DSpace at VNU: Nanostructures of C-60-Metal-Graphene (Metal = Ti, Cr, Mn, Fe, or Ni): A Spin-Polarized Density Functional Theory Study

First-principles calculations suggested that graphene decorated with benzene could exhibit interesting magnetic properties, which might potentially lead to spin-valve materials.15 The me

Nanostructures of C 60 MetalGraphene (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 C60Mgraphene (C60MG) nanostructures (M = Ti, Cr, Mn, Fe, or

Ni) The calculated binding energies suggested that C60could be mounted on a metal−

graphene surface with good bonding stability The high-spin C60CrG nanostructure

was found to be more stable than the previously reported low-spin configuration Also,

C60Ti was found to stand symmetrically upright on the graphene surface, while in the

remaining four cases, the orientation of C60M in the C60MG 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 C60M in the tilted C60

MG 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 C60Mbenzene 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 wasfirst

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 clusters2,3and

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 C60and 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 C60

-attached 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).9Our recent calculations demonstrated

that such nanostructures are indeed capable of hosting metal

nanoparticles on C60, and that resultant complexes should act as active catalysts for chemical reactions (such as OO bond activation).9

In addition to its potential roles in catalysis, the significance

of C60in hydrogen storage has been appreciated The coating of

C60with 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 C60surface, 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 fromfirst-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 C60Lix, achieving the H2-storage capacity up to 5 wt % Even for such hydrogen storage

pubs.acs.org/JPCC

21057 | J Phys Chem C 2014, 118, 21057−21065

purposes, steadying C60on a graphene sheet or other

carbon-based 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

First-principles calculations suggested that graphene decorated with

benzene could exhibit interesting magnetic properties, which

might potentially lead to spin-valve materials.15 The

metal-bridging 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

inter-nanotube junction resistance.14,17 Assuming that C60 is the

ligand, we previously examined C60CrG, 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.,14C60CrG

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

MG 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 C60MG 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

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−Ernzer-hof23−25 (PBE) functional within the generalized gradient

approximation was employed to describe the

exchange-correlation 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

kinetic-energy cutoff of 45 Ry was used for the plane-wave expansion

The semiempirical dispersion correction scheme was used to

include the nonbonding interaction between C60 and

graphene.28,29 In each structural optimization, the initial

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:

EC Mbinding60 G EG EC M EC M G

where EMG, EC60, EG, and EC60Mdenote the total energies of an optimized metal-adsorbed graphene system, C60, pure graphene supercell containing 54 C atoms, and C60M, respectively;

EC60MG represents the total energy of the complex nanostructure ECbinding60MG expresses the binding of C60 on a metal−graphene surface, while ECbinding60 MGrepresents the binding

of an MC60 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 gas-phase models of C60Mbenzene, which were assumed to bear much resemblance to the C60MG nanostructures Previously, a study of first- and second-row transition-metal binding to benzene was reported by Bauschlicher et al.32The PBE exchange-correlation functional23−25 was employed to optimize the C60Mbenzene structures with constrained spin states The triple-ζ-polarized (TZP) Slater-type basis set33−35with 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.38,39In 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:

ECbindingM benzene EM benzene EC EC M benzene

(3) where EMbenzenedenotes 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 Crbenzene, Mnbenzene, and

Febenzene are septet,41

sextet, and triplet, respectively (see Table S1, Supporting Information (SI)) EC60 and EC60MG represent the total bonding energies of C60 and the C60−M− benzene complexes, respectively

3 RESULTS AND DISCUSSION

3.1 Structural Optimization of C60MG We previously reported an upright (symmetric) structure of

C60CrG (Figure 1(b)) with a low spin polarization, which was obtained from geometry optimization using an

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upright initial geometry.9As shown in Figure 1(a), we explored

a wider area of the potential energy surface for C60CrG,

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 tofix 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 C60participated in

the coordination bonding with Cr Moreover, the C60Cr axis

was highly tilted as can be seen from a tilt angle, which was

defined as the angle between the bisector of the two MC

vectors and the approximate normal vector of the graphene

plane

In the equilibrium structure of C60MnG 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

CrG (see Figure 2(a)) As for the C60FeG

nanostruc-ture, in its most stable form, the equilibrium geometry was

similar to that of the high-spin C60CrG and C60MnG

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 CrC/MnC bonds have nearly the same z

coordinate, while the plane defined by two FeC 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 FeC linkages To describe the distortion of

