Drug Discovery Applications of Electronic Landscape Stability Diagnostics in Metal-Centered Biological Active Sites

Electronic Landscape Stability Diagnostics for Metal-Centered Biological Active Sites Version 2.0 data available at: https://doi.org/10.5281/zenodo.19163956 Benchmark Classification and Binding-State Perturbation Mapping Using Penalized Ensemble VQE Quantum Clarity LLC March 2026 Abstract We report the application of the Electronic Landscape Stability Diagnostic (ELSD) platform to a series of biologically relevant metal-centered active-site fragments, including Fe(II) porphyrin, Zn²⁺ carbonic anhydrase models, and Cu²⁺ superoxide dismutase (SOD) variants. Using a GPU-accelerated penalized variational quantum eigensolver (VQE) with multi-seed ensemble sweeps, explicit N-sector and Sz-sector enforcement, and full energy decomposition per run, we classify the electronic landscape of each system into one of four regimes: Rigid Stability, Coherent Open-Shell, Multi-Basin, or Model Pathology. Nine locked results are reported across Fe, Zn, and Cu systems, including canonical benchmarks, matched perturbation states, and one diagnostic scaffold control. A four-perturbation controlled series on the Cu²⁺ SOD active site — varying donor protonation state, donor identity, coordination number, and bound ligand — demonstrates that the dominant electronic family is preserved across all 25 runs while ensemble ruggedness spans a 21× range across the series. A matched apo/bound pair shows that water binding increases landscape ruggedness by 9.2× without changing the electronic family, providing the first binding-state classification result in the present Prometheus biological series. These findings establish three platform capabilities: (1) identification of stable, decision-grade biological benchmarks across metal centers and spin states; (2) causal mapping of perturbation-dependent ruggedness within a preserved electronic family; and (3) discrimination between fragments sharing the same electronic family but representing materially different screening models. Plain Language Summary What we did We built a computational tool that examines the electronic structure of metal-centered active sites in biological molecules — the kind found at the heart of enzymes involved in drug metabolism, cancer biology, and cellular defense. Instead of running a single simulation and accepting the result, we ran dozens of independent calculations on the same target, each starting from a different random point, and asked: do they all agree? We tested this across three different metal centers — iron (Fe), zinc (Zn), and copper (Cu) — in models that represent real drug-discovery targets. We then systematically changed one thing at a time in the copper system: the chemical character of a nearby donor molecule, the number of coordinating atoms, and whether a water molecule was bound to the metal center. Across nine locked results and twenty-five Cu perturbation runs, we recorded what happened to the electronic landscape each time. What we discovered Three things that we did not expect to find together: 1. The same tool works across very different chemical systems. Iron, zinc, and copper active sites — with different electron counts, different spin states, and different coordination environments — can all be classified by the same methodology. The electronic landscape of a closed-shell zinc site and an open-shell copper site look very different, but the tool correctly identifies and distinguishes them without needing to be reconfigured for each one. 2. Ruggedness is tunable, and the baseline is not always the most stable point. When we changed the chemical character of the donor molecule attached to the copper center — making it weaker, stronger, or removing one donor entirely — the electronic landscape changed in a systematic but non-obvious way. The unmodified baseline turned out to sit at a local maximum of ruggedness. Every perturbation we tested, in any direction, produced a tighter, more predictable landscape. This means the most "natural" configuration is not necessarily the most stable one electronically — a finding with real implications for how drug targets are modeled. 