Half-Way Bayesian Calibration for Assessing Uncertainties in Quantum Chemistry Guided Catalyst Optimization

Developments in computational chemistry have made quantum chemical modeling an essential tool for catalyst design. However, so far theoretical predictions usually lack error bars, making them almost useless in guiding high-stakes decisions. Commonly used accuracy metrics such as mean absolute error are ill-defined when selectivity depends on relative energies of dozens of closely related transition states, as often happens in catalysis. The main missing ingredient is a tool for estimating errors of a computational protocol where many computed values combine into a single prediction. Here we show how Bayesian statistics can be applied to a model case of catalyst optimization, providing a framework for assessing reliability of a computational protocol as well as for telling reliable predictions from unreliable ones even for very similar compounds. We find that a modest B97-D/TZV(2d,2p)/PCM level of theory employing a semi-local GGA-level density functional provides a standard deviation of only ~0.26 kcal/mol in relative energies of enantiomeric transition states for the model reaction. Thus, we provide a practical tool for assessing uncertainties in computational predictions and integrating them into catalyst optimization pipelines, bridging the gap between quantum chemistry and experimental catalysis design.