Δ-Machine learning toward CCSD accuracy for homohalogenated borane–phosphine adducts: screening low-energy structures from DFT and MP2 libraries

Abstract

Accurate formation energies for weak boron–phosphorus Lewis adducts are challenging because low-order correlation and density-functional methods can misrank low-energy motifs on shallow potential-energy landscapes and are sensitive to basis-set superposition error (BSSE). Herein, we combine large-scale structure-library sampling with Δ-machine learning (Δ-ML) to approach coupled-cluster accuracy for the homohalogenated adducts F₃B–PF₃, Cl₃B–PCl₃, and Br₃B–PBr₃. DFT (B3LYP-D3) and MP2 libraries comprising several thousand geometries per system are generated and used to train CCSD-referenced Δ-ML models that predict E_CCSD from low-level inputs. The resulting models reproduce CCSD energies with low errors and enable efficient screening of the full libraries, after which a compact low-energy subset is refined with targeted CCSD(T) calculations. Counterpoise-corrected results show that MP2 substantially overbinds, especially for the chlorinated and brominated adducts. At the highest level, Cl₃B–PCl₃ is found to lie at the threshold of binding, whereas Br₃B–PBr₃ remains clearly bound and F₃B–PF₃ is weakly bound. Distance-resolved scans and Morokuma-type energy decomposition analyses rationalize the distinct binding regimes across F/Cl/Br in terms of the balance between Pauli repulsion, polarization/exchange, and dispersion. The proposed workflow enables reliable coupled-cluster-level screening of weak donor–acceptor adducts at greatly reduced cost.