3. A bound ligand changes the electronic model even when it does not change the electronic family. When we added a single water molecule to the most stable copper configuration, the dominant electronic state remained identical — the same quantum mechanical solution appeared in every run. But the spread of solutions across runs increased by 9×. In practical terms: the apo (unbound) site and the water-bound site look the same qualitatively, but they are not the same model for screening purposes. One is nine times more variable than the other. That difference is invisible to conventional single-point methods. Why this matters Drug discovery programs that involve metal-centered targets — which includes a large fraction of enzyme inhibitor programs — typically assume that the computational model of the target is settled before screening begins. Our results show that this assumption deserves scrutiny. The electronic character of a metal active site can change substantially depending on protonation state, coordination number, and bound ligand, even when the changes look small on paper. More specifically: two target models can produce the same dominant electronic solution and still represent materially different screening landscapes. A team that treats the apo and ligand-bound states as equivalent is optimizing compounds against a target that may be 9× more electronically variable than their reference model suggests. The practical implication is a new kind of quality-control step that can be inserted before large-scale screening: classify the electronic landscape of the target model first, confirm it is stable and coherent, and only then commit to the screening campaign. This does not replace existing computational methods — it sits upstream of them, on the question of whether the model itself is trustworthy. 1. Platform Description 1.1 Engine All calculations were performed using the Prometheus VQE engine (prometheus_vqe_engine_penalized.py), a GPU-accelerated penalized variational quantum eigensolver built on TorchQuantum and OpenFermion-PySCF. Key parameters: Parameter Value Ansatz UCCSD depth 6 Active space 10 electrons / 10 orbitals (20 qubits) Basis set LANL2DZ (effective core potential) Pauli terms ~3100 per system Hardware NVIDIA L40S GPU (44 GB) Convergence conv=1e-6 (default), conv=1e-7 (tighter sweeps) Max iterations 300 (default), patience=30 1.2 Sector enforcement Number-sector enforcement: penalty term λ_N × (N̂ − N_target)² added to Hamiltonian. Spin-sector enforcement: penalty term λ_Sz × (Ŝz − Sz_target)² added to Hamiltonian. Standard operating points: λ_N = 2.0 Ha (Zn/Cu systems), λ_Sz = 5.0 Ha (open-shell Cu). 1.3 Quality criteria A result is locked only when all five criteria are met simultaneously across the full seed ensemble: Sector clean: |⟨N⟩ − N_target| < 0.1 and |⟨Sz⟩ − Sz_target| < 0.1 Dominant determinant probability: dom_p > 0.99 Same dominant bitstring family across all seeds Penalty contribution audited and confirmed numerical noise only (decompose_energy.py) σ and range consistent with claimed landscape classification 1.4 Classification regimes Regime σ (kcal/mol) Description Rigid Stability typically < 0.5 Single tight basin, decision-grade Coherent Open-Shell typically 0.5–2.0 Broader but single-family, trustworthy Multi-Basin > 10 Multiple competing families, sector-clean Model Pathology N/A Sector escape despite enforcement 2. Locked Results — Nine Total Three categories: canonical benchmark systems, locked perturbation states, and locked diagnostic controls. 2.1 Full results registry Canonical benchmark systems (6): System Metal σ (kcal/mol) Seeds Regime Status FePorphyrin_FeII ls Fe²⁺ d⁶ low-spin 0.3375 5 Rigid Stability LOCKED ✓ Zn_CA2 minimal Zn²⁺ d¹⁰ tetrahedral 0.0933 9 Rigid Stability LOCKED ✓ Zn_CA2 imidazole Zn²⁺ d¹⁰ + 3 imidazole 0.4367 5 Rigid Stability LOCKED ✓ Cu_SOD_minimal Cu²⁺ d⁹ 3N+1O 1.7035 5 Coherent Open-Shell LOCKED ✓ Cu_SOD_2imidazole Cu²⁺ d⁹ 2N+1O 0.0803 5 Rigid Stability LOCKED ✓ Cu_SOD_2imidazole_water Cu²⁺ d⁹ + axial H₂O 0.7419 5 Coherent Open-Shell LOCKED ✓ Locked perturbation states (2): System Metal σ (kcal/mol) Seeds Regime Status Cu_SOD_protonated Cu²⁺ d⁹, donor neutralized 0.6402 5 Tightened open-shell LOCKED ✓ Cu_SOD_acetate Cu²⁺ d⁹, donor strengthened 0.9017 5 Tightened open-shell LOCKED ✓ Locked diagnostic control (1): System Metal σ (kcal/mol) Seeds Regime Status Zn_squareplanar Zn²⁺ d¹⁰ D4h artificial 43.29 5 Multi-Basin (scaffold) LOCKED DIAGNOSTIC 2.2 FePorphyrin_FeII low-spin Fragment: Fe²⁺ + 4 porphyrin N (square planar, Fe-N=2.01 Å) + axial H₂O. Config: charge=0, mult=1 (singlet), N=10, n_orb=10. Result: σ=0.3375 kcal/mol, 5/5 seeds clean. Rigid Stability. First locked biological result. Confirms d⁶ low-spin → Rigid Stability predictive rule in biology. 