A novel quantum topological index QTI is proposed based on adjacency matrix by introducing quantum numbers and topological chemical principle on the basis of valence shell electron structure character and interaction among electrons in this paper. Topological index QTI appears uniquely to the ground state atom and has excellent structural selectivity. The index is utilized to study quantitatively the structure-property relationship of lanthanide with math model P=aQTI+b (a, b are constant). The topological index QTI is correlated with 16 physicochemical properties of lanthanides, such as effec...
