Know Your Material's Electronic Risk Profile Before You Synthesise It
Quantitative electronic landscape diagnostics — σ, trapped fraction, basin count, regime classification — for any candidate composition, in days, not months.
NMC811 cathode dopant series · LLZO solid-state electrolyte pressure sweep · LLZO Ta⁵⁺ & Nb⁵⁺ dopant screening
⚡ The Problem Standard Methods Cannot Solve
Battery materials that look stable in DFT can still fail in the field — because DFT finds the lowest energy state, not the full set of accessible states. When a real material is perturbed — by mechanical stress, Li vacancy formation, or mid-charge orbital reorganisation — it may encounter a competing electronic configuration that single-point methods never see. That hidden configuration is often the failure mode.
What's known empirically
In Ni-rich NMC, voltage hysteresis, particle cracking, and oxygen loss all intensify near 50% state of charge. In LLZO under stack pressure, ionic conductivity varies with compression in ways that suggest an electronic, not purely structural, response. The mechanisms have remained computationally opaque.
What standard methods miss
DFT and classical force fields solve for a single ground state. They cannot detect the coexistence of competing electronic configurations, the proximity of an electronic phase boundary, or the composition-dependent threshold at which a material transitions from one electronic regime to another.
🔬 Our Approach: Ensemble VQE Landscape Tomography
Rather than computing a single ground state, we run an ensemble of independent VQE optimisations across each material condition — then analyse the statistical distribution of converged solutions. The spread of those solutions, and whether they cluster into one basin or two, is the diagnostic signal. The result is not a single energy value. It is a ruggedness fingerprint that classifies the electronic regime of a material and identifies the mechanism driving it.
Multi-seed ensemble
15–35 independent VQE runs per condition from different random initialisations. Landscape topology emerges from the ensemble distribution, not any single calculation.
Symmetry-breaking probe
A controlled perturbation — Jahn–Teller distortion, compression, or vacancy formation — acts as an electronic selection field, revealing latent branches invisible at the symmetric geometry.
ELS score
Energy scatter (σ), trapped fraction, and basin count together constitute an Electronic Landscape Stability score — a topology-based descriptor orthogonal to total energy, band structure, or formation energy.
Mechanism classification
Each material is assigned to one of three electronic regimes: Bifurcation, Rigid Stability, or Resonant Activation. The regime determines the failure mode and the correct dopant strategy.
🔒 Why These Results Are Reliable
These are not single calculations. They are ensemble measurements of electronic energy landscape structure — with built-in statistical validation at every level. Every conclusion is reproducible by design.
Independent seeds
Each condition uses 15–35 independent optimisations from different random starting points with the same Hamiltonian. Consistent convergence patterns across seeds indicate genuine landscape structure, not optimiser artifacts.
Zero Hamiltonian drift
All seeds within a condition share an identical Hamiltonian. Systematic drift would be immediately visible. Across 855 valid runs, observed drift is zero — confirming numerical stability across two material classes.
Statistical metrics
Conclusions are based on σ, trapped fraction, and basin count across the full ensemble. Key basins confirmed at N=35, reproducing structures from independent seed sets. No result rests on a single data point.
Reproduces known chemistry
The platform independently recovers established experimental facts — cobalt stabilises Ni-rich cathodes, manganese resolves orbital ambiguity, NCA co-doping is electronically non-redundant. Agreement with known outcomes validates the framework before it makes new predictions.
For R&D leadership: This approach enables early-stage screening of cathode and electrolyte compositions computationally — identifying electronic instabilities before costly synthesis and cycling campaigns are performed. The ELS score provides a topology-based risk metric that no conventional DFT workflow can generate. Results are available in days. A full dopant series typically requires under 50 GPU hours.
