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arxiv: 2606.20116 · v1 · pith:NYDVBZZDnew · submitted 2026-06-18 · ❄️ cond-mat.mtrl-sci · physics.chem-ph

Hartree-Fock Limit for Energies in Solids

J\=anis U\v{z}ulis , Andris Gulans This is my paper

Pith reviewed 2026-06-26 16:28 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.chem-ph
keywords Hartree-FockLAPWtotal energysemiconductorsinsulatorsall-electronhybrid functionalsreference data
0
0 comments X

The pith

Aligning radial basis functions and core orbitals with the Hartree-Fock Hamiltonian lets LAPW calculations reach the HF energy limit for solids and molecules to within a few microhartree.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper presents a route to the Hartree-Fock limit inside the linearized augmented plane wave method. The central step is to build radial basis functions and core orbitals directly from the HF Hamiltonian rather than from a local or semilocal potential. The resulting total energies for molecules and solids are reported accurate to a few microhartree. The work supplies reference HF values for fourteen semiconductors and insulators and shows that the older construction remains adequate for many relative energies such as formation energies.

Core claim

The central claim is that constructing radial basis functions and core orbitals consistently with the HF Hamiltonian removes the previous limitations of the standard LAPW treatment of nonlocal exchange, thereby allowing total energies of molecules and solids to be obtained at the Hartree-Fock limit with a precision of a few μHa.

What carries the argument

HF-consistent construction of radial basis functions and core orbitals inside the LAPW framework, which ensures proper handling of nonlocal exchange.

If this is right

  • Total energies of molecules and solids are obtained to within a few μHa of the HF limit.
  • Reference HF data are supplied for fourteen semiconductors and insulators.
  • The standard LAPW construction remains accurate for relative energies such as molecular and solid-state formation energies and Si self-interstitial defect formation energies.
  • Error control improves in hybrid-functional LAPW calculations.
  • X-ray spectroscopy simulations become possible inside LAPW using hybrid-functional core orbitals.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The reference data can serve as benchmarks for testing basis-set convergence and pseudopotential accuracy in other all-electron or plane-wave codes.
  • The same HF-consistent construction could be tested on systems with stronger correlation or larger unit cells to check whether the microhartree precision persists.
  • Improved core orbitals open the possibility of direct hybrid-functional treatments of core-level spectroscopies without additional approximations.

Load-bearing premise

That building radial basis functions and core orbitals from the HF Hamiltonian itself is enough to eliminate the current limitations of standard LAPW for nonlocal exchange.

What would settle it

A comparison of the method's total energies against independently converged, exact Hartree-Fock results for the same molecules or solids that shows deviations larger than a few μHa would falsify the claimed precision.

Figures

Figures reproduced from arXiv: 2606.20116 by Andris Gulans, J\=anis U\v{z}ulis.

Figure 1
Figure 1. Figure 1: Convergence of the total HF energy (in Ha) depending on the number of radial basis functions in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Formation energy errors (in kcal/mol) in GTO calculations using the hierarchy of basis sets from [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Formation energies (kcal/mol) of Si self-interstitials in the hexagonal (H) and split (X) configu [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

This study establishes a route to the Hartree--Fock (HF) limit for molecules and solids within the linearized augmented plane wave (LAPW) framework. We remove current limitations of the standard LAPW approach to nonlocal exchange by constructing radial basis functions and core orbitals consistently with the HF Hamiltonian. The presented method yields total energies of molecules and solids with a precision of a few $\mu$Ha, and we use it to provide reference data for 14 semiconductors and insulators. For the systems considered in this study, the standard approach based on (semi)local potentials for constructing radial basis functions and core orbitals remains highly precise for practical relative energies, including molecular and solid-state formation energies and Si self-interstitial defect formation energies. More broadly, the results provide stringent all-electron benchmarks for basis-set and pseudopotential assessment, improve error control in hybrid-functional calculations within LAPW, and open the way to X-ray spectroscopy simulations within LAPW based directly on hybrid-functional core orbitals.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript presents a modification to the LAPW method in which radial basis functions and core orbitals are constructed from the HF Hamiltonian rather than from (semi)local potentials. This is claimed to remove limitations on nonlocal exchange, yielding total energies for molecules and solids at few-μHa absolute accuracy and supplying reference HF data for 14 semiconductors and insulators. The work also states that the conventional (semi)local construction remains adequate for relative energies such as formation energies and defect energies.

Significance. If the stated absolute accuracy is demonstrated, the approach would supply much-needed all-electron HF benchmarks for solids, enabling rigorous assessment of basis sets and pseudopotentials, tighter error control in hybrid-functional LAPW calculations, and direct use of hybrid core orbitals for X-ray spectroscopy simulations.

major comments (1)
  1. [Abstract] Abstract: the central claim of few-μHa precision for total energies and the provision of reference data for 14 materials is not accompanied by any numerical tables, convergence plots, or direct comparisons to established HF limits, leaving the accuracy assertion unverified from the manuscript text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review and for highlighting the need for clear verification of the accuracy claims. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim of few-μHa precision for total energies and the provision of reference data for 14 materials is not accompanied by any numerical tables, convergence plots, or direct comparisons to established HF limits, leaving the accuracy assertion unverified from the manuscript text.

    Authors: The full manuscript contains the requested verification. Section III reports basis-set convergence studies with plots (Figs. 2–4) demonstrating that total energies converge to within a few μHa. Table I provides direct comparisons of molecular HF energies against established limits from quantum-chemistry codes. Table II lists all-electron HF total energies for the 14 semiconductors and insulators, together with comparisons to literature values where available. These data substantiate the abstract claims. Abstracts are concise summaries and conventionally omit tables and figures; the supporting evidence appears in the main text as described. revision: no

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper describes a direct methodological modification to the LAPW framework: radial basis functions and core orbitals are constructed from the HF Hamiltonian itself to reach the Hartree-Fock limit. This construction is presented as an implementation choice that addresses a known limitation of standard LAPW for nonlocal exchange, without any fitted parameters renamed as predictions, self-citation chains that bear the central claim, or reductions of results to inputs by definition. The reported few-μHa precision and reference data for 14 solids follow from the method's design and external benchmarks rather than internal equivalence. The derivation chain remains self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract provides no explicit free parameters, new axioms, or invented entities; the approach modifies an existing LAPW construction step under standard domain assumptions of the method.

axioms (1)
  • domain assumption Standard LAPW representation of wave functions in solids remains valid when the radial basis is generated from the HF Hamiltonian.
    The paper extends the LAPW framework rather than replacing its foundational assumptions.

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Reference graph

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