Article pubs.acs.org/JPCC
Nanostructures of C60MetalGraphene (Metal = Ti, Cr, Mn, Fe, or Ni): A Spin-Polarized Density Functional Theory Study Hung M. Le,*,†,‡ Hajime Hirao,*,† Yoshiyuki Kawazoe,§,∥ and Duc Nguyen-Manh⊥ †
Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore ‡ Faculty of Materials Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam § New Industry Creation Hatchery Centre, Tohoku University, 6-6-4, Aramaki, Aoba, Sendai, 980-8579, Japan ∥ Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, 1, Lavyrentyev Avenue, Novosibirsk 630090, Russia ⊥ Theory and Modeling Department, Culham Centre for Fusion Energy, United Kingdom Atomic Energy Authority, Abingdon, OX14 3DB, United Kingdom S Supporting Information *
ABSTRACT: We used plane-wave density functional theory (DFT) to investigate the properties of C60Mgraphene (C60MG) nanostructures (M = Ti, Cr, Mn, Fe, or Ni). The calculated binding energies suggested that C60 could be mounted on a metal− graphene surface with good bonding stability. The high-spin C60CrG nanostructure was found to be more stable than the previously reported low-spin configuration. Also, C60Ti was found to stand symmetrically upright on the graphene surface, while in the remaining four cases, the orientation of C60M in the C60MG nanostructures were bent, and the geometry of each structure is somewhat different, depending on the identity of the bridging metal atom. The large geometric distortion of C60M in the tilted C60 MG nanostructures (with Cr, Fe, Mn, and Ni) is attributed to the spin polarization in the 3d orbitals and dispersion interactions between graphene and C60. Additional DFT calculations on smaller C60Mbenzene complexes with atomic-orbital (AO) basis sets provided consistent results on structural geometry and numbers of unpaired electrons. The DFT calculations using AO basis sets suggested that the C60−M unit was flexible with respect to the bending motion. The knowledge of metal-dependent geometric differences derived in this study may be useful in designing nanostructures for spintronic and electronic applications.
1. INTRODUCTION Buckminsterfullerene (C60), a spherical molecule that was first discovered by Kroto and co-workers,1 has a large surface area arising from the spherical molecular shape. This feature has proven useful in the adsorption of small metal clusters2,3 and the catalysis of small molecules.4−7 For example, Birkett et al. suggested that the adsorption of a Ni/Co layer on C60 would produce a “plausible” catalyst for the carbon nanotube synthesis.4 Braun et al. proposed an experimental procedure to attach amorphous Ru on C60 and applied it to the catalysis of the hydrogenation processes of CO and 2-cyclohexenone.5,6 C60 itself was also shown to act as a catalyst in the hydrogenation of nitro groups.7 If such attractive catalytic effects of C60 are to be further exploited for heterogeneous catalysis, then a stable hosting nanostructure may have to be established, so that the C60attached metal nanoparticles can be recovered and utilized repeatedly. This may be accomplished, for example, by steadying C60 on the surface of a graphene monolayer8 with bridging metal atom(s).9 Our recent calculations demonstrated that such nanostructures are indeed capable of hosting metal © 2014 American Chemical Society
nanoparticles on C60, and that resultant complexes should act as active catalysts for chemical reactions (such as OO bond activation).9 In addition to its potential roles in catalysis, the significance of C60 in hydrogen storage has been appreciated. The coating of C60 with Sc and Ti was reported to elevate the binding energy of hydrogen, which led to a high H2-storage capacity (up to 8 wt %).10 However, it was noted in the same study that transition metals tended to cluster on the C60 surface, thereby compromising the effectiveness of hydrogen storage. Alkali metals such as Li and Na, however, do not cluster on C60. On the basis of the results obtained from first-principles studies, it was suggested that C60Li12 was able to capture up to 60 H2 molecules,11 while C60Na8 could store 48 H2 molecules.12 Furthermore, Teprovich et al.13 experimentally demonstrated the hydrogen storage on C60Lix, achieving the H2-storage capacity up to 5 wt %. Even for such hydrogen storage Received: August 5, 2014 Published: August 18, 2014 21057
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magnetization of the metal atom was varied to ensure that the calculations yielded the most stable spin states (magnetic moment) of the nanostructures, and the Gaussian smearing was employed with a small smearing width of 0.002 Ry. In order to obtain equilibrium structures with good accuracy, the energy convergence criteria were set as 10−6 Ry. To reduce the computational cost, the scan calculations were performed with a smearing width of 0.03 Ry. Once convergence of geometry optimization was attained, the binding stability could be evaluated using the following equations:
