Over the past few decades there have been tremendous advances in the accuracy of electronic structure calculations, rigorous methods to assess proposed reaction mechanisms, and techniques to create representative models of active sites for homogeneous and ordered heterogeneous catalysts. Advances on all these fronts have greatly improved our understanding of numerous catalysts. However, most of these methods assume that the active sites are both well-defined and uniform (or are in an ensemble of uniform sites). Catalysts with quenched disorder have non-uniform active sites. Most established modeling techniques are inapplicable and many important catalysts in this category remain poorly understood. The major challenges of modeling catalysts with quenched disorder are (i) the nature of the disorder is out-of-equilibrium 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 preparation method.

In this thesis, we develop new methods to efficiently predict kinetic properties of the distribution of quenched-disordered sites and how they affect different steps of catalyst operation. We combine population balance modeling techniques with machine learning methods to learn how the population of grafted sites evolves in time. We develop a new algorithm to efficiently converge site-averaged kinetics for a given distribution of grafted sites, the Importance Learning algorithm. A combination of Importance sampling and machine Learning are used to efficiently and accurately learn activation parameters of rare sites that dominate site-averaged kinetics. Finally, we develop a protocol to create cluster models of active sites that most accurately preserve quenched degrees of freedom.

Several industrially important catalysts are single metals dispersed on amorphous supports. For example, Cr dispersed on amorphous SiO2 is used to catalyze ethene polymerization and W dispersed on amorphous Al2O3 and SiO2 is used to catalyze olefin metathesis. Despite their extensive use in the industry, these catalysts have largely been intractable to both, experimental and modeling investigations. In particular, they present the following challenges: (i) an unknown quenched disordered structure of the amorphous support, (ii) metal atoms attach to various surface grafting sites with different rates and have different activation and catalytic reaction kinetics, and (iii) only a small fraction of the sites are active. These challenges particularly render ab initio computational tools, routinely applied to study homogeneous and ordered heterogeneous catalysts, inefficient and impractical. The overarching goal of this thesis is developing computational tools to efficiently model the synthesis and reactivity of atomically dispersed catalysts on amorphous supports.

Atomically dispersed amorphous catalysts are synthesized by grafting organometallic complexes onto amorphous supports. We develop a machine learning (ML) parametrized population balance model to predict the evolving population of active sites during catalyst synthesis. We apply the population balance modeling framework to model the grafting of TiCl onto amorphous silica. Equilibrium predictions of the model agree with experimentally determined populations of grafted Ti sites. Additionally, we develop an Importance Learning (IL) algorithm to efficiently calculate the site-averaged activation barrier for amorphous catalysts. IL uses a combination of ML and importance sampling to discover rare and active catalytic sites which dominate kinetics.

Different studies have generated atomistic models of amorphous silica using different simulation protocols. Most studies have claimed that their models are representative of real silicas. Using statistical hypothesis testing, we show that different protocols lead to models with different structural features. We discuss the effects of these structural variations on the grafted catalyst and outline experimental metrics that can be used to validate models in future studies.

Finally, we present a site balance algebra to quantifying amounts of different species generated in grafting experiments. We quantify the amounts of [≡SiOTiCl3] and [([≡SiO)2TiCl2] sites obtained on grafting TiCl4 onto amorphous silica.