Evolution of Con Al clusters and chemisorption of hydrogen on Con Al clusters

RESEARCH PAPER

Evolution of ConAl clusters and chemisorption of hydrogenon ConAl clusters

Ling Guo

Received: 7 March 2012 / Accepted: 25 May 2012

� Springer Science+Business Media B.V. 2012

Abstract The growth behavior of ConAl (n = 1–15)

and the chemisorptions of hydrogen on the ground

state geometries have been studied using the density

functional theory (DFT) within the generalized gradi-

ent approximation (GGA). The growth pattern for

ConAl is Al-substituted Con?1 clusters, and it keeps

the similar frameworks of the most stable Con?1

clusters except for n = 2, 3, and 6. The Al atom

substitutes the surface atom of the Con?1 clusters for

n B 13. Starting from n = 14, the Al atom completely

falls into the center of the Co-frame. The dissociation

energy, the second-order energy differences, and the

HOMO–LUMO gaps indicate that the magic numbers

of the calculated ConAl clusters are 7, 9, and 13,

corresponding to the high symmetrical structures. To

my knowledge, this is the first time that a systematic

study of chemisorption of hydrogen on cobalt alumi-

num clusters. The twofold bridge site is identified to be

the most favorable chemisorptions site for one hydro-

gen adsorption on ConAl (n = 1–6, 8, 10), and two

hydrogen adsorption on ConAl (n = 1–7), while

threefold hollow site is preferred for one hydrogen

adsorption on ConAl (n = 7, 9, 11–15) and two

hydrogen adsorption on ConAl (n = 8–10, 12–15)

clusters. The ground state structure of two hydrogen

adsorption on Co11Al is exceptional. In general, the

binding energy of both H and 2H of ConAl (n = 1–12)

is found to increase with the cluster size. And the result

shows that large binding energies of the hydrogen

atoms and large fragmentation energies for Co11AlH

and Co12AlH make these species behaving like magic

clusters.

Keywords ConAl cluster � Hydrogenated cobalt

aluminum cluster � Stability � Electronic properties

Introduction

Bulk phase bimetallic systems provide a matter of

increasing interest in pure and applied materials

sciences and traditional fields of physics and chemis-

try. In catalytic chemistry and chemical engineering,

real catalysts mainly consist of a heterometallic or

bimetallic system, which can profoundly enhance

reactivity and selectivity. Thus, to get a deeper

understanding of the microscopic behavior of these

species, the study of bimetallic or so-called alloy

clusters provides a suitable tool, because cluster

science enables one to investigate chemical and

physical properties starting from a single atom or

molecule toward bulk phase as a function of size.

Therefore, in the last decades, a number of studies of

bimetallic clusters and diatomic molecules have been

performed (Lu et al. 2011; Zhao et al. 2011; Laguna

et al. 2010; Zanti and Peeters 2010).

L. Guo (&)

School of Chemistry and Material Science, Shanxi

Normal University, Linfen 041004, China

e-mail: [email protected]

123

J Nanopart Res (2012) 14:957

DOI 10.1007/s11051-012-0957-7

Among the candidate systems to have been con-

sidered, the bimetallic cobalt aluminum clusters have

been the topic of some experimental and theoretical

studies (Nonose et al. 1989; Menezes and Knickelbein

1991, 1993; Behm et al. 1994; Pramann et al. 2001).

Several years ago, Nonose et al. (1989) performed

chemisorptions reactivity studies of neutral AlnCom

(n [ m) and ConAlm (n [ m) clusters toward H2 using

a fast flow reactors. In that study, they found that the

doping of Con clusters with only one Al atom reveals a

remarkable increase of hydrogen chemisorptions rates

compared with pure Con clusters. On the other hand,

pure Aln clusters do not adsorb hydrogen, which is

comparable to Al bulk phase behavior. Menezes and

Knickelbein (1991, 1993) succeeded in a comprehen-

sive investigation of the size dependence of ionization

energies of these clusters. These IE studies show that

the electronic shell structure of AlnCo and AlnCo2

clusters remains similar to that of pure Aln clusters.

Behm et al. (1994) have performed resonant two-

photon ionization spectroscopy on small diatomic

AlCo aluminides. Pramann and co-workers (2001)

have measured the photoelectron spectra of small

mass-selected aluminum-rich AlnCo- (n = 8–17) and

cobalt-rich ConAlm- clusters (n = 6, 8, 10; m = 1, 2) at

photon energies of 3.49 eV with the aid of a magnetic

bottle photoelectron spectrometer.

Hydrogen adsorption on metal surfaces and clusters

is a widely studied subject that provides the opportu-

nity to gain a basic understanding of the complicated

nature of many interesting problem, such as hydrogen

embitterment of metals, catalytic processes, hydrogen

storage, etc. Technological advancement in recent

decades enables us to study and control systems

having dimensions of a few atoms. Hydrogen adsorp-

tion on such nanosystems, for example on clusters,

gives an atomic perspective of the process (Huda and

Kleinman 2006; Dhilip Kumar et al. 2009; Varano

et al. 2010). In this study, our main goal is to explore

the sequential growth of small ConAl clusters with

n = 1–15 and study hydrogen molecule adsorption

and its effect on the geometric and electronic proper-

ties of ConAl (n = 1–15) clusters. And to obtain

further insights on the nature of chemisorption, the

extensive calculations of chemisorption of H2 and

sequential hydrogen loading on the energetically

stable ConAl (n = 1–15) clusters are studied. A

detailed picture of chemisorption of H2 on ConAl

(n = 1–15) nanoclusters based on an analysis of

energies, stability, fragmentation behavior, and bond-

ing nature is presented. So the understanding of the

adsorption of H2 molecule on cobalt aluminum

clusters could give useful insight on hydrogen inter-

action with other alloy clusters.

