What Information Is Required to Learn Molecular Pauli Potentials? A Nonlocal Descriptor Hierarchy for Orbital-Free Density Functional Theory
- 1Research Computing Center
- 2University of North Carolina
- 3Department of Chemistry
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.
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BibTeX
@misc{liu2026what,
title = {{What Information Is Required to Learn Molecular Pauli Potentials? A Nonlocal Descriptor Hierarchy for Orbital-Free Density Functional Theory}},
author = {Shubin Liu},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010844/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010844/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - What Information Is Required to Learn Molecular Pauli Potentials? A Nonlocal Descriptor Hierarchy for Orbital-Free Density Functional Theory
AU - Shubin Liu
PY - 2026
DA - 2026/10/22
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010844/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010844/v1
AB - 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.
ER -