Local and nonlocal density functional theory (DFT) was used to study olefin metathesis in the TiCP2C3H4(R-1,R-2) system, in which the alkyl substituents (R-1,R-2) are at the beta-position of the metallocyclobutane ring. The structures and stabilities of the metallocyclobutanes were calculated, and the mechanism of olefin insertion and the process of ring-opening metathesis polymerization were investigated. The predicted geometries of the metallocyclobutanes agree well with experimental structures, especially those predicted by nonlocal DFT. The relative stabilities of the metallocyclobutanes were studied by calculating the energy change for the following olefin exchange reaction: TiCP2C3H4(R-1,R-2) + C2H2(R-3,R-4) --> TiCP2C3H4(R-3,R-4) + C2H2(R-1,R-2) The relative stabilities of the metallocyclobutanes are also strongly dependent upon the number and steric size of the alkyl group(s) (R-1,R-2) at the beta-position in the metallocyclobutane ring. In general, nonlocal DFT predicts olefin exchange energies that are in better agreement with the experimentally observed free energies of olefin exchange than local DFT. The quantitative agreement between the experimental and calculated Delta G's for olefin exchange are within 0.8 kcal/mol. The mechanism of metathesis was investigated by calculating the potential energy surface for olefin elimination from TiCp2C3H5(tBu). No compelling evidence was found for a local minimum corresponding to a titanium-alkylidiene-olefin complex, which is inconsistent with conclusions drawn from experimental mechanistic studies but is consistent with all prior theoretical calculations on metal assisted 2 + 2 insertions. The mechanism of cyclopentene and norbornene ring-opening polymerization was also studied.