We observe switching between open- and closed-shell states of a single molecule by changing its adsorption site on NaCl.

thermodynamically stabilized derivatives of s-indacene have been synthesized [10][11][12] . A feasible strategy to isolate congeners of otherwise unstable non-benzenoid non-alternant PCHs is through fusion of benzenoid rings at the ends of the π-system, that is, benzannelation. For example, while the parent pentalene is highly reactive, the benzannelated congener indeno [2,1-a]indene is stable under ambient conditions (Fig. 1b) 13 . However, the position of benzannelation is crucial for stability: although indeno[2,1-a]indene is stable, its isomer indeno[1,2-a]indene (Fig. 1b) oxidizes under ambient conditions 14 . Similarly, benzannelation of indacenes gives rise to the family of PCHs known as indenofluorenes (Fig. 1d), which constitute the topic of the present work. Depending on the benzannelation position and the indacene core, five isomers can be constructed, namely, indeno [2,1-b]fluorene (1)  Practical interest in indenofluorenes stems from their low frontier orbital gap and excellent electrochemical characteristics that render them as useful components in organic electronic devices 15 . The potential open-shell character of indenofluorenes has led to several theoretical studies on their use as non-linear optical materials 16,17 and as candidates for singlet fission in organic photovoltaics 18,19 . Recent theoretical work has also shown that indenofluorene-based ladder polymers may exhibit fractionalized excitations. 20 Fundamentally, indenofluorenes represent model systems to study the interplay between aromaticity and magnetism at the molecular scale 17 . Motivated by many of these prospects, the last decade has witnessed intensive synthetic efforts toward the realization of indenofluorenes. Derivatives of 1-4 have been realized in solution [21][22][23][24][25][26][27] , while 1-3 [28][29][30][31] have also been synthesized on surfaces and characterized using scanning tunneling microscopy (STM) and atomic force microscopy (AFM), which provide information on molecular orbital densities 32 , molecular structure 33,34 and oxidation state 35,36 . With regards to the open-shell character of indenofluorenes, 2-4 are theoretically and experimentally interpreted to be closed-shell, while calculations indicate that 1 and 5 should exhibit open-shell ground states 17,28,37 . Bulk characterization of mesitylsubstituted 1, including X-ray crystallography, temperature-dependent NMR, and electron spin resonance spectroscopy, provided indications of its open-shell ground state 21 . Electronic characterization of 1 on Au(111) surface using scanning tunneling spectroscopy (STS) revealed a low electronic gap of 0.4 eV (ref. 28 ). However, no experimental proof of an openshell ground state of 1 on Au(111), such as detection of orbital densities of singly occupied molecular orbitals (SOMOs) 38,39 , or spin excitations and correlations due to unpaired electrons 40,41 , was shown.
In this work, we report the generation and characterization of unsubstituted 5. Our research is motivated by theoretical calculations that indicate 5 to exhibit the largest diradical character among all indenofluorene isomers 37 . The same calculations also predict that 5 should possess a triplet ground state. Therefore, 5 would qualify as a Kekulé triplet, of which only a handful of examples exist 42-44 . However, definitive synthesis of 5 has never been reported so far. Previously, Dressler et al. reported transient isolation of mesityl-substituted 5, where it decomposed both in the solution and in solid state 37 , and only the structural proof of the corresponding dianion was obtained. On-surface generation of a derivative of 5, starting from truxene as a precursor, was recently reported 45,46 . STM data on this compound, containing the indeno[1,2-a]fluorene moiety as part of a larger PCH, was interpreted to indicate its open-shell ground state 46 . However, the results did not imply the ground state of unsubstituted 5. Here, we show that on insulating surfaces 5 can exhibit either of two ground states: an open-shell or a closed-shell. We infer the existence of these two ground states based on high-resolution AFM imaging with bond-order discrimination 34 and STM imaging of molecular orbital densities 32 . AFM imaging reveals molecules with two different geometries. Characteristic bond-order differences in the two geometries concur with the geometry of either an open-or a closed-shell state. Concurrently, STM images at ionic resonances show molecular orbital densities corresponding to SOMOs for the open-shell geometry, but orbital densities of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for the closed-shell geometry. Our experimental results are in good agreement with density functional theory (DFT) and multireference perturbation theory calculations. Finally, we observe switching between open-and closed-shell states of a single molecule by changing its adsorption site on the surface.