The article is organized as follows: A brief account

of the computational methodology is given in ‘‘Meth-

odology’’ section, followed by a detailed presentation

and discussion of the structures of different size ConAl

(n = 1–15) in ‘‘Results and discussion’’ section. In the

following section, I present the structures obtained

after adsorption of one and two atomic hydrogens.

These will provide the understanding of the interac-

tional nature and the magic behavior of hydrogen with

cobalt aluminum clusters. A summary of my findings

and conclusions are given in Summary section.

Methodology

Our calculations are carried out using density func-

tional theory (DFT) implemented in the DMol3

package (Delley 1990). We perform all-electron

spin-unrestricted calculations, using double numerical

plus polarization basis set (DNP) and the Beck’s

exchange functional and Lee–Yang–Parr correlation

functional (BLYP) (Lee et al. 1988) within general-

ized gradient approximation (GGA). The direct

inversion in iterative subspace (DIIS) approach is

used to speed up SCF convergence. I also applied

thermal smearing to the orbital occupation to speed it

up. The value of smearing is 0.005 hartree. For the

accurate calculations, I have chosen an octupole

scheme for the multipolar expansion of the charge

density and coulomb potential. The grid for numerical

integration is set as ‘‘fine.’’ The convergence criteria

for energy, energy gradient, and displacement are

1 9 10-5 Hartree, 2 9 10-3 Hartree/A, and 5 9

10-3 A, respectively.

To test the reliability of our calculation, the Co2 and

Al2 dimers are calculated. The results are summarized

in Table 1. From Table 1, it is obvious that the

calculated bond length (2.41 A), averaged binding

energy (0.25 eV/atom), and ionization potential

(6.50 eV) of Co2 with BLYP method are closest to

the experimental values (Kant and Strauss 1964; Hales

et al. 1994) of 2.31 A, 1.69 ± 0.26 eV, and 6.42 eV,

respectively. It should also be noted that the BLYP

functional has been successfully applied to several

Page 2 of 14 J Nanopart Res (2012) 14:957

123

other TM cluster systems, including Tin clusters

(Wang et al. 2004), Nin cluster (Xie et al. 2005), and

Lan clusters (Zhang and Shen 2004). Additionally, the

bond length (2.51 A), averaged binding energy

(0.94 eV/atom), and ionization potential (5.82 eV)

of Al2 (triplet state) are obtained, which are in good

agreement with the experimental values (Rosen 1970)

of 2.56 A, 0.77 ± 0.15 eV, and 6.20 ± 0.20 eV,

respectively. Therefore, the calculation method

employed is reliable and accurate enough.

Results and discussions

Structure and properties of the ConAl (n = 1–15)

clusters

In cluster physics, one of the most fundamental

problems is to determine the ground state geometry.

Accordingly, I first study the ground state structures of

the ConAl (n = 1–15) clusters, which are shown in

Fig. 1. Symmetries (sym), HOMO–LUMO gaps,

atomic averaged binding energy (Eb), the dissociation

energy (DE), the second-order energy differences

(D2E), vertical ionization potential (VIP), and vertical

electron affinities (VEA) for the most stable ConAl

(n = 1–15) clusters are all shown in Table 2. For

proper comparison, the structures of Con (2–16)

clusters have also been shown in Fig. 1 and Table 3.

For the CoAl dimer (Fig. 1[1a]) with C?v symme-

try, the optimized results indicate that the spin singlet

state is lower in total energy than the triplet and quintet

isomers by 0.55 eV and 1.80 eV, respectively. Fur-

thermore, the binding energy per atom (Eb) of the

CoAl dimer is 0.391 eV/atom larger than that of the

Co2 (Fig. 1[1a0]) one (0.25 eV/atom), the bond

lengths of CoAl and Co2 dimers are 2.454 and

2.410 A, respectively. For the Co3 cluster, three

structures (C2v, D3h, and D?h) have been discussed.

The linear structure (D?h, Fig. 1[2a0]) is found to be

the ground state, which is in agreement with the study

of Ma et al. (2006), who adopted the BLYP exchange–

correlation functional in the study. The ground state

Co2Al cluster is a spin doublet acute-angle triangular

structure (Fig. 1[2a]) with C2v symmetry, in which the

Al atom is at the apex, the Co–Co distance (2.388 A) is

a little smaller than that of the Co2 dimer (2.410 A),

and bond length of the Co–Al is 2.480 A. Five

different initial geometries have been considered for

the tetramer: tetrahedron, square, rhombus, planar

Y-like, and linear structures. A plane rhombus (C2v,

Fig. 1[3a0]) appears to be the most stable structure,

which is consistent with the calculations of Ma et al.

(2006). The ground state Co3Al cluster is a spin quartet

tetrahedral configuration (C3v, Fig. 1[3a]). For Co5,

many different initial geometries such as pyramid,

bipyramid, and capped tetrahedron, have been tried.

The triangular bipyramid structure (Fig. 1[4a0]) is

found to be the most stable structure with D3h

symmetry. The present result is in agreement with

the previous calculation (Ma et al. 2006). For Co4Al, a

spin septet distorted triangle bipyramid structure

(C2v, Fig. 1[4a]) has been proven to be most stable.

The capped trigonal bipyramid, octahedron, and

pentagonal pyramid structures have been studied to

search the ground state for Co6 cluster. A distortional

octahedral structure (Oh, Fig. 1[5a0]) is found to be the

ground state. It has an average bond length of 2.551 A.

