pubs.acs.org/JACS Article Unveiling the Multiradical Character of the Biphenylene Network and Its Anisotropic Charge Transport Isaac Alcón,* Gaetano Calogero, Nick Papior, Aleandro Antidormi, Kenan Song, Aron W. Cummings, Mads Brandbyge, and Stephan Roche* Cite This: J. Am. Chem. Soc. 2022, 144, 8278−8285 Read Online ACCESS Metrics & More Article Recommendations * sı Supporting Information ABSTRACT: Recent progress in the on-surface synthesis and characterization of nanomaterials is facilitating the realization of new carbon allotropes, such as nanoporous graphenes, graphynes, and 2D π-conjugated polymers. One of the latest examples is the biphenylene network (BPN), which was recently fabricated on gold and characterized with atomic precision. This gapless 2D organic material presents uncommon metallic conduction, which could help develop innovative carbon-based electronics. Here, using first principles calculations and quantum transport simulations, we provide new insights into some fundamental properties of BPN, which are key for its further technological exploitation. We predict that BPN hosts an unprecedented spin-polarized multiradical ground state, which has important implications for the chemical reactivity of the 2D material under practical use conditions. The associated electronic band gap is highly sensitive to perturbations, as seen in finite temperature (300 K) molecular dynamics simulations, but the multiradical character remains stable. Furthermore, BPN is found to host in-plane anisotropic (spin-polarized) electrical transport, rooted in its intrinsic structural features, which suggests potential device functionality of interest for both nanoelectronics and spintronics. ■ INTRODUCTION 2 Graphene, the two-dimensional (2D) form of sp carbon, has 1 structure, essential for practical purposes, remain to be established. In this work, we explore such aspects by combining first catalyzed a pursuit for other 2D carbon allotropes, such as principles simulations with real-space quantum transport phagraphene,2,3 graphane,4 graphynes,5−7 graphdyines,8,9 calculations. First, using density functional theory (DFT) grazynes,10,11 and 2D π-conjugated polymers.12−16 Interest- simulations, the effect of finite temperature on BPN’s ingly, some of these materials have been experimentally electronic structure is analyzed. Importantly, the calculations synthesized, confirming, in particular cases, previously reveal the existence of a spin-polarized multiradical electronic predicted electronic features such as semiconductor behavior state stable to thermal fluctuations, which could have or antiferromagnetism.9,16−19 The biphenylene network important implications for the material chemical reactivity in (BPN) is the latest member of the 2D carbon allotrope family practical use conditions (e.g., in air). Interestingly, this to be experimentally reported.20 As depicted in Figure 1a, it is electronic solution leads to a band gap opening, though this made of a combination of 4-, 6-, and 8-membered rings. Using result strongly depends on the utilized DFT functional. scanning tunneling spectroscopy measurements,20 a closing of Second, by studying the injection of electronic currents in the band gap was found upon increasing the width of large-scale BPN samples, unidirectional charge transport biphenylene ribbons, hence constituting a truly metallic 2D conduction is observed, in striking contrast to other 2D organic material. On the theoretical side, while initial hexagonal carbon allotropes, such as graphene.27,28 Transport simulations predicted BPN to be a semiconductor with a simulations of the multiradical electronic solution of BPN band gap of ca. 2 eV,21 more recent theoretical studies show reveal a spin-filtering effect with potential for spin devices. BPN to be metallic,22,23 in line with experimental findings.20 More recently, other theoretical studies have scrutinized Received: February 25, 2022 additional properties of BPN, such as its hydrogenation24 and Published: April 27, 2022 lithiation capacity,25 or the anisotropic character of thermal transport within the 2D network.26 However, other funda- mental aspects, such as the electrical transport characteristics of BPN or the effect of finite temperature on its electronic © 2022 The Authors. Published by American Chemical Society https://doi.org/10.1021/jacs.2c02178 8278 J. Am. Chem. Soc. 2022, 144, 8278−8285 Journal of the American Chemical Society pubs.acs.org/JACS Article HSE0639,40 functional within the generalized gradient approx- imation (GGA). We note that other GGA functionals with a different degree of Hartree Fock exchange (HFE) have also been tested (see the Experimental Section). Figure 2a shows the optimized atomic structure of BPN, where the primitive unit cell is indicated with a square. The resulting band structure, as shown in Figure 2b, indicates a metallic nature of the 2D material, in line with prior theoretical results22,23,25 and experimental findings.20 