2.3 Zn_CA2 minimal Fragment: Zn²⁺ + 3 donor N atoms + OH⁻ (5 atoms, donor-only). Config: charge=0, mult=1, N=10, n_orb=10, λ_N=2.0. Result: σ=0.0933 kcal/mol across 9 seeds (lam_n grid). Rigid Stability. Earlier overnight sweep (sector_penalty=0) showed N≈12 escape for 7/10 seeds; controlled lam_n rescue grid established fragment stability under adequate enforcement. 2.4 Zn_CA2 imidazole (realism-survival extension) Fragment: Zn²⁺ + 3 imidazole rings (C₃H₃N₂) + OH⁻ (27 atoms). Config: charge=0, mult=1, N=10, n_orb=10, λ_N=2.0. Result: σ=0.4367 kcal/mol, 5/5 seeds clean. Rigid Stability preserved. Identical dominant determinant |11111111110000000000⟩ in all 5 seeds. Confirms that the Zn_CA2 Rigid Stability classification survives scaffold enrichment from a donor-only minimal fragment to a chemically realistic His coordination environment. 2.5 Cu_SOD_minimal Fragment: Cu²⁺ + 3 imidazole N donors + formate carboxylate (28 atoms). Config: charge=+1, mult=2 (doublet), N=11, n_orb=10, λ_Sz=5.0, Sz_target=0.5. Result: σ=1.7035 kcal/mol, 5/5 seeds clean. Coherent Open-Shell. Dominant bitstring |11111111111000000000⟩ in all 5 seeds. No spin-sector escape. First Prometheus open-shell biological classification result. 2.6 Zn_squareplanar (diagnostic) Fragment: Zn²⁺ + 4 donor N atoms (D4h square planar, Zn-N=2.05 Å). Config: charge=0, mult=1, N=10, n_orb=10. Result: σ=43.29 kcal/mol, 5/5 seeds sector-clean (N=10 stable throughout), all 5 dominant bitstrings distinct. Multi-Basin (scaffold artifact). Intra-sector landscape fragmentation — not sector contamination. Artificial D4h ligand field creates near-degenerate orbital-ordering solutions absent in realistic geometry. The tetrahedral Zn_CA2 branch subsequently recovered the same clean family, supporting the interpretation that the square-planar multi-basin behavior is geometry-induced rather than sector-driven. 2.7 Cu_SOD_2imidazole (apo — coordination number 4→3) Fragment: Cu²⁺ + 2 imidazole N donors + formate carboxylate (21 atoms). Config: charge=+1, mult=2, N=11, n_orb=10, λ_Sz=5.0. Result: σ=0.0803 kcal/mol, 5/5 seeds clean. Rigid Stability. dom_p=0.9998–1.0000. Range=0.19 kcal/mol. An open-shell d⁹ Cu²⁺ center achieves Rigid Stability under coordination number reduction — the same regime as the closed-shell Zn and Fe benchmarks. 2.8 Cu_SOD_2imidazole_water (bound — axial water ligand) Fragment: Cu_SOD_2imidazole + axial H₂O at Cu-O=2.10 Å (24 atoms). Config: charge=+1, mult=2, N=11, n_orb=10, λ_Sz=5.0. Result: σ=0.7419 kcal/mol, 5/5 seeds clean. Coherent Open-Shell. Same dominant bitstring |11111111111000000000⟩ as apo. Water binding increased ruggedness 9.2× while preserving the electronic family. See Section 4 for matched-pair analysis. 3. Cu²⁺ SOD Perturbation Series — Four Perturbations Plus Baseline All experiments use the Cu_SOD_minimal geometry as reference. One variable changed per experiment. Same dominant electronic family |11111111111000000000⟩ in all 25 runs (5 systems × 5 seeds). Config: λ_Sz=5.0, Sz_target=0.5, sector_penalty=2.0, 5 seeds each. 3.1 Series summary Experiment Change Charge σ (kcal/mol) Range Regime Cu_SOD_protonated (Exp 1) Formate⁻ → formic acid +2 0.6402 1.61 Tightened Cu_SOD_acetate (Exp 2) Formate⁻ → acetate⁻ +1 0.9017 2.14 Tightened Cu_SOD_minimal (baseline) 3N+1O formate⁻ +1 1.7035 4.52 Coherent Open-Shell Cu_SOD_2imidazole (Exp 3) 3N+1O → 2N+1O +1 0.0803 0.19 Rigid Stability Cu_SOD_2imidazole_water (Exp 4) + axial H₂O on Exp 3 +1 0.7419 2.03 Coherent Open-Shell 3.2 Donor-strength axis (Experiments 1 and 2) The formate baseline sits at a local ruggedness maximum in the donor-strength axis. Both donor weakening (protonation, Exp 1) and donor strengthening (methylation to acetate, Exp 2) reduce ruggedness relative to the unmodified formate. This non-monotonic relationship is consistent with the formate donor occupying a ligand-field balance point where orbital degeneracy is maximally accessible, with perturbations in either direction partially resolving that degeneracy. 