Toward Efficient\nand Unified Treatment of Static and\nDynamic Correlations in Generalized Kohn–Sham Density Functional\nTheory

Accurate description\nof the static correlation poses\na persistent\nchallenge in electronic structure theory, particularly when it has\nto be concurrently considered with the dynamic correlation. We develop\nhere a method in the generalized Kohn–Sham density functional\ntheory (DFT) framework, named R-xDH7-SCC15, which achieves an unprecedented\naccuracy in capturing the static correlation, while maintaining a\ngood description of the dynamic correlation on par with the state-of-the-art\nDFT and wave function theory methods, all grounded in the same single-reference\nblack-box methodology. Central to R-xDH7-SCC15 is a general-purpose\nstatic correlation correction (SCC) model applied to the renormalized\nXYG3-type doubly hybrid method (R-xDH7). The SCC model development\ninvolves a hybrid machine learning strategy that integrates symbolic\nregression with nonlinear parameter optimization, aiming to achieve\na balance between generalization capability, numerical accuracy, and\ninterpretability. Extensive benchmark studies confirm the robustness\nand broad applicability of R-xDH7-SCC15 across a diverse array of\nmain-group chemical scenarios. Notably, it displays exceptional aptitude\nin accurately characterizing intricate reaction kinetics and dynamic\nprocesses in regions distant from equilibrium, where the influence\nof static correlation is most profound. Its capability to consistently\nand efficiently predict the whole energy profiles, activation barriers,\nand reaction pathways within a user-friendly “black-box”\nframework represents an important advance in the field of electronic\nstructure theory.