The present result is in agreement with previous

theoretical studies (Ma et al. 2006). For Co5Al, the

ground state structure is a spin state of ten and slightly

distorted octahedron configuration with Cs symmetry,

where an Al atom is at the vertex position. In the case

of Co7, a capped octahedron, a pentagonal bipyramid,

a tri-capped tetrahedron, and a bicapped triangular

bipyramid structure have been considered. The capped

Table 1 Calculated bond lengths, averaged binding energies, and vertical ionization potential and experiment results

Co2 (this work) Experimentala,b Al2 (this work) Experimentalc

Bond length (A) 2.41 2.31 2.51 2.56

Eb(eV/atom) 0.25 1.69 ± 0.26 0.94 0.77 ± 0.15

Ionization potential (eV) 6.50 6.42 5.82 6.20 ± 0.20

a Kant and Strauss (1964)b Hales et al. (1994)c Rosen (1970)

J Nanopart Res (2012) 14:957 Page 3 of 14

123

octahedron (C3v, Fig. 1[6a0]) appears as the most

stable structure. The pentagonal bipyramid (C5v,

Fig. 1[6a]) appears as the most stable structure of

Co6Al. For Co8, three different geometries of bicapped

octahedron, capped pentagonal bipyramid, and tri-

capped triangular bipyramid have been studied. The

bicapped octahedron with D2d symmetry (Fig. 1[7a0])

is found to be most stable structure. For the Co9

cluster, the distortion tricapped octahedron is found to

be the most stable structure (D3h, Fig. 1[8a0]). As the

clusters grow from Co10 to Co16, the new addition

always occurs at a site where interactions with more

atoms are available to form the close-packed structure.

Their symmetries are D4d (Co10, Fig. 1[9a0]), D4d

(Co11, Fig. 1[10a0]), C5v (Co12, Fig. 1[11a0]), Ih

(Co13, Fig. 1[12a0]), C3v (Co14, Fig. 1[13a0]), Cs

(Co15, Fig. 1[14a0]), and Cs (Co16, Fig. 1[15a0]),

respectively. The lowest energy structures of ConAl

(n = 7–13) are found to be as Al substituted the

surface atom of Con?1. Furthermore, the most stable

ConAl (n = 7–13) clusters always keep the same

frameworks as Con?1 clusters. For example, the

ground state geometry of Co7Al (Fig. 1[7a]) with Cs

symmetry is a bicapped octahedron configuration

similar to that of the Co8 configuration. For Co8Al

cluster, the lowest energy isomer (Fig. 1[8a]) with Cs

symmetry is capped tetragonal antiprism structure and

can be regarded as substitutional structure of Co9. The

1a0 1a 2a0 2a 3a0 3a

4a0 4a 5a0 5a 6a0 6a

7a0 7a 8a0 8a 9a0 9a

10a0 10a 11a0 11a 12a0 12a

13a0 013a 14a 14a 15a0 15a

Fig. 1 The calculated lowest energy structures of Con?1 and ConAl (n = 1–15) clusters


123

ground state geometries of Co9Al, Co10Al, and Co11Al

are spin 16 structure with C2v symmetry (Fig. 1[9a]),

spin 17 structure with C4v symmetry (Fig. 1[10a]), and

spin 20 structure with C5v symmetry (Fig. 1[11a]),

respectively. For Co12Al, the lowest energy structure

is the icosahedral configuration (Fig. 1[12a]) with C5v

symmetry, where the Al atom is at vertex position.

Co13Al (Fig. 1[13a]) takes the C3v structure as its

ground state. Starting from n = 14, the Al atom

completely falls into the center of the Co-frame. And

ConAl (n = 14 and 15) (Fig. 1[14a, 15a]) takes the Cs

structures as their ground states, respectively.

We now discuss the relative stability of ConAl

clusters by computing the energy that is indicative of

the stability. We compute the atomization or binding

energy (Eb) per atom, the dissociation energy (DE),

and the second-order energy differences (D2E) as,

respectively,

Eb ConAl½ � ¼ nE Co½ � þ E Al½ � � E ConAl½ �ð Þnþ 1ð Þ ; ð1Þ

DE ConAl½ � ¼ E Con�1Al½ � þ E Co½ � � E ConAl½ �; ð2Þ

D2E ConAl½ � ¼ E Conþ1Al½ � þ E Con�1Al½ �� 2E ConAl½ �: ð3Þ

In general, the Eb increases as the cluster size

grows. Small humps or dips for the specific size of

clusters signify their relative stabilities. The Eb of the

ConAl clusters (shown in Fig. 2) is calculated using

the Eq. 1, where E(Co), E(Al), and E(ConAl) represent

the energies of a Co atom, an Al atom, and the total

energy of the ConAl cluster, respectively. For com-

parison, we also plot the Eb of the host Con cluster,

Eb[Con] = (nE[Co] - E[Con])/n, in Fig. 2. As seen in

the figure, the average binding energies of the most

ConAl clusters are higher than those of the pure Con

clusters (except for n = 14). It indicates that the doped

Al atom in the Con clusters contributes to strengthen

the stabilities of the ConAl framework. The averaged

binding energy of ConAl clusters generally increases

with increasing size; it is concluded that these clusters

continue to gain energy during the growth process. In

addition, the comparison of Con with the BE curve for

ConAl clusters shows that the small clusters of ConAl

are strongly bound. As the cluster grows in size, the

difference between the BE curves of ConAl clusters

and pure Con clusters steadily diminishes, indicating

that the bonding in doped clusters is essentially similar

to that in pure clusters.

