Research Work on the Periodic Law

"Topological Study of the Periodic System"
Scientists Guillermo Restrepo, Heber Mesa, Eugenio J. Llanos, and Jose L. Villaveces carried out a topological study of the Space of Chemical Elements, SCE, based on a clustering analysis of 72 elements, each element defined by a vector of 31 properties. They looked for topological properties of the SCE such as boundaries of neighborhoods. The results show the patterns of the Periodic Table and the relationships such as the Diagonal Relationship and the Singularity Principle. The results also show that the Alkaline metals and the Noble Gases are sets that have no other elements besides themselves in their neighborhoods and that the topological boundary of the set of metals is formed by metalloids.

"Cluster Analysis of Chemical Elements"
Attempts have been recently made by Zhou et al. to study neighborhood relationships for chemical elements using cluster analysis (CA), using a set of 50 elements and 7 physical properties. Some of the clusters found are: {Co, Ni, Fe, Rh, Ru}, {Mo,Tc}, {Sc, Y, Ti}, {Ga, In, Sn}, {N, O, F, H}, {Cl, Br}, {Zn, Cd}, {Ar, Kr, Ne, He}, {Mg, Ca}, {Li, Na, K, Rb}, {Cu, Ag}, and {B, C}. The appearance of alkaline elements and noble gases stood out.

"Numerical Classification of the Chemical Elements"
Sneath did a similar study using cluster analysis using 69 elements (1-80 omitting 58-71), starting from 54 physical and chemical properties. Some of the clusters are: {He, Ne, Ar, Kr, Xe}, {N, P}, {S, Se}, {Cl, Br}, {O, F}, {B, Si, C}, {Ti, V}, {As, Sb, Te}, {Zn, Cd, In}, {Hg, Tl, Pb, Bi}, {Cr, Mn, Fe, Co, Ni}, {Rh, Pd, Pt}, {Li, Na, K, Rb, Cs}, {Be, Al}, {Mg, Ca, Sr, Ba}, and {Sc, Y, La}. Note the appearance of the alkaline earth metals, noble gases and fragments of other groups in the periodic table. 25% of Sneath's values were reportedly missing and 14 out of the 54 elements used related to the chemical elements. The rest related to their compounds.