www.elsevier.com/locate/cplett

Chemical Physics Letters 411 (2005) 279–284

Structure and electronic properties of cobalt atomsencapsulated in Sin (n = 1–13) clusters

Li Ma a,*, Jijun Zhao b, Jianguang Wang a, Qiliang Lu a,Lianzhong Zhu a, Guanghou Wang a

a National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, PR Chinab National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 224502, PR China

Received 27 March 2005; in final form 13 June 2005

Available online 5 July 2005

Abstract

A systematic theoretical study of the equilibrium geometries and energetics of cobalt atoms encapsulated in Sin (n = 1–13) clusters

and comparison with pure Sin clusters have been performed by density functional theory–generalized gradient approximation cal-

culations combined with a genetic algorithm. Our results reveal that the geometries of bare Sin clusters are substantially modified

upon doping of Co atom. Co-doping improves the stability of the clusters after nP 7. In general, the stability of SinCo clusters

increases with increasing size n. The Si9Co was found as magic-number cluster, and the enhanced stability was explained by the

18-electron rule. The magnetic moment on Co atom inside SinCo cluster is quenched in all the clusters with n P 4.

� 2005 Elsevier B.V. All rights reserved.

Clusters are particularly interesting research subjects

because the properties of cluster-based materials can

be designed by exploring the enormous variability inthe size, shape, and composition of constituent clusters

[1–3]. To fabricate cluster-assembled nanostructures, it

is critical to find out suitable building blocks that are

chemically stable and weakly interact with each other.

Silicon clusters are expected to be such building blocks

in light of the extreme importance of silicon materials

in the semiconducting industry [4]. The Si clusters had

been extensively investigated both experimentally andtheoretically [5–9]. However, pure silicon clusters are

chemically reactive [10] and thus are unsuitable for

building block of self-assembly materials. The finding

of formation of Si cage structures with the presence of

encapsulated metal atoms has given rise to considerable

interest in studying the properties of metal doped Si

clusters [11–13]. Recently, it was shown [11,13] that

0009-2614/$ - see front matter � 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2005.06.062

* Corresponding author. Fax: +86 25 83595535.

E-mail address: malibird@sohu.com (L. Ma).

encapsulating a metal atom inside silicon clusters may

stabilize the endohedral complex. These complexes can

then serve as the building blocks for cluster-assembledmaterials.

Recent experimental and theoretical findings have

demonstrated that the encapsulation of transition metal

atoms (TMAs) by Si-atoms leads to stable Si-cages, and

the cluster structure depends on many factors [14,15].

Kumar and Kawazoe [16] reported computational

results for metal encapsulated Si-cage-clusters. They

found that silicon forms fullerene-like Si16M (M = Hf,Zr) or cubic Si14M (M = Fe, Ru, Os) cage clusters,

depending upon the size of the metal atom. In addition,

they reported stable SinM (n = 14–17, M = Cr, Mo, W)

clusters in the cubic, fullerene-like, decahedral and Frank–

Kasper-polyhedron type of geometry [17]. On the other

hand, Khanna et al. [12] investigated Cr and Fe [18]

encapsulated in silicon cages, and found that Si12Cr and

Si10Fe are more stable than their neighbors. Both Si12Crand Si10Fe are consistent with the 18-electron rule and

Si is fourfold coordinated in Si12Cr. Experimentally,

280 L. Ma et al. / Chemical Physics Letters 411 (2005) 279–284

Koyasu et al. [19] studied the electronic and geometrical

structures of mixed-metal silicon MSi16 (M = Sc, Ti,

andV) clusters usingmass spectrometry and anion photo-

electron spectroscopy. They found that neutral TiSi16cluster has closed-shell electron configurationwith a large

HOMO–LUMO gap.Although there are many researches on the properties

of metal-doped silicon clusters in recent years, surely no

systematic theoretical investigation on SinCo clusters

has been done so far. In order to examine the relative

stability of Co-encapsulated Si clusters and the effect

of Co doping on the electronic and magnetic properties

of Si cage, we have carried out the computational

studies on SinCo (n = 1–13) clusters and compared withthat of Sin clusters.