purposes, steadying C60 on a graphene sheet or other carbonbased nanomaterials might be beneficial. When ligands are attached to a graphene monolayer via transition-metal atoms,14 interesting electronic and magnetic behaviors are elicited that could be used in high-mobility electronic transistors or spintronic and memory devices. Firstprinciples calculations suggested that graphene decorated with benzene could exhibit interesting magnetic properties, which might potentially lead to spin-valve materials.15 The metalbridging strategy is also useful in interconnecting single-walled carbon nanotubes (SWNTs).16 The bis-hexahapto linkages in SWNT−metal complexes were found to reduce the internanotube junction resistance.14,17 Assuming that C60 is the ligand, we previously examined C60CrG, which involves donor−acceptor interactions: 3d orbitals (acceptors) of Cr and 2pz orbitals (donors) of graphene establish coordination bonding between aromatic honeycomb rings and the metal, while C60 is capable of receiving electrons from the metal atom.9 According to the classification schemes of metal− graphene interactions discussed by Sarkar et al.,14 C60CrG could be regarded as a covalent chemisorption case because of the high binding energy (>2.0 eV). It should be noted that Cr is not the only transition-metal atom that has vacancy in the 3d shells, and therefore it may also be possible to construct C60 MG using other 3d transition metals, e.g., Ti, Mn, Fe, and Ni, as bridging atoms, which may allow magnetism to emerge in the resultant nanostructures.18 In this paper, we report a theoretical study of the C60MG nanostructure containing Ti, Cr, Mn, Fe, or Ni as M. Moreover, the interplay among the bonding orientation, spin polarization, and magnetic properties is discussed in the light of evidence obtained from electronic structure calculations. It was shown in a previous theoretical work19 that transition metal atoms could attach to different binding sites (hollow (H6), bridge, top) of graphene. In particular, the energy differences in various binding schemes of Cr and Mn were insignificant. However, we only consider the hollow-binding scheme between transition metal atoms and graphene in the current study.
ECbinding = EMG + EC60 − EC60MG 60MG
(1)
ECbinding = EG + EC60M − EC60MG 60MG
(2)
where EMG, EC60, EG, and EC60M denote the total energies of an optimized metal-adsorbed graphene system, C60, pure graphene supercell containing 54 C atoms, and C60M, respectively; EC60MG represents the total energy of the complex nanostructure. ECbinding expresses the binding of C60 on a 60MG metal−graphene surface, while Ebinding C60MG represents the binding of an MC60 complex on graphene. 2.2. Localized Atomic-Orbital-Basis Calculations. We also carried out localized atomic-orbital-basis calculations for the similar structures using the Amsterdam Density Functional (ADF)30 and Gaussian 09 (G09)31 packages for validation purposes. In these calculations, we considered the isolated gasphase models of C60Mbenzene, which were assumed to bear much resemblance to the C60MG nanostructures. Previously, a study of first- and second-row transition-metal binding to benzene was reported by Bauschlicher et al.32 The PBE exchange-correlation functional23−25 was employed to optimize the C60Mbenzene structures with constrained spin states. The triple-ζ-polarized (TZP) Slater-type basis set33−35 with large-core pseudopotential was employed in ADF calculations, while the 6-31G* basis set (for C and H)36,37 and the SDD effective core potential basis set (for metal) were used in G09 calculations.38,39 In the G09 calculation set, calculations using Grimme’s dispersion correction with Becke−Johnson damping (GD3BJ) were also included,40 while we performed two sets of calculations in ADF with and without the dispersion effect. Upon convergence, the binding energy of each structure is calculated based on the G09 or ADF results as follows:
2. COMPUTATIONAL DETAILS 2.1. Structural Optimizations Using Plane-Wave Calculations. Our model contained a total of 115 atoms in a hexagonal unit cell. A periodic graphene sheet consisting of 54 C atoms in the unit cell (with the a and b lattice parameters of 12.8 Å and c lattice parameter greater than 16.2 Å) was decorated with C60 via a bridging transition-metal atom. The distance between two C60 units due to periodicity was 5.9 Å. Also, by adopting such a large c axis, it was ensured the vacuum distance between layers in the z direction to be at least 6.9 Å. The geometry was relaxed in terms of unit-cell axes (with a constant volume) and atomic positions using density functional theory (DFT) methods20,21 implemented in the Quantum Espresso (QE) program.22 The Perdew−Burke−Ernzerhof23−25 (PBE) functional within the generalized gradient approximation was employed to describe the exchangecorrelation energy, in combination with the Vanderbilt ultrasoft pseudopotentials26,27 for C and transition metal atoms. For two-dimensional slab calculations, a k-point mesh of (6 × 6 × 1) was chosen to represent the Brillouin zone, while a kineticenergy cutoff of 45 Ry was used for the plane-wave expansion. The semiempirical dispersion correction scheme was used to include the nonbonding interaction between C 60 and graphene.28,29 In each structural optimization, the initial
ECbinding = EMbenzene + EC60 − EC60Mbenzene 60Mbenzene (3)
where EMbenzene denotes the total “bonding energy” (in ADF) or total energy (in G09) of a metal−benzene structure in its most stable spin state. According to the G09 and ADF results, the most stable spin states of Crbenzene, Mnbenzene, and Febenzene are septet,41 sextet, and triplet, respectively (see Table S1, Supporting Information (SI)). EC60 and EC60MG represent the total bonding energies of C60 and the C60−M− benzene complexes, respectively.
