According to the pi-allyl-insertion mechanism the entire catalytic cycle of 1,4-polymerization of butadiene has been theoretically studied by employing a gradient-corrected density functional method with the polybutadienylnickel(II) cation [Ni(eta(3):eta(2):eta(2)-RC12H18](+) as the precatalyst. We have investigated competitive chain propagation cycles for generation of a cis-1,4- and trans-1,4-polymer, and also anti-syn isomerization. The calculations provide a clear insight into the stereoregulation mechanism of cis-1,4-polymerization. Chain propagation proceeds via educt-like trigonal-bipyramidal transition states with an almost identical free activation energy of 12.0 kcal/mol for both the cis-1,4- and the trans-1,4-pathway. The free activation barrier for anti-syn isomerization is 19.0 kcal/mol, which takes place via pi --> sigma conversion of the butenyl group followed by rotation of the vinyl group around the (C2-C3) Single bond through a trigonal-bipyramidal transition state. Accordingly, the trans-1,4-generating cycle is suppressed by a slow anti-syn isomerization. The cis-trans selectivity is determined by the formation of an anti-butenyl structure in the catalyst complexes which together with a slow isomerization yields nearly exclusively a cis-1,4-polymer, although of an almost identical reactivity of anti- and syn-butenyl forms. The calculations confirmed the formation of a stereoregular, highly selective cis-1,4-polymer quite in accord with experimental observations.