Arghadwip Paul | Search arXiv

arXiv2026

Machine-learned Laplacian-level density functional from exact exchange-correlation potentials and energies

We present NNLap, a machine-learned Laplacian-level exchange-correlation (XC) functional that augments PBE with a neural-network correction depending on the electron density, its gradient, and its Laplacian. The model is trained on exact XC potentials and energies, obtained through inverse density-functional theory (DFT) calculations on configuration-interaction densities. Despite training on only a few systems -- five atoms and three molecules -- the model achieves remarkable accuracy on thermochemistry benchmarks, competing with the meta-GGA functionals SCAN and r2SCAN. It also attains accurate total energies, comparable to SCAN and better than r2SCAN and B3LYP. This shows that a Laplacian-level model, trained on exact XC potentials and energies, can reach the accuracy of meta-GGAs without their orbital dependence.

physics.chem-ph↗

arXiv2025

Field theoretic atomistics: Learning thermodynamic and variational surrogate to density functional theory

The Hohenberg-Kohn (HK) theorem -- the bedrock of density functional theory (DFT) -- establishes a universal map from the external potential to the energy. It also relates the electron density and atomic forces to the variation of the energy with the external potential. But the HK map is rarely utilized in atomistics, wherein interatomic potentials are defined using the molecular or crystal structure rather than the external potential. As a break from this tradition, we present a field theoretic atomistics framework where the external potential assumes the central quantity. We machine learn the HK energy map while satisfying the thermodynamic limit. Further, we obtain both forces and electron density from the variation of the HK energy map, that are exact relations. Our models attain good accuracy across diverse benchmarks and compete with state-of-the-art machine learned interatomic potentials. Through electron density, we predict accurate dipole and quadrupole moments, otherwise nontrivial for interatomic potentials. Our formulation paves the way for a scalable electronic structure surrogate to DFT.

physics.chem-ph↗