A Stochastic Search for the Structures of Small Germanium Clusters and Their Anions: Enhanced Stability by Spherical Aromaticity of the Ge10 and Ge122- Systems

Investigations on germanium clusters in the neutral, anionic, and dianion states Ge-n(x) (n = 2 12 and x = 0, -1, -2) are performed using quantum chemical calculations with the B3LYP functional and the coupled-cluster singles and doubles [CCSD(T)] methods, in conjunction with the 6-311 +G(d) basis set. An improved stochastic method is implemented for searching the low-lying isomers of clusters. Comparison of our results with previous reports on germanium clusters shows the efficiency of the search method. The Ge-8 system is presented in detail. The anionic clusters Ge-n(-/2-) are studied theoretically and systematically for the first time, and their energetics are in good agreement with available experiments. The clusters Ge-10, Ge-10(2-), and Ge-12(2-) are, in their ground state, characterized by large highest occupied molecular orbital lowest unoccupied molecular orbital gaps, high vertical and adiabatic detachment energies, and substantial average binding energies. The enhanced stability of these magic clusters can consistently be rationalized using the jellium electron shell model and the spherical aromatic character.