The ground state structures of Sin (n = 1–13) clusters

were first determined via genetic algorithm global search

based on tight-bindingmolecular dynamics (GA-TBMD)

[20] using Menon�s nonorthogonal tight-binding (NTB)

model. This procedure has been successfully applied to

the optimization of cluster geometries in our previous

work [20–23]. Based on the results of GA-TBMD globalsearch, cobalt atoms were doped in Sin clusters. Upon

relaxation,Co atomprefers to sit at the center of Sin cages.

This effect can be expected since transition metal atoms

tend to form high-coordinated compact structures. To

further optimize the geometries of Sin and SinCo clusters,

a DMOL package based on density functional theory

(DFT) was employed [24–26]. In the DMol electronic

structure calculations, all electron treatment and doublenumerical basis including d-polarization function

(DND) were chosen. The density function was treated

within the generalized gradient approximation (GGA)

[25] using PW91 exchange-correlation potential [26].

Self-consistent field calculations were done with a conver-

gence criterion of 10�6 hartree on the total energy and

electron density. In the geometry optimization, the

converge thresholds were set to 0.002 hartree/A for theforces, 0.005 A for the displacement and 10�5 hartree

for the energy change. In this Letter, spin-unrestricted

calculations were performed for all allowable spin multi-

plicities. We started with a spin-singlet configuration for

the even-electron systems (e.g., Sin clusters) and a

spin-doublet configuration for the odd-electron systems

(e.g., SinCo clusters). The atomic charges and the on-site

magnetic moment of the SinCo clusters were then studiedvia Mulliken population analysis [27].

In spite of the extensive search for ground-state

geometries of Si clusters carried out in the last two

decades, one continues to discover new structures with

lower and lower energies. Unfortunately, there are very

few experimental techniques that can directly determine

cluster structure while the physical properties of clusters

are usually sensitive to cluster size. Thus, if clusters areused for synthesizing materials, one must understand

how their tailored properties are sensitive to cluster size

and topology [12]. The evolution of the energetics of

SinCo clusters were investigated through calculating

the binding energy per atom (Eb), the energy gained

(DE) in adding a Si atom to an existing CoSin�1 cluster,

the energy gained (DE1) in adding a Co atom to an Sincluster, the vertical ionization potential (VIP), and thegap between the highest occupied and lowest unoccu-

pied molecular orbital (HOMO–LUMO). Similar calcu-

lations have also been performed for pure Sin clusters.

These energies are defined by

Eb ¼ ½nEðSiÞ þ EðCoÞ � EðSinCoÞ�=ðnþ 1Þ; ð1ÞDE ¼ EðSiÞ þ EðSin�1CoÞ � EðSinCoÞ; ð2ÞDE1 ¼ EðSinÞ þ EðCoÞ � EðSinCoÞ; ð3ÞVIP ¼ EðSinCoþÞ � EðSinCoÞ. ð4Þ

For pure Sin clusters, the energetics in above equationswas derived by moving away Co atom.

The lowest-energy structures obtained for pure Sinand equilibrium geometries of SinCo (n = 1–13) clusters

based on those bare Sin clusters are plotted in Fig. 1 for

comparison. The optimized geometries for pure silicon

clusters agree well with previously ab initio results calcu-

lations [20,28–30]. In particular, for all the pure Sinclusters investigated here, the lowest-energy structuresare the same with the Car-Parrinello molecular dynam-

ics simulated annealing results [29]. As one Co atom is

allowed to interact with the silicon clusters, there would

be some structural changes from those of the bare Sincluster and the equilibrium geometries of the SinCo

clusters evolve with cluster size n.

For smallest clusters with n 6 4, both bare Sin and

doped SinCo clusters adopt planar structures. Theequilibrium structures of SiCo, Si2Co and Si3Co can

be considered as directly adding the Co atom on the

structures of the corresponding bare Sin clusters, while

the incorporation of Co atoms leads to the structural

change from a rhombus for bare Si4 to a Co-centered

trapezia for Si4Co.

