Double-Hybrid Density Functional Theory within the Cluster-in-Molecule Local Correlation Framework for Large...

Double-hybrid density functional theory (DHDF) offers high accuracy but is often limited to small systems due to the computational cost of the perturbative second-order (PT2) correlation term. In this work, we develop a cluster-in-molecule double-hybrid density functional approach (CIM-DHDF) by combining DHDF with a local correlation framework, enabling efficient and accurate PT2 energy evaluation for large molecular systems. Benchmark calculations show that CIM-DHDF recovers more than 99.9% of the PT2 correlation energies of conventional DHDF methods across different basis sets for a representative set of benchmark systems, even when diffuse functions are included. The performance of CIM-DHDF is further demonstrated by reaction barrier height calculations for 6 large hydrogen-transfer reactions containing up to 1443 atoms, using the domain-based local pair natural orbital coupled-cluster with singles, doubles, and perturbative triples [DLPNO-CCSD(T₁)] method as the reference. Statistical analyses based on mean and maximum unsigned errors (MUEs and MaxUEs) show that double-hybrid functionals, especially the XYG3 family, consistently outperform conventional hybrid functionals in terms of overall accuracy. These results demonstrate that CIM-DHDF provides a scalable and reliable route to extending DHDF calculations to molecular systems far beyond the practical limits of canonical implementations.