Results and discussion
Synthetic strategy toward indeno[1,2-a]fluorene. The generation of 5 relies on the solution-phase synthesis of the precursor 7,12-dihydroindeno[1,2-a]fluorene (6). Details on synthesis and characterization of 6 are reported in Supplementary Figs. 1-3. Single molecules of 6 are deposited on coinage metal (Au(111), Ag(111) and Cu(111)) or insulator surfaces. In our work, insulating surfaces correspond to two monolayer-thick (denoted as bilayer) NaCl on coinage metal surfaces. Voltage pulses ranging between 4-6 V are applied by the tip of a combined STM/AFM system, which result in cleavage of one C-H bond at each of the pentagonal apices of 6, thereby leading to the generation of 5 (Fig. 1e). In the main text, we focus on the generation and characterization of 5 on insulating surfaces. Generation and characterization of 5 on coinage metal surfaces is shown in Supplementary Fig. 4.  Supplementary Fig. 12. b, Corresponding DFT-calculated spin density of 5OS (isovalue: 0.01 e -Å -3 ). Blue and orange colors represent spin up and spin down densities, respectively. c, Mean-field Hubbard local density of states map of the superposition of the SOMOs of 5OS, calculated at a height of 7 Å above the molecular plane. d, DFT-calculated bond lengths of 5OS. e, Constant-height I(V) spectra acquired on a species of 5 assigned as 5OS, along with the corresponding dI/dV(V) spectra. Open feedback parameters: V = -2 V, I = 0.17 pA (negative bias side) and V = 2 V, I = 0.17 pA (positive bias side). Acquisition position of the spectra is shown in Supplementary Fig. 7. f, Scheme of many-body transitions associated to the measured ionic resonances of 5OS. Also shown are STM images of assigned 5OS at biases where the corresponding transitions become accessible. Scanning parameters: I = 0.3 pA (V = -1.2 V and -1.5 V) and 0.2 pA (V = 1.3 V and 1.6 V). g, Laplace-filtered AFM image of assigned 5OS. STM set point: V = 0.2 V, I = 0.5 pA on bilayer NaCl, Δz = -0.3 Å. The tip-height offset Δz for each panel is provided with respect to the STM setpoint, and positive (negative) values of Δz denote tip approach (retraction) from the STM setpoint. f and g show the same molecule at the same adsorption site, which is next to a third layer NaCl island. The bright and dark features in the third layer NaCl island in g correspond to Cland Na + ions, respectively. Scale bars: 5 Å (c,g) and 10 Å (f).

Generation and characterization of indeno[1,2-a]fluorene on insulating surfaces.