💡 Electronic Bifurcation at Mid-Charge: The Root Cause
At the half-delithiated state (Li₁), the Ni-rich cluster undergoes a symmetry-hidden electronic bifurcation under a Jahn–Teller distortion probe. The energy landscape splits into two distinct basins — separated by ~8 kcal/mol — with zero overlap between the two populations of converged VQE solutions. The simulations use a Ni₂O₃Liₓ cluster model that captures the local electronic environment of the Ni–O octahedral site while remaining tractable for ensemble VQE calculations — not a full cathode lattice.
In energy-landscape terms, a basin is a stable electronic configuration the system settles into regardless of starting point. When multiple basins appear under the same perturbation, the system can toggle between competing electronic states during cycling. The most decisive result in the NMC study is that cobalt does not merely reduce this instability — it removes the second basin entirely, leaving a single stable electronic state with no competing alternative.
Pure nickel cathodes exhibit a bifurcated electronic energy landscape at mid-charge: two distinct competing states separated by 8.09 kcal/mol.
Cobalt substitution collapses this bifurcation, leaving a single stable electronic state. The second basin is absent. Gap = 0.
This provides a mechanistic, quantum-mechanical explanation for cobalt's stabilising role in Ni-rich cathodes — reproduced computationally before any dopant-specific experiment was designed to find it.
The distortion does not create the instability — it reveals it. The JT probe acts as a symmetry-breaking detector that exposes a competing electronic configuration already latent in the Ni²⁺/Ni³⁺ mixed-valence manifold. Without the probe, that branch is invisible to standard computation.
The Four-System Electronic Fingerprint
Substituting Co, Mn, and Al at the same site and applying the same probe produces four mechanistically distinct responses — a complete electronic fingerprint of the NMC chemistry family. The pattern is not coincidence: d-electron count predicts the response direction before the simulation is run.
| Dopant | d-config | B3/B0 σ ratio | Basin behaviour under B3 | Mechanism |
|---|---|---|---|---|
| Ni | d⁸/d⁷ (eg¹) | 2.22× | Bifurcates — 2 basins, 8.09 kcal/mol gap | JT splitting of eg¹ |
| Co | d⁷/d⁶ | 1.43× | Single basin, gap = 0 | Orbital branch removal |
| Mn | d³ (t₂g³) | 0.55× ↓ | Single basin — σ decreases | Ambiguity resolution |
| Al | d⁰ | 2.38× | Single basin, no bifurcation | d⁰ orbital depletion |
🔵 Electronic Phase Boundary Interpretation
The Ni-rich cathode sits near an electronic phase boundary where Jahn–Teller distortion can split the energy landscape into competing states. The four-system substitution series shows that Co, Mn, and Al each shift the system away from this boundary through three distinct electronic mechanisms. Small perturbations in real cells — strain, Li ordering, thermal fluctuations — may be sufficient to push the Ni system across this boundary. That crossing is not detectable by single-point electronic structure methods.
🧬 Co–Al Threshold Map: Composition-Dependent Landscape Smoothing
With the four single-dopant systems characterised, the operative question for a materials engineer is: at what substitution fraction does the bifurcation signal disappear? A 150-seed screening run (5 compositions × 2 conditions × 15 seeds, 100% valid) mapped the landscape ruggedness gradient across a Co–Al composition grid directly relevant to commercial NCA and low-Co NMC formulations.
Three Distinct Ruggedness Regimes
No resolved bifurcation signal was observed in this screening-level assay (N=15). Basin-count alone cannot distinguish these compositions at this ensemble size. The trapped fraction — seeds stuck more than 1 kcal/mol from the global minimum — provides the operative discriminator, revealing a clear three-regime gradient:
Co 25% alone: 0.87 — landscape remains highly rugged. Co at 25% does not materially reduce ruggedness at commercially relevant fractions.
Al 25%: 0.40 — equivalent trapped fraction at half the Co substitution level. d⁰ orbital depletion reduces ruggedness more efficiently per percentage than orbital branch removal.