C60 in C60FeG, we again define a tilt angle as shown in Figure 2(b) The behavior of C60on NiG, as shown in Figure 2(d), was somewhat similar to that in the case of C60FeG, but C60 seemed to be less tilted on Ni According to our equilibrium geometries obtained from plane-wave DFT calculations, in the most stable C60CrG, C60MnG,

C60FeG, and C60NiG nanostructures, the C60M 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 C60TiG structure (Figure 2(c)), the orientation of C60was symmetrically upright like the structure

of low-spin C60CrG

3.2 Spin-Polarized Electronic Structures and Bonding Analyses In all cases, the binding energies of the C60MG structures given by eq 1 are positive, indicating good stabilization and strong chemisorption (rather than physisorp-tion with small binding energies) of C60 on the metal− graphene complex The calculated binding energies of C60

CrG, C60MnG, and C60FeG and the correspond-ing magnetic moments are summarized in Table 1 Due to the fact that ECbinding60MG is always greater than the corresponding

ECbinding60M−G, we can state that attaching C60on a metal−graphene surface should be more favorable than attaching a C60−metal complex on graphene Even though C60M is highly tilted in high-spin C60MG nanostructures and the metal atoms form coordination bonds with only two C atoms, allfive metals turn out to be good bridging atoms that steady C60 on the graphene monolayer effectively The binding energy of the newly observed C60CrG nanostructure (2.95 eV) is indeed

Figure 1 (a) Energy profiles for the dissociation of C 60 from CrG,

obtained from energy scan calculations The CrC 60 distance is the

distance in the z direction between Cr and six lowest C atoms (b) The

previously obtained upright C 60 CrG structure 9 (c) The most

stable C 60 CrG structure, in which the C 60 tilt angle is defined as

the angle between the bisector of two CrC 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) C60MnG, (b) C 60 FeG, (c) C 60  TiG, and (d) C 60 NiG structures C 60 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 MC bonds (b⃗) and vector n ⃗ connecting the center of mass of six nearest C atoms on graphene to the metal atom.

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0.59 eV larger than that of the low-spin structure reported in a

previous study.9In 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

MG in plane-wave calculations, we performed structural

optimizations for the C60Mbenzene 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 C60Crbenzene, C60

Mnbenzene, C60Febenzene, C60Tibenzene, and

C60Nibenzene were quintet, quartet, triplet, singlet, and

singlet, respectively By contrast, the PBE/TZP calculations

with the dispersion effect using ADF predicted that singlet

C60Crbenzene was more stable than the quintet structure

(see the summary of binding energies of C60Mbenzene

structures in Table 1) These results indicate that the

singlet-quintet 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 C60Crbenzene (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

Crbenzene (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 C60Crbenzene was raised by 0.15 eV; however, the

empirical corrections increased the binding energy of singlet

C60Crbenzene by 0.20 eV, thus making it the ground state

instead With the inclusion of dispersion effects in ADF, the

binding energies of C60Mnbenzene, C60Febenzene,

C60Tibenzene, and C60Nibenzene 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 C60via 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

There were small geometric differences between the different models of the Ni and high-spin Cr complex Whereas the QE calculation predicted that in C60CrG, C60Cr was highly tilted with an angle of 36.3°, it was observed from the ADF-optimized quintet C60Crbenzene structure that the distortion of C60Cr 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 benzeneNi, QE calculations indicated that C60was tilted on NiG 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 C60MG

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* with-out 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 C60Cr 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 C60Cr 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 C60Crbenzene; 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 C60Mnbenzene, 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,

Table 1 Binding Energies and Magnetic Moments (MT) of the C60MG Structures Given by Plane-Wave Calculations, Binding Energies and Multiplicity of C60MBenzene Given by PBE/TZP with and without Dispersion Corrections in ADF and PBE/(SDD,6-31G*) with Dispersion Corrections in G09

M

binding energy (eV)

MT( μB/cell) multiplicity

ECbinding60−MG ECbinding60M−G ADF (without dispersion) ADF (with dispersion) G09

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21060

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

C60Mnbenzene was similar to QE-calculated C60FeG

in Figure 2(b); thus, there was a difference in the orientation of

C60between C60Mnbenzene and C60MnG Again, we

noted that the relative energies between triplet ground state

and excited singlet state of C60Febenzene 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 C60Febenzene was predicted to vary

from 16.8° to 23.3° (see Table S4, SI) Using small C60M

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 C60M was

changed, indicating that the C60MG 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

