Geometry, Spin Coupling, and Dielectric Control of Redox Potentials in [4Fe–4S] Clusters

Geometry, Spin Coupling, and Dielectric Control of Redox Potentials in [4Fe–4S] Clusters | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Geometry, Spin Coupling, and Dielectric Control of Redox Potentials in [4Fe–4S] Clusters Peter S. Rice, Bruno Jacob, Khushbu Agarwal, Marcel D. Baer, Simone Raugei This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8059723/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Iron–sulfur (Fe–S) clusters are common biological cofactors that facilitate vital redox reactions. Despite extensive research, the molecular basis of redox potential tuning in ferredoxin-like proteins remains a topic of ongoing debate. In this study, we combine statistical analysis of over one thousand [4Fe–4S]-containing protein structures from the Protein Data Bank (PDB) with broken-symmetry and extended broken-symmetry density functional theory to examine how cysteine ligand orientations and environmental screening affect cluster redox energies. We identified five main ligand configurations, three of which are predominant in natural structures. Among these, the adiabatic electron affinity differs by less than 0.1 V, indicating that, while geometry plays a secondary role, it allows localized fine-tuning of redox properties. In contrast, electrostatic and solvation effects primarily determine the overall potential range. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Iron-sulfur (Fe-S) clusters are among the most ancient and versatile cofactors in biology, 1 supporting an extraordinary range of redox processes that underpin life itself. Their emergence is thought to predate enzymatic catalysis, with mineral Fe-S motifs likely serving as primitive electron mediators in early metabolic networks. Indeed, the chemical environment of alkaline hydrothermal vents (rich in Fe 2+ , sulfide, and CO 2 ) has been hypothesized to provide ideal conditions for the self-assembly of such clusters, fostering the first energy-converting reactions at the origin of life. 2 – 4 Over billions of years of evolution, nature has retained and refined these motifs within proteins, embedding them in scaffolds that exquisitely tune their electronic properties. Fe-S clusters now appear in an enormous variety of biological contexts, from simple electron carriers such as rubredoxins and ferredoxins to complex catalytic centers such as the FeMo-cofactor of nitrogenase. 5 – 7 Among these, the cubane-type [4Fe-4S] cluster stands out as a paradigmatic redox module, mediating single-electron transfers over a potential range exceeding 1 V while maintaining a common inorganic core. This remarkable tunability arises from the interplay between intrinsic cluster geometry and the surrounding protein environment, including the nature of cysteine ligation, local hydrogen-bond networks, and long-range electrostatics. 8 – 14 Despite decades of structural, spectroscopic, and electrochemical investigations, a quantitative understanding of how these environmental factors modulate the redox potential of [4Fe-4S] clusters remains incomplete. Experimentally, potentials vary from approximately + 0.40 V to -0.80 V vs. SHE across different proteins (Table 1 ), suggesting that subtle geometric and electrostatic effects can dramatically shift the thermodynamics of electron transfer. However, disentangling the contributions from cluster distortions, spin coupling, and environmental polarization remains a formidable challenge for both theory and experiment. To address this question, we combine statistical analysis of Protein Data Bank 15 (PDB) structures with broken-symmetry and extended broken-symmetry density functional theory (BS-DFT and EBS-DFT). Our approach isolates the effect of ligand orientation and local dielectric screening on the redox energetics of representative [4Fe-4S] cores. By comparing more than one thousand unique cysteine-ligated clusters, we identify five dominant geometrical motifs and evaluate their adiabatic electron affinities using a wide range of exchange-correlation functionals. We further employ the Heisenberg–Dirac–van Vleck (HDvV) Hamiltonian framework to assess spin-coupling effects, providing a rigorous treatment of exchange interactions often neglected in single-determinant DFT. In doing so, we aim to quantify how much of the redox potential variability can be ascribed to intrinsic geometric differences versus environmental screening and electronic correlation. Our results contribute to this enduring question by providing