关键词: Fe-P cluster, density functional theory (DFT), ground-state structure, electronic structure

Abstract: A series of novel atomic structure of lowest-energy Fe$_{n}$P$_{13-n}$ ($n=0$-13) clusters via density functional theory (DFT) calculations and an unbiased structure search using Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) code. Our research results show that the global minimum geometry structure of neutral Fe$_{13-n}$P$_{n}$ ($n=0$-6) clusters tend to form cage structures but the lowest-energy Fe$_{13-n}$P$_{n}$ ($n=7$-13) clusters are gradually evolution from a cage structure to a chain shape geometric structure. Their geometric structure should responsible for the raise of binding energy from Fe$_{7}$P$_{6}$ to P$_{13}$ clusters rather than chemical components. This is completely different from a linear relation of the binding energy with chemical components in our previous research for Cu$_{n}$Zr$_{13-n}$ ($n=3$-10) clusters (J. Mol. Liq. 343 117603 (2021)). Hence, in order to characterize the global chemical stability of target cluster, we proposed a new parameter (${\rm jyq}=\eta /\chi $) that the chemical hardness of isolated cluster is used to be divided by its electronegativity. One of the biggest advantages of this parameter is successful coupling the ability of a resistance to redistribution of electrons and the ability to attract electrons from other system (such as atom, molecular or metallic clusters). Moreover, it is found that the P$_{13}$ cluster shows typical insulator characteristics but the Fe$_{12}$P$_{1}$ shows typical conductor characteristics, which phenomena can be attributed to the remarkable delocalized and localized electrons in Fe$_{12}$P$_{1}$ and P$_{13}$, respectively. In terms of nearly-free-electron mode, we also found that the number of electrons on Femi level ($N(E_{\rm F})$) are obviously tended to toward a lower value when Fe was replaced gradually with P from Fe$_{13}$ to P$_{13}$, and a non-magnetic can be observed in Fe$_{13}$, Fe$_{2}$P$_{11}$, Fe$_{1}$P$_{12}$, and P$_{13}$ that mainly because their perfect symmetrical between spin-up and spin-down of density of states of electrons.

Key words: Fe-P cluster, density functional theory (DFT), ground-state structure, electronic structure