Augmented Magnetic Response and Spin-Transfer in Copper Corrole/Graphene Hybrids - A DFT Study

. The search for hybrid materials with outstanding electronic performance is highly demanding Since copper corroles have emerged as versatile building blocks providing outstanding electronic, and reactivity properties, a new series of non-covalent hybrid materials were computationally investigated based on pristine graphene and A3-type copper corrole complexes. The corrole complexes contain strong electron-withdrawing fluorinated substituents at the meso positions. Our results show that the non-innocent character of corrole moiety modulates the structural, electronic, and magnetic properties of the hybrid systems. The graphene-corrole hybrids display outstanding stability via the interplay of dispersion and electrostatic driving forces while graphene act as an electron reservoir for more conductive cases. Furthermore, the hybrid structures display an intriguing magneto-chemical performance since a detailed analysis of magnetic properties evidence how structural and electronic changes contribute to the amplification of the magnetic response also for ferromagnetic and antiferromagnetic cases. This amplification is accompanied by the spin transfer which characterized by a directional spin polarization from the corrole through the graphene surface. Main results suggest that graphene-corrole hybrids are excellent candidates for technologic applications due to the ferromagnetic tendency, the augmented magnetic response, the tunability due to substituents, and the potential conductive properties. Finally, a statistical analysis of magnetic properties suggests correlations between spin transfer, augmented magnetic response, and the geometrical distortion of the copper ligand field, offering exciting hints about how to modulate the magnetic response in the studied hybrid systems.


Abstract.
The search for hybrid materials with outstanding electronic performance is highly demanding Since copper corroles have emerged as versatile building blocks providing outstanding electronic, and reactivity properties, a new series of non-covalent hybrid materials were computationally investigated based on pristine graphene and A3-type copper corrole complexes. The corrole complexes contain strong electron-withdrawing fluorinated substituents at the meso positions. Our results show that the non-innocent character of corrole moiety modulates the structural, electronic, and magnetic properties of the hybrid systems.
The graphene-corrole hybrids display outstanding stability via the interplay of dispersion and electrostatic driving forces while graphene act as an electron reservoir for more conductive cases. Furthermore, the hybrid structures display an intriguing magneto-chemical performance since a detailed analysis of magnetic properties evidence how structural and electronic changes contribute to the amplification of the magnetic response also for ferromagnetic and antiferromagnetic cases. This amplification is accompanied by the spin transfer which characterized by a directional spin polarization from the corrole through the graphene surface. Main results suggest that graphene-corrole hybrids are excellent candidates for technologic applications due to the ferromagnetic tendency, the augmented magnetic response, the tunability due to substituents, and the potential conductive properties. Finally, a statistical analysis of magnetic properties suggests correlations between spin transfer, augmented magnetic response, and the geometrical distortion of the copper ligand field, offering exciting hints about how to modulate the magnetic response in the studied hybrid systems.

Introduction.
Hybrid materials have emerged as promising materials because of their unique and outstanding properties for several domains and applications, including catalysis [1], optical devices [2,3], environmental [4], medicine [5], energy storage [6], among others. Hybrid materials consist of at least two components of different nature to combine their unique physicochemical properties and bind through covalent or non-covalent interaction [7]. In this context, graphene (G), graphene oxide (GO), doped graphene (DG), and graphene quantum dots (GQDs) has been studied due to their attractive mechanical, electrical, and photophysical properties, which can be complemented in the preparation of graphene hybrid based materials (GBMs) [8][9][10]. Covalently linked GBMs have been extensively studied, highlighting the particular advantage of the graphene moiety on increased stabilities, charge/discharge kinetics, and capacities, and increased electron transfer processes towards nonlinear optical properties [11][12][13][14]. Among the wide variety of adsorbates, macrocyclic compounds such as porphyrins and phthalocyanines appear as attractive candidates to tune up the properties of hybrid materials. For instance, G surfaces coated with Co-porphyrins and Fe-phthalocyanines showed enhancement of electron transfer process, providing highly active materials for oxygen reduction reactions [15]. Besides, high stability and large electron-conductivity of GQDs/Zn-porphyrins hybrids are observed towards photocatalytic degradation of pollutants [16]. G coated by π−π stacking with a water-soluble phthalocyanine demonstrated large synergism as a photosensitizer suitable for photothermal and photodynamic therapies [17].