As cluster size increases, three-dimensional (3-D)

structures were obtained for both bare Sin clusters andCo-doped CoSin clusters with n P 5. A trigonal prism

(D3h symmetry) was obtained for bare Si5 cluster, while

doping a Co atom inside Si5 lead to the Cs structure

shown in Fig. 1 that can be viewed as a Si2Co and a

Si3Co interconnected by sharing the Co atom. Our

lowest-energy structure for Si6 is a distorted edge-

capped trigonal prism. The equilibrium structure of

Si6Co is still based on an edge-capped trigonal prism,with one additional Si atom attached to the central Co

atom. For Si7, we obtained a pentagonal bipyramid with

D5h symmetry. With addition of a Co atom on Si7, the

equilibrium structure transforms into a Co-centered

C2v structure (Fig. 1), which can be viewed as a square

bipyramid edge-capped by two Si atoms with one Co

on the vertex. The equilibrium configuration of Si8Co

Fig. 1. The lowest-energy structures of Sin and equilibrium geometries of SinCo (n = 1–13) clusters.

L. Ma et al. / Chemical Physics Letters 411 (2005) 279–284 281

is based on a distorted Co-centered Si hexagon with twoadditional Si atoms face-capped on the upper and down

side of the hexagonal plane, while the equilibrium

configuration of Si8 is simply based on Si7 by capping

one more Si atom on its pentagonal bipyramid.

Starting from n P 9, the SinCo clusters adoptcage-like structures with Co atom stuffed in the interior

site, similar to previous calculation for other silicon clus-

ters encapsulated with other transition metal atoms

[12,16–18]. Moreover, the central Co atom form bond

282 L. Ma et al. / Chemical Physics Letters 411 (2005) 279–284

with each Si atom in all those clusters studied except for

one capped Si atom in Si13Co cluster. For example, the

equilibrium structure of Si9Co can be considered as a

distorted Si8 cube capped by one Si atom on the top,

with a Co atom encapsulated in the center of the Si8cube. Similar to Si9Co, the equilibrium structure ofSi10Co is based on a two-layered Si cage with square

and pentagon on each layer and one additional Si atom

capped on the top. As a continuation of the structural

growth pattern by Si9Co and Si10Co, the equilibrium

cage-based structure Si11Co has two layers of pentagon

and one top Si atom, with the Co atom in the center of

Si cage. For Si12Co, the upper layer by pentagon and the

top Si atoms still remain of Si11Co, but adding one moreSi atom leads to a structural reconstruction on the lower

pentagon. Those six Si atoms form two squares sharing

two atoms. In this way, there are totally three pentagons

on the Si outer cage. However, the equilibrium structure

of Si13Co is not similar to that of Si12Co. Instead, it can

be considered as a continuation of Si11Co, with two lay-

ers of pentagon and two additional Si atoms capped on

the top and bottom each. Then, there is one more Si

Table 1

Binding energy per atom (Eb), energy gained (DE) in adding a Si atom to an e

ionization potential (VIP), and HOMO–LUMO gap of Sin clusters

Cluster DE (eV) Eb (eV) D2E

Si1 0.03

Si2 3.34 1.70 �0

Si3 4.13 2.52 �0

Si4 4.56 3.04 0

Si5 3.99 3.23 �0

Si6 4.22 3.40 0

Si7 4.22 3.52 1

Si8 2.46 3.40 �2

Si9 4.78 3.55 0

Si10 4.44 3.64 1

Si11 2.74 3.59 0

Si12 2.24 3.54 0

Si13 3.11 3.58

Table 2

Binding energy per atom (Eb), energy gained (DE) in adding a Si atom to an e

Sin cluster, vertical ionization potential (VIP), HOMO–LUMO gap of SinCo

Cluster DE (eV) DE1 (eV) Eb (eV)

