Clusters Mg_n And Feco_n Cluster Structure And The Nature Of First-principles Calculations

In the study of metal clusters, there have been considerable interests in the magnesium clusters., Magnesium is an element that exhibits a transition from weak van deer Waals bonding in the diatomic molecule to metallic bonding in the bulk due to the full filled 3s² electronic shell in magnesium atom. Magnesium cluster is special appropriate for the investigation of the size deduced transition to metallicity. The addition or removal of a few electrons produces little change in bulk systems; however, such an addition or removal may have large effects in clusters and produces a large change in geometry, electronic and magnetic behavior, even lead to fragment.The magnetic transition-metal clusters, especially the iron clusters, cobalt clusters and iron-cobalt doping clusters are very attractive because of their unique electronic structures and magnetic properties. The size-depended stability, magnetic properties and other physical and chemical properties of the transition-metal clusters are significative issues to be discussed. Thus binary Fe-Co clusters have attracted theoretical and technological interest due to its unusual magnetic moment.In the present paper, using the first principle calculation based on density functional theory, we optimized some initial geometry structures of the neutral magnesium clusters Mg_n, singly charged cationic magnesium clusters Mg_n⁺, singly charged anionic magnesium clusters Mg_n^-(n=2-11) and netural binary clusters FeCo_n-1(n=2-16). For the same size n, after optimized, we obtained the most stable structure, and then discussed their electron structure and magnetic properties. The following results are obtained:(1) Mg₄, Mg₅⁺ and Mg₄^- are the turning points form planar to three-dimension structure for the most stable Mg_n, Mg_n⁺ and Mg_n^- clusters. The most stable structures of singly charged cationic Mg_n⁺ and singly charged anionic Mg_n^- clusters are not very different from those obtained for corresponding neutral clusters. Exceptions are observed for small clusters, where the ground-state geometries of Mg₃⁺ and Mg₄⁺ are linear chains due to the Jahn-Teller distortion and that of Mg₆^- is a pentagonal pyramid the reason is not clear here. The analyses of the second differences of total energy show that for for the neutral Mg_n clusters, Mg₄, Mg₇ and Mg₁₀ clusters have relative higher stability. The enhanced stability of Mg₄ and Mg₁₀ clusters is maily due to the close electronic shells 1s²1p⁶ and 1s²1p⁶1d¹⁰2s² according to the spherical jellium model. The high stability of Mg₇ is resulted from its "closed" pentagonal bipyramid structure. For the same size n, the binding energy E_b⁺ > E_b^- >E_b.It is demonstrated that on the one hand the charged clusters is more stable than the neutral clusters, on the other hand, it is show that the enhanced stability for the cationic cluster resulted from the removal of an antibonding electron is larger than that for the anionic cluster by promoting an extra electron to occupy a bonding orbital. This result also explains that the cationic magnesium clusters are easier to gain than the neutral ones in the experiment. The analyses of DOS show as cluster size increases the HOMO-LUMO gap decreases, the lowest unoccupied state and the highest occupied state are both shifting toward Fermi level E_f . The increase in interaction between valence and unoccupied states leads to an increase in s-p hybridization. So as the cluster size increase, the bonding mode of the clusters represent a transition from week van der waals bonding to the strong metal bonding.(2) The geometries prefer to planar structures for the very small FeCo_n-1(n=2-3) and Co_n(n=2-4) clusters and prefer to three-dimension structures for other size. The growth of FeCo_n-1 and Co_n clusters with large cluster size is firstly in an icosahedral pattern and then in the hep structure growth pattern. The resulting geometries show that except for n=4, 11 and 12, no considerable structural change occurs when one Co atom is replaced with Fe atom in the cluster. The replaced Fe atom favorites to occupy the surface position except for FeCo₁₃. The stability has been investigated by analyzing the binding energy per atom and the second difference in energy. The analyses of the second differences of total energy show that FeCo₅, FeCo₈ and FeCo₁₀ clusters have relative higher stability than their neighboring FeCo_n clusters and Co₆, Co₉ and Co₁₂ clusters are more stable than their neighboring Co_n clusters. The analyses of bonding energy indicate that the stability of pure Co_n clusters is weakened by the replacing of one Co atom with Fe atom. Except for n=14, the average magnetic moment of the cluster increases when replace one Co atom with Fe atom. The variation tendency in magnetic moments is resulted from the competing of the increase rate of and c>. In the size ranges n=2-4 for FeCo_n-1 and n=2-5 for Co_n, the increase rate of is faster than that of c>, so increase in the magnetic moment due to increase of is large than decrease in the magnetic moment due to increase of c> and thus results in an increase in the magnetic moment. An opposite phenomena exists in intermediate size till n=10, that is a decrease in the magnetic moment since the increase in c> dominates over the increase of . The oscillate increases of the magnetic moment for both FeCo_n-1 and Co_n cluster after n=11 are difficult to related to the relative increase rate of both and c> due to their obvious oscillation.