Similarly, porphyrin derivatives coated on GO surfaces have shown remarkable fluorescence quenching processes, indicating mostly a fastback electron transfer process on the studied hybrid, in conjunction with a computed interaction of about ~1.0 eV (22 kcal/mol) [18,19].
On the other hand, an increasing interest has been evidenced in the chemistry of corroles and their metallo-derivatives because of their unique photophysical and electrochemical properties [20][21][22]. Corroles are analogous to porphyrins but lacking the C20 meso-carbon atom at the core structure, and they have been proposed as suitable compounds in cancer therapy, sensing, organic electronics, and catalysis [23][24][25][26][27][28][29][30][31][32][33]. In this sense, new synthetic strategies for developing corrolic derivatives have been proposed, mainly substituted at the beta [23,34,35] and/or meso [23,35,36] positions of the corrolic core. Here, electron-withdrawing meso-substituents appear as an excellent strategy to increase the stability of the macrocycle, in combination with the modulation of the electron density on the core structure of the corresponding derivatives [37]. Alternatively, the binding of metal cations in the central cavity has also been explored; Fe(IV) and Cu(III) [38][39][40][41][42] corrole complexes have been recognized as exciting metallo-derivatives, where the corrolato moiety acts as a non-innocent ligand. In the particular case of Cu-corroles, this definition implies a rearrangement of the electronic structure of the π-extended macrocycle upon metalation.
Accordingly, a partial electron transfer between the metal cation and the corrolic structure occurs, stabilizing the formation of a magnetically coupled corrole 2−• /Cu(II) • radical pair instead of the formal expected Cu(III) cation [41,43,44]. Thus, quantum chemical calculations show that antiferromagnetic coupling between copper and corroles, which is predominant over the formal singlet closed-shell spin state, e.g., the Cu(III) case [41,45,46].
Despite this, few references involving corroles on non-covalent hybrid GBMs are reported.
Cobalt corroles supported on graphene-based surfaces have improved catalytic performances towards hydrogen evolution [47] and oxygen reduction reaction [33]. This behavior is explained according to the strong π- interactions in the obtained hybrids, high stability, and the fast electron transfer on the hybrid. Despite this evidence, a systematic study of the electronic and magnetic properties of copper corroles supported on graphene surfaces remains unexplored.
In this work, a series of A3-copper corroles bearing different fluoroalkyl, fluoroalkyl, and vinyl substituents at the meso positions are investigated as isolated complexes and their corresponding hybrid systems supported on a pristine graphene sheet (Fig. 1). The fluorinated substituents of the studied Cu corroles were selected since they promote the stability of the corrole structure and increase the formal high valent character of the metal center [33,37,47]. Furthermore, the nature of the substituents (noted R on Fig. 1) was selected to evaluate the effect of the aryl, alkyl, or vinyl skeleton, as well as the rigidity of the corresponding substituent on the stability of non-covalent interactions. Density functional theory (DFT) calculations were performed to gain insights into the main parameters controlling the occurrence of graphene-corrole hybrids
The stability of corrole-graphene hybrids (C-G) was characterized by the adsorption energies (Eads): Where EC, EG, and EC−G are the energy of the corrole, graphene, and corrole-graphene complexes, respectively, the higher values of Eads stand for the more stable systems. Basis set superposition error (BSSE) were corrected using the counterpoise method [56].
The nature of the intermolecular interactions was explored using the Atoms in Molecules (AIM) analysis, which allows classifying the interaction by the electron density at 38 the bond critical-point (ρBCP) of the intermolecular interactions. Under this scope, covalent bonds, coordinate covalent bond/highly polarized interactions, and weak electrostatic interactions are commonly characterized by ρBCP in the range of ~0.50 -0.10, 0.10 -0.04, and ≤ 0.01 e/Bohr 3 , respectively. Besides, the reduced gradient method was employed based on the Independent Gradient Model (IGM), which allows differentiation of the intermolecular and intramolecular interactions [57]. The AIM and IGM analyses were carried out using the wavefunction analyzer Multiwfn3.7 program [58].