As has been previously shown for semimetallic 2D π-conjugated poly- mers,12 to capture any low-lying multiradical states with periodic DFT calculations, it is necessary to choose an antiferromagnetic (AFM) initial guess.13,41 As shown in Figure 2c, upon doing so, we obtain a multiradical state with an AFM spin alignment. This multiradical character emerges from the square CBD-like units, in agreement with the radical nature of this organic compound35 and recent studies on 1D BP.38 We note that this electronic state cannot be hosted in the minimal cell (square, as shown in Figure 2a), so to obtain it, we utilized the 2 × 2 supercell, as shown in Figure 2a. More details about Figure 1. (a) BPN structure with an enlarged schematic view of its basic repeating unit. (b) Chemical structure of molecular BP, where the importance of the unit cell choice are provided in Figure S1 the square ring resembling CBD is highlighted in red. (c) Lewis and Table S1 of Supporting Information. resonance forms of CBD: the two energetically degenerate closed- The band structure of this multiradical state is shown in shell rectangular conformations are connected through an open-shell Figure 2d (a comparison with that of the non-spin-polarized (radical) transition-state with a square conformation. metallic state for the analogous supercell can be seen in Figure S2 of Supporting Information). Figure 2d suggests that the Overall, our study provides new insights into the electronic multiradical state is still metallic, which is in agreement with structure of BPN with implications for its future technological experimental findings reporting a vanishing band gap for exploitation. increasingly wider BP ribbons.20 However, the nature of this ■ RESULTS AND DISCUSSION On the Multiradical Character of BPN. The term multiradical electronic solution appears to strongly depend on the percentage of HFE, and other hybrid functionals with higher HFE, such as PBE0,42 yield a band gap opening and a biphenylene (BP) was first used for the molecular analogue semiconducting state (see Figure S3). As shown in Table 1, composed of two doubly connected phenyl rings,29,30 as this multiradical solution is the ground state of the system, represented in Figure 1b (molecular BP). This connection being −0.22 eV below the non-spin-polarized metallic solution. leads to a four-membered ring between the two phenyl rings, This value depends on the utilized DFT flavor, but both tested which resembles the cyclobutadiene structure (CBD in Figure functionals predict the multiradical configuration as the most 1b). CBD is a compound with two energetically degenerate stable electronic solution. On the other hand, the average of closed-shell rectangular conformations,31,32 as depicted in the absolute value of atomic spin populations, ⟨|μi|⟩, which can Figure 1c. It was shown, both via theoretical calculations33,34 be used as a measure of multiradical character,41 is very similar and more recently via electron paramagnetic resonance for both tested theoretical approaches (Table 1). In spite of the measurements,35 that the transition state between the two is significant energy difference with the metallic state, such of radical character (Figure 1c). This was demonstrated by the multiradical electronic solution has not been previously detection of spin-polarized triplet states populated at high predicted for BPN. As explained, this may be related to the temperatures,35 which is also in line with the high reactivity of inability of DFT to capture such a spin-polarized solution CBD and the need to utilize protecting groups to isolate and without a proper spin-polarized initial guess and the need to characterize it.36 use a supercell (e.g., 1 × 2, 2 × 2, or larger) hosting such AFM Therefore, the presence of “CBD-like” four-membered rings alignment of spins (see Figure S1). in BPN could indicate the existence of low-lying multiradical In order to study the effect of thermal fluctuations on the electronic solutions. Such states have not yet been reported for electronic configuration of BPN, we employ ab initio molecular the 2D material, but there is some indication of their existence dynamics simulations (AIMDS) at 300 K at the same level of in the analogous 0D and 1D systems. Specifically, the non- theory (see the methods section for details). In this case, an bonding character of four-membered rings in molecular BP initial spin guess of 0 is used, to avoid any bias of the system was demonstrated via molecular electrostatic potential top- toward the spin-polarized multiradical solution. As shown in ology calculations.37 Additionally, a recent study predicted the Figure 2e, we plot the time dependence of ⟨|μi|⟩ during the appearance of an antiferromagnetically aligned multiradical molecular dynamics simulation, which evidences the sponta- state in 1D BP, although this magnetic solution could not be neous appearance of a spin-polarized multiradical character detected in the on-surface