DSpace at VNU: First-principles modeling of C-60-Cr-graphene nanostructures for supporting metal clusters

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Nguyen-Manh, Phys Chem Chem Phys., 2013, DOI: 10.1039/C3CP53529K.

Physical Chemistry Chemical

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Supporting Metal Clusters

Received (in XXX, XXX) Xth XXXXXXXXX 200X, Accepted Xth XXXXXXXXX 200X

DOI: 10.1039/b000000x

5

We present a first-principles modeling study of a new class of nanomaterials in which

buckminsterfullerene (C60) and graphene (G) are bridged by Cr via coordination bonds Two

nanostructures denoted as G(C54)–Cr–C60 and G(C150)–Cr–C60 are investigated, which share many

similarities in the configuration geometries but differ in the distribution densities of Cr–C60 on the

graphene surface The binding energies between C60 and the rest of the system in these complexes are

10

calculated to be 2.59 and 2.10 eV, respectively, indicative of their good structural stability Additional

spin-polarized calculations indicate that G(C54)–Cr–C60 is weakly ferromagnetic, which is chiefly due to

the contribution from the 3d shell of Cr We then investigate three model complexes of C60–Cr–G(C54)

and a metal cluster (Ni4, Pd4, or Pt4) The binding energies of these three nanostructures are significantly

large (3.57, 2.38, and 4.35 eV, respectively) Electron density analysis along the Ni–C, Pd–C, and Pt–C

15

bonds consistently affirms that the Pt–C bond is the strongest while the Pd–C bond is the weakest The

strong Pt–C bond is attributed to the effective overlap of 5 dz2 (Pt) and 2p z (C) orbitals Partial density of

states analysis indicates that Ni4 and Pd4 substantially contribute to the strong ferromagnetism of the

complexes, whereas Pt4 is observed to be non-magnetic even when the spin-orbit coupling is taken into

account H2 dissociation on the Ni4 complex is also examined, and the estimated reaction barrier is

20

relatively low (0.76 eV)

I Introduction

Graphene is a newly discovered two-dimensional material

composed of sp2-hybridized carbon It has been proved

experimentally that a graphene nanostructure (i.e., at the

25

nanometer scale) is extremely stable and exhibits

superconductivity.1 Importantly, this two-dimensional material is

considered as a zero-gap semiconductor, despite being entirely

made of a non-metal element.2 It has been demonstrated that the

combination of graphene and metal has the potential to find

30

useful applications in electronic and spintronic devices.3, 4 As

such, the interactions between graphene and metals have

continuously attracted a great deal of attention in the research

community, and the interesting features of graphene have been

widely explored both experimentally and theoretically.5-15

35

On one hand, many experimental efforts have been made to

explore and exploit the interactions between graphene and metal

nanoparticles/surfaces There is in fact abundant interest in the

roles of metals such as Ni,5 Au, Fe, and Cr,6-8 and thus various

experimental techniques have been applied to examine how these

40

metals participate in interlayer interactions Interestingly enough,

there is a gas-sensing application of a metal-graphene structure

when the surface of graphene is decorated with Ag

nanoparticles.9

On the other hand, the establishment of high-performance

45

computing systems and the development of density functional theory (DFT) 16, 17 have enabled theoretical and computational investigations of larger nanomaterials, and such first-principles studies have made substantial contributions to the research area

of graphene-metal interactions By employing DFT, Nakada and

50

Ishii systematically investigated the atomic decorations of graphene with most of the elements on the periodic table and reported the favored binding site of each element as well as its corresponding binding energy.11 It was revealed that a specific metal element had a tendency to bind preferentially to either the

55

hexagonal (H), top (T), or bridge (B) site, as illustrated in Fig 1

Particularly, Cr, the 3d transition metal of interest in this work, preferentially binds to the H site of graphene with high chemical stability In another study, Giovannetti et al examined the interactions between graphene and noble metals such as Cu, Au,

60

Ag, and Pt, and suggested that there was a shift of 0.5 eV in the graphene Fermi level upon the formation of weak bonding interactions.12 Maassen et al performed a spintronic investigation

of graphene–Co(111) and graphene–Ni(111) interactions using first-principles modeling, and calculated the spin filtering

65

efficiencies of those two models to be greater than 80 and 60%, respectively.4 An intercalation structure and vibrational modes of graphene–alkali earth metals–graphene were also investigated.13 The adsorption of

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DOI: 10.1039/C3CP53529K

2 | Journal Name, [year], [vol], 00–00 This journal is © The Royal Society of Chemistry [year]

Pt4 on graphene and boron-substituted graphene was presented by

Wu and co-worker.15 Recently, Bui et al.14 have performed an

investigation of graphene–Cr–graphene nanostructures using the

local-spin-density approximation (LSDA)18 of DFT, and

discussed the interplays between stability and ferromagnetism

5

based on electronic structure data

Buckyball buckminsterfullerene (C60) is made of carbon atoms

and has a spherical shape This interesting molecular structure

was first discovered by Kroto and co-workers in 1985.19, 20 There

have also been proposals as to the synthesis of

10

buckminsterfullerene-based materials for catalytic purposes.21-24

Duffe et al.25 decorated C60 monolayers with Ag clusters, and

demonstrated that the resultant structures were stable and worked

very efficiently as catalysts when they were supported by gold

sink or graphite With that result in mind, in this study, we

15

suggest and examine a different way to steady C60 on a surface so

that it can be employed to carry metal clusters In fact, there has been experimental work in which graphene was utilized as a ligand to carry complex structures of Cr–benzene.26 In addition, the successful attachment of C60 to bis(benzene) chromium27 also

