Eur. Phys. J. Plus (2022) 137: 88
https://doi.org/10.1140/epjp/s13360-021-02299-7

Regular Article

Theoretical insights of structural evolution and electronic properties of Ru₂Ge_n (n = 1–16) clusters

¹ School of Electronics and Information Engineering, Taizhou University, 318000, Taizhou, Zhejiang, China
² School of Mathematics and Physics, Hebei University of Engineering, 056038, Handan, China
³ Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology), Ministry of Education, 116024, Dalian, China

^a liangxq@tzc.edu.cn
^e zhaojj@dlut.edu.cn

Received: 29 May 2021
Accepted: 17 December 2021
Published online: 4 January 2022

Abstract

We present a study on dual ruthenium atom-doped germanium clusters, Ru₂Ge_n (n = 1–16), using comprehensive genetic algorithm combined with density functional theory (DFT) calculation. The low-lying structures of Ru₂Ge_n are re-optimized by DFT calculation implemented in Gaussian09 program. For small Ru₂Ge_n with n ≤ 8, the ground state structures adopt exohedral structure with Ru dimer as core surrounding by Ge atoms, and Ge atoms tend to separate rather than aggregate to form polyhedral configurations. From cluster sizes n ≥ 9, half-encapsulated structures start to form, while the geometries of clusters with 12 ≤ n ≤ 15 are based on the regular pentagonal prism attached with extra Ge atoms. For Ru₂Ge₁₆, the geometry looks like a Ru dimer invaginated cage structure. Furthermore, we analyze their bonding characters, natural electron configurations, density of states and frontier molecular orbital. We predict that the clusters with number of Ge atom of n = 6, 8, 10, 13 have high structural and chemical stability. Interestingly, Ru₂Ge₃, Ru₂Ge₅, Ru₂Ge₇ and Ru₂Ge₉ clusters possess magnetic moment of 2 μ_B, which is different from the reported non-magnetism of monatomic doping. These results enrich the understanding of transition metal-doped Ge_n clusters.