Phosphorene–Fullerene Nanostructures: A First-Principles Study

Hybrid materials formed by carbon fullerenes and layered materials have emerged due to their advantages for several technological applications, and phosphorene arises as a promising two-dimensional semiconductor for C60 adsorption. However, the properties of phosphorenefullerene hybrids remain mainly unexplored. In this work, we employed density functional theory to obtain structures, adsorption energies, electronic/optical properties, binding (AIM, NBO), and energy decomposition analyses (ALMO-EDA) of nanostructures formed by phosphorene and fullerenes (C24 to C70). We find fullerenes form covalent and non-covalent complexes with phosphorene depending on the molecular size, showing remarkable stability even in solution. Two classes of covalent complexes arise by cycloaddition-like reactions: the first class, where short-range effects (charge-transfer and polarization) determines the stability; and the second one, where short-range effects decay to avoid steric repulsion, and balanced longrange forces (electrostatics and dispersion) favors the stability. Otherwise, high-size fullerenes (C50 to C70) only form non-covalent complexes due to strong repulsion at shorter intermolecular distances and lack of dissociation barriers. In terms of electronic properties, fullerenes act as mild p-dopants for phosphorene, increasing its polar character and ability to acquire induced dipole moments (polarizability). Also, small energy-bandgap fullerenes (<0.8 eV) largely increase the phosphorene metallic character. We also note fullerenes retain their donor/acceptor properties upon adsorption, acting as active sites for orbital-controlled interactions and maximizing the phosphorene light absorbance at the UV-Vis region. Finally, we strongly believe our study will inspire future experimental/theoretical studies focused on phosphorene-fullerene uses for storage, anode materials, sensing, phosphorene bandgap engineering, and optoelectronics.


Introduction
Among low-dimensional carbon allotropes (such as graphene and carbon nanotubes), the buckminsterfullerene molecule (C 60 ) is a class of 0-dimensional (0-D) organic compounds of spherical molecular shape and high surface area, displaying remarkable physical and chemical properties due to surface/interfacial effects and quantum confinement 1 . In particular, C 60 displays a remarkable electron acceptor character with a semiconductor bandgap. Also, C 60 is merely composed of sp 2 -hybridized carbon atoms, which confer it an electron-deficient polyalkene nature, and thus, it is chemically reactive 1 . Likewise, small fullerenes have been synthesized and characterized (e.g., from high-resolution transmission electron microscopy), which have associated an increased reactivity with attaching to substrates because of containing paired or adjacent pentagons [2][3] , and their electronic properties are significantly influenced by the shape and size 4 . The unique properties of fullerenes turn into useful building blocks for constructing supramolecular assemblies and micro/nanofunctional materials 1 . Consequently, non-covalent and covalent nanostructures have been fulfilled by depositing fullerene onto emerging low dimensional substrates such as graphene, perovskites, graphite-like carbon nitride, transitionmetal disulfides, and hexagonal boron nitride 1,5 . These hybrid nanostructures show potential applications in different technologies such as catalysis, nanoelectronics, optoelectronics, storage, batteries, solar cells, and spintronics, among others 1,5 .
Phosphorene emerged as a new generation of nanomaterials with an anisotropic 2dimensional (2-D) structure in a puckered honeycomb shape with sp 3 -orbital hybridization 6 .
Despite widespread works on hybrids of fullerenes with other 2D nanomaterials, studies on Phosphorene-Fullerene hybrids have infrequently been reported and mainly focused on C 60 adsorption. Experimentalists and theoreticians have synthesized/proposed PhosphoreneC 60 nanostructures with relevant properties for technological applications such as high specific capacity battery electrode materials 16 , solar energy conversion [17][18] , new molecular doped crystalline superlattices for semiconductor industry 19 , and heterojunction photodetectors 20 . In this way, properties of phosphorene and fullerenes are compensated synergistically; for example, it is found in photovoltaic research that fullerenes act as excellent electron acceptors in polymer solar cells, while phosphorene improves the energy alignment in the devices, which lead to improved power conversion efficiency by favoring the charge transfer and exciton dissociation 18 .
