Computational Systems Chemistry with Rigorous Uncertainty Quantification

Abstract

The success of in silico design approaches for molecules and materials that attempt to solve major technological issues of our society depends crucially on knowing the uncertainty of property predictions. Calibration is an essential model-building approach in this respect as it renders the inference of uncertainty-equipped predictions based on computer simulations possible. However, there exist various pitfalls that may affect the transferability of a property model to new data. By resorting to Bayesian inference and resampling methods (bootstrapping and cross-validation), we discuss issues such as the proper selection of reference data and property models, the identification and elimination of systematic errors, and the rigorous quantification of prediction uncertainty. We apply this statistical calibration approach to the prediction of 57Fe Mössbauer isomer shifts from electron densities obtained with density functional theory. Our findings reveal that the specific selection of reference iron complexes can have a significant effect on the ranking of density functionals with respect to model transferability. Furthermore, we show that bootstrapping can be harnessed to determine the sensitivity of such model rankings to changes in the reference data set, which is inevitable to guide future computational studies. Such a statistically rigorous approach to calibration is almost unknown to chemistry. Our study is one of the very few addressing this issue and its results can be applied by all chemists to arbitrary property models with our open-source software reBoot. In this thesis, we define a new standard for the calibration of computational results due to the rigor, transparency, and generality of our statistical approach, which is completely automatable. Black-box uncertainty quantification can also be applied to macroscopic systems by propagating the uncertainties inferred for single-molecule properties, which will ultimately allow modeling in chemistry to accelerate the discovery of important drugs, organic materials for solar cells, electrolytes for flow batteries, etc. A rather fundamental application area of this systems-focussed uncertainty quantification approach is the understanding of complex chemical reaction mechanisms, which is therefore another focus of this thesis. For an approach that accounts for all elementary processes within a reactive mixture, it is essential to know all relevant intermediates and transition states, to determine relative (free) energies, to quantify their uncertainties, and to model the systems kinetics based on uncertainty propagation. The advantage of a holistic in silico approach to chemistry is that the origin of all data can be rigorously controlled, which allows for reliable uncertainty quantification and propagation. In this thesis, we present the first automated exploration of parts of chemical reaction space based on quantum mechanical descriptors at the example of synthetic nitrogen fixation. Moreover, an extension to the exploration strategy considering uncertainty propagation through all stages of in silico modeling is presented in detail at the example of the formose reaction. It is generally hard to model the kinetics of such complex reactive systems as they usually constitute processes spanning multiple time scales. Here, we present a simple and efficient strategy based on computational singular perturbation, which allows us to model the kinetics of complex chemical systems at arbitrary time scales. To study arbitrary reaction networks of dilute chemical systems (low-pressure gas or low-concentration solution phase), we implemented a generalized scheme of our kinetic modeling approach referred to as KiNetX. Main features of the completely automated KiNetX meta-algorithm are hierarchical network reduction, uncertainty propagation, and global sensitivity analysis, the latter of which detects critical (uncertainty-amplifying) regions of a network such that more complex electronic structure models are only employed if necessary. We also developed an automatic generator of abstract reaction networks encoding chemical logic, named AutoNetGen, which is coupled to KiNetX and allows us to examine a multitude of different chemical scenarios in short time. In a final case study, we apply the insights gained from computational systems chemistry with rigorous uncertainty quantification to model the thermochemistry, kinetics, and spectroscopic properties of iron porphyrin compounds, which constitute a crucial type of active centers in metalloenzyme research.