An Energy-Corrected Fast Post-SCF Local-Hybrid Scheme for Highly Accurate Energy Differences of Large Main-Group Systems.

Local-hybrid (LH) density functionals admix exact exchange locally in real space and thereby can be powerful tools to ameliorate the usual zero-sum game between reducing self-interaction errors and modeling static correlation. But as with other hybrid functionals the practical use of LHs for large systems is limited by the cost of evaluating exact-exchange quantities self-consistently. Here we introduce an energy-corrected local-hybrid framework, EC(LH)@(m)GGA, in which a computationally expedient semi-local reference density is used for a single post-SCF evaluation with an advanced LH. Using the recent neural-network-based LH25nP LH as a prototype, we show that the EC route based on GGA or meta-GGA orbitals preserves the characteristic accuracy profile of the parent local hybrid and reaches state-of-the-art rung 4 performance on the GMTKN55 test suite (WTMAD-2 around 2.4-2.7 kcal/mol, depending on grid). The top performance of LH25nP for spin-restricted bond dissociation as a strong-correlation measure is retained in this framework. The dominant post-SCF overhead in timing is governed by the EC grid. For the practical gridsize 3, the total EC(LH)@(m)GGA cost is only about ~2-3× that of a GGA single point, typically about an order of magnitude less than a full LH SCF. Overall, EC(LH)@(m)GGA provides a simple post-SCF route to state-of-the-art rung-4 energetics at a cost close to semi-local DFT, applicable to large systems.