By leveraging the fact that SE methods already capture much of the relevant physics, the Δ-learning approach has emerged as a powerful strategy for enhancing their accuracy. In this approach, the target property is the difference between SE energies and forces and their DFT counterparts, enabling SE methods to achieve higher accuracy in physicochemical properties with minimal computational overhead. An early example of this methodology was demonstrated for a set of C 7 H 10 O 2 isomers from the GDB17 dataset . Here, a KRR model was trained to predict atomization energies at the G4MP2 level by learning the difference between G4MP2 and PM7 (62) semiempirical energies, outperforming models trained on absolute energies. Similarly, a BPNN has been used to address the limitations of the second-order density functional tight-binding (DFTB2) method in describing intramolecular hydrogen bonds and torsional potentials of glycine . Building upon this idea, the accuracy of the third-order DFTB method (64) was improved by replacing the standard atom-pairwise repulsive potential with a many-body NN repulsive potential, NN rep . This potential was trained on small molecules from the QM7-X dataset using the SchNet architecture, achieving PBE0-level accuracy for energetic, structural, and vibrational properties across diverse organic molecules containing up to nine heavy atoms.