Predicting novel atomic structure of the lowest-energy Fe_(n)P_(13-n)(n=0-13)clusters:A new parameter for characterizing chemical stability

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_7P_(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.343117603(2021)).Hence,in order to characterize the global chemical stability of target cluster,we proposed a new parameter(jyq=η/χ)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_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.