Structural and electronic properties of aluminum-based binary clusters
S. Chacko,* M. Deshpande,
†
and D. G. Kanhere
‡
Department of Physics, University of Pune, Pune 411007, India
Received 2 October 2000; revised manuscript received 5 April 2001; published 1 October 2001
We investigate the low-energy geometries and the electronic structure of several aluminum based clusters,
viz. Al
4
X
4
,( X =Li, Na, K, Be, Mg, B, and Si by first principle Born-Oppenheimer molecular dynamics
within the framework of density-functional theory. We present a systematic analysis of the bonding properties
and discuss the validity of spherical jellium model. We find that the structure of eigenstates for clusters with
metallic elements conform to the spherical jellium model. The 20 valence electron systems Al
4
Be
4
and Al
4
Mg
4
exhibit a large highest-occupied–lowest-unoccupied HOMO-LUMO gap due to shell closing effect. In clus-
ters containing alkali-metal atom, Al
4
behaves as a superatom that is ionically bonded to them. The Al-Al bond
in both Al
4
Si
4
and Al
4
B
4
clusters is found to be covalent.
DOI: 10.1103/PhysRevB.64.155409 PACS numbers: 61.46.+w, 31.15.Ar, 36.40.-c
I. INTRODUCTION
During the last few years much attention has been paid to
the study of atomic clusters from both theoretical and
experimental
1–4
sides. The areas of interest include ground-
state geometries, electronic structure, optical properties, frag-
mentation, and thermodynamic properties like melting. The
theoretical calculations are usually carried out by employing
density-functional molecular dynamics in conjunction with
simulated annealing. Extensive investigations on the geom-
etries and the electronic structure of homo-atomic clusters
with 20 atoms of Li, Na, K, Mg, B, Al, Ga, Si, etc., have
been carried out.
5–14
Similar investigations on heterogeneous
clusters are relatively few. Mixed clusters are of considerable
interest due to diverse effects like bonding,
15,16
segregation,
selective clustering, etc. It is instructive to contrast the prop-
erties of these tiny alloys with their bulk counterparts. An-
other interesting aspect concerns the validity of spherical jel-
lium model
17
SJM for mixed clusters. It is known that the
eigenvalue spectrum of alkali-atom clusters generally con-
forms to the SJM with minor modifications. This has also
been observed in the case of single impurity doped metallic
clusters of the type A
n
B ,
18–23
where depending upon the na-
ture of impurity, it either gets trapped or prefers to be on the
surface or distorts the host structure significantly. Impurities
with smaller ionic radii and strong binding with the host are
seen to get trapped in the cluster. Many investigations on
mixing and segregation effects in various mixed alkali-atom
clusters, viz. Na-K Refs. 24 and 25 and Na-Li Ref. 26,
have been reported. The ground-state geometries of several
A
4
B
4
clusters involving simple metal atoms like Li, Na, K,
Rb, Cs, Mg, Al, Sb, and other elements like Ga, Sr, Si have
been studied by Majumdar et al.
27
The lowest energy struc-
ture of all these clusters were found to be tetracapped tetra-
hedron TCP. In an ab initio orbital based investigation,
Raghavachari et al.
28
suggested a similar structure for both
Al
4
P
4
and Mg
4
S
4
clusters. A recent ab initio density-
functional calculation
29
demonstrated the high stability of
A
4
Pb
4
( A =Li, Na, K, Rb, Cs clusters, where Pb
4
forms a
tetrahedron capped by alkali atoms.
It is well established that so far as alkali-metal atoms are
concerned the SJM has been quite successful in describing
the gross electronic structure and the stability. However,
clusters of Al presents an interesting contrast. Although bulk
Al is known to be a free electron metal, several experimental
and theoretical studies indicate that small Al clusters do not
display the well known magic behavior. This and other such
issues concerning the nature of the electronic states in pure
Al clusters have been critically examined by Rao and Jena.
30
In an elaborate density-functional calculations for charged
and neutral Al clusters, they found that Al
7
+
with 20 valence
electrons is magic. Further, the electronic structure of clus-
ters containing less than 7 atoms does not resemble that of
the jellium model. They have also presented some evidence
for an effective monovalent nature in pure small Al clusters.
However, their investigation on Al
5
X
m
Ref. 31 ( X =Li, K
failed to provide any evidence of suggested monovalent na-
ture of Al. The onset of sp hybridization in pure Al clusters
and the relation of their electronic structure to the jellium
model has also been studied by Duque and Mananes
32
. Re-
cent investigations on Al
5
Na
n
Ref. 33 ( n =1–6), clearly
indicate that Al
5
Na
5
, a 20 valence electron system, to be
very stable. The spectrum of Al
5
Na
5
conforms to SJM.
Moreover, alkalization of these Al clusters
31
makes their
electronic structure jelliumlike. It also lowers the ionization
potential of the base Al
n
clusters.
34
Apart from these pecu-
liarities of Al clusters, early work on Al-Li clusters
18,35
indi-
cates an ionic bond between Al and Li. It may be recalled
that in bulk phase, aluminum forms stable alloys with vari-
ous elements like Li, Be, Mg, Si, etc., while Na and K Refs.
36 and 37 are completely immiscible in it. It also forms a
strongly bonded boride AlB
2
, whose stability mainly depend
on the strong B-B and Al-B bond. Thus it is of considerable
interest to study aluminum based mixed clusters.
In the present work, we investigate the structural and the
electronic properties of several aluminum based binary clus-
ters, viz. Al
4
X
4
clusters using Born–Oppenheimer molecular
dynamics BOMD Ref. 38 within the framework of
density-functional theory, where X ranges from simple
monovalent alkali metals Li, Na, K to divalent metals Be,
Mg and finally to semiconductors B and Si. We also present
a systematic analysis of the bonding properties and discuss
the validity of SJM.
PHYSICAL REVIEW B, VOLUME 64, 155409
0163-1829/2001/6415/1554096/$20.00 ©2001 The American Physical Society 64 155409-1