SiCo 3.29 3.29 2.52

Si2Co 4.08 4.02 3.05

Si3Co 4.08 3.97 3.31

Si4Co 3.14 2.55 3.28

Si5Co 3.80 2.36 3.37

Si6Co 3.95 2.09 3.46

Si7Co 4.56 2.42 3.60

Si8Co 3.44 3.39 3.59

Si9Co 5.35 3.95 3.76

Si10Co 4.77 4.28 3.86

Si11Co 4.06 5.59 3.88

Si12Co 3.56 6.92 3.85

Si13Co 3.36 7.17 3.82

atom face-capped on this Si12 cage, which is not directly

connected with the central Co atom. This result implies

that Si12 might be the largest cage for encapsulating Co

atom if we require all the Si atoms on the cage to form

chemical bonds with Co. For the larger SinCo clusters

with n P 13, the addition of more Si atoms will becapped on the surface of Si12Co or smaller SinCo clus-

ters and those Si atoms cannot directly form bond with

the encapsulated Co atom. Comparing to those of pure

Sin clusters with n P 9, there is substantial structural

reconstruction after encapsulating the Co atom except

for Si9 and Si10.

We now discuss the size-dependent physical

properties of these clusters. The binding energies, thefirst-order and second-order energy differences, vertical

ionization potentials (VIP), and the gaps between high-

est occupied molecular orbital (HOMO) and lowest

unoccupied molecular orbital (LUMO) for pure Sinclusters and doped SinCo clusters are listed in Tables 1

and 2 and plotted in Figs. 2–5. In cluster physics, the

second-order difference of cluster energies, D2E(n) =

E(n + 1) + E(n � 1) � 2E(n), is a sensitive quantity that

xisting Sin�1 cluster, second differences of cluster energies D2E, vertical

(eV) VIP (eV) HOMO–LUMO (eV)

8.25 1.60

.79 7.87 1.50

.43 8.29 1.26

.56 8.12 1.15

.22 8.34 2.04

.00 8.00 2.00

.76 8.18 2.13

.31 7.34 1.17

.35 7.79 2.01

.69 8.10 2.07

.51 7.20 1.12

.98 7.03 1.74

7.20 1.12

xisting CoSin�1 cluster, energy gained (DE1) in adding a Co atom to an

clusters and atomic charges of Co atom in SinCo clusters

VIP (eV) HOMO–LUMO (eV) Charge

7.36 1.22 �0.10

7.34 0.36 �0.06

7.72 0.42 �0.11

7.20 0.52 �0.32

7.22 0.50 �0.64

7.34 0.58 �0.71

7.48 0.43 �0.74

7.12 0.39 �0.79

7.84 0.34 �0.89

7.43 0.43 �0.91

6.99 0.31 �0.87

6.87 0.26 �0.83

7.10 0.27 �0.87

0 8 10 12

-2

-1

0

1

2

Cluster size n

∆ 2 E

(eV

)

2 4 6

Fig. 2. The second differences of Si cluster energies D2E(n) as a

function of the cluster size n.

0 10 12 142.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

∆E (

eV)

Cluster size n

Sin

SinCo

2 4 6 8

Fig. 3. Size dependence of the energy gained DE of Sin and SinCo

clusters.

0 2 4 6 8 10 12 14-1.0-0.8-0.6-0.4-0.20.0

Cha

rge

Cluster size n

2

4

6

8

∆E1

(eV

)

2

3

4

5

Eb

(eV

)

a

b

c

Fig. 4. Size dependence of the binding energy per atom Eb (a), energy

gained DE1 (b), atomic charges of Co atom (c) of SinCo clusters.

0 10 12 140.0

0.5

1.0

1.5

2.0

2.5

HO

MO

-LU

MO

gap

(eV

)

SinSinCo

Cluster size n

2 4 6 8

Fig. 5. Size dependence of HOMO–LUMO gap of Sin and SinCo

clusters.

L. Ma et al. / Chemical Physics Letters 411 (2005) 279–284 283

reflect the relative stability of clusters [31]. Fig. 2 shows

the second-order difference of, D2E(n), as a function of

the cluster size for pure Sin clusters. Maxima are found

at n = 4, 7, 10, implying that these clusters are more

stable than their neighboring clusters. These magicnumbers have been confirmed by anion photoelectron

spectroscopy [32], Raman [33] and infrared [34]

measurements on matrix-isolated clusters.