To experimentally explore the electronic structure of 5, we used bilayer NaCl films on coinage metal surfaces to electronically decouple the molecule from the metal surfaces. Before presenting the experimental findings, we summarize the results of our theoretical calculations performed on 5 in the neutral charge state (denoted as 5 0 ). We start by performing DFT calculations on 5 0 in the gas phase. Geometry optimization performed at the spin-unrestricted UB3LYP/6-31G level of theory leads to one local minimum, 5OS, the geometry of which corresponds to the open-shell resonance structure of 5 (Fig. 1d, Fig. 2d and Supplementary  Tables 1-7, the label OS denotes open-shell). The triplet electronic configuration of 5OS is the lowest-energy state, with the open-shell singlet configuration 90 meV higher in energy. Geometry optimization performed at the restricted closed-shell RB3LYP/6-31G level reveals two local minima, 5para and 5ortho, the geometries of which (Fig. 3b) exhibit bond length alternations in line with the presence of a para-or an ortho-QDM moiety, respectively, in the as-indacene core of the closed-shell resonance structures of 5 (Fig. 1d) 37 . Relative to 5OS in the triplet configuration, 5para and 5ortho are 0.40 and 0.43 eV higher in energy, respectively. Additional DFT results are shown in Supplementary Fig. 5. To gain more accurate insights into the theoretical electronic structure of 5, we performed multireference perturbation theory calculations ( Supplementary Fig. 6) based on quasi-degenerate second-order n-electron valence state perturbation theory (QD-NEVPT2). In so far as the order of the ground and excited states are concerned, the results of QD-NEVPT2 calculations qualitatively match with DFT calculations. For 5OS, the triplet configuration remains the lowest-energy state, with the open-shell singlet configuration 60 meV higher in energy. The energy differences between the open-and closed-shell states are substantially reduced in QD-NEVPT2 calculations, with 5para and 5ortho only 0.11 and 0.21 eV higher in energy, respectively, compared to 5OS in the triplet configuration. We also performed nucleus-independent chemical shift calculations to probe local aromaticity of 5 in the open-and closed-shell states. While 5OS in the triplet configuration exhibits local aromaticity at the terminal benzenoid rings, 5OS in the open-shell singlet configuration, 5para and 5ortho all display antiaromaticity ( Supplementary Fig. 6).
The choice of the insulating surface determines the charge state of 5: while 5 adopts neutral charge state on the high work function bilayer NaCl/Au(111) surface (irrespective of its openor closed-shell state, Supplementary Fig. 7), 5 exhibits charge bistability between 5 0 and the anionic state 5 -1 on the lower work function bilayer NaCl/Ag(111) and Cu(111) surfaces (Supplementary Figs. 8 and 9). In the main text, we focus on the characterization of 5 on bilayer NaCl/Au(111). Characterization of charge bistable 5 is reported in Supplementary Figs. 10 and 11. We first describe experiments on 5 on bilayer NaCl/Au(111), where 5 exhibits a geometry corresponding to the calculated 5OS geometry, and an open-shell electronic configuration. We compare the experimental data on this species to calculations on 5OS with a triplet configuration, as theory predicts a triplet ground state for 5OS. For 5OS, the calculated frontier orbitals correspond to the SOMOs ψ1 and ψ2 (Fig. 2a-c and Supplementary Fig. 12), whose spin up levels are occupied and the spin down levels are empty. Figure 2d shows the DFT-calculated bond lengths of 5OS, where the two salient features, namely, the small difference in the bond lengths within each ring and the notably longer bond lengths in the pentagonal rings, agree with the open-shell resonance structure of 5 (Fig. 1d). Figure 2g shows an AFM image of 5 adsorbed on bilayer NaCl/Au(111) that we assign as 5OS, where the bond-order differences qualitatively correspond to the calculated 5OS geometry (discussed and compared to the closed-shell state below). Differential conductance spectra (dI/dV(V), where I and V denote the tunneling current and bias voltage, respectively) acquired on assigned 5OS exhibit two peaks centered at -1.5 V and 1.6 V (Fig. 2e), which we assign to the positive and negative ion resonances (PIR and NIR), respectively. Figure 2f shows the corresponding STM images acquired at the onset (V = -1.2 V/1.3 V) and the peak (V = -1.5 V/1.6 V) of the ionic resonances. To draw a correspondence between the STM images and the molecular