Theoretical Investigation On Fe₃C₂ And Ga₃N₃ Clusters

Based on density-functional theory DFT calculations with the generalized gradient approximation (GGA), we optimize the geometrical structures of Fe3C2 cluster, calculate the electronic structure and vibrational frequencies. We also examine the relationship between the stability and geometry, chemical stability and magnetism of the stable structures. Another work of this paper is to seek and confirm the most stable structure of the Ga3N3 cluster, and study the main character of the stable structures.We follow the method of constructing the initial structures of FemCn cluster in the literature, and construct 108 initial structures of Fe3C2 cluster based on the stable Fe2C2 and Fe3C cluster. In order to confirm the reasonability and efficiency of the present calculational levels, we re-calculate the 16 stable structures of Fe2C2 and Fe3C clusters reported in the literature, and compare our results with those in the literature. It is confirmed that our calculation parameters are efficient in contrast with the previous results. The initial structures are subjected to geometrical optimization and frequency analysis, leading to 20 stable structures. We discussed their geometry character, chemical stability and magnetism. The result shows that the most stable structure is a non-planar in the Cs symmetry, the binding energy 482.978 kcal/mol, and the spin state 9. In our results, highly symmetric D3h structure for the cluster is not the most stable geometry and no linear structure is found to be stable. The energy gaps between HOMO and LUMO of 20 stable isomers of Fe3C2 cluster are obviously different, and can be used for different purposes in chemical interactions. The total magnetic moment is mainly located on the Fe atoms, and some of the local moments on C atoms are found to align antiferromagnetically with respect to that on the Fe atoms. When the local moments on one Fe atom align antiferromagnetically with respect to that on the other two Fe atoms, it consequentially results in the decrease of the total magnetic moment. Furthermore, it is found that all the local magnetic moments on each atom of highly symmetric D3h structure are zero. It provides references for the further investigation on the growth of FemCn cluster.Gallium nitride (GaN) plays a significant role in many important applications on microelectronic and photoelectron; as a result of this, it is very important to investigate their electronic structures and properties theoretically. For a sufficient understand of Ga3N3 cluster, we optimize 23 initial structures in the previous published results using DFT with the generalized gradient approximation in PW91,BLYP,RPBE forms. By the three functions, we have confirmed that there are 6 stable structures which have no imaginary frequencies with all the three functions. There are three different ground states in the previous published results by different authors, but none of them are the most stable structure in our study. The most stable structure of the Ga3N3 cluster we obtain is a planar structure in C2v symmetry. The energy gaps (Egap) between HOMO and LUMO of Ga3N3 cluster range from 0.599eV to 2.585eV. It is found that the Ga3N3 cluster has different chemical stability and can be used for different purposes.