Forensic SCF-Reference Validation of the LLZO Pressure-Sweep Record: Widespread Multi-Root Contamination and Scope Correction

Verdict (read first)

• Not decision-grade as originally framed: the LLZO pressure-sweep headline claims — the monotonic Li-present σ-stabilisation trend, the d⁰ "bifurcation" interpretation, and the pressure-inversion narrative — are not supported by the current evidence, because the arms required to support them show severe SCF reference-root instability large enough to explain the apparent σ/basin/IBG structure.
• Survives the first screen (exact-reference validation still pending): P3_Li1 and P4_Li1 pass the SCF-root stability check at N=20. P4_Li0 passes a targeted N=20 rerun, though an earlier full-sweep run showed minor spurious-root contamination; it is retained as a cleaner Li-vacancy endpoint candidate, root-filter / exact-reference validation pending. P3_Li1 (stable reference, published σ ≈ 14.14 kcal/mol) is the strongest remaining anomaly candidate.
• Unsupported pending reruns (not refuted): the d⁰-bifurcation and pressure-inversion interpretations are withdrawn as decision-grade claims until root-pinned or physical-root-filtered reconstructions are performed. This work does not assert that a correctly-converged calculation would be featureless.
• Methods finding: the same SCF reference-multiplicity failure mode characterised in the Fe₄N₂ correction (Zenodo 10.5281/zenodo.20264767) is present, and more widespread, in this LLZO sweep. It is documented here as a citable hazard for σ-based electronic-landscape diagnostics.

This is a corrected, superseding version of an earlier deposit. The previous version ("What Happens Inside a Solid-State Battery Electrolyte Under Pressure — A Quantum Ensemble Study") reported a pressure-driven electronic-landscape inversion, a monotonic Li-present stabilisation trend, and an unexpected d⁰ Zr⁴⁺ bifurcation in LLZO. A forensic validation applying the methodology developed for the Fe₄N₂ correction shows that most of the arms underpinning those claims suffer SCF reference-root contamination. The headline interpretations are withdrawn as decision-grade results. What survives, the limitations, and the methods finding are stated explicitly below.

1. Background and what the original deposit claimed

LLZO (Li₇La₃Zr₂O₁₂) is a leading solid-state-battery electrolyte. The original deposit ran a VQE ensemble "electronic-landscape" study on a Zr–O₄(–Li) cluster model (10e,10o, 20 qubits, UCCSD/COBYLA, LANL2DZ/6-31G) across five compression amplitudes (B0→P4) and two lithiation states (Li-present singlet, charge 0; Li-vacancy doublet, charge +1), 15 seeds per arm. It reported, as physical findings:

• A monotonic Li-present stabilisation trend: σ decreasing from 34.25 (B0_Li1) to 3.94 kcal/mol (P4_Li1).
• A pressure-driven inversion: Li-vacancy σ rising (2.57 → 6.23) while Li-present σ falls, crossing over at P4.
• An unexpected d⁰ bifurcation: 2–3 electronic basins with inter-basin gaps up to 47.7 kcal/mol in a formal closed-shell Zr⁴⁺ singlet, "warranting mechanistic investigation," supported by an N=35 confirmation run.

These were positioned as actionable (pre-synthesis dopant ranking) and as cross-material validation of the diagnostic.

2. What the validation found

The same forensic method that corrected the Fe₄N₂ deposit was applied: each arm's cluster Hamiltonian was rebuilt N=20 times from the engine's own registered LLZO geometry and configuration (geometry keys and charge/spin read from source, not assumed), and the per-build Hartree–Fock energy was clustered to detect SCF reference-root multiplicity. The diagnostic-relevant quantity is whether the SCF converges to a single physical reference across seeds, or jumps among multiple roots — in which case the published σ measures root-jumping, not an electronic landscape.

2.1 Per-arm SCF-root stability (N = 20)

(Values from the N=20 validation JSONs 20260518T192547Z, 20260519T012507Z, 20260519T013353Z, 20260519T030019Z, bundled with this record. Where two independent N=20 runs exist for an arm — B0/P1/P2_Li1 — the contamination is reproduced in both, with the spurious-root fraction varying run-to-run as expected for a stochastic spurious root; the presence and magnitude of contamination are reproducible. P3_Li1 and P4_Li1 are root-stable across two independent N=20 runs each, agreeing to the fourth decimal.)

2.2 What this means for the headline claims

The decisive observation: every contaminated arm has a physical-root HF spread of ≤ 0.10 kcal/mol — when the SCF reaches the correct reference it converges tightly. The large full spreads (36–196 kcal/mol) are produced by inconsistent convergence among distinct SCF roots — in some arms (e.g. P2_Li0, P3_Li0) the spurious root is the minority outcome, in others (e.g. B0_Li1, P1_Li1) the physical root is the minority outcome. Therefore, for the contaminated arms, the published σ is not a measure of an electronic landscape; it reflects the frequency and magnitude of SCF reference-root jumping across the seed ensemble.