Full Composition Results
| Composition | B3 trapped | Interpretation |
|---|---|---|
| Ni (ref) | 0.80 | Highly rugged — near-bifurcating character |
| Co 25% | 0.87 | Highly rugged — no resolved bifurcation signal at N=15 |
| Co 50% | 0.40 | Reduced ruggedness — single basin, no splitting observed |
| Al 25% | 0.40 | Reduced ruggedness — more efficient per % than Co |
| Co 25% + Al 25% ★ | 0.13 | Strongly stabilised — lowest trapped fraction in grid |
| Composition | σ B3 (kcal/mol) | B3/B0 ratio | Trapped B3 | Basins | Regime |
|---|---|---|---|---|---|
| A: Ni–Ni (ref) | 0.6764 | 0.882× | 0.80 | 1* | Highly rugged |
| B: Co 25% | 0.8465 | 1.365× | 0.87 | 1 | Highly rugged |
| C: Co 50% | 0.5729 | 1.262× | 0.40 | 1 | Smoother |
| D: Al 25% | 0.5711 | 1.581× | 0.40 | 1 | Smoother |
| E: Co 25% + Al 25% | 0.3813 | 0.381× ↓ | 0.13 ★ | 1 | Strongly stabilised ★ |
* No resolved bifurcation signal observed at the N=15 screening level for any composition. This is expected — the canonical Ni two-basin result required N=35. Trapped fraction, not basin count, is the operative discriminator in this run. Ni–Ni trapped=0.80 is the within-run baseline; its near-bifurcating character is confirmed separately at N=35.
★ The Co+Al Synergy Finding — and the NCA Connection
The B3/B0 ratio of 0.381× for Co+Al combined means the JT distortion reduces landscape ruggedness relative to baseline — the bifurcation channel is closed, and trapped fraction falls to its lowest value in the entire run. Co at 25% alone leaves trapped=0.87 (highly rugged). Al at 25% alone gives trapped=0.40. Co+Al together gives trapped=0.13.
This is not additive suppression. Orbital branch removal by Co and orbital depletion by Al are mechanistically orthogonal — they interact constructively, achieving a degree of stabilisation neither reaches independently at these fractions.
The NCA connection: Real NCA cathodes co-dope with both Co and Al. This ensemble screen reproduces that pairing from electronic first principles — providing a quantum-mechanical rationale for its empirical success. Co is not interchangeable with Al. The mechanisms are non-redundant, and co-doping exploits both simultaneously. This is now computationally demonstrated, not inferred.
Design boundary for cathode engineers: The trapped-fraction gradient suggests the ruggedness transition for both Co and Al independently occurs below 25% substitution. At commercially relevant dopant fractions (5–20%), bifurcation-signal suppression may already be active. Locating the exact critical fraction would establish a quantitative design boundary with direct IP implications for cost-optimised, high-Ni cathode formulations. Finer-grid follow-up at 5%, 10%, 15% is the immediate next experiment.
🔋 LLZO Solid-State Electrolyte: The Platform Generalises
After establishing the NMC cathode results, the same ensemble VQE framework was applied to a chemically different system: the LLZO solid-state electrolyte. The Zr centre in LLZO is formally d⁰ — no partially filled d-orbital manifold, no Jahn–Teller susceptibility. If the platform only worked on JT-active systems, it would have found nothing here. It found two distinct instability mechanisms, and resolved a direct design tension relevant to solid-state stack engineering.
Four distinct electronic basins confirmed at N=35. Mechanism: near-degeneracy mixing within the Zr–O bonding orbital manifold. Zr d-electrons remain in d⁰ configuration across all basins — the Li ion acts as an electronic anchor. Compression progressively lifts this near-degeneracy: σ collapses from 34.3 → 3.9 kcal/mol as pressure increases.