computational insight into how local coordination and the dielectric environment collectively shape the bio-electrochemical behavior of Fe-S clusters. The remainder of this paper is organized as follows. We first describe the statistical analysis of Protein Data Bank structures used to identify representative cysteine-ligation motifs in ferredoxin-type [4Fe-4S] clusters. These geometries form the basis for a systematic series of broken-symmetry and extended broken-symmetry DFT (BS-DFT and EBS-DFT) calculations designed to quantify the influence of ligand orientation, exchange coupling, and electronic correlation on redox energetics. We then examine solvation and dielectric effects using both continuum and explicit models to assess the relative importance of environmental screening. Finally, we integrate these results to determine the extent to which geometry, electronic correlation, and electrostatics collectively modulate the redox properties of biological Fe-S clusters, drawing connections to experimental trends and to design principles underlying bio-inspired redox catalysts. Table 1 Redox properties of a select few bacteria containing [4Fe-4S] clusters, highlighting the large variation of E0. Organism E ° (V) A. vinosum + 0.355 16 T. tepidum + 0.323 17 B. thermoproteolyticus –0.280 18 D. africanus –0.385 19 A. vinelandii –0.650 20 , -0.790 21 Computational Methods Dataset curation and structural clustering We queried the Protein Data Bank (PDB) for proteins containing [4Fe-4S] clusters ligated by four cysteine residues. From more than 2000 entries, 1049 unique, non-redundant clusters were retained after removing mutants and duplicate proteins. Five recurrent ligand-orientation motifs were identified (Fig. 1); three dominate the population and cleanly separate in principal-component space 22 (Clusters 1, 2, and 4). These motifs occur broadly across oxidoreductases ( e.g. , ferredoxins, dehydrogenases, dehalogenases, sulfite/nitrate reductases). All broken-symmetry density-functional theory (BS-DFT) calculations were performed with ORCA 6.0 23 . To focus on primary coordination effects, the cysteine ligands (Fe-SCH 2 -R) were modeled as methyl thiolates (CH 3 S − ). 24–26 Oxidized [4Fe-4S] 2+ ( S = 0) and reduced [4Fe-4S] + ( S = 1) states were considered. For [4Fe-4S] 2+ , all relevant BS solutions were examined using a two-layer picture with ferromagnetically coupled Fe pairs within each [2Fe-2S] sublayer and antiferromagnetic coupling between sublayers. 10 , 27 , 28 Dispersion was included using Grimme’s D4 scheme, 29,30 and the ma-def2-TZVP 31 basis (with diffuse functions) was used for all atoms. Geometries taken from the statistical analysis of PDB structures were initially optimized with BP86 32 , with further geometry and energy refinements surveyed with a representative set of LDA/GGA/meta-GGA/hybrid and range-separated functionals (PWLDA 33 , BP86 32 , PBE 34 , BLYP 35 , 36 , TPSS 37 , revTPSS 38 , r2SCAN 39 , B3LYP (20% HF) 36,40–42 , PBE0 (25% HF) 43 , TPSSh (10% HF) 44 , TPSS0 (25% HF) 44 , r 2 SCANh (10% HF) 45 and CAM-B3LYP 46 ). Harmonic frequency analysis verified minima and provided zero-point vibrational energy (ZPE) corrections. Redox metrics: adiabatic and vertical electron affinities We report adiabatic electron affinities with ZPE (AEA ZPE ) by optimizing both oxidation states and adding ZPE terms: $$\:\text{Ox}+{e}^{-}\to\:\text{Red},\:{\:\text{A}\text{E}\text{A}}_{\text{Z}\text{P}\text{E}}=\left(E\right(\text{O}\text{x})+\text{Z}\text{P}\text{E}(\text{O}\text{x}\left)\right)-\left(E\right(\text{R}\text{e}\text{d})+\text{Z}\text{P}\text{E}(\text{R}\text{e}\text{d}).$$ The results are summarized in Fig. 2 and Table S1 (Supporting Information). In the final section, we also evaluated the vertical electron affinities (VEA). EBS-DFT and Heisenberg–Dirac–van Vleck (HDvV) Hamiltonian Given that BS-DFT is single-determinant in nature, the resulting electronic states are not true spin eigenfunctions but linear combinations of determinants with different m S projections ( e.g. , mixtures of m S = 1/2 or 0 components). Consequently, the computed energies correspond to spin-contaminated states whose ordering and splitting can deviate from those of the proper pure-spin states. This limitation is particularly significant for low-spin configurations of Fe-S clusters, where near-degeneracy and spin frustration are common. To obtain physically meaningful spin energies and exchange couplings, the BS-DFT results were mapped onto a Heisenberg–Dirac–van Vleck (HDvV) Hamiltonian using the Extended Broken-Symmetry DFT (EBS-DFT) formalism. 