This directly undermines the headline interpretations:

• Monotonic Li-present stabilisation (σ 34.25 → 3.94). Its high-σ end — B0_Li1 (19/20 spurious, 123 kcal/mol full spread), P1_Li1 and P2_Li1 (15/20 spurious, ~37 kcal/mol) — is reference-contaminated. The apparent "stabilisation" largely tracks the spurious-root contribution diminishing toward higher compression, not a physical ordering of the electronic landscape. The trend is not decision-grade as published.
• The d⁰ "bifurcation". The published d⁰ bifurcation interpretation is not supported by the current evidence, because the corresponding arms (B0/P1/P2_Li1) show SCF reference instability large enough to explain the apparent multi-basin structure. The contaminated evidence does not support overriding the expected electronic rigidity of a formal d⁰ Zr⁴⁺ centre; the reported "2–3 basins, IBG up to 47.7 kcal/mol" coincide in magnitude with the measured spurious-root separations. The N=35 confirmation established that the scatter is reproducible, which — as in the Fe₄N₂ case — confirms an artifact is reproducible, not that the structure is physical. This is stated as unsupported pending root-pinned reruns, not as a definitive claim that the corrected calculation would be featureless.
• The pressure inversion. The inversion requires both the Li-present and Li-vacancy σ trends to be physical. The Li-present high-σ points are contaminated; on the Li-vacancy side B0_Li0 (7/20 spurious) and P1_Li0 (6/20, 196 kcal/mol full spread) are also contaminated. The crossover endpoints are individually the cleanest arms (P4_Li1 root-stable; P4_Li0 clean on a targeted rerun, caveated), but the trends leading to the crossover run through contaminated references on both sides. The inversion narrative is withdrawn as a decision-grade claim pending reconstruction on root-pinned references.

3. What survives

Two arms cleanly pass the SCF-root stability screen at N=20 across independent runs (P3_Li1, P4_Li1); a third (P4_Li0) passes a targeted rerun with a caveat:

P3_Li1 is the scientifically important survivor: a stable SCF reference with a published σ ≈ 14 kcal/mol means the ruggedness there is not a root-jump artifact. Whether that σ is a genuine VQE-landscape feature or a VQE-optimiser pathology on top of a stable Hamiltonian cannot be settled by the SCF-root screen alone and requires an independent same-active-space exact reference (see Limitations). P3_Li1 is therefore reported as surviving the first screen, exact-reference validation pending — not as a corrected physical result.

4. The methods finding

This LLZO sweep exhibits the same SCF reference-multiplicity failure mode characterised in the Fe₄N₂ correction (Zenodo 10.5281/zenodo.20264767), and more pervasively: 7 of 10 arms are contaminated, with spurious-root frequencies from 5% to 95% and spurious-root separations up to ~196 kcal/mol. The transferable lesson, consistent across both records: σ-based "electronic-landscape" diagnostics built on unconstrained SCF references can report physics-shaped artifacts; an SCF-root stability screen and an independent same-Hamiltonian exact reference are prerequisites, not optional checks. Documenting this failure mode, with the per-arm contamination quantified, is the substantive contribution of this corrected version.

5. Limitations and honest scope

• The SCF-root screen rules out one specific artifact (reference multiplicity). A UNIMODAL_STABLE arm has a well-defined reference but its published σ has not thereby been validated as physical: distinguishing a genuine rugged VQE landscape from VQE-optimiser pathology on a stable Hamiltonian requires an independent in-sector exact reference. That solver (memory-safe for the large singlet sector — the dense path is intractable, ≈64 GB for the (10e,10o, 2Sz=0) sector) is not yet run; it is the planned next step and a future version of this record.
• Accordingly, P3_Li1/P4_Li1/P4_Li0 are reported as surviving the SCF screen only. None is asserted as a confirmed physical result.
• The d⁰-bifurcation and pressure-inversion interpretations are unsupported pending reruns, explicitly not refuted. A root-pinned or physical-root-filtered reconstruction could in principle recover structure; this work does not exclude that, it only shows the original evidence is contaminated.
• The original deposit's actionable claims (pre-synthesis dopant ranking, cross-material mechanism confirmation) inherit the contamination of the arms they rest on and should not be relied upon pending the above reruns.

6. Files in this deposit

Each JSON records per-build HF energies, physical/spurious clustering, charge/spin/geometry provenance (read from the engine source, not assumed), and a self-contained summary. The proprietary VQE engine is not included (consistent with the Fe₄N₂ deposit); this record provides the validation artifacts, not a standalone re-runnable engine.

7. Citation and supersession

This version supersedes and corrects the prior deposit. The prior version's pressure-inversion, monotonic-stabilisation, and d⁰-bifurcation conclusions should not be cited or relied upon. This version should be cited for: (a) the forensic SCF-reference validation and the per-arm contamination characterisation, (b) the documented cross-record SCF reference-multiplicity failure mode (with Zenodo 10.5281/zenodo.20264767), and (c) P3_Li1 as a surviving anomaly candidate pending independent exact-reference validation.