We have studied the ethylene polymerization catalyst C5H5Nb(butadiene)Cl2 + MAO using primarily density functional theory (DFT). The active species was assumed to be C5H5Nb-(butadiene)R+. Chain initiation and propagation as well as different termination processes were modeled. The ethene coordination is very weak, and no free energy minimum was found. Insertion into the metal-alkyl bond has an energy barrier of 4 kcal/mol for R = CH3 and 6 kcal/mol for R = C2H5. The ethene insertion transition state is clearly stabilized by agostic interaction, with metal-hydrogen distances of 2.07-2.16 Å. However, in alkyl conformations these bonds are longer and correspond to only weak agostic interaction. In the absence of strong agostic interaction the resting state alkyl complexes are floppy and different conformations interconvert easily. Termination via hydrogen transfer to a coordinated ethene molecule ejecting a terminal alkene has a high energy barrier of 17 kcal/mol. An alternative termination process via β-elimination and subsequent alkene ejection is also very expensive, 43 kcal/mol. The propagation free energy barrier for the concerted reaction is 21 kcal/mol, which consists mostly (80%) of ethene coordination. The termination free energy barrier via hydrogen transfer to coordinated alkene is 30 kcal/mol and that via β-elimination is 28 kcal/mol. The free energies have been determined in a vacuum using the harmonic approximation. The key intermediates were also optimized using MP2 supplemented with single-point calculations using CCSD. These methods gave stronger complexation energies, resulting in lowering the propagation barrier by approximately 3-4 kcal/mol and increasing the β-elimination barrier by 6-7 kcal/mol. The BSSEs in MP2 and DFT complexation energies were estimated to be 15-20 and 1-3 kcal/mol, respectively, using DZ and DVZP bases.