Magneto-chemical properties were evaluated from broken symmetry solutions for antiferromagnetic (AFM) and ferromagnetic (FM) magnetic states [59]. The electronic structure of the magnetic systems was characterized by the unrestricted corresponding orbitals [60,61], which described the magnetic exchange pathways and the overlap of the corresponding magnetic orbitals. The Heisenberg -Dirac-Van Vleck spin Hamiltonian [62] that described the exchange coupling of C and C-G systems follows: Where H, J12, Ŝ1, and Ŝ2 are the spin Hamiltonian, the magnetic coupling constant between fragment 1 and 2, the spin operators for fragment 1, and the spin operator for fragment 2, respectively. The broken-symmetry approach with non-projected spin employed has been extensively used for transition metal complexes [63][64][65][66][67]. The J values were calculated as follows [68,69] Where EHS and EBS, are the electronic energy of the high spin, broken-symmetry states relative to FM and AFM states, respectively. While 〈S 2 〉HS, and 〈S 2 〉BS are the total spin for high-spin and broken symmetry states, respectively.
Finally, the geometrical distortion (gd) due to ligand field effects (concerning ideal solids) was characterized using the Shape 2.1 program [70], where the gd function is obtained as (Eq. 4): Thus, the terms gd can be compared with the ideal polyhedron composed of N vertexes.
Q0, Qk, and Pk are the mass center, distorted, and perfect vector coordinates, respectively.
The boundary conditions are between 100 ≥ gd ≥ 0, where lower limits stand for structures that match the target symmetry, and higher values stand for distorted structures [71].

Results and Discussion
The stability of copper corroles/graphene hybrids was examined considering the adsorption energy and the characterization of their intermolecular interaction. Besides, structural properties, reactivity indexes, and frontier molecular orbitals were discussed.
Finally, the magneto-chemical characterization based on the broken-symmetry approach described the enhanced magnetic response and the spin transfer.

Stability and structural properties of isolated systems
Firstly, we described the stability of graphene nanosheet and the copper corrole    On the other side, considering the non-innocent character of the corrole ligand in this type of complexes, the structure of the corrole core was analyzed based on the torsion angles (α, β, γ, δ, and ψ) to describe the planarity of the corrole macrocycle [25,45,78], which is summarized in Table 1 and depicted in were observed for KAGGIJ and RINCAS crystal structures (CSD codes) in agreement with C5 and C7, respectively, demonstrating the validity of the obtained structures. Thus, C3 and C5 are representative cases, where planarity distortion depends on the chemical and electronic effect of the meso substituents, especially for π-conjugated or aryl groups substituents (Fig. 2c). Analogous results were obtained for substituted metallo-corroles described in the literature where the values vary because of steric repulsion of substituents and the metal incorporated in the structure [25,[78][79][80]. For instance, it was shown that the planarity of Au corrole suffered significant changes after iodination; nevertheless, more substantial changes were observed after replacing gold with silver or copper [80]. According to structural searches, meso substituents are aryl groups; and only a reduced number of reported copper corroles display non-aromatic groups in these positions according to CSD search. This suggest that the hight factibility of synthesize corroles with different aromatic meso substituents can be combined with the choice of metal complexed to tune electronic and structural properties in corroles rational design.  [31]. The same tendency of ΔHL has been observed in other DFT calculations of copper corroles substituted in meso-positions [45,76].

Electronic structure and reactivity
Toward a deep understanding of the electronic properties of the studied compounds, global reactivity indexes were also analyzed. Table 2 also depicts the global indexes considering the chemical potential (μ), molecular hardness (η), and electrophilicity (ω). The maximum hardness principle states that stable systems show resistance to modification on the electron density distribution; ergo, higher molecular hardness is expected. Thus, the studied copper corroles display η values of 0.9 -1.1 eV, suggesting a similar behavior within the studied CuC series. The harder system is the fluorinated case (C1) due to the direct effect of fluorine atoms (as the harder element) over the CuC electron structure. At the same time, the lower η value is found for the alkenyl meso substituents (C7) attributable to the πconjugation of R groups with the CuC core, in agreement with the observed FMOs for this compound (Fig. S1). As observed in the last row of Table 2, the graphene nanosheet presents a considerably lower η value of 0.4 eV, which agrees with the most prominent conjugation on the whole surface, thus, providing a planar structure with enhanced electronic polarization. Additionally, μ is related to the electronegativity χ through μ = −χ; while ω represent the stabilization when the molecular system gains electrons. Hence, μ and ω are related to the relative electrophilic character [55]. With this in mind, the fluorinated alkyl chains in meso positions (C2-C4) display the more prominent electrophilic character due to the electron-withdrawing effect of these substituents. The electrophilic character is also achieved through π-conjugation in C7 due to π-conjugation of the trifluoromethylphenyl substituents, which promote the delocalization of electron density through the whole CuC core.

