Cluster World

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 well

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 Al₆ cluster.

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 icosahedron. 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.