20

demonstrates the possibility of connecting C60 and graphene using a bridging transition-metal atom (Cr) These successful experimental efforts have highly motivated us to design a complex of graphene and C60 More specifically, we employ DFT calculations to investigate a model in which buckminsterfullerene

25

and graphene are bridged by a Cr atom via coordination bonds

Then, interplays between structural stability and magnetic properties are deliberately discussed on the basis of electronic structure data

In addition, such a nanostructure may be considered as an

30

excellent candidate for supporting metal nanoparticles and may

be employed in the future design and development of nanocatalysts To examine this feature more realistically, we test the possibility of decorating the steadied buckminsterfullerene complex with a small metal cluster (of Ni, Pd, or Pt) and

35

investigate the energetic stability as well as its electronic and magnetic properties

II Buckminsterfullerene –Cr–graphene models

According to the theoretical results obtained from our previous study,14 Cr is expected to bind to the H site (indicated in Fig 1)

40

of a honeycomb hexagonal unit on graphene as well as buckminsterfullerene In addition, our previous study of graphene–Cr–graphene structures also showed that the distribution density of an attached structure (i.e Cr–C60 in this case) on the graphene surface has a significant impact on the

45

stability, magnetism, and active surface area of buckminsterfullerene The curved surface of C60 should be beneficial in improving the reacting efficiency of attached metal nanoparticles that are to act as catalysts in chemical reactions, and its attachment on graphene would enhance the recoverability of

50

the catalysts

Two graphene–Cr–C60 models are investigated in this study In the first model, a periodic sheet of graphene containing 54 C atoms per unit cell is decorated with Cr–C60 (Fig 2(a)) In the second model, we attempt to reduce the distribution density of

55

Cr–C60 by extending the area of the periodic graphene sheet so that one Cr–C60 complex exists per 150 C atoms (Fig 2(b)) For convenience, let us denote these two investigated nanostructures

as G(C54)–Cr–C60 and G(C150)–Cr–C60, respectively In both cases, the investigated systems are two-dimensional slabs, and for

60

the vacuum treatment in the z direction, we employ a unit cell with the c lattice parameter of 30 Bohr (15.86 Å) More specifically, the thickness of vacuum layer in G(C54)–Cr–C60 and G(C150)–Cr–C60 is approximately 6.34 Å

III Computational details

65

All calculations are executed using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional28, 29 as implemented in the Quantum Espresso package.30 The employed ultrasoft

pseudopotentials include the 2s, 2p valence wavefunctions for C and the 3s, 3p, 4s, 3d, and 4p valence wavefunctions for Cr.31, 32

70

The generalized gradient approximation with spin polarization is

Fig 1 Three possible adsorption sites of a metal atom on a

honeycomb unit in graphene

Fig 2 (a) The theoretical model of G(C54)–Cr–C60, where C60 is

attached on the graphene monolayer surface via coordination

bonds with Cr In this unit cell, the graphene layer contains 54 C

atoms (b) The illustrative model of G(C150)–Cr–C60, which

contains C60 attached on Cr–graphene In this unit cell, the

graphene layer contains 150 C atoms

This journal is © The Royal Society of Chemistry [year] Journal Name, [year], [vol], 00–00 | 3

employed to investigate the metal-aromatic ring (from

buckminsterfullerene and graphene) interactions The k-point

mesh for most calculations is selected as (6 × 6 × 1), which

enables computations with reasonable computational cost

However, for the studies of G(C150)–Cr–C60 and a chemical

5

reaction involving the G(C54)–Cr–C60 complex, we perform

calculations at the Γ point because the computational demand is

extremely high The kinetic-energy cutoff for plane-wave

expansion has a significant impact on energy convergence and

computing time; in this study, we employ 45 Rydberg for all

10

calculations The semi-empirical correction option for van der

Waals interactions33, 34 is also activated in our calculations in

order to improve the description of the interaction between C60

and graphene

Since the investigated systems have two-dimensional

15

extension, we employ a 2D-like unit cell for the computational

treatment That is, the structures are thought of as periodic in the

x and y directions, while the z direction is assumed to be isolated

with a vacuum layer As mentioned earlier, the c lattice parameter

is initially chosen as 30 Bohr (15.86 Å) The

Broyden-Fletcher-20

Goldfarb-Shanno35 (BFGS) algorithm is employed to optimize

the equilibrium structures with an energy-convergence criterion

of 10-5 eV/cell and a gradient-convergence criterion of 10-4

eV/Å/cell In order to optimize structures efficiently, we impose a

constraint to perform constant-volume optimizations (the fixed

25

volume is sufficiently large), but three unit-cell axes are fully

adjusted to reduce the energy

In the subsequent investigation of decorating Ni, Pd, and Pt

nanoparticles, the structural optimizations are executed within a

fixed unit cell The ultrasoft pseudopotentials are employed

30

which describe the valence wavefunctions of (4s, 4p, 3d), (5s, 5p,

4d), and (6s, 6p, 5d) for Ni, Pd, and Pt, respectively The c lattice

parameter in these cases is extended to 40 Bohr (21.17 Å)

The PBE-derived results for G(C54)–Cr–C60 are validated by

performing additional PW91 calculations.36, 37 Upon the

35

availability of reliable ultrasoft potentials, we later validate the

calculation on a complex between G(C54)–Cr–C60 and a Pt4

cluster (validation of Ni and Pd complexes is excluded because of

unavailability of reliable pseudopotentials for PW91 calculations)