3.3 Coordination number reduction (Experiment 3) Removing one imidazole donor (3N+1O → 2N+1O) produced the tightest landscape in the series (σ=0.0803, Rigid Stability). The hypothesis that under-coordination would increase orbital flexibility and broaden the landscape was not supported. Removal of one imidazole appears to reduce electronic frustration in the first coordination shell, collapsing the accessible configuration space into a single tight basin. 3.4 Ligand binding (Experiment 4) See Section 4. 4. Binding-State Classification — Matched Apo/Bound Pair 4.1 Experimental design Base: Cu_SOD_2imidazole (locked, σ=0.0803, Rigid Stability). Perturbation: axial water molecule added at Cu-O=2.10 Å (+z axis). All 21 base atoms: coordinates unchanged. Water geometry: O at (0.000, 0.000, 2.100), H-O-H=104.5°, O-H=0.957 Å. 4.2 Results Metric Cu_SOD_2imidazole (apo) Cu_SOD_2imidazole_water (bound) σ (kcal/mol) 0.0803 0.7419 Range (kcal/mol) 0.1915 2.0299 Ruggedness ratio 1.0× 9.2× dom_p range 0.9998–1.0000 0.9988–1.0000 Dominant bitstring |11111111111000000000⟩ |11111111111000000000⟩ Sector status CLEAN ✓ (5/5) CLEAN ✓ (5/5) Regime Rigid Stability Coherent Open-Shell 4.3 Interpretation Both states are sector-clean, single-family, and sector-audited. Neither is pathological. The dominant electronic family is identical. However, ensemble ruggedness increases 9.2× upon water binding. The apo and water-bound states are not equivalent models for screening: a discovery program that treats them as interchangeable is optimizing against a landscape 9× broader than its apo reference. Canonical wording: Adding a single axial water ligand to the locked Cu_SOD_2imidazole apo scaffold increased ensemble ruggedness by 9.2× (σ: 0.0803 → 0.7419 kcal/mol) while preserving the same sector-clean N=11, Sz=+0.5 dominant family and identical dominant determinant across all 5 seeds. The apo state classifies as Rigid Stability; the water-bound state classifies as Coherent Open-Shell. Both states are electronically trustworthy and single-family — but they are not equivalent models for screening. This is the first Prometheus binding-state classification result: ligand binding changes the electronic regime without changing the dominant electronic family. 5. Three Platform Capabilities Capability 1 — Benchmark validation across metal centers and spin states Prometheus identifies stable, decision-grade metalloenzyme models across chemically distinct active sites. Results span Fe(II) d⁶ low-spin, Zn²⁺ d¹⁰ in both minimal and full imidazole coordination shells, and Cu²⁺ d⁹ in multiple coordination geometries. The Zn classification survives scaffold enrichment — identical result whether run against a donor-only fragment or a full His coordination environment. All results accompanied by full sector audit and energy decomposition. No cherry-picked runs. Capability 2 — Perturbation-dependent ruggedness mapping within a preserved family Within the Cu²⁺ SOD active site, a five-experiment perturbation series — donor neutralization, donor strengthening, coordination number reduction, and ligand binding — produced σ values ranging from 0.08 to 1.70 kcal/mol (21× range) while the dominant electronic family remained identical across all 25 runs. The unmodified 3N+1O formate baseline occupies a local ruggedness maximum: every perturbation tested produced a tighter landscape. This demonstrates causal regime mapping — quantified within-system perturbation response, not cross-system comparison. Capability 3 — Binding-state discrimination Prometheus distinguishes fragments that share the same dominant electronic family but represent materially different screening models. The matched Cu apo/bound pair (σ=0.08 vs 0.74 kcal/mol) demonstrates that a ligand-binding event can shift the electronic landscape regime without inducing a family change. This distinction — same family, different ruggedness, therefore different screening model — is not detectable by single-point methods. 