Understanding the Relationship Between Kinetics and Thermodynamics in CO₂ Hydrogenation Catalysis

Catalysts that are able to reduce carbon dioxide under mild conditions are highly sought after for storage of renewable energy in the form of a chemical fuel. This study describes a systematic kinetic and thermodynamic study of a series of cobalt and rhodium bis­(diphosphine) complexes that are capable of hydrogenating carbon dioxide to formate under ambient temperature and pressure. Catalytic CO₂ hydrogenation was studied under 1.8 and 20 atm of pressure (1:1 CO₂/H₂) at room temperature in tetrahydrofuran with turnover frequencies (TOF) ranging from 20 to 74 000 h^–1. The catalysis was followed by ¹H and ³¹P NMR spectroscopy in real time under all conditions to yield information about the rate-determining step. The cobalt catalysts displayed a rate-determining step of hydride transfer to CO₂, while the hydrogen addition and/or deprotonation steps were rate limiting for the rhodium catalysts. Thermodynamic analysis of the complexes provided information on the driving force for each step of catalysis in terms of the catalyst hydricity (Δ<i>G</i>°_H^–), acidity (p<i>K</i>_a), and free energy for H₂ addition (Δ<i>G</i>°_H₂). Linear free-energy relationships were identified that link the kinetic activity for catalytic hydrogenation of CO₂ to formate with the thermodynamic driving force for the rate-limiting steps of catalysis. The catalyst exhibiting the highest activity, Co­(dmpe)₂H, was found to have hydride transfer and hydrogen addition steps that were each downhill by approximately 6 to 7 kcal mol^–1, and the deprotonation step was thermoneutral. This indicates the fastest catalysts are the ones that most efficiently balance the free energy relationships of every step in the catalytic cycle