3. RESULTS AND DISCUSSION 3.1. Structural Optimization of C60MG. We previously reported an upright (symmetric) structure of C60CrG (Figure 1(b)) with a low spin polarization, which was obtained from geometry optimization using an 21058
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Figure 1. (a) Energy profiles for the dissociation of C60 from CrG, obtained from energy scan calculations. The CrC60 distance is the distance in the z direction between Cr and six lowest C atoms. (b) The previously obtained upright C60CrG structure.9 (c) The most stable C60CrG structure, in which the C60 tilt angle is defined as the angle between the bisector of two CrC bonds (b⃗) and vector n⃗ connecting the center of mass of six nearest C atoms on graphene to the metal atom. Figure 2. Equilibrium (a) C60MnG, (b) C60FeG, (c) C60 TiG, and (d) C60NiG structures. C60 is upright on Ti by forming hexahapto bonds, while tilted in the other three cases. The C60 tilt angle is defined as the angle between the bisector of two MC bonds (b⃗) and vector n⃗ connecting the center of mass of six nearest C atoms on graphene to the metal atom.
9
upright initial geometry. As shown in Figure 1(a), we explored a wider area of the potential energy surface for C60CrG, and found that there are two distinct types of curves (denoted as “Scan 1” and “Scan 2”). Because of the difficulty in defining internal coordinates in QE calculations, the scan calculations were performed by imposing constraints to fix the z coordinates of Cr and six lowest-lying C atoms of C60 (the same z coordinates were initially assigned to these C atoms), while the x,y coordinates of those atoms and the x,y,z coordinates of other atoms are relaxed. From the scan and geometry optimization calculations, we found a new equilibrium structure as shown in Figure 1(c), which was more stable than the previous structure and had a larger spin polarization term. In the newly obtained nanostructure, a unique bonding geometry was observed, in which only two C atoms of C60 participated in the coordination bonding with Cr. Moreover, the C60Cr axis was highly tilted as can be seen from a tilt angle, which was defined as the angle between the bisector of the two MC vectors and the approximate normal vector of the graphene plane. In the equilibrium structure of C60MnG that had a large magnetic moment, Mn was bound to six C atoms in graphene and two C atoms in C60 as in the case of most stable C60 CrG (see Figure 2(a)). As for the C60FeG nanostructure, in its most stable form, the equilibrium geometry was similar to that of the high-spin C60CrG and C60MnG nanostructures; however, there was a clear difference in the orientation of C60. As shown in Figures 1(c) and 2(a), the two C atoms in the CrC/MnC bonds have nearly the same z coordinate, while the plane defined by two FeC bonds is almost perpendicular to the graphene sheet, and one C atom has a larger z coordinate than the other (Figure 2(b)). The Fe atom fully interacts with a honeycomb ring of graphene, whereas it tends to reduce coordination interactions with C60, to have only two FeC linkages. To describe the distortion of
C60 in C60FeG, we again define a tilt angle as shown in Figure 2(b). The behavior of C60 on NiG, as shown in Figure 2(d), was somewhat similar to that in the case of C60FeG, but C60 seemed to be less tilted on Ni. According to our equilibrium geometries obtained from plane-wave DFT calculations, in the most stable C60CrG, C60MnG, C60FeG, and C60NiG nanostructures, the C60M unit was tilted when it was mounted on the metal; these structures had tilt angles of 36.3°, 30.5°, 28.6°, and 15.1°, respectively. In the C60TiG structure (Figure 2(c)), the orientation of C60 was symmetrically upright like the structure of low-spin C60CrG. 3.2. Spin-Polarized Electronic Structures and Bonding Analyses. In all cases, the binding energies of the C60MG structures given by eq 1 are positive, indicating good stabilization and strong chemisorption (rather than physisorption with small binding energies) of C60 on the metal− graphene complex. The calculated binding energies of C60 CrG, C60MnG, and C60FeG and the corresponding magnetic moments are summarized in Table 1. Due to the fact that ECbinding is always greater than the corresponding 60MG binding EC60M−G, we can state that attaching C60 on a metal−graphene surface should be more favorable than attaching a C60−metal complex on graphene. Even though C60M is highly tilted in high-spin C60MG nanostructures and the metal atoms form coordination bonds with only two C atoms, all five metals turn out to be good bridging atoms that steady C60 on the graphene monolayer effectively. The binding energy of the newly observed C60CrG nanostructure (2.95 eV) is indeed 21059