6. Engineering Constraints Registry Systems excluded from benchmark use due to sector pathology: ID System Failure mode Status ENG-001 FePorphyrin_FeIII bare cation (charge=+1) Catastrophic Sz-sector collapse LOCKED ENG-002 FePorphyrin_FeII high-spin quintet (mult=5) Off-target spin-sector family LOCKED ENG-003 FePorphyrin_FeIII thiolate (charge=0, N=11) Spin-escalation despite lam_sz=50 PROVISIONAL 7. Operational Parameters 7.1 Validated operating point Parameter Value Notes Qubits 20 18: mediocre results; 22: OOM on L40S Active space (10e, 10o) Validated across all systems Pauli terms ~3100 Consistent across targets lam_N (Zn/Cu) 2.0 Ha From rescue grid; avoids HF-trapping lam_Sz (Cu open-shell) 5.0 Ha Prevents spin escalation Seeds per system 5 (minimum) 9 seeds used for Zn_CA2 rescue grid 7.2 Archiving pattern All results archived per seed: {system}_seed{N}_statevector.npz — full quantum statevector {system}_seed{N}_history.csv — VQE convergence history {system}_seed{N}_convergence.png — convergence plot {system}_seed{N}_checkpoint.pth — optimizer checkpoint 7.3 Sector audit tool decompose_energy.py — separates physical energy from sector penalty contributions, computes ⟨N⟩, ⟨Sz⟩, dominant bitstring, and dom_p from statevector. Authoritative Sz sign convention: interleaved alpha/beta spin-orbital ordering. 8. Geometry Specifications All geometries constructed from crystallographic reference bond lengths and patched into the engine via verified patch scripts (5/5 checks required before any run). System Atoms Key distances FePorphyrin_FeII 8 Fe-N=2.01 Å, Fe-O=2.10 Å Zn_CA2 minimal 5 Zn-N=2.00 Å, Zn-O=1.97 Å Zn_CA2 imidazole 27 Zn-N=2.05 Å, Zn-O=1.97 Å Cu_SOD_minimal 28 Cu-N=2.00 Å, Cu-O=1.97 Å Cu_SOD_protonated 29 +OH at O2, O-H=0.957 Å Cu_SOD_acetate 31 +CH₃ at C, C-C=1.522 Å Cu_SOD_2imidazole 21 imidazole 3 removed Cu_SOD_2imidazole_water 24 +H₂O axial, Cu-O=2.10 Å Zn_squareplanar 5 Zn-N=2.05 Å, D4h 9. Dataset Contents This deposit contains output data only. Engine source code, patch scripts, and sweep scripts are proprietary and patent-protected and are not included in this deposit. File Description README.md This document — full scientific record Zn_CA2_lam_n_grid_summary.csv Zn_CA2 rescue grid results across lam_n={1.0,2.0,5.0}, seeds {0,1,2} Zn_CA2_lam_n_grid_report.txt Rescue grid decision-gate report results/Cu_SOD_minimal_seed{0-4}_statevector.npz Cu_SOD_minimal quantum statevectors (5 seeds) results/Cu_SOD_minimal_seed{0-4}_history.csv Cu_SOD_minimal VQE convergence histories (5 seeds) results/Cu_SOD_protonated_seed{0-4}_statevector.npz Perturbation Exp 1 statevectors (5 seeds) results/Cu_SOD_protonated_seed{0-4}_history.csv Perturbation Exp 1 convergence histories (5 seeds) results/Cu_SOD_acetate_seed{0-4}_statevector.npz Perturbation Exp 2 statevectors (5 seeds) results/Cu_SOD_acetate_seed{0-4}_history.csv Perturbation Exp 2 convergence histories (5 seeds) results/Cu_SOD_2imidazole_seed{0-4}_statevector.npz Perturbation Exp 3 statevectors (5 seeds) results/Cu_SOD_2imidazole_seed{0-4}_history.csv Perturbation Exp 3 convergence histories (5 seeds) results/Cu_SOD_2imidazole_water_seed{0-4}_statevector.npz Perturbation Exp 4 statevectors (5 seeds) results/Cu_SOD_2imidazole_water_seed{0-4}_history.csv Perturbation Exp 4 convergence histories (5 seeds) results/Zn_CA2_imidazole_seed{0-4}_statevector.npz Zn_CA2 imidazole statevectors (5 seeds) results/Zn_CA2_imidazole_seed{0-4}_history.csv Zn_CA2 imidazole convergence histories (5 seeds) Total: 62 files (README + 2 grid files + 60 result files across 6 systems × 5 seeds × 2 file types) Note on reproducibility: The statevector files (.npz) contain the full 20-qubit quantum statevector for each run. Sector analysis (⟨N⟩, ⟨Sz⟩, dom_p, dominant bitstring, penalty decomposition) can be independently verified from these files using standard numpy operations without access to the Prometheus engine. Citation If you use this dataset or methodology, please cite: Quantum Clarity LLC. Electronic Landscape Stability Diagnostics for Metal-Centered Biological Active Sites: Benchmark Classification and Binding-State Perturbation Mapping Using Penalized Ensemble VQE. Zenodo, March 2026. DOI: [10.5281/zenodo.19142883] License Dataset and analysis scripts: CC BY 4.0 Engine source code (prometheus_vqe_engine_penalized.py): proprietary — not included in this deposit. Quantum Clarity LLC | Prometheus Platform | March 2026 "One biological domain. One methodology. Multiple metal-centered regimes."