IV Results and discussion

40

IV.1 The G(C54)–Cr–C60 nanostructure

In this high-densed model, there are 54 C atoms on the graphene

sheet per Cr–C60 The geometry optimization is performed on this

model using the PBE functional In order to obtain a sufficiently

relaxed structure, we set the energy conversion criterion as 10-6

45

eV and the gradient conversion criterion as 10-4 eV/Å in all three

dimensions In addition, the unit cell is simultaneously optimized

during the relaxation of atoms It is noticed from the optimized

structure that those six C atoms coordinating to Cr are slightly

pushed down from the original graphene surface In the

50

equilibrium structure, we observe that the Cr–C(graphene) bond has a length of 2.16 Å In a previous study of the graphene–Cr–

graphene nanostructure,14 one of the most stable structures (namely 1-12 GMG) had an equilibrium Cr–C bond length of 2.18 Å, which is slightly longer than the Cr–C(graphene) bond in

55

the current case The Cr–C(C60) bond has a distance of 2.20 Å, which is slightly longer than the Cr–C(graphene) distance The Cr–graphene layer distance is found to be 1.60 Å, while the Cr–

C60 distance is 1.67 Å

The structural stability of a particular nanostructure is

60

evaluated by its corresponding binding energy:

structure C

Cr graphene

60

(1)

where E graphene-Cr and

60

C

E represent the total energy of the graphene–Cr complex and C60 in the unit cell, respectively, while

E structure is the total energy of the equilibrium nanostructure In a

65

previous study,11 the graphene–Cr complex was shown to be stable; therefore, we employ the total energy of such a complex in binding energy calculations instead of using the total energy of graphene and Cr separately A positive binding energy indicates that the nanostructure of concern is energetically stable, whereas

70

a negative binding energy is an indication of structural instability

By adopting equation (1), the binding energy of G(C54)–Cr–

C60 is calculated as 2.59 eV, which indicates that it is an energetically stable nanostructure The binding energies of the previously-investigated graphene–Cr–graphene nanostructures

75

(namely 1-12 GMG) were shown to be less than 2.09 eV.14 Hence, the current case study of G(C54)–Cr–C60 suggests that steadying C60 on the graphene–Cr complex provides enhanced stability (by 0.5 eV) compared to the cases of graphene–Cr–

graphene intercalated structures The important distances

80

discussed above and binding energy of G(C54)–Cr–C60 (as well as G(C150)–Cr–C60) are summarized in Table I along with the validation data obtained from PW91 calculations for G(C54)–Cr–

C60 The difference in geometry configuration predicted by PBE and PW91 are negligible The binding energy predicted by PW91

85

is lower than the previous calculation by 16.2%; however, its magnitude is still relatively high, which indicates the structural stability of the complex

Besides analyzing the theoretical stability, we also perform electronic structure analysis to characterize the spin polarization

90

and magnetic behavior of the nanostructure From the DFT calculations of G(C54)–Cr–C60, two useful quantities, i.e., the total and absolute magnetizations, can be derived from

density-of-state (DOS) analysis For convenience, we denote them as M T

and M A , respectively The mathematical formulas of M T and M A

95

are expressed as follows:

= n n d r

= n n d r

In the above equations, n up and n down respectively describe the

Table I The important interatomic distances and binding energies for G(C54)–Cr–C60 and G(C150)–Cr–C60

Cr–C(graphene) bond (Å)

Cr–C(C60) bond (Å)

Cr–graphene separation (Å)

Cr–C60

separation (Å)

Binding energy (eV) G(C54)–Cr–C60 (PBE)

G(C54)–Cr–C60 (PW91)

2.16 2.16

2.20 2.21

1.60 1.61

1.67 1.69

2.59 2.17 G(C150)–Cr–C60 (PBE) 2.15 2.21 1.61 1.68 2.10

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DOI: 10.1039/C3CP53529K

4 | Journal Name, [year], [vol], 00–00 This journal is © The Royal Society of Chemistry [year]

numbers of spin-up and spin-down states at a certain energy

level For a particular orbital, a positive spin polarization

increases the total magnetic moment and thereby contributes to

ferromagnetism Conversely, a negative spin polarization

contributes to anti-ferromagnetism Therefore, M T is always less

5

than or equal to M A When the total and absolute magnetizations

are similar, all polarization terms are positive, and we can

conclude that all orbitals contribute to ferromagnetism

From the orbital analysis of PBE data, the total magnetization

of G(C54)–Cr–C60 is estimated as 0.55 µB/cell, which indicates

10

ferromagnetic behavior, while the absolute magnetization is 1.09

µB/cell When such magnetic moments are compared to the

magnetic moments of graphene–Cr–graphene intercalated

nanostructures examined in a previous study,14 the

ferromagnetism exhibited by G(C54)–Cr–C60 can be considered

15

fairly weak The absolute magnetization is almost twice as large

as the total magnetic moment due to the significant effect of

anti-ferromagnetic moment, which helps to reduce the overall

ferromagnetism of the nanostructure To have a more pictorial

understanding of the origin of magnetism exhibited by this

20

structure, we analyze the total DOS and partial DOS (PDOS) of

G(C54)–Cr–C60

The bonding interaction between six-membered carbon rings

(from either graphene or C60) and a transition-metal element is

dominantly formed by coordination bonds, in which the 2p z

25

orbitals from C have a tendency to donate electrons toward an

unfilled 3d orbital of the transition metal As a result, the C 2p z

and metal 3d orbitals would play important roles in the bond

formation and spin polarization In fact, Cr contributes strongly to

the ferromagnetic moment, while both graphene and C60

30

contribute to the anti-ferromagnetic moment Overall, when we sum up all magnetic terms, we are left with a weak ferromagnetic moment as a result of cancellation of the two opposing effects In addition, the electron distribution of Cr around the Fermi level (located at 0) indicates conducting behavior, suggesting that the