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Table 1. Binding Energies and Magnetic Moments (MT) of the C60MG Structures Given by Plane-Wave Calculations, Binding Energies and Multiplicity of C60MBenzene Given by PBE/TZP with and without Dispersion Corrections in ADF and PBE/(SDD,6-31G*) with Dispersion Corrections in G09 binding energy (eV) M
ECbinding 60−MG
ECbinding 60M−G
ADF (without dispersion)
ADF (with dispersion)
G09
MT (μB/cell)
multiplicity
Cr
2.95 (2.36) 2.75 3.18 3.37 3.11
1.99 (1.41) 2.10 3.01 3.16 2.69
1.96 (1.95) 2.03 1.91 2.75 2.32
2.11 (2.15) 2.22 2.12 3.14 2.70
2.16 (2.14) 2.23 2.33 3.38 2.77
4.06 (0.00) 3.11 2.00 0.00 0.00
quintet (singlet) quartet triplet singlet singlet
Mn Fe Ti Ni
There were small geometric differences between the different models of the Ni and high-spin Cr complex. Whereas the QE calculation predicted that in C60CrG, C60Cr was highly tilted with an angle of 36.3°, it was observed from the ADFoptimized quintet C60Crbenzene structure that the distortion of C60Cr was less severe (4.4−4.5°). However, the G09-optimized structure was highly distorted (with a tilt angle of 30.4° according to the definition introduced in Figure 1). The much smaller angles obtained in the ADF calculations may be due to the use of large cores. In the Ni cases, whereas the results from AO calculations indicated that C60 was not tilted on benzeneNi, QE calculations indicated that C60 was tilted on NiG with an angle of 15.1°. Despite these differences, overall, the QE plane-wave calculations and the ADF calculations gave more or less consistent trends in the distorting geometry of C60MG. For validation purposes, we carried out four additional sets of atomic-orbital DFT calculations in G09 using the hybrid B3LYP functional42 and 6-31G* basis set with/without the dispersion effect, PBE/(SDD,6-31G*) and PBE/6-31G* without considering the dispersion effect. For convenience, the relative total energies and tilt angles of all Cr, Mn, Fe, Ti, and Ni structures obtained from atomic-orbital DFT calculations are given in Tables S2, S3, S4, S5, and S6, respectively (SI). The difference between PBE and B3LYP calculations in terms of geometry distortions and relative energies can be clearly observed in the Cr, Mn, and Fe cases. Quintet C60Cr benzene was highly tilted according to the PBE/(SDD,6-31G*) calculations without dispersion effects (19.4°). When the dispersion correction was included, C60 approached closer to benzene and made a larger tilting angle (30.5°). A small distortion of C60Cr was also reported by B3LYP/6-31G* calculations, but when the dispersion correction term was introduced, C60 drew closer to benzene, and thus caused an increase in the tilt angle (25.0°). In the last calculation set, PBE/6-31G* calculations indicated a large distortion (29.5°) in quintet C60Crbenzene; however, this calculation (at the PBE/TZP level with dispersion effects using ADF) suggested that singlet was more stable than quintet, while the other calculation sets showed that the quintet state was more stable. Also, B3LYP calculations tended to give larger energy differences of 0.60−0.64 eV and favor the high spin state, whereas the PBE/(SDD,6-31G*) with/without dispersion effects indicated slight distinctions in relative energy between the two states (0.01−0.04 eV). In the case of C60Mnbenzene, the PBE calculations gave large tilt angles (13.7°−18.5°) of the quartet structure, and the relative energy of the excited doublet state compared to the quartet ground state fell in the range of 0.24−0.63 eV. Both B3LYP calculations with and without dispersion effects,
