A Parameter-Free Reference Hamiltonian for Tight-Binding Vanadium Oxides
Abstract
Density-functional tight binding has yet to yield a transferable description of vanadium oxides; for the standard second-order construction and the tested cells, we demonstrate that two of its approximations deviate by electron volts and offset each other in the band-index centroid separation between the V 3d and O 2p bands: the neutral two-centre reference omits electron-volt environmental terms, whereas the Mulliken charge model assigns the compact V 3d shell less than half of the self-consistent potential shift observed in PBE. Instead, we build a tight-binding model where the reference Hamiltonian derives from superposed neutral atoms, the full PBE exchange-correlation potential and frozen-core orthogonality, without adjustable terms, and where the orbital-resolved charge response employs three screening factors obtained from PBE linear response and an unscreened Coulomb range. Relative to the primary PAW reference, the plane-wave Harris-Foulkes energy differences of VO2 are matched by the reference energy at fixed geometry and the stated numerical settings, with signed deviations of +2.6 meV/atom for M1 relative to rutile (an energy difference of 92 meV/atom) and +6.2 and -5.2 meV/atom under 3% volume compression and expansion; the charge response reproduces 14 of 22 fitted and 5 of 8 held-out matched PBE responses within one tolerance, and 28 of the 30 within twice the tolerance, and in rutile the fitted first-radial V 3d shift is -4.39 eV, 0.47 eV more negative than PBE's -3.92 eV, whereas the tested DFTB2 charge model gives -1.53 eV. The convexity of the spinless model at fixed geometry prevents it from spontaneously differentiating symmetry-equivalent sites under the symmetries respected by its implemented operators and sampling, so within this model such differentiation in the Magnéli phases must arise from electron-lattice coupling or an explicit spin or correlation term.
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BibTeX
@misc{lu2026parameterfree,
title = {{A Parameter-Free Reference Hamiltonian for Tight-Binding Vanadium Oxides}},
author = {Jun-qiang Lu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17687},
eprint = {2610.17687},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17687},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Parameter-Free Reference Hamiltonian for Tight-Binding Vanadium Oxides
AU - Jun-qiang Lu
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.17687
UR - https://arxiv.org/abs/2610.17687
AB - Density-functional tight binding has yet to yield a transferable description of vanadium oxides; for the standard second-order construction and the tested cells, we demonstrate that two of its approximations deviate by electron volts and offset each other in the band-index centroid separation between the V 3d and O 2p bands: the neutral two-centre reference omits electron-volt environmental terms, whereas the Mulliken charge model assigns the compact V 3d shell less than half of the self-consistent potential shift observed in PBE. Instead, we build a tight-binding model where the reference Hamiltonian derives from superposed neutral atoms, the full PBE exchange-correlation potential and frozen-core orthogonality, without adjustable terms, and where the orbital-resolved charge response employs three screening factors obtained from PBE linear response and an unscreened Coulomb range. Relative to the primary PAW reference, the plane-wave Harris-Foulkes energy differences of VO2 are matched by the reference energy at fixed geometry and the stated numerical settings, with signed deviations of +2.6 meV/atom for M1 relative to rutile (an energy difference of 92 meV/atom) and +6.2 and -5.2 meV/atom under 3% volume compression and expansion; the charge response reproduces 14 of 22 fitted and 5 of 8 held-out matched PBE responses within one tolerance, and 28 of the 30 within twice the tolerance, and in rutile the fitted first-radial V 3d shift is -4.39 eV, 0.47 eV more negative than PBE's -3.92 eV, whereas the tested DFTB2 charge model gives -1.53 eV. The convexity of the spinless model at fixed geometry prevents it from spontaneously differentiating symmetry-equivalent sites under the symmetries respected by its implemented operators and sampling, so within this model such differentiation in the Magnéli phases must arise from electron-lattice coupling or an explicit spin or correlation term.
ER -