Catalytic Resonance Theory: Turnover Efficiency and the Resonance Frequency

Programmable catalysts exhibiting forced oscillation in the free energy of reacting surface species were simulated to understand the general mechanisms leading to efficient use of input energy. Catalytic ratchets with either positive or negative adsorbate scaling exhibited oscillation conditions of both high and low turnover efficiency, yielding catalytic turnover frequencies either close to or significantly lower than the applied catalyst oscillation frequency, respectively. The ‘effective rate,’ defined as the product of the catalytic turnover frequency (TOF) and the turnover efficiency (η,TOE), was limited via two catalytic mechanisms: a leaky catalytic ratchet existed when molecules repeatedly traversed backwards through the catalytic transition state upon catalyst oscillation, while a catalytic ratchet with low surface participation exhibited reduced formation of gas-phase final product due to low surface product coverage. A single applied frequency yielding maximum effective catalytic rate defined as the ‘resonance frequency’ provided maximum combined benefit for catalytic rate and efficiency.