The geometrical and electronic structures of the germanium clusters with up to 25 atoms are studied by using density-functional theory with the generalized gradient approximation. The ${\mathrm{Ge}}_n$ clusters follow a prolate growth pattern with $n>~13.$ For medium-sized clusters, we find two kinds of competing structures, stacked layered structures and compact structures. The stacked layered structures with capped tetrahedron ${\mathrm{Ge}}_9$ cluster are more stable than compact structures and other stacked structures. The size dependence of cluster binding energies, highest-occupied and lowest-unoccupied molecular orbital gap, and ionization potentials are discussed and compared with experiments.

• Received 9 May 2001

DOI:https://doi.org/10.1103/PhysRevB.64.205411