Ionic bonding in metallic clusters!
Metal clusters are a strange lot. Here the electrons are free to move
all around the cluster. Infact, they are so free that they forget which
atom they belonged to. To them all atoms look the same and appear to
form a uniform positive background. The theoretical understanding of
metal clusters has most often relied on the Jellium
model of clusters. The jellium model assumes that the valence
electrons of all the atoms in a cluster are free and see a uniform
positively charged jellium formed by the ions. This model yields shell
structure for the electronic states similar to the shell structure for
atoms. When the number of elctrons correspond to a shell closing,
i.e., 2, 8, 20, 40...., the
cluster is expected to be stable. Many simple metal clusters like Li,
Na, Be, Mg, Al have been seen to follow the jellium picture reasonably
Here we study some clusters of aluminium doped with lithium and
magnesium. We show that based on the jellium model shell filling, metal
clusters can behave like ``super-atoms''. We show that in some
situations this kind of ``super-atom'' behavior leads to such a cluster
binding ionically with another metal atom. This is an
interesting phenomenon, and can be used to investigate the extent to
which the jellium picture is valid for a particular kind of clusters.
It may also open up possibilities of designing clusters of desired
stability, by choosing the kind of bonding one wants to have.
Clusters as super-atoms
We first look at the cluster Al6Mg, where the six aluminium
atoms for an octahedron, and the Mg atom caps a triangular face, as
shown in the picture. Each Al atom has 3 valence electrons, which
makes the total number of electrons in the Al6 cluster 18.
One would recall that 18 is just two short of shell closing. A Mg atom
has two valence electrons, and will be happy to part with them. So, if
one forms a cluster Al6Mg, and the jellium picture works,
one should see a transfer of the two electrons from Mg to the
We did a Car-Parrinello molecular dynamics calculation for the
Al6Mg cluster and found out the lowest energy electronic
state. We calculated the distribution of electrons in the cluster,
i.e., the density of electrons. In three dimensions it is not possible
to plot the density as a function of x, y and z coordinates. So we
plot a constant density surface of electron distribution. This means
plotting all points in the cluster where the density has the same
particular value. The result is shown in the picture alongside. For
comparison, the constant density surface of a single Mg atom is also
plotted, at the same value as used in the Al6Mg cluster.
One can see that when the Mg atom was alone, it had a finite density
of electrons, whereas in the cluster the Mg site only appears as an
empty hole, which means that the has been a transfer of electrons from
the Mg atom to the cluster.
You might think that this phenomenon is specific to Al and Mg. To
convince you that this is not so, we take another example. We take
a Al6 clusters and two Li atoms. Lithium (Li) atom has one
valence electron which it can happily part with. So, with two Li atoms
and the Al6 cluster we should be able to observe the same
effect as in Al6Mg.
Again we take the octahedral Al6 and cap two Li
atoms on opposite sites, as shown in the figure. So, how does the constant
density surface look like in this case? In the figure alongside, a
dimple at the lower right side in the constant density surface denotes
the location of an Li atom. This indicates that the electron has been
almost completely transferred to the Al6 cluster. So, the
Jellium picture actually works.
A cluster of Aluminium behaves like a "super-atom" and follows
electronic shell filling rules like atoms. Here, the surprising fact is
that although Al, Mg and Li are metals, the bonding between the
cluster and an atom is ionic. Because of the fact that
electron transfer takes place either from the cluster to the atom or
vice-versa there is a polarization of charge between the cluster and
the atom. Such clusters where electron transfer takes place, may behave
like an ionic molecule, and hence it may be possible to form an
ionically bonded solid out of such entities. The question whether this
polarization will survive at all, if one tries to make a solid out of
such entities, remains open. However, With this picture of a cluster
ionically bonded to an atom, one can go ahead to speculate whether such
ionic bonding is possible between two clusters, thereby leading to a
formation of a ``cluster-molecule''. This is an interesting
possibility, and will have bearing on what people are trying now,
i.e., to make cluster assembled materials (see R. Palmer,
New Scientist, 22 Feb. 1997).
Are cluster-molecules possible?
To investigate this aspect we look at the following situtation. We take
an Mg atom and put two clusters, which are one electron short of its
shell closing, on its either side. Doing this, one would expect that
the two valence electrons of Mg will be transferred to the two clusters
which will close their shells using that extra electron.
Al13, containing 39 valence electrons, satisfies the
criterion of a cluster with one electron short of shell-closing. In
addition, it has a very compact closed structure of an icosahedron.
So we look at a linear chain
Al13MgAl13. Picture on the right shows the constant density surface of two Al13 clusters and an Mg atom when they are
far apart, hence not bonded. Note how Al13 forms a nice
Let us now see what happens if these three entities are brought
closer. When they are brought close together, there is bonding between
them, and the energy is lowered. Picture below shows the constant
density surface of this cluster-molecule Al13MgAl13.
Interestingly, in this case too the electrons from the Mg atom have
been transferred to the two Al13 clusters, as evident from
loss of density in the region where the Mg atom is located. So, in
effect what remains are two Al13- clusters, and a
Mg+2 ion. Hence, one can think of this entity as an
ionically bonded cluster molecule. It is highly unlikely that this is
the ground state geometry of 26 Al atoms and one Mg atom, but this
definitely is a locally stable structure, and serves to demonstrate
that it is possible to have two clusters ionically bonded to each other
through an atom.
In future one can investigate various kinds of clusters to find out
where such a senario leads to a really stable cluster-molecule. It
would be interesting to see how the chemistry of a cluster changes
depending on how it is bonded to another cluster or an atom. It
appears, one can now talk about electronegativity and electron
affinity of a cluster.