In cluster physics, the dissociation energy (DE) and

the second-order energy differences (D2E) are sensi-

tive quantities that reflect the relative stability of the

investigated clusters. The DE shows the energy that

one atom is separated from the host clusters. The

Table 2 Symmetries (sym), HOMO–LUMO gaps, atomic

averaged binding energy (Eb), the dissociation energy (DE),

the second-order energy differences (D2E), vertical ionization

potential (VIP), vertical electron affinities (VEA) (all in eV),

and the mean nearest-neighbor bond lengths between Al and

Co atoms (dAl–Co (A)) for the most stable ConAl (n = 1–15)

clusters

Cluster sym gap Eb DE D2E VIP VEA dAl–Co (A)

CoAl C?v 1.909 0.391 6.930 0.585 2.454

Co2Al C2v 0.745 0.674 1.241 -0.046 6.699 0.863 2.486

Co3Al C3v 0.504 0.827 1.284 0.196 6.634 0.917 2.538

Co4Al C2v 0.356 0.879 1.088 0.063 6.539 0.901 2.438

Co5Al Cs 0.473 0.904 1.026 -0.661 6.519 1.328 2.480

Co6Al C5v 0.824 1.015 1.687 -0.049 6.324 1.064 2.530

Co7Al Cs 0.375 1.105 1.736 0.800 6.221 1.227 2.416

Co8Al C4v 0.028 1.087 0.936 -1.037 6.221 1.257 2.549

Co9Al C2v 0.430 1.175 1.973 0.952 6.133 1.358 2.489

Co10Al C4v 0.441 1.161 1.020 -1.064 5.891 1.396 3.043

Co11Al C5v 0.334 1.238 2.084 -0.142 5.989 1.377 2.471

Co12Al C5v 0.338 1.310 2.171 -2.465 5.948 1.442 2.604

Co13Al C3v 0.593 1.530 4.637 3.557 5.859 1.687 2.562

Co14Al Cs 0.135 1.516 1.080 -0.882 5.676 2.000 2.652

Co15Al Cs 0.266 1.544 1.962 5.565 1.997 2.501


123

Table 3 Structures, binding energies of various clusters obtained using the BLYP-DFT method

Cluster Location of H Total BE (eV) BE of H (eV) dAl–Co (A) dAl–H (A) DCo–H (A)

1a CoAlH b(Co, Al) 3.029 2.248 2.430 1.910 1.600

1b CoAlH2 b(Co, Al) 5.516 4.735 2.425 1.870 1.630

2a Co2AlH b(Co, Co) 4.547 2.526 2.480 1.687

2b Co2AlH2 n-b,b(Co, Al) (Co, Co) 6.993 4.972 2.485 1.900 1.670

2c Co2AlH2 n-b,b(Co, Co) (Co, Co) 6.822 4.801 2.490 1.706

2d Co2AlH2 n-b,b(Co, Al) (Co, Al) 6.670 4.649 2.460 1.870 1.645

3a Co3AlH b(Co, Co) 6.057 2.751 2.497 1.687

3b Co3AlH h(Co, Co, Co) 5.929 2.623 2.529 1.791


3d Co3AlH2 o-b,b(Co, Co) (Al, Co) 8.343 5.037 2.517 1.745 1.693

3e Co3AlH2 n-b,h(Co, Co)(Co, Co, Co) 8.335 5.029 2.530 1.762

4a Co4AlH b(Co, Co) 7.652 3.257 2.545 1.689

4b Co4AlH2 n-b,b(Co, Co) (Co, Co) 10.278 5.883 2.565 1.690

4c Co4AlH2 o-b,b(Co, Co) (Co, Co) 10.112 5.717 2.555 1.701

5a Co5AlH b(Co, Co) 9.257 3.837 2.468 1.695

5b Co5AlH h(Co, Co, Co) 9.256 3.836 2.545 1.780


5d Co5AlH2 n-h,h(Co, Co, Co) (Co, Co, Co) 11.668 6.247 2.468 1.777

5e Co5AlH2 n-b,b(Co, Co) (Al, Co) 11.638 6.217 2.440 1.880 1.647

6a Co6AlH b(Co, Co) 11.051 3.943 2.532 1.690

6b Co6AlH h(Co, Co, Co) 10.925 3.817 2.506 1.787



7a Co7AlH h(Co, Co, Co) 12.678 3.834 2.553 1.790

7b Co7AlH b(Co, Co) 12.648 3.805 2.565 1.690


7d Co7AlH2 o-b,b(Co, Co) (Co, Co) 15.102 6.259 2.560 1.700

8a Co8AlH b(Co, Co) 14.419 4.639 2.560 1.703

8b Co8AlH h(Co, Co, Co) 14.403 4.623 2.560 1.795

8c Co8AlH2 n-h,h(Co, Co, Co) (Co, Co, Co) 16.920 7.140 2.560 1.797


8e Co8AlH2 n-b,b(Co, Co) (Co, Co) 16.798 7.018 2.560 1.693

9a Co9AlH h(Co, Co, Co) 16.229 4.476 2.550 1.790

9b Co9AlH2 n-h,h(Co, Co, Co) (Co, Co, Co) 18.771 7.018 2.550 1.790


10a Co10AlH b(Co, Co) 17.432 4.659 2.700 1.720



11a Co11AlH h(Co, Co, Co) 19.979 5.121 2.605 1.807

11b Co11AlH2 n-h,b(Co, Co, Co) (Co, Co) 22.564 7.706 2.611 1.774


12a Co12AlH h(Co, Co, Co) 22.194 5.165 2.627 1.797


12c Co12AlH2 o-h,h(Co, Co, Co) (Co, Co, Co) 24.675 7.646 2.613 1.810


123

D2E is often directly compared with the relative

abundances determined in mass spectroscopy exper-

iments. They are defined as Eqs. 2 and 3, where

E(ConAl), E(Con?1Al), E(Con-1Al), and E(Co) rep-

resent the total energies of the most stable ConAl,

Con?1Al, and Con-1Al clusters and a Co atom,

respectively. As shown in Fig. 3, particularly prom-

inent maxima of D2E are found at n = 7, 9, and 13,

indicating higher stability than their neighboring

clusters. It is observed that, for the ConAl cluster, the

DE of Co7Al (1.736 eV), Co9Al (1.973 eV), and

Co13Al (4.637 eV) clusters are higher than other

clusters. And the HOMO–LUMO gaps of Co7Al

(0.375 eV), Co9Al (0.430 eV), and Co13Al (0.593 eV)

shown in Table 2 are larger than those of their

neighboring clusters. Thus, we can conclude that the

magic clusters are found at n = 7, 9, and 13 for ConAl.