Additionally, the packing of fullerenes onto substrates must be influenced by the shape and size, which would play a key role in the properties and stability of PhosphoreneFullerene hybrids; then the physical/chemical phenomena that dominate the interaction strength is essential to be clarified. Mechanochemical reactions in a high energy mechanical milling process have been used as a strategy to form phosphorus-carbon (P−C) bonds between phosphorene and carbon materials, including C 60 , graphite, and graphite oxide 16 ; in this way, the content of the P−C bond in the phosphorene-C 60 hybrids is only 0.8%, denoting C 60 is not preferably bonded to phosphorene via covalent interactions until breaking the sp 2 C=C/C−C bonds to form defects 16 .
In addition, low-temperature scanning tunneling microscopy, X-ray, ultraviolet photoelectron, and scanning tunneling spectroscopy measurements also show that C 60 molecules are mainly physisorbed at room temperature on the honeycomb lattice of blue and black phosphorene synthesized by epitaxial growth, where an interfacial charge transfer is evidenced upon interaction with C 60 21-22 . The Phosphorene-C 60 non-covalent interaction has also been confirmed by the disappearance of the C 60 absorption band at 340 nm in phosphorene Langmuir-Blodgett films after a simple toluene wash 20 . In this regard, density functional theory (DFT) computations supported a simple physical interaction between C 60 and phosphorene characterized by strong electron density rearrangements (charge transfer) and adsorption energies of 1 eV [22][23] .
The background mentioned above indicates phosphorene could be implemented as a remarkable substrate for the assembly of novel hybrid nanostructures with carbon fullerenes.
Nevertheless, it is still not well understood yet the influence of fullerenes size on Phosphorene-Fullerene hybrids' properties, such as the stability and preferred binding mechanism (covalent/non-covalent), electronic/optical properties after bonding, and the contribution of intermolecular forces determining the adsorption stability. To answer these questions, we employed a dispersion-corrected DFT scheme to obtain adsorption energies and conformations, electronic/optical properties, electron density-based analyses, and energy decomposition analyses of PhosphoreneFullerene nanostructures, which provide deep insights into the stability, structure, adsorption mechanism, and useful potential properties for technological applications.
We consider either the covalent or non-covalent binding of fullerenes in different sizes and symmetries as representative classes, i.e., C 24 (D 6h ), C 26 (D 3h ), C 34 (C 2 ), C 36  (D 2 ), C 50 (D 3 ), C 60 (l h ), and C 70 (D 5h ); in this way, it is provided a wide family of adsorbates resulting in different assemblies for characterization.

Computational Details
We used the PBE functional with the all-electron def2-SVP basis sets for all the DFT calculations in the ORCA4.1 [24][25][26] . The PBE functional has been used to describe the interactions of phosphorene with a wide range of adsorbates. The DFT-D3(BJ) procedure included dispersion corrections into the PBE functional for energies and gradients 27  Bohr, respectively. Continuum solvent effects were included by the universal continuum solvation model (SMD) based on the quantum mechanical charge density of a solute molecule interacting with a continuum description of the solvent 28 . Excited states were obtained with the simplified time-dependent density functional theory (sTD-DFT) approach combined with the meta-hybrid TPSSh functional (10% Hartree-Fock exchange) 29-30 ; configuration state functions were included up to an energy threshold of 6.2 eV. Phosphorene nanoflakes (P 126 H 30 ) were used for adsorption studies and with a surface area of at least 1585 Å 2 considering its electron density, which is relatively larger to obtain well-converged adsorption energies concerning the fullerenes surface area (up to 456 Å 2 ). Adsorption energies (E ads ) were computed as: where E Phos , E Fullerene , and E PhosFullerene are the total energies of the free phosphorene, free fullerenes, and the complex, respectively; ZPE stands for the zero-point energy correction. Thus, the more positive the E ads values, the more stable the complex is. The counterpoise correction was used to avoid BSSE in the E ads values 31 . Adsorption energies were further decomposed by the secondgeneration energy decomposition analysis based on absolutely localized molecular orbitals (ALMO-EDA) of the Q-Chem5.2 program at the PBE-D3/def2-TZVP level 32 . Hence, the adsorption energy for one AB complex expresses as [33][34] : where E CT , E POL , E ELEC , and E DISP stand for the energy lowering due to charge-transfer (inter and intramolecular charge flow between fragments), polarization (induced electrostatics), Coulombic attractions (classical intermolecular electrostatics), and dispersion forces (van der Waals interactions), respectively. E DISP is obtained with the dispersion-free revPBE functional. g inter =| IGM,inter |||, where  stands for the electron density gradient and  IGM,inter is an upper limit to  as defined by Lefebvre and co-workers 36 . AIM, IGM (based on the Hirshfeld partition), CM5 charges, and wavefunction analyses were performed in Multiwfn3.7 37 .

