Towards Efficient and Unified Treatment of Static and Dynamic Correlations in Generalized Kohn-Sham Density Functional Theory

Accurate description of the static correlation poses a persistent challenge for electronic structure theory, particularly when it has to be concurrently considered with the dynamic correlation. We develop here a ground breaking method in the generalized Kohn-Sham density functional theory (DFT) framework, named R-xDH7-SCC15, which achieves an unprecedented accuracy in capturing the static correlation, while maintaining a good description of the dynamic correlation on par with the state-of-the-art DFT and wave function theory methods, all grounded in the same single-reference black-box methodology. Central to R-xDH7-SCC15 is a novel, general-purpose static correlation correction (SCC) model applied to the renormalized XYG3-type doubly hybrid method (R-xDH7). The SCC model development pioneers a hybrid machine learning strategy that ingeniously harmonizing symbolic regression with nonlinear parameter optimization, to strike a balance between enhanced generalization capability, rigorous numerical accuracy, and retained interpretability of the SCC model. Extensive benchmark studies confirm the robustness and broad applicability of R-xDH7-SCC15 across a diverse array of chemical scenarios. Notably, it displays exceptional aptitude in accurately characterizing intricate reaction kinetics and dynamic processes in regions distant from equilibrium, where the influence of static correlation is most profound. Its capability to consistently and efficiently predict energy profiles, activation barriers, and reaction pathways within a user-friendly “black-box” framework, signifies a paradigm shift in our ability to model and comprehend complex chemical transformations, thereby marking a significant stride in the field of electronic-structure theory.