Accurate Coupled Cluster Energies via Machine Learning: Delta Learning Extrapolated from Wavefunction and Density-Functional Theory

Abstract

The absolute energies of molecules are essential in many areas, such as atmospheric chemistry, thermochemistry, kinetics, catalysis, reaction predictions, and the study of reactive intermediates. Traditionally, energies were determined through elaborate quantum mechanical computations. Depending on the size of the molecule, only computations at a low level of theory can be carried out, such as methods based on density functional theory. Small molecules can be calculated using a wave function based method, like the coupled cluster theory, often referred to as the gold standard of computational chemistry, especially when the CCSD(T)/cc-pVTZ theory level is used. With the exponential development of the computing power of special accelerator cards (graphics cards), machine learning has experienced a real upswing and is often found in the everyday language under the buzzword "artificial intelligence". In this work, two methods were developed to predict accurate molecular energies of molecules using statistical models. Starting from a lower theory level, which requires significantly less computing power, the models were able to predict the differences in energies to the higher theory level. Such an approach is known as Delta-Learning. This not only saves time but also enables the prediction of energies for large molecules, which could not be calculated quantum mechanically. In the first publication, a database of 540 molecules was generated using the CCSD(T) method to train a model that can predict from the CCSD method to the CCSD(T) method and has an accuracy of 0.25 kcal mol–1. The subsequent work achieved with a database size of 8000 molecules the prediction of the CCSD(T)/cc-pVTZ energy based on density functional based properties with a mean absolute error of <1 kcal mol–1 with twentyfold time saving.