Structure and stability.
We place fullerenes initially 5 Å away from the phosphorene surface; at least ten orientations for each molecule were considered according to its symmetry. The PhosFullerene systems form two groups of stable complexes depending on the fullerene size ( On the other side, the C 50 , C 60, and C 70 fullerenes are physisorbed onto phosphorene with positive adsorption energies of up to 1.0 eV, denoting stable adsorption that compares to the stability reached by C 36 and C 40 via chemisorption (Fig. 1c). Note also adsorbed fullerenes could be further stabilized by neighboring molecules onto phosphorene through strong moleculemolecule interactions, arising two-dimensional self-assembly in the physisorption regime as reported for C 60 adsorption 19 . Compared to our results, periodic vdW-KBM calculations and molecular dynamics simulations have reported non-covalent PhosC 60 complexes with E ads values of 0.7 and 1.0 eV, respectively 19,23 ; then, our results agree with previous reports.
Additionally, UV-VIS-NIR absorbance, temperature scanning tunneling microscopy, and scanning tunneling spectroscopy measurements indicate that C60 molecules physically adsorb on phosphorene, where desorption occurs with annealing 400 K 20-21 . As can be seen, E ads =0.9 eV for PhosC 60 complexes agrees with the experimental favorable non-covalent adsorption of fullerenes on phosphorene-based materials. Furthermore, the C 60 adsorption stability increases at least 30% compared to related 2D materials such as graphene, where E ads 0.7 eV is reported for GrapheneC 60 non-covalent complexes [40][41][42][43][44] . Therefore, phosphorene serves as excellent support for fullerenes to form new hybrid nanostructures, ensuring a stable interaction.
We also compute the potential energy surface (PES) of non-covalent complexes to search for possible states where chemisorption occurs (Fig. 1d). PES begins at intermolecular distances states will have a short lifetime and poor stability due to the lack of dissociation barrier to reach the non-covalent states. This behavior is different from graphene and carbon nanotubes, where C 60 fullerenes reach highly stable chemisorbed states at room temperature due to the relatively high dissociation barrier to reach the physisorbed states (E  >0.7 eV) 39,45 . The absence of an energy barrier to reach chemisorbed states is a consequence of phosphorene nonplanarity due to its shape of structural ridges; in contrast, the chemical GrapheneC 60 attachment requires a high energy barrier due to the lack of local puckering in the graphene structure 39,41 .
Regarding stability in solvent media, almost all PhosFullerene complexes) show high stability in different solvents, independent of the solvent polarity (Fig. 2). In this way, solvation energies cause a slight penalty in the adsorption energies (30%). The exception is the PhosC 44 and PhosC 70 complexes, whose stability is decreased up to 96% in high/medium polar solvents due to differences in solute-solvent polarity with respect to the free fragments. Consequently, solvents with low dielectric constants would be adequate for PhosC 44 and PhosC 70 dilution, e.g., toluene and n-hexane. Another key point to emphasize, phosphorene can be sensitive and  oxidized underwater and oxygen conditions 46 . However, phosphorene oxidation does not imply that fullerene adsorption will be hindered, and new synthetic techniques are developed to improve the stability of phosphorene layered materials for several applications [47][48] . Despite the latter, recent reports highlight the physisorption of C 60 during an assembly at the air-water interface contribute to protecting phosphorene thin films from oxidation and inhibiting the overlapping stacking or agglomeration of phosphorene nanosheets in solvents 20 .