orbital densities, we consider tunneling events as many-body electronic transitions between different charge states of 5OS (Fig. 2f). Within this framework, the PIR corresponds to transitions between 5 0 and the cationic state 5 +1 . At the onset of the PIR at -1.2 V, an electron can only be detached from the SOMO ψ1 and the corresponding STM image at -1.2 V shows the orbital density of ψ1. Increasing the bias to the peak of the PIR at -1.5 V, it becomes possible to also empty the SOMO ψ2, such that the corresponding STM image shows the superposition of ψ1 and ψ2, that is, |ψ1| 2 + |ψ2| 2 (ref. 39 ). Similarly, the NIR corresponds to transitions between 5 0 and 5 -1 . At the NIR onset of 1.3 V, only electron attachment to ψ2 is energetically possible. At 1.6 V, electron attachment to ψ1 also becomes possible, and the corresponding STM image shows the superposition of ψ1 and ψ2. The observation of the orbital densities of SOMOs, and not the hybridized HOMO and LUMO, proves the open-shell ground state of assigned 5OS. Measurements of the monoradical species with a doublet ground state are shown in Supplementary Fig. 13. Here, the molecule is adsorbed on top of a defect on the surface. For an example of a 5para species adsorbed adjacent to a third layer NaCl island, see Supplementary Fig. 15. f, Selected bonds labeled for highlighting bond order differences between 5para and 5ortho. For the bond pairs a/b, c/d and e/f, the bonds labeled in bold exhibit a higher bond order than their neighboring labeled bonds in 5para. g, Laplace-filtered AFM images of 5 on bilayer NaCl/Cu(111) showing switching between 5OS and 5para as the molecule changes its adsorption position. Switching from 5para to 5OS was induced by scanning at 1.1 V, while switching from 5OS back to 5para took place by scanning at -2.2 V. The faint protrusion adjacent to 5 is a defect that stabilizes the adsorption of 5. STM set point: V = 0.2 V, I = 0.5 pA on bilayer NaCl, Δz = -0.3 Å. STM and STS data in c and d are acquired on the same species, while the AFM data in e is acquired on a different species. Scale bars: 10 Å (d) and 5 Å (e,g).
Unexpectedly, another species of 5 was also experimentally observed that exhibited a closedshell ground state. In contrast to 5OS, where the frontier orbitals correspond to the SOMOs ψ1 and ψ2, DFT calculations predict orbitals of different shapes and symmetries for 5para and 5ortho, denoted as A1 and A2 and shown in Fig. 3a and Supplementary Fig. 12. For 5ortho, A1 and A2 correspond to HOMO and LUMO, respectively. The orbitals are inverted in energy and occupation for 5para, where A2 is the HOMO and A1 is the LUMO. Figure 3e shows an AFM image of 5 that we assign as 5para. We experimentally infer its closed-shell state first by using qualitative bond order discrimination by AFM. In high-resolution AFM imaging, chemical bonds with higher bond order are imaged brighter (that is, with higher frequency shift Δf) due to stronger repulsive forces, and they appear shorter 34,47,48 . In Fig. 3f, we label seven bonds whose bond orders show significant qualitative differences in the calculated 5ortho, 5para (Fig. 3b) and 5OS (Fig. 2d) geometries. In 5para, the bonds b and d exhibit a higher bond order than a and c, respectively. This pattern is reversed for 5ortho, while the bond orders of the bonds ad are all similar and small for 5OS. Furthermore, in 5para bond f exhibits a higher bond order than e, while in 5ortho and 5OS bonds e and f exhibit similar bond order (because they belong to Clar sextets). Finally, the bond labeled g shows a higher bond order in 5para than in 5ortho and 5OS. The AFM image of assigned 5para shown in Fig. 3e indicates higher bond orders of the bonds b, d and f compared to a, c and e, respectively. In addition, the bond g appears almost point-like and with enhanced Δf contrast compared to its neighboring bonds, indicative of a high bond order (see Supplementary Fig. 14 for height-dependent measurements). These observations concur with the calculated 5para geometry (Fig. 3b). Importantly, all these distinguishing bond-order differences are distinctly different in the AFM image of 5OS shown in Fig. 2g, which is consistent with the calculated 5OS geometry (Fig. 2d). In the AFM images of 5OS ( Fig. 2g and Supplementary Fig. 10), the bonds a-d at the pentagon apices appear with similar contrast and apparent bond length. The bonds e and f at one of the terminal benzenoid rings also exhibit similar contrast and apparent bond length, while the central bond g appears longer compared to assigned 5para.
