The germanium clusters Ge n (n = 1–6) and their anions: structures, thermochemistry and electron affinities

Abstract

Six different hybrid and pure density functional theory (DFT) methods have been employed to study the structures, electron affinities, and dissociation energies of the (n = 1–6) species. The basis set used is of double-ζ plus polarization quality with additional s- and p-type diffuse functions, denoted DZP++. The geometries are fully optimized with each DFT method independently. Located were 20 structures of the neutral Ge n clusters and 12 structures of the anionic clusters. The ground states of Ge n and clusters in this work are in good agreement with available experiments. Three types of electron affinities reported are the adiabatic electron affinity (EAad), the vertical electron affinity (EAvert), and the vertical detachment energy (VDE). The first Ge–Ge dissociation energies D e(Ge n −1–Ge) for Ge n and both D e(–Ge) and D e(Ge n −1–Ge−) for the species have also been reported. Previously observed trends in the prediction of bond lengths by DFT methods are also demonstrated for the germanium clusters and their anions. Generally, the Hartree–Fock/DFT hybrid methods predict shorter and more reliable bond lengths than the pure DFT methods. The most reliable adiabatic electron affinities, obtained at the DZP++ BP86 level of theory, are 1.55 (Ge), 1.97 (Ge2), 2.24 (Ge3), 2.08 (Ge4), 2.29 (Ge5) and 2.07 eV (Ge6), among which those for Ge2, Ge3 and Ge6 are in good agreement with experiment. However, for Ge5 the predicted electron affinity is somewhat smaller than the available experimental values. Average electron affinity differences with the best experiments are 0.10 eV for the B3LYP method and 0.12 eV for BP86. The first dissociation energies for the neutral germanium clusters predicted by the B3LYP method are 2.87 (Ge2), 3.22 (Ge3), 3.80 (Ge4), 3.12 (Ge5) and 3.37 eV (Ge6). Compared to the available experimental dissociation energies for Ge2, the theoretical predictions are very reasonable. For the vibrational frequencies of the Ge n series, the DZP++ B3LYP method produces reliable predictions with a relative error of ∼2% with respect to available experimental values. In addition to the earlier finding that the BHLYP method is the most reliable for geometries, we conclude that the BP86 or B3LYP methods do the best for electron affinities, with B3LYP preferable for dissociation energies and vibrational frequencies among the six DFT methods.