Spin density and magnetic properties
Regarding the spin density distribution, the Cu center displays values of 0.6 a.u. in agreement with other works related to the magnetic properties of Cu(II) complexes (showing one unpaired electron) [67,81]. Besides, the spin density surface (Fig. S1) is located mainly on the CuC core, and the surface shape resembles the 3dx2-y2 orbitals as is proper of Cu(II) center in a square-planar ligand field [41,76]. In this sense, part of spin density is localized onto Cu(II). In contrast, the resting spin density is delocalized along with the corrole core showing a non-innocent and magnetic character.
Because of the non-innocent character of the corrole ligand, multiplicity studies were performed to evaluate the spin state of the minimum energy structures showing different values in each case ( Table 2). The spin density surfaces are plotted in Fig. S1 according to minimum energy spin states. A ferromagnetic nature is found in compounds C1, C2, C3, C6, and C7, which display triplet spin-state (2S+1=3) and positive values of the magnetic exchange constant (J), oscillating between 3 to 82 cm -1 . Conversely, an antiferromagnetic ground state is found for compounds C4 and C5. Noteworthy is the antiferromagnetic behavior of C5 since it displays the stronger coupling of -1168 cm -1 that agrees with the high overlap between α and β unrestricted corresponding orbitals (UCOs), reaching 25 % on the whole molecule (Fig. 3a). This overlap is allocated on the Cu center, in contrast to the strong ferromagnetic case (C7), showing no overlap on the metal center and reaching only 1.25 % of overlapping on the whole molecule (Fig. 3b). It is necessary to note that the relationship between overlapping magnetic orbitals and the antiferromagnetic nature of the coupling is revisited in Goodenough-Kanamori's model to understand the magnetic behavior of complexes in solid-state [82,83]. Thus, the orthogonality and overlapping between magnetic orbitals are essential descriptors for exploring magnetic properties from a chemical point of view. Nonetheless, other structural parameters also act onto the orbital orthogonality and overlapping, such as planarity of the ring, which can affect the magnetic exchange between corroles, as found in the literature for bis-copper corroles [84]. For this reason, the geometrical distortion (gd,  (Fig. S2). Lastly, we highlighted that even the non-innocent character of corroles is strongly dependent on the planarity of corrole, substituent steric effects, and the metal center [85], corroborating the significant influence of structural and chemical modification on the electronic properties of corroles.
Additionally, the stacked conformation has been corroborated for the corrole adsorption onto metallic surfaces such as Au (111), Ag (111), and Pt(111) [76,[87][88][89][90]. Remarkably, the noncovalent adsorption of corroles and corrolato onto Ag(111) displayed adsorption energies in the range of 2.8 -4.7 eV [88]. Furthermore, the π-electron conjugation between radical corroles and the surface increases the stabilization due to aromatic effects [88]. Significant correlations were found between Eads, |ΔEINT|, and the number of carbon atoms in each copper corrole (Fig. S3). The adsorption energy per carbon atom (Eads/C) displayed an average value of ~90 meV/atom, indicating that more substantial stabilization will be achieved for larger R substituents. For instance, the lower stabilization is obtained for the C1-G hybrid, while the more considerable stabilization for the C7-G hybrid. Moreover, ΔEPREP represents the energy penalty due to the deformation of graphene and copper corroles during the adsorption process. Thus, higher deformation is observed in the hybrids with aromatic substituents. This observation can be related to the steric effects in the aromatic R substituents, compared to the non-aromatic fluoroalkyl substituents, where the latter present a lower rotational barrier (similar to alkyl groups) than π-conjugated groups. For instance, the vinyl group rotation in C7-G suffers steric impediment between phenyl hydrogen atoms and corrole outer hydrogen atoms, while the C=C double bond cannot rotate freely. Thus, the preparation energy involved in the deformation increases for the aromatic substituents during the stacking process. As an illustration of the structural changes, the torsion angles reflect the increase of planarity of the corrole cores, which can be observed by the decrease of α, β, γ, δ, and ψ angles ( Table 3). Thus, the increase of planarity is due to electronic interactions with the graphene surface, similarly to the study of copper corroles adsorbed onto Au(111) surface [76] and for non-metallated corroles adsorbed onto Ag(111) surface [88].   Table 3).
