Catalytic Resonance\nTheory: Turnover Efficiency and\nthe Resonance Frequency

Programmable catalysts exhibiting forced oscillation\nin the free\nenergy of reacting surface species were simulated to understand the\ngeneral mechanisms leading to efficient use of the input energy. Catalytic\nratchets with either positive or negative adsorbate scaling exhibited\noscillation conditions of both high and low turnover efficiency, yielding\ncatalytic turnover frequencies either close to or significantly lower\nthan the applied catalyst oscillation frequency, respectively. The\n“effective rate”, defined as the product of the catalytic\nturnover frequency and the turnover efficiency (η<sub>TOE</sub>), was limited via two catalytic mechanisms: a leaky catalytic ratchet\nexisted when molecules repeatedly traversed backward through the catalytic\ntransition state upon catalyst oscillation, while a catalytic ratchet\nwith low surface participation exhibited reduced formation of a gas-phase\nfinal product due to low surface product coverage. A single applied\nfrequency yielding a maximum effective catalytic rate defined as the\n“resonance frequency” provided maximum combined benefit\nfor catalytic rate and efficiency.