Toward 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 in electronic structure theory, particularly when it has
to be concurrently considered with the dynamic correlation. We develop
here a 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 general-purpose
static correlation correction (SCC) model applied to the renormalized
XYG3-type doubly hybrid method (R-xDH7). The SCC model development
involves a hybrid machine learning strategy that integrates symbolic
regression with nonlinear parameter optimization, aiming to achieve
a balance between generalization capability, numerical accuracy, and
interpretability. Extensive benchmark studies confirm the robustness
and broad applicability of R-xDH7-SCC15 across a diverse array of
main-group 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 the whole energy profiles, activation barriers,
and reaction pathways within a user-friendly “black-box”
framework represents an important advance in the field of electronic
structure theory.