In this regard, we have explored the nature of chemical bonds using the AIM method to detect specific interactions between both components. However, the extended number of intermolecular interactions present values of ρBCP in the range of 0.001 − 0.013 |e/Bohr 3 |, indicating that the very weak electrostatic interactions that contribute to the stabilization.
Nonetheless, the interaction mechanism in C-G hybrids should be driven by Van der Waals forces derived from π-conjugation of corroles interacting with graphene in a parallel displaced πstacking. With this in mind, the non-covalent interactions were explored using the independent gradient model to characterize the dispersive driving force pictorially ( Fig.   S4 and Fig. 5). The regions of strong stabilization [red colored for sign(λ2)ρ negative values] are mainly located below fluorine, and H-π interactions form stabilizing interactions, while subtle stabilizing regions are located below copper and nitrogen atoms that belong to CuN4 core (Fig. 5).

Conversely, repulsive interactions [blue colored for sign(λ2)ρ positive values]
between Cu−N bonds and graphene are observed, and especially the most intense steric repulsion is observed between twisted phenyl group and graphene nanosheet in C5-G hybrid.
Considering IGM surfaces size, there is some correspondence with the Eads tendency since C5-G, C6-G, and C7-G hybrids are the more stable systems. The latter can be explained considering that the sum of an extended number of low stabilizing interactions achieves a valuable contribution to the whole stabilization. This point suggests that the dispersion forces are presumably the driving forces for the interaction of C-G hybrids, considering the πstacking prevalence in all the current studied hybrids.

Electronic structure and reactivity of C-G hybrids
The electronic structure of C-G hybrids is revised regarding the FMOs surfaces for α,β-frontier molecular spin-orbitals, and the global reactivity descriptors (Fig. S5 and Table   4). In the C-G hybrids, the copper corroles participate more actively for the α,β frontier molecular spin-orbitals, in contrast with the isolated copper corroles. This kind of distribution has been reported previously for the adsorption studies of 2D nanomaterial [91]. Indeed, four different cases are observed for the α,β-ΔHL depending on the corroles participation: reaching up to 0.9 eV, close to the isolated graphene nanosheet (ΔHL=0.8 eV, Table 2) in correspondence with a significant contribution to the α and β spin-orbitals. Table 4. Electronic properties of C-G hybrids. ΔHL, μ, η, and ω are expressed in eV. Besides, the increase of planarity supports the π−π stacking with graphene-based surfaces [92]. The frontier molecular spin-orbitals are affected in similar corroles adsorbed onto

Magneto-chemical properties
Regarding the magnetic properties of the C-G hybrids, the unpaired electrons can be distributed within the whole system, including the graphene platform. Indeed, the spin density surface of C-G hybrids is mainly allocated on both copper corroles and the edge of the graphene nanosheet (Fig. S5). Indeed, spin density delocalization/polarization mechanism is present in all the cases that agree with other studies, especially for graphene nanoribbons indicating that electronic structure is in line with experimental evidence [94,95].
On the other side, it is essential to differentiate the charge transfer (QCT) vs. spin-transfer phenomena since the spin density (ρS) is the difference between α and β spin density: ρS=ρα−ρβ. In this sense, the QCT parameter does not differ between α and β electrons, but spin density transfer can occur with QCT = 0 if the spin density location is balanced [76,96]. In the cases of C2-G, C3-G, and C4-G hybrids, charge transfer/spin density delocalization coincides, analogous to forming a transient corrole radical due to an electron transfer [88].
Ag (111) surface transfers electron and spin density to corrole due to dispersion and aromatic driving forces. In this sense, the aromatic character of the fragment of the C-G hybrid arises as other stimuli to reach higher magnetic coupling.
Since the spin density is allocated on graphene, this effect modified the magnetic behavior substantially. The spin-transfer occurs on graphene by the interaction with corroles.