0.59 eV larger than that of the low-spin structure reported in a previous study.9 In Table 1, we also present the total magnetic moment exhibited by each structure when DFT calculations were executed with a smearing width of 0.002 Ry. To verify the interesting geometric trends observed for C60 MG in plane-wave calculations, we performed structural optimizations for the C60Mbenzene models with the PBE functionals and atomic-orbital basis sets, using ADF and G09 software. According to the results obtained from the PBE/TZP calculations without dispersion effects using ADF and the PBE/ (SDD,6-31G*) calculations with dispersion corrections using G09, the most stable spin states of C60Crbenzene, C60 Mnbenzene, C60Febenzene, C60Tibenzene, and C60Nibenzene were quintet, quartet, triplet, singlet, and singlet, respectively. By contrast, the PBE/TZP calculations with the dispersion effect using ADF predicted that singlet C60Crbenzene was more stable than the quintet structure (see the summary of binding energies of C60Mbenzene structures in Table 1). These results indicate that the singletquintet spin-state splitting is sensitive to the method employed. In fact, we examined several different methods and found that the PBE method tends to give the singlet ground state, especially when effective core potential is not used (SI Table S2). The calculated binding energies from both ADF without dispersion effects and G09 with dispersion effects suggested that quintet C60Crbenzene (S = 2) was the most stable structure with a binding energy of 1.96 eV (ADF) or 2.16 eV (G09), while the closest metastable configuration of C60 Crbenzene (singlet (S = 0), with no geometry distortion) had a slightly lower binding energy (1.95 eV given by ADF without dispersion effects and 2.14 eV given by G09). With the inclusion of dispersion effects in ADF, the binding energy of quintet C60Crbenzene was raised by 0.15 eV; however, the empirical corrections increased the binding energy of singlet C60Crbenzene by 0.20 eV, thus making it the ground state instead. With the inclusion of dispersion effects in ADF, the binding energies of C60Mnbenzene, C60Febenzene, C60Tibenzene, and C60Nibenzene were also raised by 0.19−0.39 eV. In general, it can be observed that with dispersion effects included, the binding energies obtained from ADF calculations were closer to the corresponding binding energies given by G09 calculations. Overall, the binding energy trend obtained from atomic-orbital calculations is not very different from that obtained from QE calculations. In terms of geometry, all QE, ADF, and G09 calculations predicted that Cr, Mn, Fe, and Ni interacted with C60 via two C atoms in the most stable ground states. Meanwhile, Ti made a low-spin configuration, in which the metal atom formed bis-hexahapto bonds with both graphene and C60, which is very similar to the case of the low-spin Cr complex. 21060
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Table 2. Mulliken Charges and Spin Densities (in Parentheses) of Benzene, M, and C60 Given by PBE/TZP (ADF) and PBE/ (SDD,6-31G*) with GD3BJ Correction (G09) for Four BenzeneMC60 Complexes PBE/TZP without dispersion corrections (ADF) benzene benzeneCrC60 (quintet) benzeneCrC60 (singlet) benzeneMnC60 (quartet) benzeneFeC60 (triplet) benzeneTi−C60 (singlet) benzeneNi−C60 (singlet)
0.33 (0.19) 0.30 (0.00) 0.21 (−0.17) 0.21 (−0.14) 0.19 (0.00) 0.25 (0.00)
M 0.51 0.02 0.38 0.24 0.44 0.16
(4.18) (0.00) (3.45) (2.21) (0.00) (0.00)
PBE/(SDD,6-31G*) with dispersion corrections (G09)
C60
benzene
−0.84 (−0.37) −0.32 (0.00) −0.59 (−0.28) −0.45 (−0.07) −0.63 (0.00) −0.41 (0.00)
0.31 (0.14) 0.48 (0.00) 0.29 (−0.19) 0.38 (−0.17) 0.28 (0.00) 0.47 (0.00)
however, predicted that the tilt angles were very small (0.1°) and the energy difference between the two states was much larger (>1.1 eV). It should also be noted that the geometry of C60Mnbenzene was similar to QE-calculated C60FeG in Figure 2(b); thus, there was a difference in the orientation of C60 between C60Mnbenzene and C60MnG. Again, we noted that the relative energies between triplet ground state and excited singlet state of C60Febenzene were higher (0.58−0.65 eV) according to the hybrid B3LYP calculations, while PBE gave smaller energy differences (0.24−0.44 eV). The tilt angle of triplet C60Febenzene was predicted to vary from 16.8° to 23.3° (see Table S4, SI). Using small C60M benzene, we also checked how energy changes with respect to the change in the position of C60 (SI Figures S10−S12). It was found that the stability of the system changed significantly when C60 dissociated from M−benzene. However, the energy change was not significant when the angle of C60M was changed, indicating that the C60MG are relatively flexible with respect to the bending motion. In its most stable form, C60 seemed to stand upright on Ni−benzene via two Ni−C interactions. The tilt angle in all cases were very small (0.0− 0.7°). This is different from the geometry observed in C60 NiG (with a tilt angle of 15.1°), which might be a result of strong dispersion interactions between C60 and graphene. All PBE and B3LYP calculations predicted that the energy difference between the