47 This procedure reconstructs the spin ladder by comparing the energies of high-spin and broken-symmetry solutions to extract pairwise exchange constants \(\:{J}_{ij}\) between Fe centers, followed by diagonalization of the Hamiltonian: $$\:\widehat{H}=-2\sum\:_{i<j}{J}_{ij}{\widehat{s}}_{i}\bullet\:{\widehat{s}}_{j}$$ where \(\:{\widehat{s}}_{i}\) is the spin operator on the spin site i , yielding spin eigenstates and total-spin energies consistent with a multideterminant description. Continuum solvation: dielectric-response scans Environmental screening was modeled using the SMD continuum, scanning dielectric constants from e = 1 (vacuum) to e = 80 (∼water). Both BS-DFT and EBS-DFT show rapid AEA ZPE stabilization at low e , approaching a plateau near e ≈ 15, consistent with protein-like interiors; the across-cluster spread remains small (~ 0.1 eV) relative to solvent shifts. Explicit solvation and hybrid QM/MM protocols To capture first-shell specificity, we constructed an SPC/E water droplet (up to 5953 water molecules) and equilibrated it for 100 ns in the canonical (NVT) ensemble, with the D 2d -like Cluster 4 at the center. We evaluated VEA using: (i) all-QM water (QM is calculated at the BP86-D4/ma-def2-TZVP level of theory), (ii) hybrid QM/MM with waters as point charges, (iii) QM/MM(+ QM H 2 O) by progressively promoting waters within radial cutoffs (3–15 Å) into the QM region, (iv) QM + SMD ( e = 78), and (v) QM/MM + CPCM(+ QM H 2 O) hybrid treatments. Results and Discussion Overview The electronic structure and redox properties of [4Fe-4S] clusters were examined using the five representative ligand configurations derived from statistical analysis of ferredoxin-type proteins. For each configuration, BS-DFT and EBS-DFT calculations were performed in both oxidized ([4Fe-4S] 2+ , S = 0) and reduced ([4Fe–4S] + , S = 1) states. The adiabatic electron affinities with zero-point correction (AEA ZPE ) were computed using a range of exchange-correlation functionals, and additional dielectric and solvation models were used to probe environmental screening effects. This multi-tiered approach allows for a systematic comparison of how intrinsic geometric features, spin coupling, and medium polarization collectively modulate the redox thermodynamics of Fe-S clusters. Structural Diversity in Biological [4Fe-4S] Clusters A comprehensive survey of the Protein Data Bank identified more than two thousand Fe-S-containing proteins, of which 1049 unique [4Fe-4S] cores were selected after removing redundant and mutant entries. Principal component analysis (PCA) of the cysteine-ligation vectors revealed five distinct geometric motifs, differing primarily in the orientation of the C–S–Fe bonds relative to the cubane core (Fig. 1). Among these, three configurations account for the majority of observed structures and correspond to ligand orientations that recur across diverse enzyme families, including ferredoxins, dehydrogenases, and reductases. Despite subtle geometric differences, all clusters preserve the [4Fe-4S] cubane core framework with average Fe–Fe distances of 2.70 ± 0.05 Å and Fe-S distances of 2.28 ± 0.03 Å. Variations in cysteine orientation primarily affect the outer-sphere topology and, consequently, the directionality of potential hydrogen-bond networks and local electrostatics. These structural descriptors, therefore, provide a physically grounded set of models for assessing the effects of geometry on intrinsic redox energetics. Probing the influence of the ligation environment with BS-DFT The electronic structure of [4Fe-4S] clusters is characterized by the presence of Fe(II) and Fe(III) ions that are anti-ferromagnetically coupled through bonding to S 2− ions. Broken-symmetry DFT (BS-DFT) is widely used to treat these strongly correlated species. To assess how the methyl thiolate ligand orientation influences the redox properties of the five [4Fe-4S] clusters (Fig. 1), we have computed the adiabatic electron affinity with zero-point energy corrections (AEA ZPE ) for several commonly used exchange-correlation functionals. From Fig. 2 , it is found that the absolute AEA ZPE is highly sensitive to the choice of functional. For any given cluster, the range across the different functionals is calculated to be between 1.19 eV and 1.38 eV (maximum for cluster 4), indicating that functional choice dominates the absolute scale. Electronic Structure and Redox Energetics Broken-symmetry DFT (BS-DFT) and extended broken-symmetry DFT (EBS-DFT) calculations were