Electronic Landscape Stability Diagnostics of the Iron Porphyrin CO₂ Reduction Redox Ladder: A Reproducibility-Certified Ensemble VQE Benchmark

Plain-Language Summary

Converting CO₂ into useful fuels and chemicals using electricity is one of the most promising strategies for addressing climate change. Iron porphyrin molecules — a class of synthetic catalysts inspired by biological enzymes — are among the leading candidates for driving this conversion. Despite decades of study, scientists have disagreed about the electronic structure of the key active states of these catalysts, because standard computational tools give inconsistent answers depending on how the calculation is set up.

We addressed this problem using a quantum chemistry framework called ELSD (Electronic Landscape Stability Diagnostics), which runs five independent calculations per state rather than one, and measures how consistent the results are. Inconsistency is the signal — it tells you the state is electronically unreliable or that the model is inadequate. Consistency is the certification.

We tested each step of the iron porphyrin catalytic cycle — the resting state, the singly-reduced intermediate, the doubly-reduced active species, and the CO₂-bound adduct — and classified each state as either electronically trustworthy or not. We found that the doubly-reduced active state and the CO₂ adduct are both electronically stable and reproducible, provided the computational model is large enough to capture the surrounding ring structure. The intermediate singly-reduced state, by contrast, fails regardless of model size — its instability is a genuine physical property of that electronic configuration.

This is the first time the iron porphyrin CO₂ reduction pathway has been characterised using a reproducibility-certified ensemble method. The result establishes which states can be trusted as a foundation for further computational study of the catalytic mechanism, and demonstrates that decades of inconsistency in the literature were at least partly caused by different groups using different model sizes and unknowingly finding different solutions to the same problem.

Overview

This dataset presents a reproducibility-certified ELSD characterisation of the iron porphyrin CO₂-reduction redox ladder using Electronic Landscape Stability Diagnostics (ELSD), a penalized variational quantum eigensolver (VQE) workflow that classifies metal-centred electronic states by reproducibility across independent optimizer trajectories rather than by single converged solutions alone.

Iron porphyrins are among the most studied molecular electrocatalysts for CO₂-to-CO conversion. Prior DFT and spectroscopic work established the importance of reduced Fe porphyrin states and the ligand-centred, antiferromagnetically coupled character of the doubly-reduced manifold. This dataset adds a different diagnostic layer: it quantifies whether a state is simultaneously sector-clean, determinant-dominant, and reproducible across independent seeds.

The record includes per-seed statevectors, run logs, convergence artifacts, sector-audit outputs, and campaign-level summary metrics for all four phases of the benchmark.

Scientific Contribution

ELSD separates three properties that are often conflated in single-convergence workflows:

• Sector purity — correct particle number and spin projection
• Dominant determinant character — single-reference-like vs multi-reference
• Cross-seed energy reproducibility — landscape smoothness across independent initializations

By requiring all three simultaneously, ELSD distinguishes electronically clean states from electronically reproducible states. In this Fe porphyrin campaign, that distinction proved consequential: a minimal doubly-reduced fragment appeared determinant-pure but energetically split, while controlled fragment extension collapsed the spread and restored rigid reproducibility.

The novelty of this dataset is not the assignment of the doubly-reduced Fe porphyrin state as ligand-centred and antiferromagnetically coupled — that interpretation is already established in the literature. The contribution is a reproducibility-based classification of the redox ladder, including controlled separation of intrinsic instability from fragment-induced pseudo-ruggedness.

Goal

The central question this campaign addresses is not "what is the energy of each reduced Fe porphyrin state" — DFT has addressed that repeatedly. The question is: which states in the iron porphyrin CO₂ reduction redox ladder are electronically trustworthy enough to build on?

Trustworthy here means decision-grade under ELSD: sector-clean, determinant-consistent, and reproducible across five independent optimizer trajectories from random initializations. States that pass are candidates for further mechanistic study. States that fail — whether by spin escalation or landscape bimodality — are flagged with a mechanistic diagnosis of why.

What We Found

The redox ladder is non-monotonic in electronic trustworthiness:

• The resting state (FeII_ls) is electronically stable and reproducible. It is the clean anchor for the entire ladder.
• The singly-reduced state (FeI) fails in both a minimal and an extended fragment. The physical quartet state is energetically preferred over the doublet target by more than 5 Ha — a robust, intrinsic constraint within the present active-space lane, not a truncation artifact.
• The doubly-reduced state (red2_AF) appears bimodal in a minimal fragment (σ=8.5646 kcal/mol) but locks cleanly at Rigid Stability (σ=0.3035 kcal/mol) when the fragment is extended to include the pyrrole alpha-carbon core. The Phase 1 bimodality was truncation-induced, not physical.
• The CO₂-bound adduct built on the extended doubly-reduced scaffold locks at Rigid Stability (σ=0.3555 kcal/mol) — a 1.17× perturbation relative to the unbound state, within the same reproducibility band. The dominant determinant family and singlet landscape are preserved through CO₂ coordination.

