  In this paper we report the structure of the Li4Ge4 cluster as a function of
charge transfer and polarizability. We find that for small charge transfer (Q <
0.5) this cluster has the expected cubic structure: a Ge4 tetrahedron with a Li
ion attached at large distance to each face. With increasing charge transfer Q
> 0.5 the structure of Li4Ge4 changes: for relative small polarizability of the
Ge ion the Ge4 breaks up into two Ge2 pairs separated by the four Li. For
larger polarizability there are three possibilities: 1) for full charge
transfer the Li ions break up the Ge subcluster into four separated ions; 2)
for smaller values of the charge transfer we still have the structure with two
Ge2 pairs and 3) for intermediate values of, charge transfer the Ge sublattice
forms a structure with two opposite bonds of the Ge4 tetrahedron cluster
broken. These are the only stable geometries found. For large Ge polarizability
we find that all structures become unstable: the size of the induced dipole
moment becomes larger than the diameter of Ge. Based on this phase diagram of
Li4Ge4 we discuss the structure of other A4M4 alkali(= A)--tetralide (= M) (=
group 14) clusters, and related solid state structures
