Microkinetic modeling of CO2 hydrolysis over Zn-(1,4,7,10-tetraazacyclododecane) catalyst based on first principles: Revelation of rate-determining step

Abstract

Density functional theory (DFT) calculations were used to study the mechanism of CO2 hydrolysis by Zn-(1,4,7,10-tetraazacyclododecane), also referred to as zinc–cyclen, and evaluate the associated thermodynamic and kinetic parameters. A microkinetic model was then built based on the kinetics and thermodynamics derived from first principles. The model describes the sigmoidal dependence of the observed reaction rate constant on pH, which is similar to behavior observed for CO2 hydrolysis catalysts in nature, i.e., human carbonic anhydrase. The inflection point is identical to the pKa value of the zinc–cyclen complex, in good agreement with previous results. The overall reaction rate constant was calculated to be 3055M−1s−1, which is in excellent agreement with the range of experimental values reported (2691.5–3300M−1s−1). Importantly, though, the microkinetic model quantifies how the reaction rate and the associated overall rate constant varies as a function of time, underscoring that observed overall rate constants are a function of the species’ concentrations used to extract them, which may not be the initial conditions. The decrease in initial reaction rate over 0–12ms was ascribed to the decrease in the concentration of the catalytic form, Zn-OH−, which was primarily converted to Zn-HCO3−. Through calculating the ratio of the net rate to the forward rate of each elementary reaction, the rate-limiting step of the catalytic cycle was identified as the adsorption of CO2. To aid in the interpretation of the complex microkinetic model, an analytical rate expression was derived based on a simplified potential energy surface comprised of three major regions: the adsorption of CO2, the release of HCO3− via displacement by water, and the deprotonation of Zn-H2O. Analysis showed quantitatively how the observed reaction rate constant depends not only on how fast a CO2 molecule is captured but also on how deep the Zn-HCO3− sits.