Structure And Physical Properties Of Binary Alloy TMB_n(TM=Sc,Co;B=K,Ca) Clusters

Cluster research began in the 1970s.With the improvement of theoretical knowledge and experimental techniques,the research on clusters has made a breakthrough in the1990s.From this period on,the clusters developed further vertically and showed many interesting physical and chemical properties.Cluster research has developed from simple unit clusters to alloy clusters with rich element types.In the study of these alloy clusters,the doping of transition metal atoms with unique d-electron shells gives rise to some interesting properties.It has been reported that simple 3d transition metal atoms doped into alkali and alkaline earth metal clusters Sc Li_n,Sc Na_n,VNa_n,VLi_n,and Ti Na_n can improve the stability and magnetic moment of host clusters.In this paper,the ground state structure,stability,electronic configuration and magnetic properties of Sc M_n(M=K,Ca,n=2-12)and CoK_n(n=2-12)clusters are studied by using first principles combined with particle swarm optimization(PSO).First,we systematically studied the geometric structure,stability and magnetic properties of the first simple transition metal Sc atom doped alloy ScK_n clusters.The geometric structure of the ScK_n(n=9-12)cluster was studied with the increase of K atoms,and the Sc atoms moved from the vertex to the central position.By calculating the average binding energy E_b,fragmentation energy E_f and second-order energy difference?²E,we can see that doping a transition metal Sc atom can improve the thermodynamic stability of the host K_n cluster.The thermodynamic stability of ScK₈ and ScK₁₂ clusters is stronger than that of other adjacent clusters.According to the analysis of magnetic characteristics,the small size ScK_n(n=2-8)clusters have small magnetic moments of 1 and 2?_B.The small magnetic moments also exhibit odd pair oscillations,and the total magnetic moments are mainly source from the Sc-3d atomic orbitals.The magnetic moments in the caged ScK_n(n=9-12)clusters are 2,3,4,5?_B,respectively.The main source of these stepwise enhancement magnetic moments is the strong interaction between all K atoms and Sc.Bonding analysis of ScK₁₂ clusters with high magnetic moment 5?_B showed that ScK₁₂ had five 13-center double electron bonds(13c-2e)and five 13-center single electron bonds(13c-1e).Which made ScK₁₂ have the electronic configuration of1S²1P⁶1D⁵2S².Bonding analysis also verifies that the interaction between Sc and K is the main source of the large magnetic moment.In the same way,the ground state structure,stability and magnetic properties of CoK_n(n=2-12)clusters are studied.By studying the ground state structure of the CoK_nclusters,it shows that all the structures except CoK₂ are three-dimensional.The thermodynamic stability,chemical stability and magnetic stability of these ground state structures are calculated.The results show that the thermodynamic stability of CoK_n(n=4,6,8,9)clusters is stronger than that of other adjacent clusters.It was shows that the chemical stability of CoK₄ and CoK8 clusters was stronger than that of other adjacent clusters.CoK₄ clusters with high thermodynamic stability and high magnetic moment of5?_B are choiced as magnetic superatoms in CoK_n clusters.According to the Mulliken population analysis of CoK_n(n=2-12)clusters,the total magnetic moments of clusters are higher than the local magnetic moments of Co atoms when n=4,5,7.The larger total magnetic moment in CoK_n cluster is due to whether the electron spin direction of Co-3d atom is consistent with that of K atom.For other CoK_n(n=2-3,9-12)clusters with smaller magnetic moments,the total magnetic moments are mainly caused by the inconsistency of electron spin directions between the Co-3d atom and the K atom.In this paper,for study magnatic moment,the molecular orbitals,the average bond length between Co-K atoms and the charge transfer of Co atoms are comprehensively considered.The positive interaction between Co and K atoms is the main reason for the enhancement of magnetic moment.In the same way,the ground state structure,stability and magnetic properties of transition metal Sc doped alkaline earth metal Sc Ca_n(n=2-12)clusters have been systematically studied.The electron configuration of Ca atom is 4s² state,and the doping of Sc atom makes the geometric structure of Sc Ca_n cluster develop to the densely packed structure.The ground state structure is three-dimensional except that Sc Ca₂ is planar.The thermodynamic stability,chemical stability and magnetic stability of Sc Ca_n clusters were calculated.The results show that the binding energy generally increases with the increase of Ca atoms.When n=9,the thermodynamic stability is the best compared with other adjacent clusters,and the binding can be maintained at a certain size starting from Sc Ca₁₀.The second-order energy difference(?²E)is very similar to the curve fluctuations of the fragmentation energy(E_f),especially at very low energy points(n=5,7,9).The values calculated for magnetic stability are all greater than zero,indicating that in the whole system,the charge is not easily transferred from one spin orbital in the HOMO to the other spin orbital of the LUMO,and all of them have good magnetic stability.Mulliken analysis and electron configuration analysis show that the total magnetic moment of the Sc Ca_n(n=2-8)cluster is 1?_B,which is mainly derived from the 3d atomic orbitals of the SC.When n=9-12,the total magnetic moment of Sc Ca_n clusters is also 1?_B.With the increase of Ca atoms,the contribution of Ca atoms to the total magnetic moment increases gradually,and plays a leading role in the magnetic moment.This result is consistent with the conclusion that the cage structure will enhance the interaction between Sc and K atoms and the effect of alkali metal atom K on the total magnetic moment gradually increases in magnetic research of ScK_n clusters.