singlet ground-state and triplet excited state was in the range of 1.21−1.32 eV. In the most stable configuration of C60Tibenzene (singlet), C60 was seen to stand symmetrically upright on Ti, similar to the singlet C60 Crbenzene case, which was consistent with the structure of C60TiG given by QE calculations. In terms of energy, all PBE calculations predicted a more significant energy difference between the singlet ground-state and triplet excited state (0.29−0.55 eV), while the two B3LYP calculation sets predicted much smaller energy differences (0.01−0.03 eV). To gain a deeper understanding of such distortion behavior of C60, we analyzed the molecular orbital diagrams obtained from ADF AO calculations without the dispersion effect. As summarized in Table 2, the Mulliken charge distribution analysis from PBE/TZP (ADF) and PBE/(SDD,6-31G*) (G09) showed that C60 had a negative charge in the C60 Mbenzene complex in all cases, indicating that M−benzene donated electrons to C60. In the most stable form, C60Cr benzene had a spin multiplicity of quintet (four unpaired electrons). The singlet C60Crbenzene was less stable (with no unpaired electrons as shown in Figure 3(b)). In a previous study, Sahnoun and Mijoule reported that bis(benzene) chromium adopted the singlet spin state in its most stable form.41 Unlike benzene, the unique spherical shape of C60 allows its rolling on Cr to obtain a more stable geometric configuration having a tilted CrC60 moiety. The orbital
M 0.30 −0.33 0.21 −0.03 0.20 −0.14
(4.15) (0.00) (3.43) (2.23) (0.00) (0.00)
C60 −0.61 (−0.29) −0.15 (0.00) −0.51 (−0.24) −0.35 (−0.06) −0.48 (0.00) −0.32 (0.00)
Figure 3. Energy diagrams of the Cr 3d shells in (a) the quintet (most stable) and (b) singlet (less stable) C60Crbenzene structures given by PBE/TZP without dispersion corrections in ADF. In the quintet structure, 3dyz is doubly occupied, while the other 3d shells are singly occupied. In the singlet state, 3dz2, 3dxy, and 3dx2−y2 are doubly occupied, whereas 3dxz and 3dyz are unoccupied.
diagram in Figure 3(a) shows that only the 3dyz-type orbital is doubly occupied, and this orbital should be mainly used for the electron donation to C60 (Figure S1, SI). Indeed, we observed above that the two C atoms in the CrC bonds had nearly the same z coordinate in C60CrG (Figure 1(c)). However, the other d orbitals are singly occupied, and thus a hexahapto coordination of C60 will result in large repulsion between these singly occupied d orbitals (especially 3dxz and 3dz2) and occupied orbitals of C60. To alleviate this repulsion, C60 changes its geometry to a more tilted one (Figure 1(c)). In terms of the electronic structure, the overall multiplicity (quintet) in ADF calculations is consistent with the relatively large total magnetic moment obtained by QE calculations (4.06 μB/cell as shown in Table 1). In the low-spin C60Crbenzene (Figure 3(b)), both the 3dxz and 3dyz orbitals are unoccupied, while 3dz2, 3dxy, and 3dx2−y2 subshells are doubly occupied. The 3dz2-type orbital will be used for the electron donation to C60. Furthermore, the empty Cr 3dxz and 3dyz subshells can establish two pairs of donor−acceptor interactions effectively with highest-occupied orbitals of C60. These charge-transfer interactions allow the low-spin C60Crbenzene complex to have an upright geometry, and the relatively small charge of C60 (−0.32 given by ADF and −0.15 given by G09 as reported in Table 2) results from the back-donation effect. The most stable spin multiplicities of C60Mnbenzene and C60Febenzene were predicted as quartet (S=3/2) and triplet (S = 1), respectively. Quartet C60Mnbenzene had three unpaired electrons that occupied the 3dxy, 3dz2, and 3dyz, while the 3dxz and 3dx2−y2 orbitals were doubly occupied, as shown in the energy diagram in Figure 4(a). In the case of C60Febenzene, the spin state was triplet, and both 3dxz and 3dyz were singly occupied (Figure 4(b)). The single 21061
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(i.e., C60Febenzene) structure was “isolobal” to carbine and had two unpaired electrons occupying a1 and b2 levels (Figure 6).43 For Cr and Mn (d6, d7 respectively), more
Figure 4. Energy diagrams of the 3d shells in (a) quartet C60Mn benzene and (b) triplet C60Febenzene given by PBE/TZP without dispersion corrections in ADF. In the Mn complex, 3dxz and 3dx2−y2 are fully occupied, while the other 3d orbitals are singly occupied. In the Fe structure, the single occupations of 3dxz and 3dyz result in the distortion of C60.
