Structure And Stability Of TiB_n, ScB_n And Ti_mB_n Clusters

With the development of clusters research, the doped clustersbegan to attract wide attention. The doped heteroatom can changethe structures and properties of clusters. Thus, it is expected touncover the formation mechanism and the stability rule of thedoped clusters theoretically. These results of research will providesome theoretical guidance for the application of these clusters.In this paper, the structures and stabilities of TiB_n（n=1-12）、ScB_n（n=1-12） and Ti_mB_n（m+n=8, m≤n） have been systematicallyinvestigated by using the density theory （DFT） at theB3LYP/6–311+G（d） level. All the results are summarized as follows.The growth behaviors, stabilities, and electronic properties ofthe TiB_nclusters, n up to 12, are investigated theoretically at theB3LYP level by employing 6-311+G（d） basis sets. Ab initio moleculardynamic （MD） simulation also confirmed that our proposed TiB_n（n=1-12） clusters are global minimum. Our investigations show that（1） The equilibrium structures of B_nclusters are fundamentallychanged due to the doped the Ti atom. The 3D configurationsbecome the ground state structures for the TiB_n（n≥5） clusters.Starting from n≥9, the nest-like structure dominates the growthpattern of the TiB_nclusters. The spin multiplicity of the groundstate of TiB_nis 6、1、2、5、2、3、2、3、2、1、2、3, respectively. （2）Theaverage atomic binding energies, fragmentation energies, second-order energy differences and HOMO-LUMO gaps arecalculated and discussed. The doping of the Ti atom improves thestability and metallicity, but reduces the energy gap in most casesexcept n=7. the magic numbers of the TiB_nclusters are 3, 8, 10. （3）NBO analyses show that electron always transfers from the Ti to theB atoms. There are strong overlap between d orbitals of Ti atom andp orbitals of B_nclusters.The growth behaviors, stabilities, and electronic properties ofthe ScB_nclusters, n up to 12, are also investigated theoretically atthe B3LYP level by employing 6-311+G（d）basis sets. Ab initiomolecular dynamic simulation also confirmed that our proposedScB_n（n=1-12） clusters are global minimum. Our Calculation showsthat （1） The equilibrium structures of B_nclusters are fundamentallychanged due to the doping of the Sc atom. The 3D configurationsbecome the ground state structures for the ScB_n（n≥5） clusters.Starting from n≥9, the nest-like structure dominates the growthpattern of the ScB_nclusters. The spin multiplicity of the groundstate of ScB_nis 5、2、1、2、1、2、1、2、1、2、1、2, respectively. （2）the magic numbers of the ScB_nclusters are 3, 7, 10. （3） NBOanalyses show that Charge always transfers from the Sc to the Batom with the increase of size and indicates that Sc acts as anelectron donor in all ScB_nclusters. There are strong overlapbetween d orbrtals of Sc atom and p orbrtals of B_nclusters.the structures and stabilities of Ti_mB_n（m+n=8, m≤n） clusters arealso investigated by DFT calculations. Ab initio molecular dynamicsimulation also confirmed that our proposed Ti_mB_n（m+n=8, m≤n）clusters are global minimum. The results show that the B-B bonds are favored in the ground state structures of Ti_mB_n（m+n=8, m≤n）clusters. The Ti_mB_nclusters form the 3D structures rather thanplanar or linear. In the lowest-energy structure of Ti₄B₄、Ti₃B₅、Ti₂B₆、Ti₁B₇, Ti atoms cap on the vertex of bipyramid strctures. The dopingof the Ti atoms enhance the stability and the clusters can continueto gain energy when the Ti atoms increase. Electronic analysisshowed that the Ti_mB_n（m+n=8, m≤n） clusters with even n havesmaller energy gap than those with odd n. NBO analysis shows thatCharge always transfers from the Ti to the B atom.This work was supported by National Basic Research （973）Program of China （No. 210CB635110） and National Natural ScienceFoundation of China （21031003）.