Error-Controlled Quantum Chemical Exploration of Reaction Networks

For a detailed analysis of a chemical system, all relevant intermediates and elementary reactions on the potential energy surface (PES) connecting them need to be known. An in-depth understanding of all reaction pathways would allow one to study the evolution of a system over time, given a set of initial conditions (e.g., reactants and their concentrations, temperature, and pressure) and propose derivatives of the original reactants to avoid undesired side reactions. Manual explorations of complex reaction mechanisms employing quantum-chemical methods are slow and error-prone. In addition, due to the high dimensionality of PESs exhaustive exploration is generally unfeasible. However, to rationalize, for instance, the formation of undesired side products or decomposition reactions, unexpected reaction pathways need to be uncovered. In this thesis, we present a computational protocol that constructs reaction networks, consisting of intermediates and transition states, in a fully automated fashion. Starting from a set of initial reagents new intermediates are explored through intra- and intermolecular reactions of already explored ones. This is done by assembling reactive complexes based on heuristic rules derived from conceptual electronic-structure theory and exploring the corresponding approximate reaction path. A subsequent path refinement leads to a minimum-energy path which connects the new intermediate to the existing ones to form a connected reaction network. Tree traversal algorithms are then employed to detect reaction channels and catalytic cycles. We apply our protocol to the formose reaction to study different pathways of sugar formation and to rationalize its autocatalytic nature. Furthermore, we investigate the Schrock dinitrogen-fixation catalyst and discover alternative pathways of catalytic ammonia production. To be able to draw reliable conclusions from the generated reaction networks, accurate relative energies between intermediates and transition states are required. To date, density functional theory (DFT) is the only method that is computationally feasible for the exploration in this detail. However, DFT often fails to provide sufficiently accurate results, especially for systems containing transition metals. In this thesis, we apply a framework based on Bayesian statistics that allows for error estimation of properties calculated with DFT. Instead of considering only the best-fit parameters of an approximate density functional, we assign a conditional probability distribution to the continuous set of parameters from which a confidence interval can be calculated for any observable. We assess our approach at two challenging chemical systems: catalytic nitrogen fixation and the formose reaction. Finally, to overcome the lack of systematic improvability of approximate quantum chemical methods we apply Bayesian statistical learning. This new approach allows for the systematic, problem-oriented, and rolling improvement of quantum chemical results through the application of Gaussian processes. Due to its Bayesian nature, reliable error estimates are provided for each prediction. A reference method of high accuracy will be employed to provide a new data point if the uncertainty associated with a particular calculation is above a given threshold. This data point is then added to a growing data set in order to continuously improve the model, and as a result, all subsequent predictions. Previous predictions are validated by the updated model to ensure that uncertainties remain within the given confidence bound, which we call backtracking. We demonstrate our approach with the example of a complex chemical reaction network