The effect of group IIIB transition metals on the formation of closed-structure germanium clusters: a computer-aided experiment conducted in the framework of the density functional theory

Abstract

Purpose. The paper discusses the modelling results of the spatial structure and electronic properties of the clusters MeGe16 - and MeGe20 - (Me = Sc, Y, Lu). It considers the possibility of the synthesis of fullerene-like clusters and clusters with other types of closed structures. Comparative
calculations were carried out in the framework of the density functional theory using the SDD basis and three different potentials: B3LYP, B3PW91, and PBEPBE. The authors analysed the infl uence of the chosen potential on the modelling results of the spatial structure of clusters and their electronic spectra. The validity of theoretical methods was assessed by comparing the calculated electronic spectra with the experimental results on photoelectron spectroscopy.
Results The main isomer of the clusters MeGe^-₁₆ is the Frank-Kasper polyhedron for all of the three encapsulated metal atoms. For the cluster ScGe^-₂₀ , an isomer with a prismatic structure is detected experimentally. Endohedral structures have noticeably smaller average binding energies, yet, since their electronic spectra are in good agreement with the experimental spectra (although worse than the spectra of a prismatic isomer), their existence is likely. The main isomers of the YGe^-₂₀ and LuGe^-₂₀ clusters have endohedral structures, which can be observed with equal probability in the experiment, since their total spectrum ideally agrees with the experimental one.

Differences in the structure of the main isomers of the clusters MeGe^-₂₀ are associated with the size of the scandium, yttrium, and lutetium atoms. The scandium atom has a noticeably smaller atomic radius (1.63 Å) than the Y and Lu atoms (1.78 and 1.72 Å respectively); therefore, with alarge number of germanium atoms in the cluster ScGe^-₂₀ the scandium atom cannot stabilize a closed germanium lattice, and the formation of endohedral clusters becomes almost impossible. 

Conclusions. For the clusters MeGe^-₁₆ , calculations in all three potentials gave identical results. For the clusters MeGe^-₂₀ , the calculation in the potential B3LYP detected a shift in the highest average bond energies toward fullerene-like structures. The Frank-Kasper structures were the least stable in this calculation. The calculation using the PBEPBE potential showed almost the same binding energies of the Frank-Kasper structures and the fullerene-like structures. The B3PW91-calculation demonstrated a small energy difference between these two types of structures.

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