35

nanostructure is metallic When we further analyze the 3d shell of

Cr and 2p z orbitals of C (from graphene and C60), it is shown that

all 3d spins align ferromagnetically (Fig 3 and Table II) In

particular, we observe that the 3 2

z

d orbital of Cr exhibits the

largest ferromagnetic contribution The 2p z subshells of C, which

40

mainly donate electrons toward the 3d orbitals of Cr to form

coordination bonds, align anti-ferromagnetically with respect to

the 3d shell of metal (Table II) Indeed, its conducting behavior

can be examined in this plot, where the 3d z2 contribution to the spin-down state is dominant at the Fermi energy, demonstrating

45

metallic behavior of this nanostructure The magnetic contributions of individual subshells from PW91 are found to agree excellently with the PBE data, as shown in Table II

In this first structure, we have successfully attached C60 on top

of Cr in the graphene–Cr complex, and the resulting

50

nanostructure is seen to be very stable (when compared with the previously studied graphene–Cr–graphene intercalation nanostructures14) Also, from the spin-polarized analysis, it is found that G(C54)–Cr–C60 exhibits a weak ferromagnetic moment In the experimental synthesis of such nanostructures,

55

another possibility should be considered that C60 can attach directly to the graphene surface via van der Waals interaction,38 while Cr may accidentally bind to C60 without establishing any coordination interactions with graphene Therefore, a testing case

is performed, in which we consider a direct decoration of

60

graphene with the C60–Cr complex (also illustrated in Fig 2(a))

At convergence of geometry optimization, Cr does not occupy the

H site on C60; in fact, it prefers to bind to the B site of two C The honeycomb unit in C60 is not superposed with that in graphene like the previous case (G(C54)–Cr–C60) According to our binding

65

energy calculation, the new structure (G(C54)–C60–Cr) is stable with a positive binding energy of 1.40 eV; however, this is still lower than the binding energy of G(C54)–Cr–C60 by 54%

Interestingly, a strong ferromagnetic moment is observed (4.54

µB/cell) In this paper, we do not perform further analysis of

70

magnetism for this less stable structure

The distribution density of the Cr–C60 group on graphene may vary depending upon the experimental conditions; therefore, we believe that it is beneficial to explore the configurational and structural stability of a less-densed G–Cr–C60 nanostructure

75

IV.2 The G(C150)–Cr–C60 nanostructure

In this low-densed G–Cr–C60 nanostructure, the graphene sheet has one Cr–C60 unit per 150 C atoms in the two-dimensional unit cell, which means that the distribution density of the Cr–C60

Table II Main orbital contributions (µB) to total magnetization in G(C54)–Cr–C60

PBE

PW91

-0.065 -0.072

-0.130 -0.122

0.750 0.748

2s 2p z 2p x

(2p y) 2s 2p z

2p x

(2p y)

s + p

orbitals 3d z2 3d x2−y2

(3d xy)

3d zx

(3d zy) PBE 0.002 -0.075 0.004 -0.048 -0.068 -0.029 0.008 0.440 0.115 0.036

PW91 0.001 -0.080 0.004 -0.004 -0.068 -0.027 0.008 0.426 0.120 0.041

Fig 3 Spin-polarized PDOS of the G(C150)–Cr–C60

nanostructure and PDOS of Cr 3d and C60 2p z subshells The

Fermi level is located at 0 It can be obviously seen that the

ferromagnetism is mainly caused by the spin polarization of Cr

This journal is © The Royal Society of Chemistry [year] Journal Name, [year], [vol], 00–00 | 5

cluster is lower than that in the former case The C60–Cr cluster is

similarly attached to the central H site of the graphene monolayer

(Fig 1) The geometry optimization of G(C150)–Cr–C60, however,

is computationally too demanding Therefore, to achieve

convergence within a reasonable computational time, we lower

5

the energy and gradient convergence thresholds to 10-5 eV and

10-4 eV/Å, respectively

In the converged geometry, the average equilibrium Cr–

C(graphene) bond length is 2.15 Å, which is almost the same as that in G(C54)–Cr–C60 The bond length between Cr and C in C60

10

(2.21 Å) is also observed to be very similar to that of the previous nanostructure (2.20 Å) When we only consider the z direction, the Cr–C60 separation is found to be 1.68 Å, while the Cr–

graphene separation is approximately 1.61 Å In general, even when we extend the hosting graphene sheet (or in other words,

15

we reduce the distribution density of Cr–C60), the key geometrical features are similar in the two nanostructures

The theoretical calculations of total energies for G(C150)–Cr–

C60 at Γ point produce a binding energy of 2.10 eV according to equation (1) As a consequence, we conclude such a

20

nanostructure to be less energetically stable than the previously investigated structure (G(C54)–Cr–C60) Nevertheless, the magnitude of binding energy is still relatively large, which suggests good structural stability

IV.3 Attachments of a metal cluster on G(C54)–Cr–C60

25

The decoration of a graphene monolayer surface with C60–Cr complexes may offer many promising applications, especially in chemical catalysis The role of G–Cr–C60 structures in chemical reactions remains uncertain, and we do not seek for a definite conclusion in this paper However, such structures are capable of

30

supporting one or multiple nanoscaled metal clusters, which might be active enough to catalyze chemical processes, especially organic reactions.39-42 In this study, we demonstrate the possibility of attaching nano-clusters of three active metals in the Nickel group (group 10), i.e., Ni, Pd, and Pt Owing to the high