NiG (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 C60Tibenzene (singlet), C60 was seen to

stand symmetrically upright on Ti, similar to the singlet C60

Crbenzene case, which was consistent with the structure of

C60TiG 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

Mbenzene complex in all cases, indicating that M−benzene

donated electrons to C60 In the most stable form, C60Cr

benzene had a spin multiplicity of quintet (four unpaired

electrons) The singlet C60Crbenzene 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 CrC60 moiety The orbital

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 CrC bonds had nearly the same z coordinate in C60CrG (Figure 1(c)) However, the other d orbitals are singly occupied, and thus a hexahapto coordination of C60will result in large repulsion between these singly occupied d orbitals (especially 3dxz and 3dz2) and occupied orbitals of C60 To alleviate this repulsion, C60changes 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 (4.06μB/cell as shown in Table 1)

In the low-spin C60Crbenzene (Figure 3(b)), both the 3dxz and 3dyz orbitals are unoccupied, while 3dz2, 3dxy, and 3dx2

−y 2subshells 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 C60Crbenzene 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 C60Mnbenzene and C60Febenzene were predicted as quartet (S=3/2) and triplet (S = 1), respectively Quartet C60Mnbenzene had three unpaired electrons that occupied the 3dxy, 3dz2, and 3dyz, while the 3dxz and 3dx2

−y 2 orbitals were doubly occupied, as shown in the energy diagram in Figure 4(a) In the case of

C60Febenzene, the spin state was triplet, and both 3dxz

and 3dyz were singly occupied (Figure 4(b)) The single

Table 2 Mulliken Charges and Spin Densities (in Parentheses) of Benzene, M, and C60Given by PBE/TZP (ADF) and PBE/ (SDD,6-31G*) with GD3BJ Correction (G09) for Four BenzeneMC60Complexes

PBE/TZP without dispersion corrections (ADF) PBE/(SDD,6-31G *) with dispersion corrections (G09)

benzene CrC 60 (quintet) 0.33 (0.19) 0.51 (4.18) −0.84 (−0.37) 0.31 (0.14) 0.30 (4.15) −0.61 (−0.29) benzene CrC 60 (singlet) 0.30 (0.00) 0.02 (0.00) −0.32 (0.00) 0.48 (0.00) −0.33 (0.00) −0.15 (0.00) benzene MnC 60 (quartet) 0.21 ( −0.17) 0.38 (3.45) −0.59 (−0.28) 0.29 ( −0.19) 0.21 (3.43) −0.51 (−0.24) benzeneFeC 60 (triplet) 0.21 (−0.14) 0.24 (2.21) −0.45 (−0.07) 0.38 (−0.17) −0.03 (2.23) −0.35 (−0.06) benzene Ti−C 60 (singlet) 0.19 (0.00) 0.44 (0.00) −0.63 (0.00) 0.28 (0.00) 0.20 (0.00) −0.48 (0.00) benzene Ni−C 60 (singlet) 0.25 (0.00) 0.16 (0.00) −0.41 (0.00) 0.47 (0.00) −0.14 (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) C 60 Crbenzene structures given by PBE/TZP without dispersion corrections in ADF In the quintet structure, 3d yz is doubly occupied, while the other 3d shells are singly occupied In the singlet state, 3d z2, 3d xy , and 3d x2−y 2 are doubly occupied, whereas 3d xz and 3d yz are unoccupied.

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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 C60Fe axis

Both C60Tibenzene and C60Nibenzene were

observed to establish singlet multiplicities (no unpaired

electrons) even though the C60M 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 C60Tibenzene (Figure 5(a)), the 3dxy

and 3dx2

−y 2 orbitals were doubly occupied at the same energy

levels, and the remaining 3d-like subshells were unoccupied In

the C60Nibenzene case, all five 3d-like orbitals are fully

occupied (Figure 5(b))

The number of unpaired electrons in each C60M

benzene case could also be explained by adopting the

hybrid-orbital electron occupation schemes for metal−ligand

com-plexes 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, C60Mnbenzene, C60Febenzene,

C60Nibenzene, and high-spin C60Crbenzene could

be regarded as ML4 structures, which had three t2g and two

other hybrid bonding orbitals (a1and b2) Indeed, the d8ML4

(i.e., C60Febenzene) 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

electrons would be withdrawn from t2g However, for Ni (d10), two additional electrons should be added to complete the a1 and b2orbitals and a close-shell configuration was obtained As

a result, we observed the most stable spin states of quintet, quartet, and singlet for C60Crbenzene, C60Mn benzene, C60Nibenzene, respectively (also illustrated in Figure 6) C60Tibenzene, 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 C60MnG exhibited a magnetic moment of 3.11μB/cell, whereas C60FeG gave a magnetic moment of 2.00μB/cell The magnetic moments of high-spin and low-spin

