Structure, stability, charge transfer, chemical bonding, and spectroscopic properties of Ga atom-doped neutral Mg_n (n=2-12) clusters have been systematically investigated by CALYPSO and density functional theory. All cluster structures are based on "tetrahedral" and "yurt-like" growth except for GaMg2. The ground state isomer of GaMg with high symmetry strcture is predicted to be the best-fit candidate for the "magic" cluster because of its excellent stability. Natural bond orbital calculations reveal that Ga and Mg atoms play the role of electron acceptor and donor in all ground state isomers, while the orbitals in both Ga and Mg are sp-hybridized. Most importantly, chemical bonding studies based on atom-in-mole ular theory have shown that the lowest-energy state of GaMg₄ is so special in that it is not only the critical size for the appearance of Mg-Mg covalent bonds but also the only cluster that has both Ga-Mg covalent and non-covalent bonds. Finally, theoretical calculations of IR and Raman spectra of all ground state isomers indicate that the spectra of these clusters are observable in the low-frequency band, and thus they can be identified by spectroscopic experiments. Furthermore, the bond heterogeneity of the Ga-Mg in the GaMg₄ ground state isomer has also been specically investigated, includingfixed GaMg₄ structure with Mg atoms added in different directions as well as ab initio molecular dynamics sampling at different temperatures.

The structure, stability, charge transfer, and chemical bonding properties of palladium-doped magnesium clusters, PdMg n (n = 2-20), are comprehensively researched by CALYPSO software within first-principles DFT computations. It is shown that the cluster structure evolved from a tetrahedral-based structure to a cage-like structure, and interestingly, the single Pd atom always immerses in the Mg n clusters except for PdMg 2 and PdMg 3. Stability studies indicate that PdMg 4 , PdMg 7 , PdMg 10 , and PdMg 15 clusters have relative robust stability and can be identified as 'magic' clusters. Most importantly, chemical bonding studies reveal that Pd-Mg is always non-covalent bond (closed-shell) interaction in all PdMg n (n = 2-20) clusters, and PdMg 6 and PdMg 7 are the critical sizes at which Mg-Mg covalent interactions occur. The geometric structure database of transition metal-doped Mg clusters will be enriched by this study, and it also provides, at least theoretically, new members of cage-like structures for magnesium-based hydrogen storage nanomaterials.

Beryllium doped small-sized magnesium and its ion clusters are fully studied in this work. CALMPSO software was used to search for BeMg^Q _n (Q = 0, ±1, n = 2–12) clusters’ structures. The structural optimization with density functional theory (DFT) of BeMg^Q _n clusters was performed by two functionals B3PW91/6-311G(d,p) and PBE0/6-311G(d,p). Although the structures of clusters are diverse, their geometries with 3D structures can be summarized as two types of growth mechanism based on tetrahedron and tower-like. Calculations of the size dependence of the lowest energy state of BeMg^Q _n clusters using the two functionals, including average binding energy, second-order energy difference, HOMO–LUMO energy gap, VIP and VEA, coincidentally indicate that BeMg⁰ ₉, BeMg⁺¹ ₉ and BeMg⁻¹ ₈ are the local most stable clusters. For providing theoretical guidance for future experimental observations, the theoretical computations and simulations of BeMg⁻¹ _n clusters’ PES and BeMg^Q _n (Q = 0, ±1, n = 2–12) clusters’ IR and Raman spectra were performed. Finally, ELF, MO and DOS analyses of the local most stable clusters were carried out, and it was found that their stability mainly originated from the σ-type covalent bond formed by the interaction between the s- and p-orbitals of Be and Mg atoms.