Uncertainty Quantification for <i>In Silico</i> Chemistry

The rapid growth of worldwide computing power has transformed <i>in silico</i> chemistry into a discipline that is integrated into the daily work of many chemists. Nowadays, researchers find it increasingly straightforward to predict a wide range of molecular properties and chemical processes at reasonable computational cost. The resulting abundance of data generated by quantum chemistry, molecular dynamics simulations, and chemical machine learning naturally raises questions about accuracy, precision, and reliability as well as the systematic treatment of errors and uncertainties. Addressing these questions through rigorous mathematical frameworks is at the heart of uncertainty quantification. In the past years, the incorporation of uncertainty quantification into <i>in silico</i> chemistry has gained attention, motivated by its ability to provide deeper insights into chemical phenomena. In this review, we establish a common language for uncertainty quantification with respect to <i>in silico</i> chemistry, introduce the key mathematical formalisms, and survey the growing body of work that applies uncertainty quantification across different areas of <i>in silico</i> chemistry.