Abstract: Using optimum valence bond scheme which reduces the computation effort, we study systematically the properties of the critical structures (critical points) of small clusters (up to four atoms) of elements in the second and third row of the periodic table. We also show the evolution process of the clusters from two atoms to four atoms. By examining the electronic structures of all clusters, we can understand why the four-atom clusters for specific elements can have three-dimensional structures with Td symmetry. More interestingly, comparing the variation of the binding energy of such small clusters with the melting points and boiling points of corresponding pure element materials, we can understand the effect of the critical structures in the melting and boiling processes.

Keywords: 
• optimum valence bond scheme /
• critical structure of clusters /
• cluster /
• first-principle molecular dynamics /
• material properties