arXiv subjects

Timo Lebeda

Publications and source records attributed to Timo Lebeda.

6 recordsLinked to original sources

arXiv2026

Rationalizing defect formation energies in metals and semiconductors with semilocal density functionals

The study of defects in materials is of utmost importance for technological applications and the design of new materials. In this work, we analyze the performance of density functional approximations on two prototypical sets of defective systems: monovacancies in eight fcc metals, and interstitials in the semiconductor Si-diamond. Specifically, we compute defect formation energies using the local density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, the meta-generalized gradient approximations (meta-GGAs) strongly constrained and appropriately normed (SCAN), its regularized version (r2SCAN), the Lebeda-Aschebrock-Kummel (LAK) meta-GGA, and the Heyd-Scuseria-Ernzerhof screened hybrid functional. For metals, the local density approximation shows better performance compared to the other approximations, whereas for silicon, the meta-generalized gradient approximation Lebeda-Aschebrock-Kummel yields outstand- ing accuracy, surpassing the hybrid functional and approaching the results of more computationally demanding Quantum Monte Carlo methods. To rationalize the different performances, we study the semilocal ingredients rs, s and {\alpha} in both the pristine and defective structures. We identify critical regions that indicate the observed trends of the defect formation energies and pave the way for improving density functional approximations.

cond-mat.mtrl-sci↗

arXiv2026

Meta-generalized gradient approximation made in the Hartree gauge

In density functional theory (DFT), exact constraints, fundamental mathematical properties of the exchange-correlation (XC) energy and its underlying XC hole, along with paradigm systems such as the uniform electron gas and the hydrogen atom have been instrumental in developing exchange- correlation (XC) density functional approximations (DFAs). However, since the spatial XC energy density is not uniquely defined, its exact constraints can only be formulated within a chosen gauge and are therefore seldom utilized in DFA construction. Here, we propose a meta-generalized gradient approximation for the exchange energy, explicitly constructed within the Hartree gauge, using the hydrogen atom's exchange energy density for gauge alignment in core and asymptotic regions. By formulating DFAs at the XC energy density level, this approach expands reference datasets for machine learning and establishes a foundation for more accurate nonlocal density functionals requiring gauge alignment.

cond-mat.mtrl-sci↗

arXiv2025

Electron Localization in Non-Compact Covalent Bonds Captured by the r2SCAN+V Approach

In density functional theory, the SCAN (Strongly Constrained and Appropriately Normed) and r2SCAN functionals significantly improve over generalized gradient approximation functionals such as PBE (Perdew-Burke-Ernzerhof) in predicting electronic, magnetic, and structural properties across various materials, including transition-metal compounds. However, there remain puzzling cases where SCAN and r2SCAN underperform, such as in calculating the band structure of graphene, the magnetic moment of Fe, the potential energy curve of the Cr2 molecule, and the bond length of VO2. This research identifies a common characteristic among these challenging materials: non-compact covalent bonding through s-s, p-p, or d-d electron hybridization. While SCAN and r2SCAN excel at capturing electron localization at local atomic sites, they struggle to accurately describe electron localization in non-compact covalent bonds, resulting in a biased improvement. To address this issue, we propose the r2SCAN+V approach as a practical modification that improves accuracy across all the tested materials. The parameter V is 4 eV for metallic Fe, but substantially lower for the other cases. Our findings provide valuable insights for the future development of advanced functionals.

cond-mat.mtrl-sci↗

arXiv2025

Artificial Symmetry Breaking by Self-Interaction Error

Symmetry is a cornerstone of quantum mechanics and materials theory, underpinning the classification of electronic states and the emergence of complex phenomena such as magnetism and superconductivity. While symmetry breaking in density functional theory can reveal strong electron correlation, it may also arise spuriously from self-interaction error (SIE), an intrinsic flaw in many approximate exchange-correlation functionals. In this work, we present clear evidence that SIE alone can induce artificial symmetry breaking, even in the absence of strong correlation. Using a family of one-electron, multi-nuclear-center systems $ \mathrm{H}^+_{n \times \frac{+2}{n}}(R) $, we show that typical semilocal density functionals exhibit symmetry-breaking localization as system size increases, deviating from the exact, symmetry-preserving Hartree-Fock solution. We further demonstrate that this localization error contrasts with the well-known delocalization error of semilocal density functionals and design a semilocal density functional that avoids the artifact. Finally, we illustrate the real-world relevance of this effect in the \ch{Ti_{Zn}v_O} defect in ZnO, where a semilocal density functional breaks the $C_{3v}$ symmetry while a hybrid density functional preserves it. These findings highlight the need for improved functional design to prevent spurious symmetry breaking in both model and real materials.

cond-mat.mtrl-sci↗

arXiv2024

How Semilocal Are Semilocal Density Functional Approximations? -Tackling Self-Interaction Error in One-Electron Systems

Self-interaction error (SIE), arising from the imperfect cancellation of the spurious classical Coulomb interaction between an electron and itself, is a persistent challenge in modern density functional approximations. This issue is illustrated using the prototypical one-electron system $H_2^+$. While significant efforts have been made to eliminate SIE through the development of computationally expensive nonlocal density functionals, it is equally important to explore whether SIE can be mitigated within the framework of more efficient semilocal density functionals. In this study, we present a non-empirical meta-generalized gradient approximation (meta-GGA) that incorporates the Laplacian of the electron density. Our results demonstrate that the meta-GGA significantly reduces SIE, yielding a binding energy curve for $H_2^+$ that matches the exact solution at equilibrium and improves across a broad range of bond lengths over those of the Perdew-Burke-Ernzerhof (PBE) and strongly-constrained and appropriately-normed (SCAN) semilocal density functionals. This advancement paves the way for further development within the realm of semilocal approximations.

cond-mat.mtrl-sci↗

arXiv2020

A numerical stability analysis for the Einstein-Vlasov system

We investigate stability issues for steady states of the spherically symmetric Einstein-Vlasov system numerically in Schwarzschild, maximal areal, and Eddington-Finkelstein coordinates. Across all coordinate systems we confirm the conjecture that the first binding energy maximum along a one-parameter family of steady states signals the onset of instability. Beyond this maximum perturbed solutions either collapse to a black hole, form heteroclinic orbits, or eventually fully disperse. Contrary to earlier research, we find that a negative binding energy does not necessarily correspond to fully dispersing solutions. We also comment on the so-called turning point principle from the viewpoint of our numerical results. The physical reliability of the latter is strengthened by obtaining consistent results in the three different coordinate systems and by the systematic use of dynamically accessible perturbations.

gr-qc↗