By analogy with QCT, the spin-transfer (ρST) can be quantified summing the atomic spin density of each atom that compose a fragment. In this sense, the ρST of the graphene fragment will reveal how corroles can generate a magnetic response over the platform. The ρST values suggest that an integer spin is transferred to graphene (Fig. 6a). For instance, no spin-density is transferred for C1-G, and C6-G hybrids; close to one spin was transferred for C2-G, C3-G, C4-G, and C5-G hybrids, while two spins were transferred to C7-G hybrid. Because of the π-conjugated character of graphene, the spin density is delocalized along the nanosheet, but a directional spin polarization is observed, especially for the ferromagnetic hybrids ( Fig.   6b and Fig. S5). Interestingly, correlations were observed when comparing the geometrical distortion of CuN4 core (gd) with spin transfer (Fig. S6). Besides, the stability descriptors are also related to spin-transfer since electronic hardness (kinetic stability), and adsorption energy (thermodynamic stability) show significant correlation parameters (Fig. S6). These results suggest that the spin transfer process is associated with the structural and electronic properties of the copper corroles, indicating that spin transfer to graphene is a complex process that involves several variables. On the other hand, the magnetic response of most systems increases in terms of the absolute value, being the ferromagnetic nature more strongly favored. The C5-G hybrid shows the stronger ferromagnetic coupling of +3316 cm -1 with no overlap between corresponding magnetic orbitals ( Table 5). The strong ferromagnetism agrees with the low overlap between magnetic orbitals and the increase of planarity for copper corroles since the planarity of the corrole ligand supports the π-conjugation where the orbitals are orthogonal to the 3dx2-y2 proper of Cu(II) centers stabilizing the ferromagnetic states. Conversely, the C3-G hybrid displays a more robust antiferromagnetic behavior with −1869 cm -1 and a high % S 2 of magnetic orbitals reaching up to 63 %. Comparatively, a set of copper corroles adsorbed on Au (111) reported magnetic couplings between −909 to +1784 cm -1 , suggesting that the magnetic properties of copper corroles are highly modulable by the incorporation of new substituents [76]. These magnetic behaviors were reported for silver corroles where πconjugation also interacts with the 4dx2-y2 orbital of Ag(II), but the higher torsional angles in the distorted structure obstruct the ferromagnetic coupling. Consistently, a previous study reports the strong antiferromagnetic coupling of non-metalated corroles adsorbed onto Ag (111), reaching up to −2371 cm -1 [89]. Table 5. Magnetic properties of C-G hybrids and copper corroles employing the hybrid geometry (C*). Multiplicity (2S+1), exchange coupling constant (J), and the overlap (S 2 ) between corresponding magnetic orbitals. J is expressed in cm -1 . The characterization of corresponding magnetic orbitals evidences the exchange pathway between the magnetic centers. In fact, the C5-G hybrid outstands by the substantial magnetic response due to the high stabilization of the high-spin state (triplet state) and its consequent null overlap between α,β-UCOs. Indeed, the surface of α-UCO is allocated onto corroles while β-UCO is distributed on graphene lacking contact between both magnetic orbitals (Fig. 7a), and the unpaired electrons cannot interact by a direct magnetic pathway.
Indeed, the unpaired electrons can interact antiferromagnetically through the exchange pathway with no resistance. Considering the current evidence, the graphene nanosheet is presented as a platform able to act as an amplifier of the magnetic response that directs/conducts the spin transfer through its structure. The magnetic properties were compared with structural and electronic properties to get a deeper insight into C-G hybrids. Hence, the statistical analysis of these properties allows us to determine the most important variables through correlation analysis. For instance, a strong correlation between the electrophilicity and the overlap of corresponding magnetic orbitals (S vs. ω plot in Fig. S7) suggests that a more considerable overlap supports the stabilization of additional electron density. Even more, following this line of analysis, the correlation between ΔJ and ω demonstrate that high electrophilic C-G hybrids support the augmented antiferromagnetic response (ω vs. ΔJ plot in Fig. S7). That is why the C3-G hybrid presents the augmented antiferromagnetic response after adsorption. Furthermore, similar analysis indicates that the geometrical distortion of the CuN4 (in isolated copper corroles) and its variation concerning C-G hybrids (gd and ∆gd, respectively) is involved in the augmented magnetic response due to graphene interaction (plots relative to ΔJ in Fig.   S7). In consequence, the explanation of the augmented magnetic response of C-G hybrids is consistent with the magneto-chemistry either by analyzing the chemical structure, the electronic properties, the corresponding magnetic orbitals, and the respective hybrid stabilization during the adsorption process.

