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

Article
pubs.acs.org/JPCC

Nanostructures of C60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 C60 could 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 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 OO 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 C60Lix, achieving the H2-storage
capacity up to 5 wt %. Even for such hydrogen storage
Received: August 5, 2014
Published: August 18, 2014
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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 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.,14 C60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.

ECbinding
= EMG + EC60 − EC60MG
60MG

(1)

ECbinding
= EG + EC60M − EC60MG
60MG

(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 C60M, respectively;
EC60MG represents the total energy of the complex
nanostructure. ECbinding
expresses the binding of C60 on a
60MG
metal−graphene surface, while Ebinding
C60MG represents 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 gasphase 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.32 The
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
set33−35 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
= EMbenzene + EC60 − EC60Mbenzene
60Mbenzene
(3)

where EMbenzene 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 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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Figure 1. (a) Energy profiles for the dissociation of C60 from CrG,
obtained from energy scan calculations. The CrC60 distance is the
distance in the z direction between Cr and six lowest C atoms. (b) The
previously obtained upright C60CrG structure.9 (c) The most
stable C60CrG structure, in which the C60 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) C60FeG, (c) C60
TiG, and (d) C60NiG 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 MC
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 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 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 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 nanostructure, 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 C60 on 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 C60 was 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 physisorption 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 corresponding magnetic moments are summarized in Table 1. Due to the
fact that ECbinding

is always greater than the corresponding
60MG
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 C60M is highly tilted in
high-spin C60MG 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 C60CrG nanostructure (2.95 eV) is indeed
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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
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 C60CrG, C60Cr was highly
tilted with an angle of 36.3°, it was observed from the ADFoptimized 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 C60 was
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* 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 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,

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
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 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 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 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.
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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 BenzeneMC60 Complexes
PBE/TZP without dispersion corrections (ADF)
benzene
benzeneCrC60 (quintet)

benzeneCrC60 (singlet)
benzeneMnC60 (quartet)
benzeneFeC60 (triplet)
benzeneTi−C60 (singlet)
benzeneNi−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
C60Mnbenzene was similar to QE-calculated C60FeG
in Figure 2(b); thus, there was a difference in the orientation of
C60 between 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

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) C60Crbenzene 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 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 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 C60Crbenzene (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 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−y2 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
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(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

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, 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 C60Crbenzene, C60Mnbenzene, C60
Febenzene, and C60Nibenzene).

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

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 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
3.11 μB/cell, whereas C60FeG gave a magnetic moment of
2.00 μB/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 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 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 lowspin 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−y2 and the nearly empty 3dxz and
3dyz orbitals as shown in Figure 7(b).
In C60MnG (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 MnC60 in high-

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, 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 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 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, 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 (a1 and b2). Indeed, the d8 ML4
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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
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, C60 is 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
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
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 C60 tilting 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.

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
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.

spin C60MnG compared to that in quartet C60−Mn−
benzene. Similarly to the previous spin density of benzene
MnC60 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
FeG (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 C60MG
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

■

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 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 (highspin and low-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.

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 C60Tibenzene (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

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail:
*E-mail:
Notes

The authors declare no competing financial interest.
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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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