Binding Energy and Electronic Structure of Sc₁₃ Clusters

The binding energy and electronic structure of the cube octahedral, truncated hexagonal bipyramidic and icosahedral Sc₁₃ clusters are investigated by using discrete variational-self consistent charge X_a method （DV-SCC-X_a）. Based on the calculation of total binding energy, the equilibrium bond lengths of the clusters were determined. By comparing the binding energy of the clusters at equilibrium bond lengths, we verified the Knight’s suggestion that the icosahedral Sc₁₃ cluster is most energetically stable of all the cluster mentioned above. Calculated and analyzed the energy spectrums and densities of states of the clusters, it is shown that the icosahedral Sc₁₃ cluster still has an Jahn-Teller distortion tendency, due to its degenerate ground state ²T_1u, which is not the ²A_g supposed by Knight. In addition, the results for clusters were compared and discussed with experiments and theories for bulks.