Beyond the Wade-Mingos Rules in Bare 10- and 12-Vertex Germanium Clusters:  Transition States for Symmetry Breaking...

The lowest energy structures of bare Gen(z) clusters (n = 10, 12; z = -6, 0, +2, +4) obtained using density functional theory (DFT) at the hybrid B3LYP level often are relatively low-symmetry polyhedra not readily recognizable by the Wade-Mingos rules. However, such optimized structures may arise from higher symmetry transition states through symmetry breaking processes. Thus the lowest energy structures for the Ge10(6)(-) and Ge12(6)(-) clusters with hyperelectronic arachno 2n + 6 skeletal electron counts are derived from pentagonal and hexagonal prism transition states, respectively, and retain the pentagonal and hexagonal faces of the prisms upon symmetry-breaking optimization. In addition, a variety of capped cube, prism, and antiprism transition states are found for the hypoelectronic Ge10(4+), Ge12, and Ge12(4+) clusters, which go to low-energy low-symmetry optimized structures, typically Cs or Ci, upon following the normal modes of the imaginary vibrational frequencies.