Two basins. Orbital analysis reveals the mechanism: 0.31 electrons toggle from a Zr–O bonding hybrid into a Zr-4d antibonding orbital. A discrete charge-transfer resonance activated specifically by vacancy + compression together — not generic optimiser scatter. The nominally d⁰ configuration is broken.
| Arm | σ (kcal/mol) | Basins | Px/B0 ratio | Trend |
|---|---|---|---|---|
| B0_Li1 (baseline) | 34.25 | 4 | 1.000× | Near-degeneracy manifold |
| P4_Li1 (max compression) | 3.94 | 2 | 0.115× | ↓ Monotonic collapse — compression orders landscape |
| B0_Li0 (vacancy, baseline) | 2.57 | 2 | 1.000× | Vacancy baseline |
| P4_Li0 (vacancy + max compression) | 6.23 | 2 | 2.421× | ↑ Monotonic rise — charge-transfer resonance activated |
The LLZO inversion: the same pressure simultaneously stabilises and destabilises
Stack-pressure-like compression produces opposite electronic landscape responses depending on Li occupancy. Li-present sites become more electronically ordered as pressure increases. Li-vacancy sites become more electronically disordered. In a solid-state cell, the mechanical compression required for ionic contact may be the same pressure activating an electronic instability at vacancy sites. That inversion is not visible to DFT — and it is directly actionable for stack-pressure optimisation and electrolyte formulation.
LLZO Dopant Screening: Ta⁵⁺ and Nb⁵⁺ Partial CT Suppression
With the pressure sweep establishing the baseline landscape and identifying the charge-transfer (CT) resonance mechanism at vacancy sites, the logical next question is whether aliovalent dopants can suppress this instability. Two candidates with established ionic conductivity benefits in the literature were screened using the same ensemble VQE protocol: Ta⁵⁺ and Nb⁵⁺ substituting at the Zr site.
Landscape σ reduced to 1.65 kcal/mol vs 3.89 kcal/mol baseline. Single basin retained. Trapped fraction drops from 0.733 to 0.320. The charge-transfer resonance is substantially attenuated. Partial CT suppression confirmed.
Landscape σ reduced to 2.79 kcal/mol vs 3.89 kcal/mol baseline. Two basins persist, but both trapped fraction and σ are reduced relative to undoped Zr. A weaker but quantifiable suppression effect. Partial CT suppression confirmed.
| Dopant | σ (kcal/mol) | σ / Zr baseline | Basins @5 kcal | Trapped | Verdict |
|---|---|---|---|---|---|
| Zr⁴⁺ (baseline) | 3.89 | 1.000× | 2 | 0.733 | CT-active reference |
| Ta⁵⁺ | 1.65 | 0.423× | 1 | 0.320 | Partial suppression ✓ |
| Nb⁵⁺ | 2.79 | 0.718× | 2 | 0.440 | Partial suppression ✓ |
Design implication for solid-state electrolyte engineers
Ta⁵⁺ produces stronger electronic landscape stabilisation than Nb⁵⁺ by this metric — a distinction not visible to ionic conductivity measurements alone. Both dopants suppress the charge-transfer resonance partially, not completely: the underlying mechanism remains active, just attenuated. This quantified gap between partial and complete suppression defines the next design target: a composition or co-dopant strategy that closes the remaining instability. The platform can evaluate any candidate — Ta/Nb composition sweep, co-doping combinations, or novel dopant classes — before a single synthesis run is attempted.
📐 Three Electronic Landscape Regimes — A Unifying Framework
The combined NMC and LLZO data reveal something deeper than two separate discoveries. In both systems, external perturbations act as electronic selection fields — forcing the material to resolve a latent ambiguity in its quantum arrangement. How a material answers that selection question determines which regime it occupies, and which failure mode it is susceptible to.
Two electronic branches remain viable under perturbation. Large σ, high trapped fraction, multi-basin landscape. In cells: voltage hysteresis, rate sensitivity, cracking at the bifurcation window.
Single basin retained. Landscape narrows or maintains under perturbation. Reached by removing the bifurcation channel (Co/Al in NMC) or by compression ordering (Li1-LLZO). In cells: stable cycling, low hysteresis.
Stable until a specific charge-transfer channel is activated. A discrete two-state toggle appears — not classical JT, not generic roughening. In cells: threshold-gated instability, pressure- or vacancy-concentration-dependent.