In Tables 1 and 2, it can be seen that the energy gain

DE in SinCo clusters are larger than that of Sin clusters

for n P 7, which is also clearly shown in Fig. 3. This

demonstrates that the encapsulating Co atom in Si cages

can improve the stability of the clusters. In other words,when one additional Si atom is added to the cluster, it is

energetically more favorable to attach to Sin�1Co cluster

and to form SinCo cluster rather than to attach at Sin�1

cluster and to form Sin cluster. From Tables 1 and 2, we

also note that Si9Co has the largest DE value and the

largest VIP value among all the SinCo clusters studied.

The maximum on ionization potential is a common

feature for the magic-number clusters. All these effectsmake the Si9Co cluster more stable than the other SinCo

clusters studied. Such enhanced stability can be

explained by the 18-electron rule. The outer-shell elec-

tron configuration of Co atom is 3d74s2 and all the nine

valence electrons participate bonding. On the other

hand, each Si atom contributes one electron to bond

with the central Co atom. Thus, the Si9Co cluster consti-

tutes the 18-electrons complete shell, similar to theSi12Cr [12] and Si10Fe [18] clusters found previously.

However, it should be pointed out that although Si9Co,

Si12Cr and Si10Fe are consistent with the 18-electron

rule, the 18-electron rule has its certain limitation.

Sen and Mitas [35] found that electron shell filling (18-

electron rule) is only one of the factors that determine

the cluster stability. The stability depends on other

factors as well (size of TM atom, etc.).

284 L. Ma et al. / Chemical Physics Letters 411 (2005) 279–284

It is noteworthy that the HOMO–LUMO gaps of Sinclusters are consistently reduced by adding the doped

Co atom (Fig. 5). A detailed analysis of the electronic

levels shows that the HOMO and LUMO are composed

of Co d-states mixed with Si p-states. Therefore, that is

the pd-hybridization responsible for the reduction ofband gap with addition of Co. This may provide a valu-

able means of controlling the band gap of Sin clusters by

appropriately choosing a transition metal atom and

doping it inside the Sin cluster. The atomic charges of

Co atom are also listed in Table 2. The amount of

charges transfer from Co atom to Si atoms increase with

increasing cluster size and it reaches the largest value till

n = 10 (Fig. 4c). The magnetic properties of SinCo clus-ters were also studied. It is found that all of the clusters

studied prefer the lowest spin states, that is doublet

multiplicity. Sen and Mitas [35] studied the TM atom

encapsulated in a Si12 hexagonal prism cage. They also

found the spin multiplicity is doublet for odd number

of electrons. The magnetic moment of Co is quenched

in all the n P 4 clusters. In n 6 3 clusters, the magnetic

moment of Co is 1.87, 1.53, 1.51 lB, respectively, whilefor the free Co atom it is 3 lB. It can be inferred that

the quenching effect comes from the influence of Si

caging. This effect on the magnetic moments of transi-

tion metal atoms can have significant implications in

spintronics applications.

In summary, a systematic theoretical study of the

equilibrium geometries and energetics of Co-encapsu-

lated Sin (n = 1–13) clusters have been performed byDFT–GGA calculations combined with a genetic algo-

rithm and the results have been compared with pure

Sin clusters. Our results reveal that the geometries of

bare Sin clusters are substantially modified after Co

atom doped inside the Sin clusters. Co doping improves

the stability of the Sin clusters for n P 7. In general, the

binding energy of SinCo clusters increases along with

cluster size n. The Si9Co cluster was identified as amagic-number cluster. The origin of the enhanced stabil-

ity is consistent with the 18-electron rule. The magnetic

moment of Co atom is quenched in all the clusters with

n P 4. This Si caging effect on the magnetic moments of

transition metal atoms can have significant implications

in spintronics applications.

Acknowledgments

This work was financially supported by the National

Natural Science Foundation of China (Grant Nos.

90206033, 10274031, 10474030, 60478012, 10021001),

the Foundation for University Key Teacher by the

Ministry of Education of China (Grant No. GG-430-

10284-1043), as well as the Analysis and Measurement

Foundation of Nanjing University.

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