NN-Dx: Chemically adaptive dispersion physics for density-functional theory

<title>Abstract</title> <p> London dispersion is essential to molecular structure, recognition and condensed-phase stability, yet remains inaccurately modelled by many density-functional approximations. Existing density-free corrections recover the required long-range interaction efficiently, but their accuracy is constrained by fixed response models and globally parametrized damping functions. Here we introduce NN-Dx, a chemically adaptive dispersion correction that embeds equivariant machine learning within a D4-inspired analytical framework. The model predicts environment-dependent modifications to atomic dynamic-polarizability spectra, charge response, Becke-Johnson damping, pairwise scaling and Axilrod–Teller–Muto three-body interactions, while preserving the explicit asymptotic form of the dispersion energy. Across nine density functionals, NN-Dx reduces the mean absolute errors of default DFT-D4 by 70–91% on held-out noncovalent-interaction benchmarks, with seven functionals achieving errors below 0.08 kcal mol ⁻¹ . On neutral and charged DES15K subsets, error reductions reach 82–92%. For PBE0 on a common hydrogen, carbon, nitrogen and oxygen subset, NN-Dx achieves a mean absolute error of 0.051 kcal mol ⁻¹ , approximately thirteenfold lower than published machine-learned exchange-hole dipole moment models. NN-Dx also reproduces reference binding curves without spurious stationary points and provides analytical derivatives for stable, energy conserving molecular dynamics. </p>