Electronic Landscape Stability (ELS) — a new class of screening metric
Basin count, trapped fraction, and σ variance across optimiser seeds together constitute an Electronic Landscape Stability score — a topology-based descriptor orthogonal to total energy, band structure, or formation energy. Materials can be classified by which regime they occupy. The platform does not find ground states. It performs electronic landscape tomography.
The central principle
Across both Ni-rich cathodes and LLZO electrolyte motifs, external perturbations act as electronic selection fields that either split, collapse, or redirect the set of accessible quantum states. Ensemble VQE diagnostics provide a direct way to classify that response — and therefore to classify the intrinsic electronic stability regime of a material before it is ever synthesised or cycled.
Plain English
Some battery materials are stable because they have one clear electronic answer to perturbation. Others are unstable because small disturbances make the electrons “hesitate” between multiple possible arrangements. A third class switches into a new orbital configuration when pushed hard enough. This platform detects which kind of material you are dealing with — before it is ever cycled in a cell.
Screen your next material before your next synthesis run
The ensemble VQE diagnostic platform is available to battery manufacturers, materials developers, and solid-state battery companies under three engagement models. Identifying electronic instability at the composition-screening stage eliminates the most expensive category of experimental failure — building and cycling a material whose electronic landscape was always going to generate the failure mode you find three months later.
Submit candidate compositions or dopant strategies. Receive quantitative ELS diagnostic reports: σ, trapped fraction, basin count, regime classification. No source code shared. Turnaround in days. ~3–4 GPU hours per condition.
Full platform deployed on your hardware. Run unlimited diagnostics internally across your candidate pipeline. Annual license + royalty on filed patents arising from platform-guided discoveries.
Complete acquisition including source code, methodology, all validated run data (855 runs across NMC and LLZO), and patent rights. Lump sum + inventor royalty. Transfers the full IP estate.
Companies developing solid-state batteries — including those using LLZO-class electrolytes under stack pressure — face a specific challenge: the same mechanical compression required for ionic contact may differentially activate electronic instabilities at vacancy coordination sites. The LLZO results here demonstrate this inversion quantitatively, and show that Ta⁵⁺ suppresses the charge-transfer resonance more effectively than Nb⁵⁺ at equivalent substitution. If you are working on stack-pressure optimisation, dopant selection, or interface engineering in solid-state cells, the ensemble VQE platform provides an electronic risk profile for any candidate composition — before your next synthesis run.
Full technical results and platform specifications available under mutual NDA. Patent pending.
⚡ Why This Matters: Connecting Electronic Regime to Failure Mode
Electronic landscape regime is not an abstract classification — it maps directly onto the failure modes observed in real cells. Each regime predicts a characteristic degradation signature, and the connection provides a mechanistic link that neither DFT nor empirical testing alone can establish.
Voltage hysteresis
Path dependence in charge/discharge curves is consistent with the system toggling between competing electronic basins — the Regime 1 signature.
Rate sensitivity
A bifurcation threshold crossed by thermal or mechanical fluctuations would create strong sensitivity to cycling rate and temperature, independent of ionic transport limitations.
Crack formation
Electronic instability under local strain is consistent with particle cracking concentrated at mid-charge — the known failure window for Ni-rich chemistries.
Why Co and Mn help
First direct computational demonstration that Co and Mn suppress the instability through mechanistically distinct electronic pathways — orbital branch removal vs ambiguity resolution.
Why NCA works
The Co+Al synergy result provides a quantum-mechanical explanation for NCA's empirical performance advantage — two non-redundant, orthogonal suppression mechanisms acting simultaneously.
The distortion threshold insight: The amplitude ladder experiment shows the Ni landscape first stabilises under small distortions before bifurcating at larger ones. The instability is not inevitable — it is triggered at a specific perturbation amplitude. Small perturbations near this threshold in real cells could push the system across the electronic boundary without it being detectable by conventional diagnostics.