It is worth pointing out that the relative stability of the

Co13Al cluster in terms of the calculated dissociation

energy and the second-order difference of cluster

energy are both the strongest among all different sized

clusters. The high stability of Co13Al cluster might

stem from its highly symmetric geometry.

Experimentally, the electronic structure is probed

through measurements of ionization potentials, elec-

tron affinities, polarizabilities, etc. Therefore, we also

study these quantities to understand their evolution

with size. These quantities are determined within

BLYP for the lowest energy structures obtained within

the same scheme.

The vertical ionization potential (VIP) is calculated

as the self-consistent energy difference between the

cluster and its positive ion with the same geometry.

The VIP is plotted in Fig. 4 as a function of cluster

size. In general, the VIP decreases for n = 1–15. Also

shown in Fig. 4 are the VIPs of pure Co clusters. These

have also been calculated at the BLYP level of theory,

with structures optimized at the same level of theory.

The comparison of the two curves shows that replac-

ing one Co in Con cluster with Al, to give Con-1Al,

results in the approximate values of VIPs for most

clusters except for CoAl and Co2Al, which have

smaller VIPs than the corresponding Con clusters.

-3.2-2.4-1.6-0.8

00.81.62.43.2

44.85.6

n

Ene

rgy/

eV

ΔE

Δ2E

0 2 4 6 8 10 12 14 16

Fig. 3 Size dependence of the second-order energy difference

and the dissociation energy of the lowest energy ConAl

(n = 2–15) clusters

Table 3 continued

Cluster Location of H Total BE (eV) BE of H (eV) dAl–Co (A) dAl–H (A) DCo–H (A)

13a Co13AlH h(Co, Co, Co) 23.886 2.465 2.562 1.800


14a Co14AlH h(Co, Co, Co) 25.547 2.801 2.543 1.806


15a Co15AlH h(Co, Co, Co) 27.208 2.500 2.511 1.810


dAl–Co, dAl–H, and dCo–H are the mean nearest-neighbor bond lengths between Al and Co atoms, Al and H atoms, and Co and H atoms.

Location of H is represented by symbols n, o, b, t, and h which mean neighboring, opposite, bridge, top, and hollow site, respectively

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Eb/e

V

n

ConAl

Con+1

0 2 4 6 8 10 12 14 16

Fig. 2 Size dependence of average binding energy of the

lowest energy ConAl and Con?1 clusters


123

We have also calculated vertical electron affinities

(VEA) for these clusters (see Fig. 5) by assuming the

geometry for the charged cluster to be the same as for

the neutral one. Figure 5 shows that the VEA values of

the ConAl clusters increase as the number of atoms

increase except at n = 5 with a local maximum. A

comparison of the VEAs of ConAl clusters and pure

Co clusters shows that the most ConAl have the higher

values of VEAs than those of Con. It is interesting to

point out that the large-sized clusters usually have

smaller VIPs and larger VEAs as compared with the

small-sized clusters, implying that it is much more

difficult to ionize the smaller clusters than the larger

ones but much easier to attach an electron to the larger

clusters than to the smaller ones.

Hydrogen on ConAl (n = 1–15)

The optimized geometries for the adsorption of one

and two H atoms on small ConAl (n = 1–15) clusters

are shown in Fig. 6. In Table 4, structures, binding

energies of various ConAlHm (n = 1–15; m = 1, 2)

clusters obtained using the BLYP-DFT method are

displayed for the isomers shown in Fig. 6. In Table 4,

total BE is the binding energy of ConAlHm, using the

following equation:

Eb ConAlHm½ � ¼ nE Co½ � þ E Al½ � þ mE H½ �� E ConAlHm½ � ð4Þ

and BE of H is the difference of the binding energy of

ConAlHm and ConAl.

For the chemisorptions of one or two H on the

ConAl cluster, there are three possible adsorption sites:

onefold on top, twofold edge, and threefold hollow

site. The calculation result shows that the twofold edge

and threefold hollow adsorption configurations are

energetically most stable.

It is seen that the BE of H on CoAlH (4.735 eV) is

different to that of H on CoAl (2.248 eV). This shows

that both CoAlH and CoAlH2 have the different

stability.

The ground state corresponding to Co2AlH cluster

(Fig. 6[2a]) is a spin singlet with a Co–H bond length

of 1.687 A and the H atom takes the bridge adsorption

with the Co and Co atoms. The Cs isomer (Fig. 6[2b])

with two H atoms bridging in Co, Co atoms and Co, Al

atoms is found for the most stable geometry of

Co2AlH2 cluster. Other optimized geometries are also

considered for this cluster, for example, occupied

different places of Al, Co atoms (Fig. 6[2c]) and Co,

Co atoms (Fig. 6[2d]). None of them are more stable

than the ground state structure.

Two optimized geometries are found for Co3AlH

cluster, both of the same multiplicity, doublets.