35

computational demand, the G(C54)–Cr–C60 complex will be decorated with only one metal cluster (of Ni/Pd/Pt)

There have been a number of first-principles modeling studies

of Ni, Pd, or Pt nanoparticles Ni nanoparticles were found to assist the initial growth of carbon nanotubes.43 In a previous

40

study reported by Kacprzak and co-workers,44 γ-alumina was decorated with Pd9 clusters Nanoscaled Pt, an active catalytic material, was intensively investigated by Kumar and Kawazoe using first-principles modeling methods.45 There are, in addition, two other studies in which spin-orbit coupling was taken into

45

account by non-collinear calculations to describe spin polarization more accurately.46, 47 In this study, three metal clusters of reasonably small size, Ni4, Pd4, and Pt4, are chosen for illustration purposes From our preliminary DFT calculations, it is suggested that Ni4 and Pd4 structures favorably adopt the

50

tetrahedral configuration rather than the planar rhombus structure, while Pt4 favorably adopts the rhombus configuration However, when binding to C60, the rhombus structure of Pt4 is distorted, and

it is then converted to tetrahedral Hence, we will consider the attachment of tetrahedral Ni4/Pd4/Pt4 on the C60–Cr–G complex

55

Geometry optimization is performed to explore binding stability and electronic/magnetic properties It should be noticed that during the optimizations of metal cluster–(C60–Cr–G) complexes, we neglect the change in unit cell to simplify the optimization and reduce the computational cost Interestingly, we

60

learn from the optimized result on Ni4–(C60–Cr–G) that three Ni atoms have direct interactions with C60 (in the C60–Cr–G complex, as shown in Fig 4) More specifically, each of the three

Ni atoms at the Ni4/C60 interfacial layer (i.e., bottom layer of the tetrahedron) favorably assumes the B positions (described in Fig

65

Fig 4 Decoration of the (C60–Cr–graphene) complex with a

tetrahedral metal cluster B1 is the bond between two inner metal

atoms, while B2 is the bond between the vertex and a 2nd-layer

metal atoms

Fig 5 Spin-polarized PDOS of the Ni4–(C60–Cr–graphene)

complex and PDOS of Ni4 3d and C60 2p z subshells From the

plot, all 3d orbitals are shown to be ferromagnetic, while 2p z of

C60 is weakly anti-ferromagnetic

Table III Metal–C, metal–metal distances and binding energies

in X4–C60–Cr–G(C54) (X = Ni/Pd/Pt)

X Distances (Å) Binding energy (eV) X–C B1 B2

Ni 2.01 2.38 2.32 3.57

Pd 2.20 2.74 2.67 2.38

Pt 2.14 2.72 2.65 4.35

* See Fig 4

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1) and coordinates to two C atoms in the honeycomb ring Closer

inspection shows that the Ni–C bond length is approximately 2.01

Å, which is shorter than the previous Cr–C bond (2.20 Å) The

bond between two Ni atoms at the Ni4/C60 boundary (B1 as

indicated in Fig 4) is somewhat affected by the interaction with

5

C60, and the bond length is consequently 2.38 Å When there is

no effect from C60, the distance between the vertex Ni and a

bottom-layer Ni (B2) is slightly more compressed (2.32 Å) In

Table III, we summarize the calculated bonding distances for all

complexes in which three metal clusters (Ni4, Pd4, and Pt4) are

10

individually attached on C60–Cr–G

The binding energy of Ni4–(C60–Cr–G) structure is then examined in order to evaluate its theoretical stability From earlier calculations in this study, it is expected that the C60–Cr–G complex is energetically stable and can be synthesized

15

experimentally Therefore, we will systematically use the total energy of the whole C60–Cr–G base structure for the calculations

of binding energy, which is expressed as follows:

) (60

C

20

where

G Cr C

E − −

60

represents the total energy of the C60–Cr–G base

structure, E metal is the total energy of the investigated metal cluster (Ni4 in this case), and

) (C60Cr G metal

E − − − is the total energy of the produced structure The binding energy of Ni4–(C60–Cr–G) is estimated to be 3.57 eV, which indicates that the complex is

25

energetically stable

The total and absolute magnetizations for Ni4–(C60–Cr–G) are computed as 2.82 and 3.85 µB/cell, respectively It is Ni4 that significantly increases these magnetization values for the complex Recall that from the base structure optimization of

30

G(C54)–Cr–C60, the total magnetization is only 0.55 µB/cell From spin-polarized calculations, the Ni4 cluster aligns ferromagnetically, while C60 behaves as a weak anti-ferromagnetic residue (as shown in Fig 5) Also, it is observed that Cr and graphene have little influence on the overall spin

35

polarization For convenience, we summarize the ferromagnetic/anti-ferromagnetic moments of graphene, Cr, C60, and Ni4 (plus Pd4 and Pt4) and show the details in Table IV

The spin polarizations of Ni4 3d, 4s and C60 2p z are carefully examined, and the main orbital contributions to total

40

magnetization are shown in Table V The 4s shell of Ni4 only contributes little (0.03 µB/cell) to the ferromagnetism, while the

