Theoretical Study On Pentagonal Icositetrahedron Cluster Of Cu₆C₃₂and Au₆C₃₂

In recent years,significant progress has been made in the study of cluster structures.Research on carbon fullerenes,gold fullerenes,and metal carbon cages have made great strides.Especially in recent years,people have shown great interest in exploring the structure and properties of metal carbon cages because of their unique properties and wide applications in nanomaterials.In this paper,the first-principles calculations based on density functional theory are used to study the related properties of CU6C32 and Au6C32 clusters.The research results are of great help for understanding the structural stability and electronic properties of Cu6C32 and Au6C32 clusters,and are helpful to expand the types of high-symmetry polyhedral molecular clusters,and provide theoretical basis for future experimental studies.The results of the study are as follows:1)Both Cu6C32 and Au6C32 are hollow,pentagonal tetrahedral cage-like structures with Ih symmetry.At the PBE level,the average bond lengths of the M-C bonds of the two clusters are 1.966 A and 2.090 A,respectively,and the average bond lengths of the C-C(1)bonds are 1.387 A and 1.391 A.The average bond length of the C-C(2)bond is 1.442 A and 1.453 A,in which the three bond lengths of Au6C32 are all longer than the corresponding CU6C32 bonds,which corresponds to the larger cluster size.Compared with the C-C bond length in diamond(1.545 A),the average C-C bond length of both clusters is shorter.2)Their structural stability was studied by vibrational frequency analysis and Ab initio molecular dynamics.On the one hand,there are no imaginary frequencies in the frequency analysis of the two structures,indicating that they have better dynamic stability.On the other hand,Ab initio molecular dynamics simulations show that Cu6C32 and Au6C32 can still maintain the original geometric topology when the effective temperature is about 976.9 K and 1014.5 K,indicating that they have good thermal stability.3)Electronic structure analysis showed that the HOMO-LUMO energy gaps of CU6C32 and Au6C32 were 1.208 and 1.155 eV,respectively,indicating that they have relatively high chemical stability.From the HOMO and LUMO orbital diagrams of the two structures,it can be seen that there are distinct d-orbital features on Cu and Au.The analysis of the densities of the two structures shows that it is the hybrid of the d orbital of the metal atom M(M = Cu,Au)and the s-p orbital of the C atom that makes these molecules have a good structural stability.Through NBO analysis,it is known that in both cluster structures,the ? bond and ? bond are formed between the C atom and the metal atom M(M = Cu,Au)and the C and C atoms,which is a stable cage structure very important.