Further compelling evidence for the closed-shell state of assigned 5para is obtained by STM and STS. dI/dV(V) spectra acquired on an assigned 5para species exhibit two peaks centered at -1.4 V (PIR) and 1.6 V (NIR) (Fig. 3c). STM images acquired at these biases ( Fig. 3d) show the orbital densities of A2 (PIR) and A1 (NIR). First, the observation of A1 and A2 as the frontier orbitals of this species, and not the SOMOs, strongly indicates its closed-shell state. Second, consistent with AFM measurements that indicate good correspondence to the calculated 5para geometry, we observe A2 as the HOMO and A1 as the LUMO. For 5ortho, A1 should be observed as the HOMO and A2 as the LUMO. We did not observe molecules with the signatures of 5ortho in our experiments.
We observed molecules in open-(5OS, Fig. 2) and closed-shell (5para, Fig. 3) states in similar occurrence after their generation from 6 on the surface (out of 47 molecules, 23 and 24 molecules corresponded to 5OS and 5para, respectively). We could also switch individual molecules between open-and closed-shell states as shown in Fig. 3g and Supplementary Fig.  15. To this end, a change in the adsorption site of a molecule (whether 5OS or 5para) was induced by STM imaging at either of the ionic resonances, which often resulted in movement of the molecule. The example presented in Fig. 3g shows a molecule that was switched from 5para to 5OS and back to 5para. The switching is not directed, that is, we cannot choose which of the two species will be formed when changing the adsorption site. Out of 22 instances where the molecules moved, 14 resulted in switching between 5OS and 5para, while in 8 instances there was no switching of the ground state. Furthermore, we observed 5OS and 5para in equal yield upon changing the adsorption site. The molecule in Fig. 3e is adsorbed on top of a defect that stabilizes its adsorption geometry on bilayer NaCl. At defect-free adsorption sites on bilayer NaCl, that is, without a third layer NaCl island or atomic defects in the vicinity of the molecule, 5 could be stably imaged neither by AFM nor by STM at ionic resonances ( Supplementary Fig. 9). Without changing the adsorption site, the state of 5 (open-or closedshell) never changed, including the experiments on bilayer NaCl/Ag(111) and Cu(111), on which the charge state of 5 could be switched (Supplementary Figs. 8 and 9). Also on these lower work function surfaces, both open-and closed-shell species were observed for 5 0 and both showed charge bistability 36 between 5 0 (5OS or 5para) and 5 -1 (Supplementary Figs. 10 and 11). The geometrical structure of 5 -1 probed by AFM, and its electronic structure probed by STM imaging at the NIR (corresponding to transitions between 5 -1 and the dianionic state 5 -2 ), is identical within the measurement accuracy for the charged species of both 5OS and 5para. When cycling the charge state of 5 between 5 0 and 5 -1 several times, we always observed the same state (5OS or 5para) when returning to 5 0 , provided the molecule did not move during the charging/discharging process.

Conclusions
Based on our experimental observations we conclude that indeno[1,2-a]fluorene (5), the last unknown indenofluorene isomer, can be stabilized in and switched between an open-shell (5OS) and a closed-shell (5para) state on NaCl. For the former, both DFT and QD-NEVPT2 calculations predict a triplet electronic configuration. Therefore, 5 can be considered to exhibit the spin-crossover effect, involving magnetic switching between high-spin (5OS) and low-spin (5para) states, coupled with a reversible structural transformation. So far, the spin-crossover effect has mainly been observed in transition-metal-based coordination compounds with a near-octahedral geometry 49 , with relatively few examples of polycyclic conjugated hydrocarbons exhibiting the effect 50 . The observation that the switching between open-and closed-shell states is related to changes in the adsorption site but is not achieved by chargestate cycling alone, indicates that the NaCl surface and local defects facilitate different electronic configurations of 5 depending on the adsorption site. Gas-phase QD-NEVPT2 calculations predict that 5OS is the ground state, and the closed-shell 5para and 5ortho states are 0.11 and 0.21 eV higher in energy. The experiments, showing bidirectional switching between 5OS and 5para, indicate that a change in the adsorption site can induce sufficient change in the geometry of 5 (leading to a corresponding change in the ground state electronic configuration) and thus induce switching. Switching between open-and closed-shell states in 5 does not require the formation or dissociation of covalent bonds 51 , but a change of adsorption site on NaCl where the molecule is physisorbed.