Interaction of H twofold edge site of Co (Fig. 6[3a])

with Cs symmetry is favorable as compared with a

threefold on the hollow of Co3Al with C3v symmetry

(Fig. 6[3b]) by 0.128 eV. The BE is small (2.751 eV)

that it is easy to make further interaction with

hydrogen atom. To confirm this, I carried out calcu-

lation on Co3AlH2. Three configurations for H are

studied: (i) where both H atoms are bridging with two

Co atoms (Fig. 6[3c]), (ii) where one H atom is

bridging with two Co atoms and another one with Co

and Al atoms (Fig. 6[3d]), and (iii) where one H atom

0 2 4 6 8 10 12 14 160.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Ver

tical

ele

ctro

n af

fini

ty/e

V

n

ConAl

Con+1

Fig. 5 Size dependence of VEAs of the lowest energy ConAl

and Con?1 clusters

5.2

5.4

5.6

5.8

6.0

6.2

6.4

6.6

6.8

7.0

7.2

7.4

7.6V

ertic

al I

oniz

atio

n Po

tent

ial/e

V

n

ConAl

Con+1

0 2 4 6 8 10 12 14 16

Fig. 4 Size dependence of VIPs of the lowest energy ConAl

and Con?1 clusters


123

1a 1b 2a 2b 2c 2d

3a 3b 3c 3d 3e

4a 4b 4c

5a 5b 5c 5d 5e

6a 6b 6c 6d

7a 7b 7c 7d

8a 8b 8c 8d8e

9a 9b 9c 10a 10b 10c

11a 11b 11c 12a 12b 12c

13a 13b 14a 14b 15a 15b

Fig. 6 Relaxed structures

of ConAlHm (n = 1–15;

m = 1, 2). Black, gray, and

white balls are used for Co,

Al, and H, respectively


123

is bridging with two Co atoms and another one is in the

hollow site of Co, Co, Co atoms making the Cs

structures as shown in Fig. 6[3e]. The energy differ-

ence of the first two of these is 0.248 eV (Table 4).

Also the Cs structure 3e lies 0.256 eV higher in energy

than the 3c structure. The BE for 2H is 5.285 eV

(Table 4) and it shows that interaction between two

hydrogens on Co3Al is not attractive. This energy is

higher than the dissociation energy of H2 (4.60 eV).

Accordingly, hydrogen is likely to be dissociated on

Co3Al. The distance between two hydrogens on Co3Al

in the lowest energy state is 3.139 A as compared with

the bond length of 0.75 A in H2. Therefore, two

hydrogens are in a dissociated configuration. It is

worth mentioning that the thermodynamics of

hydrogen uptake and release (physical adsorption) is

actually ruled by the combined effect of adsorption

enthalpy and entropy. But it is necessary to indicate

that it is only favored by the enthalpy change for the

chemical adsorption. Entropy effects may not favour

this reaction.

The Co4AlH is a spin quartet and its structure, the

same as the small clusters Co2Al and Co3Al, prefers

the bridge site of Co, Co atoms (Fig. 6[4a]). In the case

of two H on Co4Al, the structure with two H atoms

taking twofold bridge site on two neighboring Co, Co

atoms (Fig. 6[4b]) is the ground state. And the

structure with two H atoms on the bridge site of

opposite Co, Co atoms (Fig. 6[4c]) is the low-lying

one.

Table 4 Fragmentation

energies of ConAlHm

clusters with the product

Con-pAlHm-q, p = 1 and 2,

and q = 1

All the values mean the

parent cluster has a larger

binding energy than the sum

of the BE of the products

Cluster (ConAlHm) Con-1AlHm ?Co Con-2AlHm ?Co2 Con-1AlHm-1 ?CoH

2a Co2AlH 1.518 2.074 1.576

2b Co2AlH2 1.478 2.234 1.774

3a Co3AlH 1.510 2.539 1.845

3c Co3AlH2 1.597 2.585 1.853

4a Co4AlH 1.595 2.615 2.155

4b Co4AlH2 1.687 2.795 2.030

5a Co5AlH 1.605 2.710 2.672

5c Co5AlH2 1.567 2.765 2.003

6a Co6AlH 1.793 2.909 3.440

6c Co6AlH2 1.894 2.972 2.291

7a Co7AlH 1.627 2.931 3.380

7c Co7AlH2 1.608 3.012 2.106

8a Co8AlH 1.742 2.879 3.385

8c Co8AlH2 1.573 2.691 2.052

9a Co9AlH 1.810 3.061 4.295

9b Co9AlH2 1.850 2.933 2.161

10a Co10AlH 1.203 2.523 3.489

10b Co10AlH2 1.856 3.216 2.207

11a Co11AlH 2.547 3.260 5.015

11b Co11AlH2 1.937 3.303 2.942

12a Co12AlH 2.215 4.272 5.146

12b Co12AlH2 2.169 3.616 2.563

13a Co13AlH 1.693 3.418 4.667

13b Co13AlH2 1.693 3.372 2.041

14a Co14AlH 1.660 2.863 1.690

14b Co14AlH2 1.559 2.762 1.908

15a Co15AlH 1.663 2.833 2.272

15b Co15AlH2 1.679 2.748 1.927


123

Similar to ConAl discussed earlier, one H is most

favorable on a bridge site of Co, Co atoms (Fig. 6[5a])

in Co5Al cluster, and it is with a binding energy of only

0.001 eV stronger than that of the threefold hollow

adsorption of Co, Co, Co atoms (Fig. 6[5b]). The BE

(3.837 eV) of H on Co5Al is also one of the smallest

among all the clusters studied. Accordingly, Co5AlH

should have small abundance. Two H prefer the bridge

sites of adjacent Co, Co atoms (Fig. 6[5c]). Isomers

with two H on the threefold hollow site of Co, Co, Co

atoms (Fig. 6[5d]) and two H on the different bridge

sites of Al, Co and Co, Co atoms (Fig. 6[5e]) have

0.177 and 0.207 eV higher energies, respectively.

