Single-atom centers on amorphous supports include catalysts for polymerization, partial oxidation, metathesis, hydrogenolysis, and more. The disordered environment makes each site different, and the kinetics exponentially magnifies these differences to make ab initio site-averaged kinetics calculations extremely difficult. This work extends the importance learning algorithm for efficient and precise site-averaged kinetics estimates to ab initio calculations and multistep reaction mechanisms. Specifically, we calculate site-averaged proton transfer relaxation rates on an ensemble of cluster models representing Brønsted acid sites on silica−alumina. We include direct and water-assisted proton transfer pathways and simultaneously estimate the water adsorption and activation enthalpies for forward and backward proton transfers. We use density functional theory (DFT) to obtain a site-averaged rate, somewhat like a turnover frequency, for the proton transfer relaxation rate. Finally, we show that importance learning can provide orders-of-magnitude acceleration over standard sampling methods for site-averaged rate calculations in cases where the rate is dominated by a few highly active sites.

‘Secondary’ effectiveness factors are developed for reactions in series that are useful for controlling the yield of the intermediate product (B).

Amyloid fibrils are thought to grow by a two-step dock-lock mechanism. However, previous simulations of fibril formation (i) overlook the bi-molecular nature of the docking step and obtain rates with first-order units, or (ii) superimpose the docked and locked states when computing the potential of mean force for association and thereby muddle the docking and locking steps. Here, we developed a simple microkinetic model with separate locking and docking steps and with the appropriate concentration dependences for each step. We constructed a simple model comprised of chiral dumbbells that retains qualitative aspects of fibril formation. We used rare events methods to predict separate docking and locking rate constants for the model. The rate constants were embedded in the microkinetic model, with the microkinetic model embedded in a population balance model for “bottom-up” multiscale fibril growth rate predictions. These were compared to “top-down” results using simulation data with the same model and multiscale framework to obtain maximum likelihood estimates of the separate lock and dock rate constants. We used the same procedures to extract separate docking and locking rate constants from experimental fibril growth data. Our multiscale strategy, embedding rate theories, and kinetic models in conservation laws should help to extract docking and locking rate constants from experimental data or long molecular simulations with correct units and without compromising the molecular description.

Small molecules often exhibit multiple metastable conformers in solution while their crystal structures incorporate only one of the conformers. Several studies have hypothesized that slow conformer interconversion could impede the kinetics of crystal growth. This study develops coupled species and population balances to model the kinetics of conformer interconversion and crystal growth in a mixed suspension mixed product removal crystallizer at steady-state. To isolate the effects of slow interconversion, we develop, nondimensionalize, and solve two models. One model includes finite interconversion rates and the other "control" model assumes rapid interconversion such that the conformers are at equilibrium with each other in solution. Finally, we develop and analyze a version of the model in which the incorrect conformer can block sites for attachment of the growth conformer. The models show that slow interconversion causes unequal supersaturations of the two conformers in solution and reduces the total crystal volume fraction in solution, but does not alter the crystal size distribution.

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