synthesized material,38 potentially that remains stable throughout the entire simulation run and due to electron doping by the metallic surface. stays similar to the value of ⟨|μi|⟩ at 0 K (Table 1). A similar To evaluate the possible existence of such multiradical states situation is found when using the PBE0 functional (see Figure in BPN, we optimized the atomic and electronic structure of S4). However, in agreement with our results at 0 K (Table 1), the 2D material with DFT calculations. These calculations the electronic band gap varies with the DFT functional. The utilize periodic boundary conditions and the hybrid HSE06 functional predicts a minor gap opening below 0.1 eV 8279 https://doi.org/10.1021/jacs.2c02178 J. Am. Chem. Soc. 2022, 144, 8278−8285 Journal of the American Chemical Society pubs.acs.org/JACS Article Figure 2. (a) Optimized atomic structure of BPN using the HSE06 DFT functional. A 2 × 2 supercell is shown, with the primitive unit cell indicated with a black square. (b) Electronic band structure of the metallic state in BPN using the primitive unit cell. (c) Atomically resolved spin population map of the multiradical state in the 2 × 2 BPN supercell (spin-up: blue and spin-down: red). The size and color intensity are proportional to the spin population value. (d) Multiradical state band structure (spin-up: blue dashed line and spin-down: red dashed line). Note that spin-up/spin-down bands are perfectly superimposed. (e) Average of the absolute atomically partitioned spin population, ⟨|μi|⟩, during 4 ps of an ab initio molecular dynamics simulation at 300 K using the HSE06 functional and (f) associated electronic band gap. Table 1. Energy Difference between the Multiradical (Rad) multiradical state in BPN is stable at finite temperature, which and the Closed-Shell Metallic (Met) Electronic Solutions, is consistent with the 0 K results (Table 1) that show that this Average of the Absolute Value of Atomic Spin Populations is the ground state of the system, well below the non-spin- in the Multiradical State (⟨|μi|⟩) and Associated Electronic polarized solution. Radical or multiradical organic (carbon- Band gaps as Calculated with Either HSE06 or PBE0 DFT based) systems are known to be highly chemically reactive Functionals, Considering 2 × 2 Supercellsa species,43,44 thus requiring a particular chemical functionaliza- HSE06 PBE0 tion to protect the radical centers (e.g., via sterical ERad − EMet (meV) −223.8 −399.1 hindrance45). Since BPN is a planar material, our predictions ⟨|μi|⟩ 0.12 0.14 suggest that it might become a highly chemically reactive band gap (eV) 0.00 0.23 system under practical use conditions (e.g., at finite temper- a See the methods section for details. ature in air) and implies a potential need to encapsulate it (e.g., between inert hexagonal boron−nitride layers46) in order to stabilize it for use in solid-state electronic devices. Finally, such during the AIMDS (Figure 2f), whereas PBE0 leads to a steady multiradical nature should make BPN prone to charge-transfer band gap of ca. 0.45 eV (Figure S4). The increase in these effects when in contact with metallic substrates, such as values with respect to those at 0 K (Table 1) may originate recently demonstrated for fully planar organic radical from electronic localization caused by thermal vibrations. compounds deposited on Au or Ag.47 As it may be seen in These results suggest that the material’s band gap could significantly change with increasing temperature, potentially Figure S5 in Supporting Information, doping the material with leading to a metal → semiconductor transition. Further holes or electrons may lead to the full depletion of its spin- experimental characterization would be of high interest to polarized multiradical character (making it a closed shell), clarify this point, or whether BPN exhibits thermally activated which is in line with recent findings with 1D BP.38 This band gap fluctuations. highlights the need to transfer the 2D carbon material to In any case, in spite of the highlighted discrepancies between insulating surfaces, such as NaCl (regularly used for graphene the different tested functionals, one may conclude that the nanoribbons48,49), in order to detect the multiradical nature 8280 https://doi.org/10.1021/jacs.2c02178 J. Am. Chem. Soc. 2022, 144, 8278−8285 Journal of the American Chemical Society pubs.acs.org/JACS Article Figure 3. (a) Basic transport setup to calculate electronic transmission along the x-direction (left panel) and y-direction (right-panel) in BPN. Normalized transmission spectra (by channel width, in Å) along each direction for (b) metallic and (c) the multiradical electronic solution of BPN. We utilized 2 × 2 supercells for these calculations, as schematically shown in (a). Note that spin-up/spin-down transmission curves are perfectly superimposed for the multiradical case. Bond current maps of injected currents (E − EF = 0.5 eV) in large-scale devices made of BPN in (d) the