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Supported single-atom catalysts show a large range of activities and selectivities that depend on the local environment of the catalytic sites. A theory-based optimization strategy is presented that is based on a density functional theory determination of the transition states and intermediates for a low-dimensional coordinate representation of the heterogeneity of the active sites. The approach is applied to a vanadium catalyst on an amorphous SiO2 support that involves a large kinetic network described using a full chemistry model. Without assuming a priori scaling relations or mechanism reduction, the optimal state of heterogeneity is found to lie at atomic configurations where the activation energies for two distinct key chemical processes are equal. It is found a posteriori that the behavior of the system is consistent with linear free energy scaling relations in the randomness parameters. The energetic span theory proves quite useful in reducing the full chemistry model to a small number of key reactions. The use of a nonlinear optimization algorithm in combination with energetic span theory provides significant simplification in treating disordered systems. 

A recent experiment at the Dalian Coherent Light Source (DCLS) has provided measurements of the partial cross sections for the photodissociation of water vapor over an unprecedented range of wavelengths in the vacuum ultraviolet (VUV) region. It was found that the three body dissociation channel, H + H + O( 3 P/ 1 D), becomes prominent at wavelengths shorter than the Lyman α-line at 121.6 nm. The present work explores the kinetic consequences of this discovery for several astrophysically motivated examples. The irradiation of a dilute low-temperature gas by unscreened solar radiation, similar to early stage photochemical processing in a comet coma, shows significant increase in the production of O 2 -molecules at shorter times, <1 day, that might physically correspond to the photochemical reaction zone of the coma. Several examples of planetary atmospheres show increased O-atom production at high altitudes but relatively little modification of the equilibrium O 2 concentrations predicted by conventional models.