The BE (3.943 eV) of H on the bridge site of two

Co, Co atoms of Co6Al (Fig. 6[6a]) is the ground state

structure of Co6AlH. The fragmentation energy (see

below) is also small and this gives further support for

the instability of Co6AlH. Accordingly, it may not

have large abundances. And the structure (Fig. 6[6b])

with hydrogen on a hollow site of Co, Co, Co atoms

lies only 0.125 eV high in energy. For two hydrogen

atoms on Co6Al, several configurations are studied.

These include bridge of Co, Co atoms in the neigh-

boring triangle (Fig. 6[6c]), hollow of Co, Co, Co

atoms in the adjacent triangle (Fig. 6[6d]) The calcu-

lated BE’s given in Table 4. The most favorable

adsorption sites of Co6AlH2 are structure 6c. The two

H have a similar configuration as in ConAlH2 (n = 3,

4, 5). The BE for 2H is 6.331 eV and it shows that

interaction between two hydrogen on Co6Al is more

attractive than clusters discussed earlier. This energy

is also higher than the dissociation energy of H2

(4.60 eV). Accordingly, hydrogen is likely to be

dissociated on Co6Al. The distance between two

hydrogens on Co6Al in the lowest energy state is very

long as compared with the bond length of 0.75 A in

H2. Therefore, two hydrogens are also in a dissociated

state on Co6Al.

One hydrogen adsorption of Co7Al is favorable on

the hollow of the Co, Co, Co atoms (Fig. 6[7a]). The

BE (3.834 eV) of H on Co7Al is one of the largest

among all the clusters studied. Isomer with H on the

bridge site of Co, Co atoms (Fig. 6[7b]) is 0.03 eV

higher in energy. The small HOMO–LUMO gap

(0.681 eV) is likely to make further interaction of

hydrogen with this cluster energetically not so favor-

able. To confirm this, some calculations are carried out

on Co7AlH2. Several initial configurations are con-

sidered for two hydrogens. These include H atoms on

the bridge of adjacent Co, Co atoms in the lower part

of the Co7Al cluster (Fig. 6[7c]). This has the lowest

energy. The HOMO–LUMO gap is lower (0.807 eV)

and the addition of one more hydrogen to Co7Al leads

to a gain of 6.504 eV, an increase of more than

2.67 eV in the BE of H as compared with one

hydrogen on Co7Al. The other calculated position for

two hydrogens on Co7Al is one on bridge of two

distant Co atoms (Fig. 6[7d]). The energy difference

of the isomers (Fig. 6[7c, 7d]) is 0.24 eV.

Co8Al has Cs symmetry (Fig. 6[8a]). I can very

roughly decompose this structure into two interacting

entities. That is the structure Co4Al and Co4 are

bridged with Co–Co bonds. I anticipate that, similar to

Co4Al, this cluster would not favor to react with one

hydrogen. Indeed I find that, the BE of H is 4.639 eV

different from Co4Al of 2.107 eV. One H is favorable

on the bridge site of Co, Co atoms of Co8Al

(Fig. 6[8a]). Structure Fig. 6[8b] with H atom on a

hollow site of Co, Co, Co atoms is only 0.02 eV less

stable. Therefore, the interaction depends very sensi-

tively on the electronic and atomic structures of

clusters. Adsorption of two hydrogen is studied on a

few selected sites which included two neighboring

faces with H atoms on the hollow Co, Co, Co atoms

(Fig. 6[8c]), the two H atoms on the hollow sites of

adjacent Co, Co, Co atoms (Fig. 6[8d]), and two

bridge sites of neighboring Co, Co atoms in the Co8Al

cluster (Fig. 6[8e]). We find that the 8c isomer has the

lowest energy. The BE of this isomer is 7.140 eV,

which is larger than the ConAl cluster discussing

earlier.

H adsorption on hollow Co, Co, Co atoms

(Fig. 6[9a]) is the most stable structure of Co9AlH

with a binding energy of 4.476 eV. The ground state

corresponding to Co9AlH2 cluster is the geometry

Fig. 6[9b] with an average Al–Co bond length of

2.550 A, which is the same as Co9AlH. Two H prefer

the hollow sites of adjacent Co, Co, Co atoms. Two H

adsorption on distant hollow site of Co, Co, Co atoms

(Fig. 6[9c]) is a substable structure with a binding

energy of only 0.04 eV less than the ground state.

One H is favorable on the bridge site of Co, Co

atoms of Co10Al (Fig. 6[10a]). Structure Fig. 6[10b]

with two H atoms on a neighboring hollow site of Co,

Co, Co atoms is the ground state corresponding to

Co10AlH2 cluster. The structure with two H atoms on

the bridge of Co, Co atoms of the neighboring

triangles Fig. 6[10c] is 0.576 eV less stable.


123

H adsorption on hollow Co, Co, Co atoms of

Co11Al (Fig. 6[11a]) is the most stable structure of

Co11AlH with a binding energy of 5.121 eV. And the

lowest energy structure for Co11AlH2 clusters is the

structure Fig. 6[11b] with two neighboring H atoms

adding on the hollow site of Co, Co, Co atom and the

bridge site of Co, Co atom. Structure Fig. 6[11c] with

two H atoms on a neighboring hollow site of Co, Co,

Co atoms is only 0.044 eV less stable.

Adsorption of single hydrogen on the hollow site of

Co, Co, Co atoms (Fig. 6[12a]) is considered to be the

ground state structure of Co12AlH. The BE (5.165) of

H on Co12Al is the largest among all the clusters

above. However, the HOMO–LUMO gap is small

(0.308 eV). The small HOMO–LUMO gap is likely to

make further interaction of hydrogen with this cluster

energetically so favorable. To confirm this, calcula-

tions on Co12AlH2 are carried out. Several initial

configurations are considered for two hydrogens.

