Grafting metal complexes onto amorphous supports: from elementary steps to catalyst site populations via kernel regression

Ab initio computational studies have made tremendous progress in describing the behavior of molecular (homogeneous) catalysts and crystalline versions of heterogeneous catalysts, but not for amorphous heterogeneous catalysts. Even widely used industrial amorphous catalysts like atomically dispersed Cr on silica remain poorly understood and largely intractable to computational investigation. The central problems are that (i) the amorphous support presents an unknown quenched disordered structure, (ii) metal atoms attach to various surface grafting sites with different rates, and (iii) the resulting grafted sites have different activation and catalytic reaction kinetics. This study combines kernel regression and importance sampling techniques to efficiently model grafting of metal ions onto a non-uniform ensemble of support environments. Our analysis uses a simple model of the quenched disordered support environment, grafting chemistry, and catalytic activity of the resulting grafted sites.