What Information Is Required to Learn Molecular Pauli Potentials? A Nonlocal Descriptor Hierarchy for Orbital-Free Density Functional Theory
Year: 2026
Type: preprint
Abstract: Practical orbital-free density functional theory (OF-DFT) for molecules remains limited by the unknown Pauli contribution to the noninteracting kinetic energy. Here, we ask what information a density representation must contain for a machine-learned (ML) Pauli potential to drive an orbital-free Euler solution toward its Kohn–Sham (KS) reference. For C2H2, a frozen KS-derived Pauli-potential oracle yields an OF energy within 3.15 mHa of the KS reference, establishing the numerical accuracy attainable within the chosen finite representation. Coordinate-conditioned neural networks demonstrate that the Paulipotential field is learnable but do not provide a density-functional representation. Replacing coordinates with semilocal density descriptors leads to severe failure for both multilayer perceptron (MLP) and Kolmogorov–Arnold network (KAN) models. A descriptor-space identifiability analysis reveals the underlying cause: sparse representations leave approximately 14% of grid points ambiguous, whereas an atom-reaching 60-component nonlocal environment reduces this fraction to approximately 1.4%. Correspondingly, progressively adding nonlocal density information reduces the KAN energy deviation from −4594 to −16.0 mHa, while geometry-informed bond-centered descriptors further reduce it to −0.9 mHa. Applied independently to C2H4, the same descriptor strategy remains effective, yielding deviations of +24.0 and −13.5 mHa for KAN and MLP, respectively. Companion models also recover the principal spatial features of the Pauli energy density and strong covalent interaction profile. These results identify the resolution of descriptor ambiguity through extended and chemically structured nonlocal density information as a central representational requirement for molecular OF-DFT.
Source: ChemRxiv
Author: Shubin Liu
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223173189