metallic state and (e) the multiradical state. Areas with high current density are shown in bright yellow, and those with low or no current density are depicted in dark purple (see color bars). (f) Net spin polarization map of bond currents (spin-up: blue and spin-down: red) for the BPN device in the multiradical state and zoomed view around the injection site (in yellow). Small red dots at the bottom of each large-scale device indicates the point of injection (d,e,f). herein predicted, and to be able to measure its transport graphenes50−52 or in the so-called grazynes.10,11 A recent study properties (see below). of BPN has also predicted that phonons (i.e., thermal energy) On the Anisotropic Charge Transport of BPN. are transported differently along the two in-plane directions.26 Contrary to graphene and other hexagonal carbon allotropes, However, till date, the electronic transport characteristics of BPN has an atomic periodic structure, which is anisotropic in this novel 2D material remain to be investigated. the x−y plane. Specifically, the six-membered rings are To gain insights into this, we have carried out transport connected via single C−C bonds along the x-direction, calculations based on the Green’s function method (see the whereas they are connected via two C−C bonds along the y- Experimental Section for details) for each of the two possible direction (see Figure 2a) which form the CBD-like ring. It has electronic solutions of BPN; namely, the non-spin-polarized already been shown, via large-scale transport simulations, that state and the multiradical one. We note that an initial AFM structurally anisotropic carbon 2D materials lead to anisotropic spin guess had to be used in order to obtain the multiradical electronic transport, such as in the case of nanoporous state, as explained above. As schematically represented in 8281 https://doi.org/10.1021/jacs.2c02178 J. Am. Chem. Soc. 2022, 144, 8278−8285 Journal of the American Chemical Society pubs.acs.org/JACS Article Figure 3a, we first construct small devices that allow us to Despite the fact that our tested DFT functionals are able to compute the electronic transmission along each in-plane capture this multiradical state, they disagree about the direction. We normalize the transmission by the width of corresponding band gap, so that no conclusive semi- each channel, to ensure that the comparison is independent of conductor/metallic behavior can be associated to it. This our unit cell choice. As can be seen in Figure 3b,c, BPN may be indicative of an electronic structure (band gap) that is displays a preference for electron transport through the CBD- sensitive to and tunable by external means such as mechanical like unit (y-direction) rather than through the single C−C strain, doping, nonequilibrium currents, or chemical function- bonds connecting the hexagonal rings (x-direction), for both alization. Finally, quantum transport simulations demonstrate electronic solutions. This goes in line with prior theoretical the anisotropic character of electronic transport in BPN. The results showing the metallic character of hexagonal rings when spatial spreading of injected currents follows a Talbot connected via CBD-like square units37 and suggests that BPN interference pattern, which is a key feature of carbon 2D may behave as an array of weakly coupled 1D BP38 channels. materials behaving as arrays of weakly coupled 1D nano- To assess such a hypothesis, we simulate the spatial electronic channels.11,50 Additionally, this feature appears for distribution of injected currents in large-scale devices made both the non-spin-polarized metallic and multiradical states of of BPN, modeled with DFT-parametrized tight binding (TB) BPN, suggesting that transport anisotropy is intrinsically linked Hamiltonians, which capture the low-energy spectra of the to the structural in-plane anisotropy of the 2D material. Due to material (see the Experimental Section for details). Figure S6 the spin-polarized character of the multiradical configuration, shows the benchmark of such DFT-parametrized TB models we find a strong spin-filtering effect of injected currents, which separately for each electronic solution. As seen in Figure 3d,e, could potentially serve for spintronic applications.58 injected currents in BPN mainly propagate along the y- Overall, our study provides new insights into fundamental direction (i.e., through the BP 1D wires) for both the metallic characteristics of BPN which are key for its applicability in and multiradical electronic configurations. However, to a future technologies. The herein revealed multiradical nature of minor degree, they also spread along the x-direction, which BPN has important consequences regarding the chemical arises from the electronic coupling between the 1D channels. stability of this novel 2D organic material. This highlights the The resulting conic-shaped bond-current distribution is known need to seek for strategies to stabilize it upon