DFT study on structure and stability of clusters

The structures and stabilities of the neutral and the positively/negatively charged Mg-doped boron clusters, i.e., MgB n ± m (n = 1–7 and m = 0, 1), have been studied at the UB3LYP/6-311+G* level. Several possible multiplicities of each cluster were tested to determine the most stable structure among the isomers. For the neutral clusters, when n ⩽ 5, the lowest-energy geometry is in favor of a planar structure. From n = 6 on, the most stable geometry tends to be quasi-planar or three-dimensional. When the clusters are positively or negatively charged, the lowest-energy structures of the clusters with some sizes change dramatically from their neutral analogs, such as MgB 7 - , MgB 2 - and MgB 3 + . The average binding energy per atom, fragmentation energy and second order energy difference were evaluated. The results indicated that the neutral and cationic clusters possess higher stability when n = 3 and 5, and the anionic is more stable only at n = 3. The adiabatic ionization potential (AIP) and adiabatic electron affinity (AEA) were also calculated for the neutral clusters to investigate their electronic properties. MgB6 has both the highest AIP and adiabatic AEA. Odd–even alteration was found in the HOMO–LUMO gap energy for the neutral and cationic clusters. NBO analysis was done to study the natural population.