Electronic properties.
Relevant electronic properties of the PhosFullerene complexes are displayed in Table 1.   displays an analogous (r) pattern but with a low magnitude due to the weak electron-transfer.
The electron density rearrangements also induce dipole moments in the range of 0.54.3 Debye ( D , Table 1); note all free systems are non-polarized in their free states ( D 0). The induced dipole moments show a directly proportional correlation to the charge transfer magnitude (Fig.   3d). Also, dipole polarizability  of the complexes increases compared to free phosphorene (>6.47·10 -22 esu vs. 6.17·10 -22 esu, Table 1), denoting an improving ability to acquire an electric dipole moment in proportion to external perturbations such as an electric field. Likewise, the polarizability of complexes increases as the polarizability of free fullerenes increases, which is directly proportional to the electron density volume of fullerenes.
Considering that electron transfer could be responsible for changes in the substrate energy levels because of the charge doping, we analyze the bandgap of the systems ( Table 1) In the final analysis, deposition of small fullerenes could be an efficient strategy for modulation of phosphorene bandgap via molecular doping, i.e., increasing its metallic character.
The bandgap modulation mechanism is mainly due to LUMO stabilization and HOMO destabilization for PhosC 24 to PhosC 40 complexes because of the high charge transfer (Fig. 4).
In the case of complexes PhosC 44  Regarding the topology of frontier molecular orbitals in the complexes (Fig. 4), covalent complexes show the HOMO located in both phosphorene and fullerene moieties due to the orbital interactions. However, the fullerene contribution to the HOMO decreases as the chemical bonding character decreases until it almost disappears in non-covalent complexes. Conversely, LUMO is almost entirely located in fullerene for all the complexes. Thus, fullerenes act as active sites for orbital-controlled interactions, mainly retaining their donor/acceptor properties when chemisorbed on phosphorene. While fullerene mainly will act as acceptor sites when physisorbed on phosphorene.

Interaction mechanism.
We provide a quantitative and readily physical interpretation of the adsorption mechanism by examining the specific role of the stabilizing effects into the adsorption energies and employing the EDA method. The attention is focused on the stabilizing contributions of Eq. is high in PhosC 24 (43%) in spite that the whole intermolecular charge transfer is low (0.08|e|, Table 1), which could be caused by strong intrafragment electron density rearrangements and bond polarization in the [4+4]-cycloaddition as noted from the high E POL contribution (32%).
The AIM analysis allows assessing the binding mechanism from the values of electron density ( i ) at intermolecular bond critical points [BCPs, points in space at which the first derivatives of the electron density vanish (r)=0, Fig. 6]. Accordingly, the covalent complexes reveal short-range intermolecular CP bonding with  i values of  i 0.100.14 e/Bohr 3 , which associate to polarized covalent bonding by sharing electrons (red numbers in Fig. 6a-b). Natural bond orbital analyses (NBO) reveal at least 60% of the CP bond density is polarized to fullerene carbon atoms due to their strong acceptor character. Therefore, the polarized covalent bonding in covalent complexes agrees with the high E CT and E POL contributions. In the molecular orbital picture, the bonding occurs when interacting carbon atoms of fullerenes hybridize from sp 2 sp 3 , forming CP polarized covalent bonds with the low-occupied lone-pair 3p orbitals of phosphorus atoms in the substrate. Additionally, BCPs appear at long-range CP interactions ( i 0.02 e/Bohr 3 ), which are associated with weak electrostatic interactions (blue numbers in Fig. 6a-b). In this regard, EDA shows the electrostatic term (E ELEC ) reaches the third largest contribution to the stability (17-31%). The electrostatic contribution emerges from the electronsufficient carbon atoms of fullerenes, which acquire a negative charge that electrostatically attracts the electron-deficient phosphorous atoms of phosphorene as noted from electron density rearrangements [see the ∆ρ(r) surface, Fig. 3a-c].