Outlook for technological applications
This work provides a conceptual perspective for exploring the stability, electronic properties, and magnetic response of copper corroles deposited onto a graphene surface.
Moreover, the discussed results provide a consistent basis for future theoretical/experimental studies on corrole/graphene hybrids. Regarding the applicability of metallo-corroles in catalysis, molecular electronics, sensing, optics, and spintronics, the understanding of their properties is a prominent challenge that should support the rational design of the material.
Besides, experimental studies have supported the use of graphene for spintronics due to attractive advantages in spin transport measurements compared to metals and semiconductors. For instance, graphene presents favorable physical characteristics at room temperature [97][98][99], such as longer spin lifetimes, larger spin signal, and longer spin diffusion lengths than copper, aluminum, silver, and highly doped silicon [100][101][102][103][104][105]. On the other side, spin-injection and spin-transport in graphene are crucial for designing new magnetic devices, especially if it is considered the strongly diamagnetic behavior as pristine nanosheets. However, cooperative magnetic ordering can be introduced to graphene as a result of vacancy defects, incorporation of light adatoms (hydrogen and fluoride), incorporation of heavy adatoms, substitutional doping using light or heavy atoms, molecular doping, and coupling to a ferromagnetic substrate. Thus, the induction of magnetic moment in graphene is a prominent goal toward developing spin logic devices [106][107][108][109].
Eventually, graphene would substitute the conventional ferromagnetic thin films since single-atomic permanent ferromagnets are more scalable than thin films with thicknesses of less than 200 nm, which present the desired changes in magnetic properties such as more significant magnetic anisotropy and dynamic magnetic response a. In addition, experimental evidence demonstrates graphene as a versatile platform for spintronic application due to the ability to turn on/off the Kondo effect by electrical control, adsorption magnetic molecules [113]. Kondo resonance signals are associated with the magnetic coupling between the unpaired spins of the paramagnetic molecules and the conduction band electrons of the metal substrate. Thus, when a little portion of paramagnets is deposited on a conductive material (metals, graphene, carbon quantum dots, among others), at low temperature, some electric resistance deviation occurs because of the mentioned magnetic coupling [114]. Regarding the applicability of C-G hybrids, the ferromagnetic coupling is desired since the system displays the spin oriented in the same direction, which allows to univocally interact with an electric current in spin valves or other spintronic devices. In this sense, the enhanced magnetic response for ferromagnetic hybrids is the desired condition for future magnetic application. Besides, the intermolecular interactions of the C-G hybrid suggest that spin transfer to graphene platform is directionally polarized to the nanosheet edges. Henceforth, graphene incorporates an active magnetic nature without losing the chemical integrity, unlike other strategies to get magnetization such as vacancy defects, substitutionally or adatom doping, or chemical reactions to couple a ferromagnet [106,107]. Clearly, the molecular deposition or adsorption process involves milder conditions that mainly support the desired magnetic behavior preserving the structural integrity of the systems.
Finally, the improvement in magnetic devices not only point to miniaturizing but rather to energy efficiency, decrease energy consumption, reduction of heat dissipation, while increasing information capabilities can be achieved [110]. In this sense, the overcoming of the challenge of generate new devices at the technological limits, increase the efficiency, increase the computing capabilities, decrease the energy demand, and help environment.
Thus, the augmented ferromagnetic response allow to orient the spins applying a external field while the orientation is more resistant to thermal disordering [111] enhancing the info writing process (Fig. 8a). Moreover, the non-innocent character of the ligand may and the tunable conductivity in the hybrid complex suggest a high sensitivity to any perturbation. In effect, copper porphyrins and copper phthalocyanines have been used to detect gases such as ammonia and nitrogen oxide [112] but it is expected that non-innocent character of corroles support the sensing since a wide area is sensible to any perturbation (Fig. 8b).
Besides, the tunability of the frontier molecular orbital gap suggest that conductivity can be tuned to enhance the electronic communication for corrole-based hybrid materials.
Therefore, the study of copper corroles-graphene hybrids is not only a prominent challenge rather also a rich field for the development of new magnetic, sensing, and optical applications. There are no competing interests to declare by the authors of this article.