These include two H atoms on the hollow sites of

Co, Co, Co atoms in the adjacent Fig. 6[12b] and

opposite triangle faces Fig. 6[12c] of Co12Al. The

isomer Fig. 6[12b] is 0.058 eV more stable than the

Fig. 6(12c) isomer.

For ConAlH (n = 13–15), the ground states reveal

hollow site H bonding to the Co, Co, Co atoms

(Fig. 6[13a, 14a, 15a]). Hollow site on the neighboring

Co, Co, Co triangles is found for the ground state

structures of ConAlH2 (n = 13–15) (Fig. 6[13b, 14b,

15b]).

Stability and fragmentation behavior

To check the stability of the lowest energy isomers,

vibrational frequencies for selected clusters have been

calculated using the BLYP/DNP level of theory. It is

found that the lowest energy isomers of all kinds of

clusters discussed earlier have all real frequencies and

are, therefore, stable. Figure 7 shows the plot of the BE

of one and two H atoms on ConAl clusters. The BE is

large for H with n = 8, 11, and 12 of ConAlH atoms.

And, for 2H, clusters with n = 5, 8, and 10 have higher

BE’s. The stability of these complexes is further

studied from the fragmentation energies (Table 5).

Channels with Con-1AlHm, Con-2AlHm, or Con-1-

AlHm-1 molecule being one of the fragments have

been studied. It is noted that in all these processes, the

fragmentation energy is the largest for Co12AlH and

therefore, I expect it to be among the most stable

species. Also the fragmentation energy for Co11AlH is

next largest for all these channels, suggesting it to be

other stable cluster.

Bonding nature

To understand the bonding nature of hydrogen on

cobalt aluminum clusters, the bond lengths in both

hydrogenated clusters and pure cobalt aluminum

clusters are discussed. From Table 2, one finds that

the Al–Co bond lengths increase generally as the size

of the cluster increases. The Al–Co, Al–H, and Co–H

bond lengths for the adsorption on ConAl clusters are

in the range of 2.383–2.705, 1.745–1.910, and

1.600–1.810 A, respectively. Thus, one can conclude

that these bond lengths evolve very slowly with cluster

size. In addition, the nearly constant value for Co–H

and Al–H bond lengths on different clusters at specific

adsorption sites suggests the similar nature of bonding

of H in different clusters. From Table 4 and Fig. 6, one

can also see that one hydrogen adsorption on ConAl

(n = 1–6, 8, 10) and two hydrogen adsorption on

ConAl (n = 1–7) take the twofold bridge site as their

most favorable chemisorptions site. While threefold

hollow site is preferred for one hydrogen adsorption

on ConAl (n = 7, 9, 11–15) and two hydrogen

adsorption on ConAl (n = 8–10, 12–15) clusters.

The ground state structure of two hydrogen adsorption

on Co11Al is an exception.

0 2 4 6 8 10 12 14 160

1

2

3

4

5

6

7

8

9

Bin

ding

Ene

rgy

of H

ydro

gen

/eV

n

ConAlH

ConAlH

2

Fig. 7 Binding energies of H (down) and 2H (up) atoms on

ConAl clusters


123

Summary

The geometrical structures, stabilities, VIPs, VEAs of

the ConAl and Con?1(n = 1–15) clusters and the

adsorption behaviors, binding energies and fragmen-

tation energies of ConAlHm(n = 1–15, m = 1,2) have

been investigated by the GGA functional at the DNP

level. The results are summarized as follows:

(1) The optimized geometries show that Al atom

substitutes the surface atom of the Con?1 clusters

for n B 13 and it keeps the similar frameworks

of the most stable Con?1 clusters except for

n = 2, 3, and 6. Starting from n = 14, the Al

atom completely falls into the center of the Co-

frame.

(2) The dissociation energy, the second-order

energy differences, and the HOMO–LUMO gaps

of the most stable ConAl clusters indicate that the

magic numbers are n = 7, 9, and 13, corre-

sponding to the high symmetrical structures.

(3) The result on hydrogen interaction with cobalt

aluminum clusters has been presented. Hydrogen

undergoes chemisorptions and interacts strongly

with cobalt aluminum clusters. One hydrogen

adsorption on ConAl (n = 1–6, 8, 10) and two

hydrogen adsorption on ConAl (n = 1–7) take

the twofold bridge site as their most favorable

chemisorptions site. While threefold hollow site

is preferred for one hydrogen adsorption on

ConAl (n = 7, 9, 11–15) and two hydrogen

adsorption on ConAl (n = 8–10, 12–15) clusters.

The ground state structure of two hydrogen

adsorption on Co11Al is exceptional.

(4) There is a slight increase in the mean Al–Co

bond lengths after H adsorption on the lowest

energy sites of the most ConAl clusters. In

addition, the nearly constant value for Co–H and

Al–H bond lengths on different clusters at

specific adsorption sites suggests the similar

nature of bonding of H in different clusters. In

general, the binding energy of H and 2H of

ConAl (n = 1–12) are both found to increase

with the cluster size. And the result shows that

large binding energies of the hydrogen atoms and

large fragmentation energies for Co11AlH and

Co12AlH make these species behaving like

magic clusters.

Acknowledgments This work was financially supported by

the National Natural Science Foundation of China (Grant No.

20603021), Youth Foundation of Shanxi (Grant No.

2007021009), and the Youth Academic Leader of Shanxi.

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Documents

Evolution of Con Al clusters and chemisorption of hydrogen on Con Al clusters