A Renormalized Doubly Hybrid Method Enhanced with Machine Learning for a Unified Treatment of Static and Dynamic Correlations

The 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 renormalized XYG3-type doubly hybrid method, named R-xDH7, which effectively captures a large portion of the static correlation alongside a broad range of the dynamic correlation, showing a marked improvement over contemporary state-of-the-art doubly hybrid (DH) density functional theory methods. By utilizing a hybrid machine learning algorithm that synergistically combines symbolic and nonlinear parameter regression, we further devise a general-purpose model for the static correlation correction (SCC) specifically adapted to R-xDH7. The resultant R-xDH7-SCC15 method achieves an unprecedented accuracy in capturing the static correlation, while maintaining a good description of the dynamic correlation on par with the best DH approximations. Extensive benchmark studies validate the robustness and transferability of R-xDH7-SCC15 across diverse chemical systems. Notably, it displays exceptional aptitude in providing precise characterizations of complex reaction mechanisms beyond the equilibrium regions where static correlation effects are significant. These findings signify a substantial enhancement in the predictive power of computational chemistry, marking a significant stride in the field of electronic-structure theory.