3d shells (especially 3d z2) account for the majority of the overall ferromagnetism As shown in detail in Table V, all orbital

contributions of 3d subshells align ferromagnetically More

45

specifically, the polarization of 3 2

z

d contributes 0.68 µB/cell

(27.9% of the 3d polarization), while 3d zx and 3d zy are observed

to make identical contributions of 0.31 µB/cell (12.9% of the 3d

polarization), and 3d x2−y2 and 3d xy exhibit similar contributions

of 0.56 µB/cell (23.2% of the 3d polarization) Orbital

50

contributions to the total magnetization from Ni4 and C60 can be

seen also from Fig 5, in which the PDOS diagrams of all 3d

subshells of Ni4 and 2p z of C60 are shown

When Pd4 is supported by C60–Cr–G, the structural configuration shares many similarities to the previously

55

investigated Ni4-decorated structure as shown in Fig 4 In fact, our calculations show that the Pd–C bond is 2.20 Å, which is longer than the Ni–C bond in the previous structure by 9.45%

Table IV Partial magnetizations (µB) of graphene, Cr, C60, and metal cluster (Ni4/Pd4/Pt4)

Total Graphene Cr C60

Metal cluster

Ni4 on (C60–Cr–G) 2.82 -0.07 0.69 -0.22 2.42

Pd4 on (C60–Cr–G) 2.20 -0.07 0.76 -0.04 1.56

Pt4 on (C60–Cr–G) 0.58 -0.07 0.77 -0.12 0.00

Table V Orbital contributions to the total magnetization from

C60 2p z and a metal cluster (Ni4/Pd4)

C60 Metal cluster

2p z s d z2 d x2−y2

(d xy)

(d zy)

Ni4 (4s and 3d) on

(C60–Cr–G) -0.19 0.03 0.68 0.56 0.31

Pd4 (5s and 4d) on

(C60–Cr–G) -0.04 0.07 0.71 0.21 0.19

Fig 6 Spin-polarized DOS of the Pd4–(C60–Cr–G) complex and

PDOS of Pd4 4d and C60 2p z subshells The latter shows that all

4d orbitals align ferromagnetically, while 2p z of C60 contributes

a small anti-ferromagnetic moment

Fig 7 Spin-polarized DOS of the Pt4–(C60–Cr–G) complex It is

shown that there is no spin polarization in Pt4

This journal is © The Royal Society of Chemistry [year] Journal Name, [year], [vol], 00–00 | 7

The bond between two Pd atoms at the the Pd4/C60 boundary

(labeled B1 in Fig 4) is 2.74 Å, which is significantly longer than

the corresponding Ni–Ni bond (2.38 Å) by 15.13% Likewise, the

B2 distance in the Pd4 complex (2.67 Å) is also longer than the

corresponding Ni–Ni distance (2.32 Å) Subsequently, the

5

binding energy is calculated using equation (4) to evaluate the

theoretical stability of this structure The binding energy is

calculated as 2.38 eV, which reveals that the decoration of C60–

Cr–G with Pd4 results in a complex less stable than the Ni4

-decorated complex Still, this binding energy is relatively large,

10

which indicates good stability of Pd4–(C60–Cr–G)

The total and absolute magnetizations computed for this

nanostructure are 2.20 and 2.90 µB/cell, respectively Compared

to the previous case of Ni4, the structure resulting from Pd4

attachment on C60 tends to exhibit smaller spin polarization and

15

therefore produces a lower total magnetic moment with

ferromagnetic alignment From the DOS analysis of spin

polarization, it can be obviously seen that there is a large

difference between spin-up and spin-down states of the Pd4

cluster, which gives rise to the major ferromagnetism exhibited

20

by the whole structure In addition, we also observe a small ferromagnetic-moment contribution from Cr Graphene and C60 unsurprisingly align anti-ferromagnetically; however, such opposing behavior is not significant enough to surpass the ferromagnetism of the overall structure The

ferromagnetic/anti-25

ferromagnetic moments of graphene, Cr, C60, and Pd4 are listed in Table IV

We then examine the orbital-resolved spin polarization of the

4d and 5s shells of Pd4 as well as the 2p z orbital of C60 The main

orbital contributions to total magnetization from Pd 4d, 5s and

30

C60 2p z are shown in Table V In the case of Pd4, it is recognized

that the ferromagnetic moment resulting from 5s (0.07 µB/cell) is

somewhat higher than that from the 4s orbital of Ni4 (previously reported as 0.03 µB/cell), but it is still considerably small The PDOS of 4d x2−y2 is very similar to that of 4d xy, while the PDOS

35

of 4d zx and 4d zy are almost identical In the 4d shells of Pd4, we

observe some major distinctions from the 3d shells of Ni4 More specifically, the contributions from 2 2

y x

d − (d xy ) and d zx (d zy) are relatively small when compared to those for Ni4 In fact, the ferromagnetic contributions from 2 2

y x

d − (d xy ) and d zx (d zy) are 0.21

40

µB/cell (13.8 % of the 4d polarization) and 0.19 µB/cell (12.6%), respectively, while the highest and dominant contribution comes from 2

z

d , which is 0.71 µB/cell (47.1%) For illustration

purposes, the plot of PDOS of all 4d subshells of Pd4 and 2p z of

C60 is shown in Fig 6

45

The optimized structure of Pt4–C60–Cr–G is observed to be similar to that of Ni4–C60–Cr–G and Pd4–C60–Cr–G in the previous cases From our DFT calculations, the Pt–C bond distance is 2.14 Å The bond distance between two bottom-layer

Pt atoms (B1 in Fig 4) is 2.72 Å, which is close to the Pd–Pd

50

bond distance in the previous case The B2 bond distance is 2.65

Å, which is slightly shorter than the corresponding Pd–Pd bond (2.67 Å) The binding energy is calculated as 4.35 eV, and we can thus conclude that Pt4–(C60–Cr–G) is the most stable nanostructure of the three examined cases