Our results should have implications for single-molecule devices, capitalizing on the altered electronic and chemical properties of a system in π-diradical open-shell and closed-shell states such as frontier orbital and singlet-triplet gaps, and chemical reactivity. For possible future applications as a single-molecule switch, it might be possible to also switch between open-and closed-shell states by changing the local electric field, such as by using chargeable adsorbates 52 .

Methods
Scanning probe microscopy measurements and sample preparation. STM and AFM measurements were performed in a home-built system operating at base pressures below 1×10 -10 mbar and a base temperature of 5 K. Bias voltages are provided with respect to the sample. All STM, AFM and spectroscopy measurements were performed with carbon monoxide (CO) functionalized tips. AFM measurements were performed in non-contact mode with a qPlus sensor 53 . The sensor was operated in frequency modulation mode 54 with a constant oscillation amplitude of 0.5 Å. STM measurements were performed in constantcurrent mode, AFM measurements were performed in constant-height mode with V = 0 V, and I(V) and Δf(V) spectra were acquired in constant-height mode. Positive (negative) values of the tip-height offset Δz represent tip approach (retraction) from the STM setpoint. All dI/dV(V) spectra are obtained by numerical differentiation of the corresponding I(V) spectra. STM and AFM images, and spectroscopy curves, were post-processed using Gaussian low-pass filters.
Au(111), Ag(111) and Cu(111) surfaces were cleaned by iterative cycles of sputtering with Ne + ions and annealing up to 800 K. NaCl was thermally evaporated on Au(111), Ag(111) and Cu(111) surfaces held at 323 K, 303 K and 283 K, respectively. This protocol results in the growth of predominantly bilayer (100)-terminated islands, with a minority of third layer islands. Sub-monolayer coverage of 6 on the surfaces was obtained by flashing an oxidized silicon wafer containing the precursor molecules in front of the cold sample in the microscope. CO molecules for tip functionalization were dosed from the gas phase on the cold sample.

Mean-field Hubbard calculations.
Tight-binding/mean-field Hubbard calculations have been performed by numerically solving the mean-field Hubbard Hamiltonian with nearest-neighbor hopping Here, , † and , denote the spin selective ( ∈ {↑, ↓} with ̅ ∈ {↓, ↑}) creation and annihilation operator at neighboring sites and , = 2.7 eV is the nearest-neighbor hopping parameter, = 3.5 eV is the on-site Coulomb repulsion, , and 〈 , 〉 denote the number operator and mean occupation number at site , respectively. Orbital electron densities, , of the theigenstate with energy have been simulated from the corresponding state vector , , by where denotes the atomic site index, and 2 is the Slater 2pz orbital for carbon.
Density functional theory calculations. Gas-phase DFT was employed using the PSI4 program package 55 . All molecules with different charge (neutral and anionic) and electronic (open-and closed-shell) states were independently investigated. The B3LYP exchangecorrelation functional with 6-31G basis set was employed for structural relaxation and singlepoint energy calculations. The convergence criteria were set to 10 −4 eV Å −1 for the total forces and 10 −6 eV for the total energies.
For the on-surface DFT calculations shown in Supplementary Fig. 16, we employed the FHIaims 56 package. Molecules in the open-and closed-shell states were first independently investigated in the gas phase. The optimized molecular geometries were then optimized on a 9×9 bilayer NaCl slab in a cluster-type calculation. Molecular geometries in the gas phase were optimized with the really tight basis defaults. For the on-surface calculations we used light basis for NaCl atoms, and really tight basis defaults for atoms in the molecule. For structural relaxation, we employed the B3LYP exchange-correlation functional using the Vosko-Wilk-Nusair 57 local-density approximation, as implemented in the FHI-aims package.
