Site-averaged kinetics for catalysts on amorphous supports: An importance learning algorithm

Ab initio calculations have greatly advanced our understanding of homogeneous catalysts and crystalline heterogeneous catalysts. In contrast, amorphous heterogeneous catalysts remain poorly understood. The principal difficulties include (i) the nature of the disorder is quenched and unknown; (ii) each active site has a different local environment and activity; (iii) active sites are rare, often less than ∼20% of potential sites, depending on the catalyst and its preparation method. Few (if any) studies of amorphous heterogeneous catalysts have ever attempted to compute site-averaged kinetics, because the exponential dependence on variable activation energy requires an intractable number of ab initio calculations to converge. We present a new algorithm using machine learning techniques (metric learning kernel regression) and importance sampling to efficiently learn the distribution of activation energies. We demonstrate the algorithm by computing the site-averaged activity for a model amorphous catalyst with quenched disorder.