Most of polymerization reactions with Ziegler catalysts operate through the 'non-living' mechanism, whereas lanthanide catalysts show a living-mechanism character. The degree of 'livingness' in a polymerization reaction is generally investigated through kinetics and the product analysis rather than by direct analysis of a catalyst. We have developed a new insight for judging the 'livingness' in polymerization reaction in aspect of electronical properties of the active chain ends of Li, Ni and Nd catalysts for 1,3-butadiene polymerization using the frontier orbital analysis. The frontier orbitals of the Ni catalyst are different from those of the Li and Nd based catalysts. The HOMO of the Ni catalyst has mostly the d-orbital (Ni) character while the LUMO has the p-orbital (C-alpha and C-gamma atoms) as well as the d-orbital (Ni) character. The pi-butenyl coordination at the Ni catalyst is eta(1)-type but those of the Nd and Li catalysts are eta(3). The atomic charge (+0.003) on the Ni atom and the atomic charge (-0.14) on C-alpha of the Ni catalyst are much lower than those of the Nd catalyst (Nd + 1.09, C-alpha - 0.56). (C) 2003 Elsevier Ltd. All rights reserved.