In addition, we used the van der Waals scheme by Tkatchenko and Scheffler 58 . The convergence criteria for on-surface calculations were set to 10 -3 eV Å -1 for the total forces and 10 -2 eV for the total energies. For the NaCl slab, we constrained the atoms at the edges of the slab, while the atoms located in the top NaCl layer away from the edges were allowed to relax.
We also studied 5 in the gas phase and adsorbed on bilayer NaCl in a 5×5 surface cell using periodic, plane-wave DFT calculations with VASP 59,60 . We employed the optB86b version of the van der Waals density functional 61-64 , a plane-wave energy cutoff of 600 eV, and a 2×2 Monkhorst-Pack k-point mesh for the surface cell. The NaCl slab was constructed with a bulk lattice constant of 5.64 Å. Structural relaxations of molecule and top NaCl layer (with fixed bottom layer) were performed until residual forces were below 10 -2 eV Å -1 . The VASPcalculated adsorption sites and their qualitative differences in energy for the open-and closedshell states were found to be consistent with the other DFT calculations shown in the main text and the supplementary information.
Multireference calculations. Multireference calculations were performed on the DFToptimized geometries using the QD-NEVPT2 level of theory 65,66 , with three singlet roots and one triplet root included in the state-averaged calculation. A (10,10) active space (that is, 10 electrons in 10 orbitals) was used along with the def2-TZVP basis set 67 . Increasing either the active space size or expanding the basis set resulted in changes of about 50 meV for relative energies of the singlet and triplet states. These calculations were performed using the ORCA package 68 .

Nucleus-independent chemical shift (NICS) calculations.
Isotropic nucleus-independent chemical shift values were evaluated at the centre of each ring using the B3LYP exchangecorrelation functional with def2-TZVP basis set using the Gaussian 16 software package 69 .

Experimental details
Starting materials (reagent grade) were purchased from TCI and Sigma-Aldrich and used without further purification. Reactions were carried out in flame-dried glassware and under an inert atmosphere of purified Ar using Schlenk techniques. Thin-layer chromatography (TLC) was performed on Silica Gel 60 F-254 plates (Merck). Column chromatography was performed on silica gel (40-60 µm). Nuclear magnetic resonance (NMR) spectra were recorded on a Bruker Varian Mercury 300 or Bruker Varian Inova 500 spectrometers. Mass spectrometry (MS) data were recorded in a Bruker Micro-TOF spectrometer. The synthesis of compound 6 was developed following the two-step synthetic route shown in Supplementary Fig. 1, which is based on the preparation of methylene-bridge polyarenes by means of Pd-catalyzed activation of benzylic C-H bonds 1 .