performed on each of the five representative ligand configurations to assess how geometric variation and spin coupling affect the intrinsic redox energetics of the [4Fe–4S] 2+/+ couple. Figure 2 and Table S1 summarize the computed adiabatic electron affinities with zero-point correction (AEA ZPE ) obtained using a series of exchange-correlation functionals spanning local, semi-local, hybrid, and range-separated levels of theory. In general, semi-local functionals (LDA/GGA/meta-GGA) yield AEA ZPE values ~ 0.70 eV more negative than hybrid functionals. This observation is consistent with delocalization/self‑interaction error artificially stabilizing anionic species for semi-local functionals. In contrast, hybrid functionals reduce this stabilization and are known to under-bind excess electrons (reduced states) in systems containing delocalized electrons. In such clusters with strong screening effects, unscreened HF exchange can significantly widen HOMO-LUMO gaps and minimize diffuse charge states. Across all functionals, the absolute AEA ZPE values fall within the range of -3.2 eV / -4.3 eV, consistent with previous gas-phase estimates for cubane-type clusters. 13 The spread (𝜎) among functionals is substantial (up to about 0.5 eV), reflecting the expected sensitivity to exchange mixing and self-interaction error. In contrast, the geometric dependence is minimal: the variation in AEA ZPE between the five ligand orientations is less than 0.1 eV. This finding demonstrates that while the cysteine-ligand geometry contributes a measurable but secondary effect, the dominant factors governing the redox energy are the intrinsic Fe-S electronic structure and the broader electrostatic environment. Such modest geometric modulation nevertheless provides a possible mechanism for fine-tuning redox potentials within a protein fold, consistently with the empirical observation that site-specific mutations can induce small but reproducible potential shifts. The spin-coupling analysis reinforces this picture, as shown by the calculated spin-ladders for all clusters (Fig. 3 ). For both oxidation states, all clusters exhibit a low-spin ground state arising from antiferromagnetic coupling between two ferromagnetically aligned [2Fe-2S] subunits. 52 , 53 The energy separation between adjacent spin states follows a linear trend with total spin quantum number S ( S + 1), well described by an isotropic Heisenberg model with the exchange constants of approximately − J ox = 193–208 cm − 1 and − J red = 109–113 cm − 1 ( Figure S1 ), which is within the range of previous literature reports. 24 , 52 , 53 The ratio of these two states, J Ox / J Red ≈ 1.71, indicates that the coupling is significantly stronger in the oxidized state than in the reduced state for all clusters, 23,51,52 consistent with greater Fe(III)–Fe(III) coupling. In the reduced state, the spin levels are closer in energy than in the oxidized state, indicating a smaller spin gap and a weaker effective antiferromagnetic exchange. The small variation of the J (< 0.002 eV) across the five geometries confirms that local ligand orientation exerts only a minor perturbation on the electronic coupling within the [4Fe-4S] core. These results validate the use of the HDvV framework as an effective phenomenological description of exchange interactions, while highlighting that true spin-state energetics are primarily governed by the delocalized Fe–S network rather than by any specific Fe–S–C orientation. The EBS-DFT and BS-DFT are compared in Table 2 . As can be seen, the explicit consideration of spin-coupling effects makes the absolute AEA ZPE more negative (average over all clusters = -4.387 eV) for all clusters relative to BS-DFT (average over all clusters = -4.217 eV). Overall, the DFT results reveal a clear hierarchy of influences on redox energetics: (1) the choice of exchange–correlation functional and treatment of electronic correlation have the largest quantitative impact; (2) environmental screening and solvation (addressed below) provide the next-most significant modulation; and (3) ligand geometry contributes a smaller, yet non-negligible, fine-tuning effect within approximately 0.1 V. This hierarchy establishes the baseline for evaluating how the surrounding protein matrix further tunes redox properties through electrostatic polarization and hydrogen-bond interactions. Table 2 Calculated adiabatic electron affinity (AEAZPE) calculated using broken symmetry DFT (BS-DFT) and extended broken symmetry DFT (EBS-DFT) for all five [4Fe-4S] clusters using BP86-D4/ma-def2-TZVP. AEA ZPE / eV Method #1 #2 #3 #4 #5 Δ(Max-Min) BS-DFT -4.239 -4.187 -4.188 -4.270 -4.203 0.082 EBS-DFT -4.439 -4.341 -4.378 -4.430 -4.346 0.098 Dielectric and Solvation Effects To quantify the influence of environmental polarization on redox energetics, we examined the variation in the adiabatic electron affinity (AEA ZPE ) as a function of the surrounding dielectric constant ( e ) using the SMD continuum model, complemented by explicit and hybrid QM/MM simulations. These calculations reveal that the solvent and protein environment play a far more substantial role in modulating the redox properties of [4Fe-4S] clusters than variations in ligand geometry. 