It is necessary to note E CT and E POL contributions mainly decay as the intermolecular distances increase due to the connection to orbital overlap, becoming E CT and E POL mostly short-range terms. In that case, the combined contribution of short-range terms defines two classes of covalent complexes (Fig. 5b): into close interaction. As a result, the strong stabilization gained by short-range contributions decay and weak long-range E ELEC and E DISP effects compensate the steric destabilization; consequently, lower adsorption energies are reached compared to the first class of covalent complexes (Fig. 1b).
Focusing now on non-covalent complexes (PhosC 50 , PhosC 60 , and PhosC 70 ), the stabilizing part of the adsorption energy mainly arises from permanent Coulombic electrostatic and dispersion driving forces (E ELEC +E DISP , up to 90%, Fig. 5a). In this regard, the minimization of dispersion and electrostatic interactions also plays a key role in forming organic molecular crystals, phthalocyanine self-assemblies, and DNA nucleobase patterns onto phosphorene-based substrates, standing for 85% of the stability 19, 59-61 . It can be pointed out although phosphorene is not a -electron system, it behaves with a similar attractive ability than graphene or carbon nanotubes to bind aromatic molecules, where fullerenes adsorb by - stacking [39][40][41][42][43][44][45] . In this regard, the 3D g inter isosurface representation of weak intermolecular interactions is visually displayed for PhosC 60 complex as a representative case and compared against GrapheneC 60 (Fig. 7a). The weak interaction pattern shows a similar shape in both forces for C 60 stabilization onto phosphorene (Fig. 7a). According to AIM analyses, non-covalent complexes displays two type of electrostatic interactions (Fig. 6c-d  found at this point the fullerene size at which chemisorption is no longer allowed, which is set between C 44 and C 50 (Fig. 5c). This limit arises because the intermolecular separations must increase to decrease the repulsion energy; consequently, physisorption is a stable state at longer intermolecular distances for bigger fullerenes (C 50 , C 60 , and C 70 ). Therefore, E PAULI is the primary driving force that compensates all the stabilizing effects to establish the energetically optimal intermolecular separation between phosphorene and fullerenes.
Finally, destabilizing terms mainly arise from Pauli repulsion; however, the covalent complexes involve geometrical preparation energies E PREP due to the required orbital penalty due to weak structural changes to reach the covalent bonding, the low RMSD values show that the electronic/structural rearrangements are low-scale and are not prohibited.

Outlook of PhosFullerene nanostructures.
This work provides a first pivotal stepping-stone to exploring the immense possibilities of the proposed nanostructures in future theoretical/experimental studies. All analyses considered, in addition to comparisons with related hybrid structures, show some interesting potential uses for PhosFullerene nanostructures. For instance, covalent PhosFullerene complexes display a graphene nanobud-like structure and strong electron transfer in the PhosFullerene direction. In this regard, graphene nanobuds have shown potential uses in energy and gas storage devices with high stability at room temperature, new spintronics, position sensing, and graphene band structure engineering 38-39, 54, 62 . Furthermore, Li adsorption was enhanced for graphene-C 60 nanobuds by the high electron affinity of C 60 and the charge transfer from graphene to C 60 55, 63 .
Accordingly, the strong charge transfer in the PhosFullerene direction turns covalent complexes into remarkable candidates to be studied as novel storage and anode materials in Li/Na-ion battery applications.
Additionally, orbital analyses show that fullerenes act as active sites for orbital-controlled interactions, mainly retaining their donor/acceptor properties when chemisorbed on phosphorene.