Synthesis of 7,12-dihydroindeno[1,2-a]fluorene (6)
The complex Pd(OAc)2 (7 mg, 0.03 mmol) was added over a deoxygenated mixture of terphenyl 11 (90 mg, 0.27 mmol), K2CO3 (114 mg, 0.83 mmol) and ligand L (26 mg, 0.06 mmol) in NMP (2 mL). The resulting mixture was heated at 160 °C for 4 h. After cooling to room temperature, H2O (30 mL) was added, and the mixture was extracted with EtOAc (3x15 mL). The combined organic extracts were dried over anhydrous Na2SO4, filtered, and evaporated under reduced pressure. The reaction crude was purified by column chromatography (SiO2; hexane:CH2Cl2 9:1) affording compound 6 (8 mg, 11%) as a white solid.    14 . As shown in the table, for the entire Δz range, LCPD values above 5 for the state corresponding to V > 0.2 V (5 -1 ) are larger than for the state corresponding to V < -0.2 V (5 0 ). This indicates that the steps in the Δf(V) spectra correspond to charge state transitions. The identity of the states as 5 -1 and 5 0 is confirmed by the observation of the presence (5 -1 ) or absence (5 0 ) of NaCl/metal interface-state scattering by the respective species ( Supplementary  Fig. 9). LCPD values on bilayer NaCl are shown for reference. The hysteretic behavior of the charging (5 0 → 5 -1 )/discharging (5 -1 → 5 0 ) process relates to the reorganization energy 13 . Within the hysteresis loop, 5 is charge bistable and can be imaged both in its neutral and anionic states. Open feedback parameters: V = 1.1 V, I = 0.2 pA. Acquisition positions of the Δf(V) spectra on 5 and on bilayer NaCl (not shown here) are marked by filled circles in the in-gap STM image of 5 -1 (V = 0.2 V, I = 1 pA). Note that in its neutral state, this species corresponds to 5OS. Scale bar: 5 Å. On bilayer NaCl/Ag(111) and bilayer NaCl/Cu(111) (Supplementary Fig. 9), 5 exhibits charge bistability. This contrasts with 2, an isomer of 5, which was found to adopt a neutral charge state on bilayer NaCl/Cu(111) 3 . This difference results from the different frontier orbital gaps of 2 and 5, and the relative alignment of the frontier orbitals with respect to the Fermi level of the surface 15 . In the absence of any adjacent third layer NaCl island, adsorbates or defects on the surface, 5 moves under the influence of the tip during image acquisition 17 . This causes the apparent bisection of the leftmost ring in the AFM images of both 5 0 and 5 -1 . On the defect-free NaCl surface, 5 always showed this movement and in addition, exhibited mobility when increasing the bias voltage to obtain orbital density images. For these reasons, we could not characterize the electronic configuration of 5 on the defect-free NaCl surface. In general, 5 seems to be less stably adsorbed than its isomer 2 (ref. 3 ) on NaCl. This may be related to the lower symmetry of 5, and the symmetry and geometry of 5 not matching well with the NaCl surface 17 . It could also be related to the existence of different metastable adsorption sites and orientations of 5 on NaCl, possibly allowing smaller movement steps for translations and rotations. Scale bars: 20 Å (a-d) and 5 Å (e-h). Note that in f and g, the molecule had translated along the edge of the third layer NaCl island toward the bottom-left of the scan frame. Scale bars: 10 Å (e-j) and 5 Å (a,b). Gas-phase DFT calculations predict 7 to be roughly 50 meV lower in energy than 8. Among 17 monoradical species that were generated and analyzed on the metal and NaCl surfaces, eight corresponded to 7 and nine corresponded to 8, indicating that they are formed with roughly equal probabilities from voltage pulse-induced dehydrogenation of 6.  A and B). The relative energies of 5OS, 5para and 5ortho states in sites A and B are tabulated. The two adsorption sites on bilayer NaCl and the relative stability of the corresponding states in the table were also confirmed with planewave DFT using periodic boundary conditions with one molecule adsorbed on a 5×5 surface slab.

Supplementary
Supplementary Fig. 17 | Experimental adsorption site determination of 5 using AFM data. a-e, AFM images of five 5para species. f-j, AFM images of five 5OS species. The overlaid lattices (in green) visualize the NaCl lattice. Crossing points correspond to Na + (Cl -) sites of the second (third) NaCl layer. 5 is adsorbed on bilayer NaCl/Cu(111) in a-d, i and j, on bilayer NaCl/Au(111) in e and h, and on bilayer NaCl/Ag(111) in f and g. Apart from a, where 5 is adsorbed next to a defect on the NaCl surface, 5 is adsorbed next to a third layer NaCl island in all cases. Scale bars: 5 Å.
The important finding and observation of on-surface DFT calculations is that the energy differences between 5OS and 5para change substantially at different adsorption sites. Likely, these changes are even more pronounced for adsorption near third layer NaCl islands, adsorbates, or defects, compared to the defect-free NaCl surface.