11 , 13 , 24 , 54 , 55 Continuum dielectric response In the continuum SMD model, the AEA ZPE increases monotonically with e , reflecting progressive stabilization of the reduced state through dielectric screening. As shown in Figs. 4 a and b , the AEA ZPE rises sharply from vacuum ( e = 1) to e ≈ 10–15, after which it approaches a plateau. This plateau corresponds to the effective dielectric constant of a protein interior ( e ≈ 15), suggesting that most of the environmental polarization responsible for redox tuning originates from the immediate protein shell rather than from bulk solvent. The total stabilization between e = 1 and e = 80 amounts to roughly 0.4 eV − 0.5 eV, an order of magnitude larger than the geometry-driven shift discussed above. This stabilization corresponds closely to the 0.4–0.8 V redox window observed across ferredoxins, suggesting that dielectric screening alone can explain most of the biological tuning range. Thus, electrostatic screening represents the dominant physical lever controlling the thermodynamics of the [4Fe-4S] 2+/+ couple. The difference between the two methods is largest for e < 10 and decreases at higher ε (Fig. 4 c ) . This observation can be explained by the fact that BS‑DFT over‑delocalizes the added electron more than EBS‑DFT, generating a more anisotropic charge density distribution. The dielectric interacts differently with these changes in charge density and stabilizes them unevenly across orientations, hence the larger low ε spread for BS‑DFT. Increasing e effectively screens delocalized charges, while EBS‑DFT already mitigates spurious anion over‑stabilization in vacuum, leaving less for the dielectric to screen. From Fig. 4 d, several interesting observations can be made regarding the response to changes in the dielectric medium. Small increases in e from vacuum produce disproportionately large stabilization, accentuating differences between orientations with varying effective charge density distributions after reduction. This is one possible explanation why the max-min plots show the largest discrepancy at low ε and then collapse quickly as ε increases. In these plots, the small bump near very low e for both BS-DFT and EBS-DFT is caused by a crossover in which a given cluster configuration is the most or least stabilized. When two AEA ZPE curves cross, the max-min develops a local extremum. Across all e , the cluster orientation ranking is preserved, and the across‑cluster spread remains small (on the order of 0.1 eV), i.e., this is much smaller than the solvent‑induced shift going from vacuum. Explicit and hybrid solvation models To capture local hydrogen‑bonding effects beyond a continuum description, we computed the vertical electron affinity (VEA) of the D 2d ‑like [4Fe-4S] cluster (Cluster 4) in an equilibrated SPC/E water droplet, shown in Fig. 5 . The VEA values were evaluated using a series of increasingly sophisticated models as a function of an increased water droplet radial cutoff ( r cutoff ): (i) full QM treatment of all water molecules (at the BP86-D4/ma-def2-TZVP level of theory); (ii) QM/MM with water represented as point charges (q(O) = -0.82 e and q(H) = + 0.41 e ); (iii) QM/MM with an increasing number of QM water molecules (> QM H 2 O) within 3–15 Å of the cluster; (iv) QM with SMD implicit solvent ( ε = 78); and (v) QM/MM + CPCM with increased number of QM waters (> QM H 2 O) representing a hybrid explicit-implicit model. As shown in Fig. 5 , all approaches exhibit the same general trend wherein the VEA increases as more water molecules are treated at the QM level. A QM/MM model that represents water only as point charges underestimates this stabilization because it lacks short‑range polarization and charge transfer. Adding CPCM to QM/MM supplies the long‑range reaction field and reaches the large cutoff‑radius limit with fewer QM waters. The implicit SMD model provides a bulk‑screened