A theoretical study of the symmetry concerted Diels-Alder analogue reactions of Zr-2 with ethylene and 1,3-butadiene is carried out. The optimized structures of the complexes indicate breaking of one of the multiple bonds in Zr-2 and 1,3-butadiene and the formation of a six-membered ring in agreement with symmetry concerted models. Thus the reaction of ethylene with Zr-2 is thermally forbidden, while it is allowed for the butadiene case. This is explained based on the natural orbitals picture. The presented potential energy surfaces are useful for the interpretation of possible reactions in both ground and excited states.