C60CrG nanostructures were 4.06 and 0.00 μB/cell, respectively Also, the total magnetic moments in both C60

TiG and C60NiG were found to vanish Those magnetic quantities are consistent with the spin states of C60M 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 C60shown 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 C60CrG 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 low-spin C60CrG 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

−y 2and the nearly empty 3dxzand 3dyzorbitals as shown in Figure 7(b)

In C60MnG (MT = 3.11 μB/cell), high positive spin-polarization terms were found in all 3d subshells (see Figure 7(c)) Unlike atomic-orbital calculations in ADF, the plane-wave 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 MnC60in

high-Figure 4 Energy diagrams of the 3d shells in (a) quartet C60Mn

benzene and (b) triplet C60Febenzene given by PBE/TZP

without dispersion corrections in ADF In the Mn complex, 3dxzand

3dx2

−y 2 are fully occupied, while the other 3d orbitals are singly

occupied In the Fe structure, the single occupations of 3dxzand 3dyz

result in the distortion of C60.

Figure 5 Energy diagrams of the 3d shells in (a) singlet C60Ti

benzene and (b) singlet C60Nibenzene given by PBE/TZP

without dispersion corrections in ADF In the Ti complex, 3dxyand

3dx2

−y 2 are fully occupied, while the other 3d orbitals are unoccupied.

In the Ni structure, all 3d-like orbitals are fully occupied.

Figure 6 Electron occupations of the hybrid orbitals in the ML4 structures (quintet C60Crbenzene, C 60 Mnbenzene, C 60  Febenzene, and C 60 Nibenzene).

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spin C60MnG compared to that in quartet C60−Mn−

benzene Similarly to the previous spin density of benzene

MnC60given 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 infive 3d subshells were found in C60

FeG (summarized in Table 3) The spin-up states in 3dxzand

3dyzare 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 C60Tibenzene (Figure 5(a)),

because we could observe electron density of 3dxy and 3dx2

−y 2

below the Fermi level, while the other 3d subshells were almost

empty Figure 7(f) clearly demonstrates nonmagnetism, in

which allfive 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

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

C60CrG, C60MnG, and C60FeG nanostructures

in their most stable ground states are severely tilted, while

C60NiG is less tilted Only two C atoms of C60 are involved in the bonding with the metal atom in these nanostructures However, C60is well balanced in the previously reported nonpolarized C60CrG and the new C60TiG 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

C60to 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

C60Crbenzene, C60Mnbenzene, C60Febenzene,

C60Tibenzene, and C60Nibenzene agreed very well with the magnetic moments predicted by plane-wave calculations Moreover, the distortion of the C60M 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

C60Cr 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 C60tilting was found in C60CrG, C60MnG, and C60FeG (larger magnetic moments), while a low tilting of C60 was found in nonmagnetic C60NiG 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 MG 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

*S Supporting Information

ADF total bonding energies, G09 total energies, energy diagrams of benzene−M of different spin states, the XYZ coordinates of C60Crbenzene (quintet and singlet), C60

Mnbenzene, C60Febenzene, C60Tibenzene, C60

Nibenzene, and the crystal structures of C60CrG (high-spin and low-(high-spin), C60MnG, C60FeG, C60TiG,

C60NiG are all provided in one document file This material is available free of charge via the Internet at http:// pubs.acs.org

Corresponding Authors

*E-mail: hung.m.le@hotmail.com

*E-mail: hirao@ntu.edu.sg

Notes

The authors declare no competingfinancial interest

Figure 7 Spin-polarized PDOS of (a) Cr (high-spin), (b) Cr

(low-spin), (c) Mn, (d) Fe 3d, (e) Ti, and (f) Ni 3d orbitals in the C 60 

MG 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.

Table 3 Spin Polarization Terms (μB) of the M 3d Orbitals,

Graphene, and C60in Four Investigated C60MG

Structures Obtained from Plane-Wave Calculations Usingσ

= 0.002 Ry

3dz2 3dxz 3dyz 3dx2

−y 2 3dxy G C60 Cr

(high spin)

0.93 0.68 0.59 0.78 0.87 0.24 −0.23

Cr

(low spin)

0.00 0.00 0.00 0.00 0.00 0.00 0.00

Mn 0.92 0.71 0.56 0.74 0.64 −0.30 −0.31

Fe 0.29 0.75 0.67 0.24 0.26 −0.19 −0.13

Ti 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Ni 0.00 0.00 0.00 0.00 0.00 0.00 0.00

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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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