Structures and properties of neutral gallium clusters: A theoretical investigation
Authors: Drebov Nedko , Weigend Florian , Ahlrichs Reinhart 
Published: August 2011

A systematic and unbiased structure search based on a genetic algorithm in combination with density functional theory (DFT) procedures has been carried out to locate low-energy isomers of \documentclass[12pt]{minimal}\begin{document}$\rm Ga_n$\end{document} Ga n up to n = 25. For the smaller clusters up to n = 8 results are checked by coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) employing a quadruple zeta type basis set. The CCSD(T) calculations confirm a \documentclass[12pt]{minimal}\begin{document}$\rm ^3 \Pi _u$\end{document}Πu3 ground state for the dimer. \documentclass[12pt]{minimal}\begin{document}$\rm Ga_3$\end{document} Ga 3 has a doublet ground state 0.2 eV below two quartet states, whereas two isoenergetic triplet states are predicted for \documentclass[12pt]{minimal}\begin{document}$\rm Ga_4$\end{document} Ga 4 with \documentclass[12pt]{minimal}\begin{document}$\rm D_{4h}$\end{document}D4h and a rhombus structure (\documentclass[12pt]{minimal}\begin{document}$\rm D_{2h}$\end{document}D2h). Three low-lying isomers with doublet electronic states are found for \documentclass[12pt]{minimal}\begin{document}$\rm Ga_5$\end{document} Ga 5: a W-structure (\documentclass[12pt]{minimal}\begin{document}$\rm C_{2v}$\end{document}C2v), a planar envelope (\documentclass[12pt]{minimal}\begin{document}$\rm C_s$\end{document}Cs) at 0.015 eV, and a non-planar envelope (\documentclass[12pt]{minimal}\begin{document}$\rm C_1$\end{document}C1) 0.086 eV above the ground state. A triplet state for a trigonal prism (\documentclass[12pt]{minimal}\begin{document}$\rm D_{3h}$\end{document}D3h) and a singlet for an open prism (\documentclass[12pt]{minimal}\begin{document}$\rm C_{2v}$\end{document}C2v) are computed with virtually identical energy for \documentclass[12pt]{minimal}\begin{document}$\rm Ga_6$\end{document} Ga 6. The global minimum for \documentclass[12pt]{minimal}\begin{document}$\rm Ga_7$\end{document} Ga 7 is a capped trigonal prism (\documentclass[12pt]{minimal}\begin{document}$\rm C_s$\end{document}Cs) and that for \documentclass[12pt]{minimal}\begin{document}$\rm Ga_8$\end{document} Ga 8 a distorted cube in \documentclass[12pt]{minimal}\begin{document}$\rm D_{2h}$\end{document}D2h. DFT provides a fair agreement with CCSD(T), deviations in dissociation energies are up to 0.2 eV for n ⩽ 8. The structures for \documentclass[12pt]{minimal}\begin{document}$\rm Ga_n$\end{document} Ga n are mostly irregular for n ⩾ 9, those for \documentclass[12pt]{minimal}\begin{document}$\rm Ga_{12}$\end{document} Ga 12 to \documentclass[12pt]{minimal}\begin{document}$\rm Ga_{17}$\end{document} Ga 17 can be derived from the truncated decahedron with \documentclass[12pt]{minimal}\begin{document}$\rm D_{5h}$\end{document}D5h symmetry though highly distorted by Jahn-Teller effects, for example. For \documentclass[12pt]{minimal}\begin{document}$\rm Ga_{18}$\end{document} Ga 18 to \documentclass[12pt]{minimal}\begin{document}$\rm Ga_{23}$\end{document} Ga 23 we find stacks of five- and six-membered rings as global minima, e.g., 5-1-5-1-6 for \documentclass[12pt]{minimal}\begin{document}$\rm Ga_{18}$\end{document} Ga 18. \documentclass[12pt]{minimal}\begin{document}$\rm Ga_{24}$\end{document} Ga 24 and \documentclass[12pt]{minimal}\begin{document}$\rm Ga_{25}$\end{document} Ga 25 consist of layers with packing sequence ABCBA similar to those found for clusters of aluminum. The most important feature of computed cohesive energies is a rapid increase with n: for \documentclass[12pt]{minimal}\begin{document}$\rm Ga_{25}$\end{document} Ga 25 it reaches 2.46 eV, the experimental bulk value is 2.84 eV. Particularly stable clusters for \documentclass[12pt]{minimal}\begin{document}$\rm Ga_n$\end{document} Ga n are seen for n = 7, 14, and 20.