Structure determination of Gen− (n = 4–30) clusters

Determining the structures of germanium clusters can assist in comprehending the origins of the structures and properties of germanium bulk. As a result, it can pave the way for designing semiconductor materials with exceptional properties. Herein, we investigated the structural evolution and electronic properties of germanium clusters Ge_n⁻ (n = 4–30) at density functional theory (DFT) level. Low-lying isomers of these clusters have been globally searched by using a homemade genetic algorithm coupled with DFT calculations. The ground-state structures of all these Ge cluster anions have been identified by comparing the experimental and simulated photoelectron spectra (PES). In the studied size range of n = 4–30, the Ge clusters follow a simple growth pattern. From Ge₄⁻ to Ge₉⁻, a nine-atom tricapped trigonal prism (TTP) is stepwisely formed. The resulting TTP unit is then capped with the remaining excess atoms in the size range of n = 10–17. Ge₁₈⁻ to Ge₃₀⁻ result from two TTP units by incorporation of additional adatoms into the waist. The vertical detachment energy (VDE) curve for Ge_n⁻ displays a general increasing trend, while the HOMO–LUMO gap results are in an opposite trend. The average binding energies increase as the size increases, indicating that it is conducive to the formation of large clusters. It is found that sizes n = 7, 10, 13, 15 are the magic numbers.