55

Inspection of the total and absolute magnetizations reveals that the Pt4 is a weakly ferromagnetic material (0.58 and 1.12 µB/cell, respectively) Compared to the previous two cases, this structure exhibits a smaller degree of spin polarization with ferromagnetic alignment As shown in Fig 7, the spin-up and spin-down DOS

60

of the Pt4 cluster (we also examine the spin-up and spin-down states of each Pt atom) virtually coincide, indicating that this cluster is purely non-magnetic As mentioned earlier, the total and absolute magnetizations of the G(C54)–Cr–C60 base structure are 0.55 and 1.08 µB/cell, respectively Therefore, we can

65

conclude from our DFT calculations on Pt4–(C60–Cr–G) that the ferromagnetism comes mainly from the base structure (G(C54)–

Cr–C60), rather than from the metal cluster (Pt4)

In the case of the Pt4 cluster, it is important to perform non-collinear calculations with spin-orbit coupling to account for the

70

relativistic effect due to 6s-5d hybridization Such calculations were previously reported in two theoretical investigations of Ptn

nanoclusters.46, 47 In those studies, tetrahedral Pt4 itself was shown to be antiferromagnetic with a total magnetic moment of 2.71 µB Our benchmark calculations for Pt4 show that the

75

antiferromagnetic moment is 2.52 µB, which is in good agreement with the previous result However, for the large-sized Pt4–(C60–

Fig 8 Spin-polarized PDOS of one M–C pair (M = Ni/Pd/Pt)

Fig 9 Electron density distribution on the plane containing the

Ni–C/Pd–C/Pt–C bond

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DOI: 10.1039/C3CP53529K

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Cr–G), the non-collinear calculations with spin-orbit interactions

become prohibitive Therefore, we instead choose to examine the

Pt4–C60 structure in order to verify the reported magnetic

property Interestingly enough, when C60 is decorated with

tetrahedral Pt4, the non-collinear calculations with spin-orbit

5

coupling once again indicate that Pt4–C60 is non-magnetic Such

observations are sufficient to verify our previous calculations,

and we conclude that the weak ferromagnetic moment of Pt4–

(C60–Cr–G) mainly originates from Cr, while the Pt4–C60

complex is observed to be non-magnetic

10

A validation check is also made between PBE and PW91

calculations for the Pt4 complex From the PW91 data, we can

conclude that the difference in geometric configuration is small,

and we also observe a weak magnetic moment (0.58 µB/cell)

given by Pt4–(C60–Cr–G) The binding energy given by PW91

15

calculations suggests that Pt4–(C60–Cr–G) is very stable with a

positive energy of 4.81 eV, which is 10.5% higher than the

PBE-predicted binding energy

At this point, we have observed from binding energy

calculations that Ni4–(C60–Cr–G) is more stable than Pd4–(C60–

20

Cr–G) by 1.19 eV (3.57 eV versus 2.38 eV), while the total

magnetic moment of Ni4–(C60–Cr–G) is larger than that of Pd4–

(C60–Cr–G) by 0.62 µB Therefore, we believe that there is an

interplay between binding energies and ferromagnetic moments

when C60, which is supported by Cr–G, is decorated with Ni4 and

25

Pd4 The decoration of Pt4, on the other hand, exhibits weak

ferromagnetism (in fact, spin-polarization calculations indicate

that Pt4 is non-magnetic) while its binding energy is surprisingly

the largest of the three investigated cases

In order to clarify this unexpected observation, we carefully

30

examine the PDOS plots of three C–M pairs (with M being Ni,

Pd, or Pt) as shown in Fig 8 We can see that in the unpolarized

Pt–C case, both spin-up and spin-down states of Pt 5 dz2 and C

2p z significantly overlap, which implies that there is a strong

donor-acceptor interaction, or a stable coordination bond A

35

comparison shows that DOS distributions in the Ni and Pd cases

are very similar to each other (Fig 8) However, there is a

distinction because the 3 2 2

y x

d − subshell of Ni tends to receive

greater electron density from C 2p z Indeed, this behavior would

cause not only an increase in spin polarization but also formation

40

of a stronger bond between Ni and C Another piece of evidence

can be found that supports the bond-strength argument, when we

inspect the electron density distribution on the plane that contains

a metal-carbon bond (Fig 9) It is shown that the highest electron

density is observed in the middle of a Pt–C bond, while the

45

lowest electron density is observed in the middle of Pd–C, which

is consistent with the previous binding energy observations In

addition, there is a significant electron density around Ni due to

the acceptance of many electrons from C60 This observation

implies the strong overlap of Ni 3d–C 2p z, which causes strong

50

ferromagnetism

IV.4 Assessment of catalytic capability

As stated earlier, one goal of developing the C60–Cr–graphene

base structure in this study is the use in chemical reaction

catalysis In order to illustrate the catalytic capability of the

55

proposed nanostructure, we investigate a dissociation reaction of

H2 on Ni4–(C60–Cr–G(C54)) It is reported elsewhere that the

cleavage of H–H bond requires as much as 104.2 kcal/mol (4.52

eV).48 In this

Fig 10 H–H bond cleavage on Ni4–(C60–Cr–G) The activation energy for this reaction is estimated as 0.76 eV The pure dissociation of H–H bond requires about 4.52 eV

illustration, we will consider a simple mechanism in which the H2

60

molecule initially bonds to Ni (by a Ni–H bond), then another Ni attracts the remaining H atom and forms Ni–H interaction At the end, H–H completely dissociates, and two H atoms bind to different sites of the Ni4 cluster

