DFT calculations show that H₂ and CO₂ activation by bridged phosphane/borane frustrated Lewis pairs (FLPs) experience a one-step concerted mechanism with small reaction barriers. In addition, we found that some bridged FLPs can effectively catalyze the hydrogenation of carbon dioxide by two possible pathways: (1) CO₂ hydrogenation can happen immediately after H₂ activation through a concerted pathway; (2) CO₂ activation happens first and metathesis of H₂ and reductive elimination follow step-by-step. Based on our DFT calculations, bridged FLPs without electron donating substitutions on the B's adjacent carbon site possess a facile H₂ activation process, and bridged FLPs with longer carbon chains or bulky substitutes on the carbon chains possess lower reactivity than the bridged FLPs with shorter carbon chains and smaller substituents. Bridged FLPs with unsaturated carbon chains, such as Mes₂PCHPhCB-(C₆F₅)₂ and Mes₂PCCH₃CHB(C₆F₅)₂, are more prepared to react with H₂ than the others with saturated carbon chains. The same happens for CO₂ activation, but most barriers for CO₂ activation are higher than H₂ activation. However, for CO₂ hydrogenation, our calculations demonstrate that quite stable intermediates are formed after H₂ activation, followed by high barriers for the concerted CO₂ hydrogenation. The total barriers for the first kind of pathway with alkyl chain bridged FLPs are from 27–37 kcal mol⁻¹, while most of the other pathways have higher barriers. Mes₂PCH₂CH₂B-(C₆F₅)₂ shows a smaller barrier for CO₂ hydrogenation with CO₂ activation first than the other pathway and other FLPs. Most of our calculation results are consistent with the experimental observations.