value close to, but generally below, the converged explicit result because it does not capture directional hydrogen bonding. Including explicit QM waters that hydrogen‑bond to exposed sulfur sites yields a modest additional stabilization, beyond a solvation radius of roughly 12 Å. Further, QM waters have a negligible impact, indicating that first‑shell and near‑surface interactions dominate. Overall, QM/MM + CPCM reproduces the cutoff‑radius plateau and gives slightly higher VEAs than the purely implicit model, consistent with cooperative hydrogen bonding and local polarization. Implications for biological environments These results establish that the surrounding medium can tune the [4Fe-4S] redox potential by several tenths of a volt, an effect far exceeding that of local geometric distortion. The protein matrix effectively acts as an electrostatic dielectric, screening charge localization upon reduction and thereby stabilizing the Fe-S core. Variations in the local polarity, hydrogen-bond networks, or proximity to charged residues are thus expected to provide powerful yet reversible mechanisms for modulating electron-transfer thermodynamics within ferredoxins and related enzymes. The small sensitivity of the Fe-S cubane to ligand orientation, coupled with its pronounced responsiveness to the dielectric environment, may explain why nature employs this scaffold as a robust yet tunable redox module across a broad potential range. In multi-center enzymes such as hydrogenases and nitrogenases, where electron flow is coupled to proton translocation or substrate activation, such dielectric gating likely dictates both directionality and rate. Conclusions The results presented here establish a clear quantitative hierarchy among the factors that modulate the redox energetics of [4Fe-4S] clusters in ferredoxin-type proteins. The systematic combination of statistical structural analysis, broken-symmetry (BS-DFT), and extended broken-symmetry DFT (EBS-DFT), and dielectric modeling allows each contribution (geometric, electronic, and environmental) to be evaluated on the same energetic scale. This workflow can be automated, enabling systematic, reproducible multi-state electronic-structure studies of Fe-S redox landscapes across various motifs and environments with minimal manual intervention. 59 Principal component analysis of 1049 unique [4Fe-4S] clusters from the Protein Data Bank identified five recurrent ligand-orientation motifs, three of which dominate natural occurrences. Despite differences in the orientation of the cysteine C–S–Fe vectors, the intrinsic [4Fe-4S] core geometry remains remarkably invariant. When these five representative motifs were optimized at the BS-DFT level, the resulting adiabatic electron affinities (AEA ZPE ) differed by less than 0.1 eV, a variation an order of magnitude smaller than the experimentally observed potential range among ferredoxins. This small but finite effect quantifies the extent to which ligand orientation can fine-tune redox potentials within an otherwise electronically rigid cubane scaffold. The spin-coupling analysis confirms that all clusters share the same qualitative magnetic topology: two ferromagnetically coupled [2Fe-2S] subunits that interact antiferromagnetically to produce an overall low-spin ground state. The extracted exchange constants, − J ox = 193–208 cm − 1 for [4Fe-4S] 2+ and − J red = 109–113 cm − 1 for [4Fe-4S] 2+ , differ by less than 0.002 eV across the five motifs. Thus, both the magnetic exchange pattern and the overall spin ladder are insensitive to the local cysteine geometry, underscoring the inherent electronic resilience of the Fe-S framework. This finding supports the notion that, within proteins, ligand orientation primarily serves as a fine-tuning variable rather than a determinant of redox-state stability. In contrast, the surrounding dielectric environment exerts a far more substantial influence on the redox energetics. Continuum SMD calculations (Fig. 4 ) show that increasing the dielectric constant from e = 1 to e = 80 stabilizes the reduced state by 0.4 eV − 0.5 eV. The stabilization rises steeply at low e and plateaus at e ≈ 15, corresponding to the upper range of effective permittivity of a protein interior. 