The singly-reduced Fe¹⁺ intermediate is the sole robustly non-canonical rung. The doubly-reduced active species and its CO₂ adduct are electronically decision-grade under the present construction.

Methodology

All calculations were performed with the Prometheus Platform penalized VQE engine using sector-enforcement penalties for particle number (λ_N=2.0 Ha) and spin projection (λ_Sz=5.0 Ha). Standard operating lane:

• Active space: 10 electrons / 10 orbitals (20 qubits)
• Ansatz: UCCSD, depth 6
• Basis: LANL2DZ with Fe ECP
• Hardware: NVIDIA L40S GPU (44.988 GB VRAM)
• Ensemble size: 5 seeds per lockable system (1 seed for ENG-007 diagnostics)
• σ convention: population standard deviation (ddof=0) throughout

After every seed, a mandatory sector audit was performed. A result is classified as locked canonical only if all five criteria are satisfied simultaneously:

1. ⟨N⟩ and ⟨Sz⟩ within ±0.1 of target for all seeds
2. dom_p > 0.99 for all seeds
3. Same dominant bitstring family across all seeds
4. Penalty contributions confirmed as numerical noise only
5. σ and energy range consistent with the claimed landscape regime

Fragment comparisons follow a strict one-variable rule: when testing fragment extension, only fragment size changes. Charge, multiplicity, active-space size, and core geometric constraints are held fixed, isolating the contribution of fragment truncation.

Campaign Structure

Phase 1 — Minimal-fragment redox ladder: Three states tested in minimal coordination fragments: FePorphyrin_FeII_ls (8 atoms), FePorphyrin_FeI (8 atoms), FePorphyrin_red2_AF (5 atoms). Results: FeII_ls locked Rigid Stability (σ=0.3375); FeI spin-escalated to Sz=+2.0 (ENG-007); red2_AF sector-clean but energetically split (σ=8.5646, Multi-Basin).

Phase 2 — Fragment-extension test on the doubly-reduced state: red2_AF extended from 5 to 21 atoms (one variable changed). σ collapsed 28.2× to 0.3035 kcal/mol. Phase 1 bimodality confirmed as truncation artifact. FePorphyrin_red2_AF_ext locked Rigid Stability.

Phase 3 — Fragment-extension rescue test on the singly-reduced state: FeI extended from 8 to 24 atoms (one variable changed). Spin escalation to Sz=+2.0 persisted identically (E_Sz_penalty ≈ 3138 kcal/mol). ENG-007 confirmed robust within the present lane — not a truncation artifact.

Phase 4 — CO₂ adduct on the clean doubly-reduced state: η¹-C-bound bent CO₂ added axially to red2_AF_ext (Fe–C=2.00 Å, C–O=1.23/1.18 Å, O–C–O=132°, literature-consistent initialization). σ=0.3555 kcal/mol — 1.17× relative to unbound state. Same dominant bitstring family as unbound red2_AF_ext across all seeds. Locked Rigid Stability.

Key Results

The three locked canonical results cluster tightly (σ=0.3035–0.3555 kcal/mol), establishing that the catalytically relevant states — resting, doubly-reduced active species, and CO₂ adduct — are electronically reproducible under the present construction.

The campaign further distinguishes two mechanistically distinct failure modes:

• Truncation-induced pseudo-ruggedness (red2_AF minimal): bimodality collapses upon controlled fragment extension. The physical state is tractable; the minimal model was insufficient.
• Intrinsic wrong-sector preference (FeI): spin escalation persists regardless of fragment size within the current lane. A genuine active-space constraint, not a modelling artifact.

Scope and Limitations

All results are scoped to the 10e/10o active space, UCCSD depth 6, LANL2DZ basis, pyrrole alpha-carbon fragment extension strategy, and 20-qubit VQE lane. The ENG-007 constraint applies within this modelling lane and should not be generalised to all possible embeddings or active spaces. CO₂ adduct geometry parameters are literature-consistent initialization choices for diagnostic testing, not claims of a fully optimised experimental structure. All σ values use ddof=0.

Related Work

This dataset extends the Prometheus Platform ELSD benchmark series into a catalytic domain. The companion drug-discovery dataset (36 locked canonical results across Cu²⁺, Zn²⁺, and Fe²⁺ metalloenzyme targets) is available at DOI 10.5281/zenodo.19212485. The associated ELSD manuscript is currently under review at ACS Omega (ao-2026-034064).

Citation

If you use this dataset, please cite the Zenodo record and the associated Prometheus Platform manuscript (ACS Omega ao-2026-034064, under review).

Quantum-Clarity LLC · Prometheus Platform · March 28, 2026 Dataset frozen March 28, 2026. All σ values: population standard deviation (ddof=0).