Figure 6. Electron occupations of the hybrid orbitals in the ML4 structures (quintet C60Crbenzene, C60Mnbenzene, C60 Febenzene, and C60Nibenzene).
occupation of each of these d orbitals will again cause repulsion against the occupied orbitals of C60, thus resulting in a severe distortion of the C60Fe axis. Both C60Tibenzene and C60Nibenzene were observed to establish singlet multiplicities (no unpaired electrons) even though the C60M bonding configurations were completely different (Ti formed hexahapto bonds with C60 while Ni was bound to two C atoms in C60). Because of having hexahapto bonds with C60, the Mulliken charge on Ti (0.44 as given by ADF or 0.20 as given by G09) was more positive than the charge of Ni (0.16 as given by ADF, or even −0.14 as given by G09). As shown in the molecular orbital energy diagram of C60Tibenzene (Figure 5(a)), the 3dxy
electrons would be withdrawn from t2g. However, for Ni (d10), two additional electrons should be added to complete the a1 and b2 orbitals and a close-shell configuration was obtained. As a result, we observed the most stable spin states of quintet, quartet, and singlet for C60Crbenzene, C60Mn benzene, C60Nibenzene, respectively (also illustrated in Figure 6). C60Tibenzene, however, could be considered as ML6 because Ti was bound to a honeycomb ring in C60 by hexahapto bonds (three additional ligands), which strongly preferred to to have a close-shell configuration (singlet). In terms of magnetic alignments, spin-polarized QE calculations using plane-wave basis sets predicted that the most stable C60MnG exhibited a magnetic moment of 3.11 μB/cell, whereas C60FeG gave a magnetic moment of 2.00 μB/cell. The magnetic moments of high-spin and low-spin C60CrG nanostructures were 4.06 and 0.00 μB/cell, respectively. Also, the total magnetic moments in both C60 TiG and C60NiG were found to vanish. Those magnetic quantities are consistent with the spin states of C60M benzene given by ADF and G09 calculations. In addition, the trend in the spin polarization of graphene and C60 was similar to the trend in spin distribution of benzene and C60 shown in Table 2. The magnetic behaviors of those investigated nanostructures can also be seen from the partial density of states (PDOS) of the 3d orbitals. In the stable C60CrG structure (quintet) having a tilted geometry, high spin polarizations in the 3d orbitals were observed, which contribute significantly to the total magnetic moment of 4.06 μB/cell. As shown in Figure 7(a), five 3d subshells are highly polarized with the dominance of spin-up states. Among five 3d subshells, 3dz2 is the most polarized orbital, while we also notice significant spin polarizations in 3dxz and 3dyz. However, in metastable lowspin C60CrG with no geometry distortion of C60, no spin polarization was observed in the Cr 3d orbitals, i.e., the doubly occupied 3dz2, 3dxy, and 3dx2−y2 and the nearly empty 3dxz and 3dyz orbitals as shown in Figure 7(b). In C60MnG (MT = 3.11 μB/cell), high positive spinpolarization terms were found in all 3d subshells (see Figure 7(c)). Unlike atomic-orbital calculations in ADF, the planewave calculations indicated that both 3dxz and 3dyz had significant spin polarizations (0.71 and 0.56 μB, respectively), which resulted in a more severe distortion of MnC60 in high-
Figure 5. Energy diagrams of the 3d shells in (a) singlet C60Ti benzene and (b) singlet C60Nibenzene given by PBE/TZP without dispersion corrections in ADF. In the Ti complex, 3dxy and 3dx2−y2 are fully occupied, while the other 3d orbitals are unoccupied. In the Ni structure, all 3d-like orbitals are fully occupied.
and 3dx2−y2 orbitals were doubly occupied at the same energy levels, and the remaining 3d-like subshells were unoccupied. In the C60Nibenzene case, all five 3d-like orbitals are fully occupied (Figure 5(b)). The number of unpaired electrons in each C60M benzene case could also be explained by adopting the hybridorbital electron occupation schemes for metal−ligand complexes proposed by Hoffmann.43 The six-membered ring of benzene bound to M could be considered as three ligands (L3), while the C60-edge connection could be considered as another ligand. Therefore, C60Mnbenzene, C60Febenzene, C60Nibenzene, and high-spin C60Crbenzene could be regarded as ML4 structures, which had three t2g and two other hybrid bonding orbitals (a1 and b2). Indeed, the d8 ML4 21062
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polarizations and tilting behavior of C60 besides the effect of strong C60−graphene dispersion interactions.
