When do machine-learned exchange-correlation improvements inherit into density-functional tight binding?

2026-08-14

AI Summary

This study addresses the challenge of effectively transferring machine learning functional improvements to density-functional tight-binding (DFTB), which often leads to bandgap prediction deviations. We propose a "transferability" metric to quantify inheritance and pre-screen parameterization feasibility. Our analysis reveals that on-site conventions dominate bandgap errors; consequently, modifying on-site terms and polarization shells significantly enhances bandgap accuracy for covalent semiconductors. These corrections reduce errors by 16%–40%. Furthermore, we release parameter sets for 23 elements alongside a pre-testing protocol. Collectively, this work provides both a theoretical foundation and practical tools for high-precision DFTB parameterization, facilitating more reliable electronic structure predictions in computational materials science.

Abstract

Machine-learned exchange-correlation functionals correct band gaps at near-semilocal cost, while density-functional tight binding reaches the $10^3$-$10^6$-atom regime; combining them assumes that a better parent yields a better parameterization, but we show it does not. Current-generation functionals are orbital-dependent generalized Kohn-Sham operators, whereas the parameterization channel is built on a multiplicative potential, preventing exact representation. Using the transfer ratio, the surviving fraction of a parent-level change, we find anti-transfer: coherently negative ratios across four covalent semiconductors move the gap in the wrong direction, consistent with a molecular proxy and an r$^2$SCAN control. The minimal-basis overgap is dominated by the on-site convention rather than basis incompleteness; correcting the on-site block removes most of it, while one $d$-polarization shell closes a further $16$-$40%$, depending on the placement of the empty $d$ level, which no free-atom eigenvalue uniquely fixes. Occupied-manifold enhancements, ionic and closed-shell repulsive potentials, and rocksalt-oxide gaps inherit, whereas elemental and III-V covalent networks inherit neither gaps nor repulsive potentials and oxide networks inherit only the latter. We screen 23 elements and release the parameter sets, showing that the transfer ratio provides a cheap pre-test before any parameterization campaign.

Problem

• Density-functional tight binding
• Machine-learned exchange-correlation
• Transfer ratio
• Band gap
• Parameterization

Innovation

• Transfer ratio
• Anti-transfer
• Density-functional tight binding
• Machine-learned exchange-correlation
• On-site convention