integration in as the Talbot interference pattern; a key characteristic of solid-state devices via, for instance, encapsulation in van der optical waveguides,53,54 which has also been recently reported Waals heterostructures (e.g., between inert hBN layers46). On for electronically anisotropic carbon 2D materials that behave the other hand, knowledge about the transport properties of as 2D arrays of nanoelectronic 1D channels.50 Thus, the BPN is also essential for its applicability in carbon electronics, results, as shown in Figure 3, confirm that BPN belongs to this which is one of the main technological areas where this novel class of nanostructured carbon 2D materials. Finally, if material bears particular potential.20 ■ we look at the normalized difference of bond currents between the two spin channels for the multiradical solution (Figure 3f), EXPERIMENTAL SECTION we see that injected currents are strongly spin-polarized in this Periodic DFT calculations have been used to optimize both the state. This stems from the local spin polarization at the atomic and electronic structure of BPN. Different hybrid exchange particular injection site (see the atomic position in yellow in correlation functionals within the GGA59 that were tested include the zoomed view of Figure 3f), and so injecting at a different HSE0640 and PBE0.42 We note that hybrid functionals have been position changes the sign and degree of spin polarization (see shown to properly reproduce experimentally measured magnetic Figure S7). Experimentally, such a spintronic effect could be coupling coefficients for carbon-based multiradical oligomers,41,60 as realized by injecting currents with a magnetically polarized Fe- well as to capture low-lying multiradical states for 1D38 and 2D13 functionalized scanning tunneling microscopy tip.55 carbon nanomaterials (later on experimentally reported16), which are ■ missed when using pure GGA61 or LDA12 approaches. The non-spin- CONCLUSIONS polarized metallic solution was obtained via spin-restricted calcu- lations, whereas the multiradical solution is generated via spin- To conclude, our theoretical studies combining first principles unrestricted calculations and setting an antiparallel spin initial guess. DFT calculations with quantum transport simulations have Both the atomic coordinates and in-plane cell vectors are optimized revealed key electronic properties of the BPN. By establishing a separately for each electronic solution and DFT functional. We use a connection with molecular BP, and in particular with CBD, we tier-1 light numerical atom-centered orbital (NAO) basis set,62 as have demonstrated the emergence of the radical character in implemented in the Fritz Haber Institute ab initio molecular the square rings embedded in BPN. Our findings thus simulations package (FHI-AIMS).63,64 Optimizations for the primary unit cell (2 × 2 supercell) were carried out employing a 30-30-1 (15- demonstrate that BPN displays a spin-polarized multiradical 15-1) Γ-centered Monkhorst Pack (MP) k-grid, using convergence ground state, which was missed in prior studies on such 2D criteria set to 10−5 eV for the total energy and 10−2 eV/Å for the organic material.21−25 A similar situation was previously maximum force component per atom. Optimized cell vectors and reported for post-graphene organic Dirac materials (e.g., atomic coordinates for each electronic solution, using HSE06, are graphynes8) where low-lying multiradical states were also provided in the Supporting Information. Band structures and missed,13 which highlights the need to consider such type of atomically partitioned spin populations (using the Hirschfeld multiradical spin-polarized configurations when modeling method65) are generated in a following single-point calculation over carbon-based metallic (or semimetallic) 2D materials. As we the fully optimized structures, using a 100-100-1 (50-50-1) Γ- mentioned above, a proper spin-polarized initial guess is centered MP k-grid for the primary (2 × 2) unit cell. Other quantities such as total energies and electronic band gaps are extracted from necessary to capture such multiradical electronic solutions in these last single-point calculations. AIMDS are run in FHI-AIMS for DFT. By running AIMDS, we have found that the multiradical each tested DFT functional at 300 K for 4 ps, using the Bussi− character emerges spontaneously under thermal fluctuations Donadio−Parrinello thermostat,66 a 6-6-1 Γ-centered MP k-grid, and (i.e., it is thermodynamically stable), in agreement with other a Tier-1 light NAO basis set. These AIMDS are carried out in a spin- studied multiradical 1D56 and 2D organic polymers.41,57 unrestricted configuration, setting an initial spin guess of 0. 