4. CONCLUSIONS In summary, the plane-wave DFT calculations show that the C60CrG, C60MnG, and C60FeG nanostructures in their most stable ground states are severely tilted, while C60NiG is less tilted. Only two C atoms of C60 are involved in the bonding with the metal atom in these nanostructures. However, C60 is well balanced in the previously reported nonpolarized C60CrG and the new C60TiG nanostructures. According to the calculated binding energies (>2 eV), all investigated nanostructures are stable at their most stable ground states. Moreover, it was also shown that attaching C60 to a metal−graphene surface is more energetically favored than decorating graphene with C60−metal complexes. The most stable spin states predicted by ADF and G09 calculations for C60Crbenzene, C60Mnbenzene, C60Febenzene, C60Tibenzene, and C60Nibenzene agreed very well with the magnetic moments predicted by plane-wave calculations. Moreover, the distortion of the C60M axis in Cr-, Mn-, and Fe-involving structures was also found by ADF and G09 calculations with various extents. The use of PBE/ TZP with large-electron−core pseudopotential with/without dispersion corrections in ADF predicted a smaller distortion of C60Cr on benzene (4.5−4.5°), while the use of PBE/ (SDD,6-31G*) with GD3BJ corrections in G09 suggested a larger tilting angle (30.5°). The PDOS of 3d orbitals obtained from plane-wave calculations and the molecular energy diagrams obtained from ADF calculations jointly explained the number of unpaired electrons, thus yielded predictions of magnetic behavior of the investigated nanostructures. A higher degree of C60 tilting was found in C60CrG, C60MnG, and C60FeG (larger magnetic moments), while a low tilting of C60 was found in nonmagnetic C60NiG. Therefore, besides the effect of dispersion interactions between C60 and graphene, there is a correlation between the 3d spin polarizations and the tilting orientation of C60 on MG. Indeed, such geometry distorting behavior encourages us to examine the possibility of using multiple metal atoms (rather than just one) to improve the binding between C60 and graphene.
Figure 7. Spin-polarized PDOS of (a) Cr (high-spin), (b) Cr (lowspin), (c) Mn, (d) Fe 3d, (e) Ti, and (f) Ni 3d orbitals in the C60 MG nanostructures. The Fermi level is positioned at 0. The electron occupations shown in the PDOS are in good accordance with the corresponding energy diagrams in Figures 3, 4, and 5.
spin C60MnG compared to that in quartet C60−Mn− benzene. Similarly to the previous spin density of benzene MnC60 given by ADF and G09 calculations, the plane-wave calculations predicted that both graphene and C60 gave antiferromagnetic contributions. In the Fe case, various degrees of spin polarizations in five 3d subshells were found in C60 FeG (summarized in Table 3). The spin-up states in 3dxz and Table 3. Spin Polarization Terms (μB) of the M 3d Orbitals, Graphene, and C60 in Four Investigated C60MG Structures Obtained from Plane-Wave Calculations Using σ = 0.002 Ry Cr (high spin) Cr (low spin) Mn Fe Ti Ni
3dz2
3dxz
3dyz
3dx2−y2
3dxy
G
0.93
0.68
0.59
0.78
0.87
0.24
−0.23
C60
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.92 0.29 0.00 0.00
0.71 0.75 0.00 0.00
0.56 0.67 0.00 0.00
0.74 0.24 0.00 0.00
0.64 0.26 0.00 0.00
−0.30 −0.19 0.00 0.00
−0.31 −0.13 0.00 0.00
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ASSOCIATED CONTENT
S Supporting Information *
ADF total bonding energies, G09 total energies, energy diagrams of benzene−M of different spin states, the XYZ coordinates of C60Crbenzene (quintet and singlet), C60 Mnbenzene, C60Febenzene, C60Tibenzene, C60 Nibenzene, and the crystal structures of C60CrG (highspin and low-spin), C60MnG, C60FeG, C60TiG, C60NiG are all provided in one document file. This material is available free of charge via the Internet at http:// pubs.acs.org.
3dyz are occupied to a large extent below the Fermi level, which causes high spin polarization terms (≥0.67 μB), whereas the other 3d orbitals are less polarized (≤0.3 μB). This trend is consistent with the diagram in Figure 4(b). The PDOS of Ti 3d (Figure 7(e)) also establishes good agreement with the previous energy diagram of C60Tibenzene (Figure 5(a)), because we could observe electron density of 3dxy and 3dx2−y2 below the Fermi level, while the other 3d subshells were almost empty. Figure 7(f) clearly demonstrates nonmagnetism, in which all five 3d subshells of Ni are doubly occupied. This is consistent with the predicted electron occupations from ADF calculations in Figure 5(b). Because of nonpolarization, the tilting angle of C60 in the Ni complex (15.1°) seemed less significant than the other cases (Cr, Mn, Fe), which had larger spin polarization terms in the 3d shells. At this point, it could be concluded that there was a correlation between metal 3d spin
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest. 21063
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ACKNOWLEDGMENTS The authors thank the High-Performance Computing Centre at Nanyang Technological University and the Institute for Materials Research at Tohoku University (HS2014-18-01) for computer resources. H.H. thanks a Nanyang Assistant Professorship and an AcRF Tier 1 Grant (RG3/13).
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