While fullerene mainly will act as acceptor sites when physisorbed on phosphorene. Also, fullerenes increase the metallic character of phosphorene. The latter suggest fullerenes could act as signal amplifiers for specific redox applications considering that phosphorene-based materials based sensors to determine prostate-specific antigen, hemoglobin, clenbuterol, and polychlorinated biphenyls, reaching an excellent specificity, chemical stability, low detection limits, and reproducibility [64][65][66] . The electrochemical amplification mechanism emerges from the good charge transfer in the hybrid material, an enhanced electrical conductivity of the electrode, and the excellent electrocatalytic activity of the deposited molecules upon adsorption 65 .
Therefore, our results open avenues for the study of PhosFullerene hybrids in electrochemical biosensing.
On the other hand, charge-doping and bandgap changes reveal phosphorene conductance can be tailored by deposition of fullerenes. Since the bandgap value is directly proportional to the conductance (   HL /kT, where k is the Boltzmann constant and T the temperature), our results define a framework to explore the charge-transport and optoelectronic response of Phos-Fullerene nanostructures. As an illustration, the increased charge transport of graphene due to C 60 deposition [54][55] , and the strong electron-accepting characteristics of C 60 causing a hole-doped nature in graphene, lead to hybrid structures allowing photogenerated carriers for highperformance photodetector devices 50 . It is also noticed that a larger electron transfer in the PhosFullerene direction is responsible for lower bandgap values, resulting in a higher conductance. In this way, functionalized fullerenes with strong acceptor functional groups could be implemented to maximize the electron transfer and charge transport. conversion efficiency 18 . In addition, C 60 allowed absorption in the visible range for mm-scale heterojunction phosphorene-based photodetectors, where synergistic effects enable high photoresponse from the visible to near-infrared spectrum 20 . Accordingly, synergistic properties of PhosFullerene complexes could inspire experimental/theoretical studies on its uses for future generation solar energy harvesters or as active layers within photodetector devices. To support these points, we verified the UV-Vis spectrum of the proposed nanostructures in n-hexane as a solvent commonly implemented to study the fullerene absorbance (Fig. 8). Intrinsic phosphorene shows a wide absorbance from the infrared, which increases in intensity below 500 nm as recorded from UV-vis spectrophotometry 67 . In comparison, most free fullerenes absorb high molar absorption coefficients at the UV region below  abs <400 nm (Fig. 5a). PhosFullerene nanostructures almost resemble the absorption spectra of free phosphorene (Fig. 5b), but a remarkably improved absorption at higher frequencies is reached ( abs 400-500 nm). Then, fullerenes maximize the phosphorene absorbance at the UV-Vis region, denoting the emerging synergistic effects for optoelectronics and photodetectors.

Conclusions
We have computationally elucidated the structure, stability, and interaction mechanisms of phosphorene-fullerene nanostructures, which form covalent and non-covalent complexes depending on the fullerene size and outstanding stability compared to related 2D materials, even in solution. Two classes of covalent complexes arise by cycloaddition-like reactions of up to [4+4] order: the first class (C 24 C 34 ), where short-range stabilizing effects dominate; and the second one (C 36 C 44 ), where short-range effects decay to avoid steric repulsion, and balanced long-range forces favor the stability. High-size fullerenes (C 50 C 70 ) form non-covalent complexes due to strong repulsion at shorter intermolecular distances and lack of dissociation barriers.
Furthermore, fullerenes act as mild p-dopants for phosphorene, increasing its polar character and ability to acquire induced dipole moments (polarizability). Also, small energy-bandgap fullerenes (<0.8 eV) largely increase the phosphorene metallic character. We also note fullerenes retain their donor/acceptor properties upon adsorption, acting as active sites for orbital-controlled interactions and maximizing the phosphorene absorbance at the UV-Vis region. Future work should focus on relevant applications of the proposed nanostructures for storage, anode materials in Li/Na-ion batteries, electrochemical sensing, bandgap engineering, and/or optoelectronics.