8282 https://doi.org/10.1021/jacs.2c02178 J. Am. Chem. Soc. 2022, 144, 8278−8285 Journal of the American Chemical Society pubs.acs.org/JACS Article In order to run the transport simulations, we obtained the Recerca i Estudis Avançats, Barcelona 08070, Spain; multiradical and metallic electronic solutions of BPN within the Siesta Email: stephan.roche@icn2.cat DFT package. Here, we utilized the PBE functional, a single-ζ basis set with 0.02 Ry energy shift, norm-conserving Troullier−Martins Authors pseudopotentials, and a real-space mesh cutoff of 400 Ry. The same Gaetano Calogero − CNR Institute for Microelectronics and convergence criteria and MP k-grids used in FHI-AIMS calculations were utilized to optimize both the atomic and electronic structure of Microsystems (CNR-IMM), Catania 95121, Italy; BPN within Siesta. Transport simulations were modeled by extracting orcid.org/0000-0003-3610-3231 the onsite and coupling elements of pz orbitals from the converged Nick Papior − Computing Center, Technical University of DFT Hamiltonians and overlap matrices, to parametrize efficient TB Denmark, Kongens Lyngby DK-2800, Denmark models (see DFT benchmark in Figure S6), which was carried out Aleandro Antidormi − Catalan Institute of Nanoscience and using the Python-based open-source SISL code.67 Transmission along Nanotechnology (ICN2), CSIC and BIST, Bellaterra, x (y) was obtained by repeating the BPN 2 × 2 supercell three times Barcelona 08193, Spain; orcid.org/0000-0002-5266- along each direction (see Figure 3a) using 350 (200) k-points along 8147 the transverse periodic direction. Large-scale BPN devices were built Kenan Song − Physical Science and Engineering Division, King by tiling the unit cell along both in-plane directions until obtaining a sample length of approximately 50 × 45 nm2, leading to devices Abdullah University of Science and Technology (KAUST), composed of more than 79,000 atoms. The TBtrans code,68 based on Thuwal 23955, Saudi Arabia the Green’s function formalism,69,70 was used to simulate quantum Aron W. Cummings − Catalan Institute of Nanoscience and transport on these large devices. 2D bond-current maps are used to Nanotechnology (ICN2), CSIC and BIST, Bellaterra, represent the spatial distribution of injected currents, utilizing a color Barcelona 08193, Spain; orcid.org/0000-0003-2307- map proportional to the current magnitude flowing from each atom 497X (i.e., high current: bright yellow and low to zero current: dark purple). Mads Brandbyge − Department of Physics, Technical More details on this type of device calculations can be found University of Denmark, Kongens Lyngby DK-2800, elsewhere.50,51,71 Denmark; Center for Nanostructured Graphene (CNG), The application of electrostatic gates was simulated via a fixed plane of charge parallel to the BPN layer and placed 3.5 Å below it, as Kongens Lyngby DK-2800, Denmark; orcid.org/0000- previously carried out in other studies.52,72 This was carried out with 0002-0126-9824 the PBE functional, as implemented in the Siesta code. These Complete contact information is available at: calculations were carried out using a 2 × 2 unit cell and applying https://pubs.acs.org/10.1021/jacs.2c02178 gates, ranging from +1 electron per cell (n-doping) to −1 electron per cell (p-doping), as shown in Figure S5 in Supporting Information. For each tested gate, the atomic structure and cell parameters of the Notes periodic network were fully optimized, thus also capturing the The authors declare no competing financial interest. ■ relaxation of the material due to the addition/subtraction of charge. ■ * ASSOCIATED CONTENT sı Supporting Information ACKNOWLEDGMENTS I.A. is grateful for a Juan de la Cierva postdoctoral grant (FJC2019-038971-I) from the Spanish Ministerio de Ciencia e The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.2c02178. Innovación. Financial support by Villum Fonden (00013340) is gratefully acknowledged. ICN2 is funded by the CERCA Unit cell choice for AFM alignment and 1 × 2 supercell Programme from Generalitat de Catalunya and is supported by results; band structure for the non-spin-polarized the Severo Ochoa program from Spanish MINECO (grant no. solution using HSE06; band structure for the spin- SEV-2017-0706). The Center for Nanostructured Graphene polarized multiradical solution using HSE06 and PBE0, (CNG) is sponsored by the Danish National Research respectively; values of spin population and band gap Foundation (DNRF103). S.R. acknowledges funding from during AIMDS using HSE06 and PBE0, respectively; the European Union Seventh Framework Programme under effect of electrostatic gates on BPN multiradical grant no. 881603 (Graphene Flagship). ■ character; benchmark of DFT-parametrized TB models; spin polarization bond current maps for large-scale BPN devices in the multiradical solution upon injecting at REFERENCES different atomic positions; and cell vectors and atomic (1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, coordinates for the optimized BPN structure in the non- Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric Field Effect spin-polarized and spin-polarized solutions, respectively, in Atomically Thin Carbon Films. 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