🧪 Computational Screening Framework
The confirmed systems define a mechanism-class framework. Candidate dopants can be assigned a predicted electronic regime before simulation based on d-electron count and ligand-field logic. The prediction is testable, the mechanism is traceable, and the result is a design rule rather than a single data point.
Mechanism classes
Class A (eg-active): Likely to bifurcate — Ni³⁺-like d⁷, Cu²⁺-like d⁹.
Class B (branch-removing): Suppresses — Co confirmed, Rh/Ir analogues predicted.
Class C (ambiguity-resolving): Stabilises — Mn confirmed, Cr³⁺ predicted.
Class D (d-depleted): Single-basin roughening — Al confirmed, Mg²⁺, Ti⁴⁺ predicted.
Design rule
Prefer dopants that remove the Ni eg¹ branch (Class B), resolve ambiguity without creating new branches (Class C), or deplete the local d-manifold (Class D). The class is predictable from d-electron count before the simulation runs.
For co-doping: combining Class B + Class D achieves synergistic reduction in landscape ruggedness beyond what either achieves independently. The Co+Al result demonstrates this quantitatively and provides the mechanistic basis for understanding NCA.
Next targets: Cr³⁺ (Class C), Mg²⁺/Ti⁴⁺ (Class D), finer Co/Al grid at 5–15%.
| Dopant / Composition | Predicted class | Predicted / measured response | Status |
|---|---|---|---|
| Ni (d⁷) | Class A | Bifurcates — 8.09 kcal/mol gap | ✅ Confirmed |
| Co (d⁷/d⁶) | Class B | Bifurcation signal not observed; single basin, gap=0 | ✅ Confirmed |
| Mn (d³) | Class C | Stabilises — σ decreases 0.55× | ✅ Confirmed |
| Al (d⁰) | Class D | Single-basin roughening, gap=0 | ✅ Confirmed |
| Co 25% + Al 25% | B + D synergy | Trapped=0.13 — lowest ruggedness in grid; bifurcation signal not observed | ✅ Confirmed |
| Cr³⁺ (d³) | Class C | Mn-like stabilisation | 🔬 Predicted |
| Mg²⁺ (no d) | Class D | Al-like roughening | 🔬 Predicted |
| Ti⁴⁺ (d⁰) | Class D | Al-like or mixed | 🔬 Predicted |
| Cu²⁺ (d⁹) | Class A | Potentially Ni-like or worse | ⚠️ Caution |
🌐 Broader Vision
This work is part of the Quantum Clarity electronic-structure platform — applying GPU-accelerated ensemble VQE to materials problems where electronic topology determines behaviour. The two material classes studied here — a Jahn–Teller-active cathode and a nominally d⁰ electrolyte — were chosen precisely because they represent opposite ends of the electronic complexity spectrum. The platform works across both.
The output is not a single prediction. It is a ruggedness fingerprint that ranks compositions, identifies mechanisms, generates testable design rules, and classifies the electronic phase boundary a material operates near. Two material classes. One platform.
Battery cathodes
NMC, NCA, and LNMO families. Screen dopants for mid-charge instability suppression. Co–Al threshold mapping for cost-optimised co-doping formulations.
Solid-state electrolytes
LLZO-class and beyond. Stack-pressure response mapping, vacancy-site CT resonance screening, dopant ELS comparison across aliovalent candidates.
Transition-metal catalysis
JT-active sites appear across CO₂ reduction, water oxidation, and C–H activation. The bifurcation diagnostic applies wherever eg degeneracy is at play.
Electronic topology mapping
Beyond stability ranking — mechanism classification. The platform identifies which electronic phase boundary a system operates near, not just whether it is stable.
📊 Campaign Metrics
Connect & Collaborate
Results are in preparation for submission to ACS Energy Letters / Journal of Power Sources. Dataset publication pending. Interested in an electronic risk profile for your cathode or electrolyte candidates?
Coming soon: Zenodo dataset · Cr³⁺ and Mg²⁺ validation runs · finer Co/Al composition grid at 5–15% · Ta/Nb composition sweep for LLZO