Because of the high structural complexity (119-atom catalyst

65

complex with an addition of 2 H atoms), we only perform Γ calculations to examine the potential energy profile The initial reactant structure of (H2–Ni4 complex) and the final product structure (in which each H is connected to one Ni) are first optimized, and the nudged-elastic-band (NEB) numerical

70

method49 is employed to locate the transition state

As shown in Fig 10, the final product is less stable than the initial structure (H2–Ni4 complex) by 0.73 eV The transition state

is 0.03-eV higher in energy than the final product, which means that it requires about 0.76 eV to break the H–H bond and the

75

presence of Ni4 in this case assists in lowering the original reaction barrier Therefore, we believe that the nanostructures developed in this work are potentially capable of activating chemical reactions

V Summary

80

In this study, we present a first-principles modeling study of a new class of two-dimensional materials, in which buckminsterfullerene (C60) is attached to the surface of graphene via Cr coordination bonds We investigate two nanostructures, G(C54)–Cr–C60 (more densed) and G(C150)–Cr–C60 (less densed),

85

which differ in the distribution ratio of the Cr–C60 complex on the surface, as shown in Fig 2 Sharing many similarities in geometry and having relatively high binding energies, the two investigated structures are both predicted to be energetically stable Spin polarization analysis shows that G(C54)–Cr–C60 is

90

weakly ferromagnetic, to which the 3d shells of Cr make a dominant magnetic contribution The 2p z spins of C from both graphene and C60, on the other hand, align anti-ferromagnetically (contributing negative magnetic moments)

Following the successful optimization of graphene–Cr–C60

95

structures, we then examine the potential decoration of C60 with small metal clusters, which might confer catalytic activity to the

This journal is © The Royal Society of Chemistry [year] Journal Name, [year], [vol], 00–00 | 9

complex The metal clusters of interest in this study are

tetrahedral Ni4, Pd4, and Pt4 At convergence of optimizations,

three metal atoms from the cluster (Ni4/Pd4/Pt4) coordinatively

bind to a honeycomb ring in C60 as shown in Fig 4 The binding

energy of each nanostructure is then evaluated to examine the

5

theoretical stability of the complex Our DFT calculations show

that the attachment of Ni4 and Pt4 is more favorable than the

attachment of Pd4 to G(C54)–Cr–C60 This result is consistent with

a previous study showing that Pd has a tendency to interact

weakly with a graphene surface in comparison to atomic Ni and

10

Pt.11 For the Ni4 decoration, the strong binding energy is more

correlated with the strong magnetic behavior of Ni 3d orbitals In

the Pt4 case, even though the whole complex is non-magnetic, we

observe the highest binding energy of the three cases, and

accordingly conclude that the hybridization effect between 2p z

15

(from C60) and 5 2

z

d (from Pt) is very effective in forming coordination bonds due to interactions between both spin-up and

spin-down states To deliver more evidence to confirm the high

stability of Pt4 attachment, we perform electron density analysis

on the planes containing the Ni–C, Pd–C, or Pt–C bonds Our

20

theoretical data (illustrated in Fig 9) actually imply that the Pt–C

bond is stronger than the other ones, while the Pd–C bond is the

weakest Nevertheless, all calculated binding energies for the

three investigated cases are still relatively large, which leads us to

believe that the suggested complexes are thermodynamically

25

stable

The Ni4 and Pd4 clusters contribute strong ferromagnetic

moments to the resultant complexes Classified as a moderately

stable structure, Ni4–(G(C150)–Cr–C60) exhibits the strongest

ferromagnetism, while the computed total magnetic moment of

30

Pd4–(G(C150)–Cr–C60) is lower than that in the Ni case Overall,

we find that the 3d shells of Ni4 as well as the 4d shells of Pd4

strongly contribute to the magnetism On the other hand, Pt4 is

observed to be non-magnetic (from calculations with/without

spin-orbit coupling), and the total magnetic moment of Pt4–

35

(G(C150)–Cr–C60) is found to be very similar to that of the

G(C150)–Cr–C60 base structure; thus, the magnetism is produced

mainly from the spin polarization of the Cr 3d shells To validate

the theoretical prediction given by PBE calculations, we

additionally perform PW91 calculations for C60–Cr–G(C54) and

40

its decoration with Pt4 Overall, very good consistency is

observed, and we conclude that PBE calculations are reliable

In experimental synthesis, a metal cluster may be employed to

steady C60 on the graphene surface rather than a single bridging

transition-metal atom (Cr) considered in this study Such

45

nanostructures may have good structural stability, and we believe

that it is beneficial to extend further investigations for such

complexes in the future

An illustrative example is presented when we employ Ni4–

(C60–Cr–G) to activate H2 dissociation According to the reaction

50

barrier estimation, it only requires 0.76 eV to break the stable H–

H bond, which indicates potential applications of such

nanostructures in chemical catalysis

Acknowledgement

We thank Vietnam National University in Ho Chi Minh City

55

(VNU-HCM) for their support in this work, and also

acknowledge supercomputing support from the Institute for

Materials Research, Tohoku University, Japan during the course

of this research H.H thanks a Nanyang Assistant Professorship

Notes and references

60

1 Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore E-mail: hung.m.le@hotmail.com

2 Faculty of Materials Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam

65

3 New Industry Creation Hatchery Centre, Tohoku University, 6-6-4, Aramaki, Aoba, Sendai, 980-8579, Japan

4

Theory and Modeling Department, Culham Centre for Fusion Energy, United Kingdom Atomic Energy Authority, Abingdon, OX14 3DB, UK

70

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