Density functional theory together with Car-Parrinello ab initio molecular dynamics simulation has been used to investigate the free energy profiles (FEP) of monomer capture in Grubbs- and SHOP-type olefin polymerization catalysts. The FEPs along the reaction coordinates at 300 K were determined directly by a point wise thermodynamic integration technique. Comparison between potential energy profile (PEP) and the FEP has been made. The results show that, for both catalysts, the PEP for the monomer ethylene uptake by the metal center is a typical Morse curve without energy barrier. However, a small barrier (1.8 kcal/mol for Grubbs catalyst and 2.4 kcal/mol for SHOP catalyst) exists on the FEP. The pi complexation energy on the FES at 300 K is higher by 10-12 kcal/mol over that on the PES. The differences between FES and PES are due to entropy contribution. Slow growth simulations on the ethylene capture process show that the ethylene attacks the metal center by an asynchronous mode. This indicates that the forming of the pi-bonding between the metal and ethylene is initiated by electrophilic attack of the metal to one of the ethylene carbons.