The results from density functional theory (DFT) studies into C–H bond activation, hydrogen transfer, and alkyne–to–vinylidene isomerization are presented in this work. The reaction mechanism for the reductive elimination (RE) of methane from [ κ3- TpPtIV(CH3)2H (1)] (Tp = hydridotris(pyrazolyl)borate) by oxidative addition (OA) of benzene to form [ κ3-TpPtIV(Ph)2H] (19) was investigated through DFT calculations. For 31 density functionals, the calculated values for the barriers to methane formation (Ba1) and release (Ba2) from 1 were benchmarked against the experimentally reported values of 26 (Ba1) and 35 (Ba2) kcal•mol-1, respectively. The values for Ba1 and Ba2, calculated at the B3LYP/DZP level of theory, are 24.6 and 34.3 kcal•mol-1, respectively. The best performing functional was BPW91 where the m.a.e. for the calculated values of the two barriers is 0.68 kcal•mol-1. Classic and newly proposed mechanisms for metal-mediated hydrogen transfer (HT) were analyzed with density functional theory (DFT) and Bader's "Atoms In Molecules" (AIM) analysis. Seven sets of bonding patterns that characterize theconnectivity in metal-mediate HT were found from the analysis of representative models for σ-bond metathesis ( σBM), oxidative addition / reductive elimination (OA/RE), and alternative mechanisms. The mechanism for the formation of the alkynyl, vinylidene complex, [(PiPr3)2Rh(CCPh)(CC(H)(Ph))] (2), by the addition of two equivalents of phenylacetylene (PA) to [( η3-C3H5)Rh(PiPr3)2] (1) was studied through DFT calculations. Two experimentally observed intermediates on the reaction coordinate are the η2-PA, alkynyl complex, [(PiPr3)2Rh( η2-HCCPh)(CCPh)] (Ia) and the fivecoordinate, pseudo square-pyramidal, RhIII–H complex, [(PiPr3)2Rh(H)(CCPh)2] (Ib), and were found to be in equilibrium. The relative energies of Ia, Ib, and 2 (relative to 1 + 2PA) depend on the phosphine that was used in the calculation; the predicted product is 2 with PiPr3 and PEt3 but Ia with PMe3, PMe2Ph, PMePh2, PPh3, and PH3. The equilibrium between Ia and Ib was calculated with PEt3 and one conformation of PiPr3. We investigated the mechanism for the formation of 2 from Ia, and a lower energy pathway where the π-bound PA of Ia slips to bind through the σ-C–H bond prior to the formation of 2 through hydrogen migration was found.