CBH-BDC Enhanced Δ‑ML for Predicting the Accurate Standard Enthalpy of Formation

The standard enthalpy of formation (Δ f H °) is a fundamental thermodynamic property that is essential for understanding various physicochemical processes. Our group recently developed the connectivity-based hierarchy with the bond difference correction (CBH–BDC) method for calculating the accurate Δ f H °. However, it encounters challenges in high-accuracy electron energy calculations and is restricted by BDC parameters that are limited to specific elements. In this work, we introduce a CBH–BDC enhanced delta machine learning (Δ-ML) approach that utilizes effective and interpretable molecular descriptors derived from connection-based hierarchy fragments and BDC, enabling the accurate prediction of Δ f H ° while bypassing high-level quantum calculations. The approach is validated using 464 species with experimental Δ f H ° and applied to extrapolate Δ f H ° from density functional theory (DFT) accuracy to CCSD(T) accuracy for 120,416 stable organic molecules in the QM9 database. It demonstrates significant improvements in accuracy, enabling the construction of a high-quality Δ f H ° database for chemical deep learning.