56 This behavior indicates that most of the polarization responsible for tuning the redox potential originates from the first few solvation shells and the local protein matrix, rather than from bulk solvent. Explicit-solvent and QM/MM(+ QM H 2 O) calculations refine this picture by capturing the microscopic origins of the dielectric response. Inclusion of hydrogen-bonding interactions from water molecules or polar residues near the cluster further stabilizes the reduced state relative to the continuum model. Beyond a solvation radius of ~ 12 Å, the incremental effect becomes negligible, demonstrating that first-shell and near-surface polarization dominate the environmental contribution. Together, these results suggest that small variations in the local dielectric constant, driven by changes in side-chain charge, hydration, or backbone orientation, can readily account for the 0.5–1.0 V redox span observed experimentally across biological [4Fe-4S] centers. Combining these analyses yields a physically transparent model for redox tuning in Fe-S proteins. The intrinsic cubane core defines a narrow energetic baseline determined primarily by Fe-S covalency and spin exchange. Ligand geometry introduces a secondary modulation (~ 0.1 V), likely exploited by proteins to align the redox potentials of adjacent cofactors for efficient electron transfer. Environmental polarization, through dielectric screening 13 , 24 , 54 , 55 and local hydrogen-bond networks, 57,58 provides the dominant energetic control, enabling shifts of several tenths of a volt without altering the inorganic core. The protein scaffold thus functions as an electrostatic gate, stabilizing or destabilizing charge localization and thereby controlling both thermodynamics and kinetics of electron transfer. The quantitative hierarchy electronic rigidity < geometric fine-tuning < environmental control rationalizes why ferredoxins, hydrogenases, and nitrogenases can employ the same Fe-S cubane framework to span redox potentials from + 0.3 V to -0.8 V versus SHE. It also clarifies the apparent dichotomy between structural conservation and functional diversity in Fe-S enzymes: the cubane core provides stability and electronic continuity. In contrast, the protein matrix provides tunability through electrostatics and solvation. In summary, the present results delineate the physical factors that enable proteins to exploit the intrinsic resilience of Fe-S clusters while tailoring their redox properties through environmental polarization. This interplay between structure, electronic coupling, and electrostatics remains a guiding principle for the bio-inspired design of electrocatalysts and electrochemical materials. Declarations Author contributions P.S.R, M.D.B, and S.R. designed the research. P.S.R, B.J., K.A., M.D.B, and S.R. conducted the study. P.S.R., M.D.B, and S.R. wrote the paper. All authors reviewed the manuscript. Funding This research was supported by the Generative AI (GenAI) for Science, Energy, and Security Science & Technology Investment under the Laboratory Directed Research and Development (LDRD) Program at Pacific Northwest National Laboratory (PNNL) and the U.S. DOE, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, Physical Biosciences Program under awards FWP 66476 (S.R. and M.B.). A portion of the research was performed using resources available through Research Computing at PNNL. PNNL is a multiprogram national laboratory operated by Battelle for the Department of Energy under Contract No. DE-AC05-76RLO 1830. Data availability All data supporting the findings of this study are available within the paper and its Supplementary Information. Conflict of interest The authors declare no competing interests. Ethical approval Not applicable. Consent to participate Not applicable. Consent to publish Not applicable. References Johnson DC, Dean DR, Smith AD, Johnson MK, STRUCTURE, FUNCTION, AND FORMATION OF BIOLOGICAL IRON-SULFUR CLUSTERS (2005). Annu. Rev. Biochem. 74 (Volume 74, 2005), 247–281. https://doi.org/10.1146/annurev.biochem.74.082803.133518 Martin W, Baross J, Kelley D, Russell MJ (2008) Hydrothermal Vents and the Origin of Life. Nat Rev Microbiol 6(11):805–814. https://doi.org/10.1038/nrmicro1991 Mansy SS, Cowan JA (2004) Iron – Sulfur Cluster Biosynthesis: Toward an Understanding of Cellular Machinery and Molecular Mechanism | Accounts of Chemical Research. Acc Chem Res 37(9):719–725. https://doi.org/10.1021/ar0301781 Fontecave M, Ollagnier-de-Choudens S (2008) Iron–Sulfur Cluster Biosynthesis in Bacteria: Mechanisms of Cluster Assembly and Transfer. Arch Biochem Biophys 474(2):226–237. https://doi.org/10.1016/j.abb.2007.12.014 Noodleman L, Norman JG, Osborne JH, Aizman A, Case DA (1985) Models for Ferredoxins: Electronic Structures of Iron-Sulfur Clusters with One, Two, and Four Iron Atoms. J Am Chem Soc 107(12):3418–3426. https://doi.org/10.1021/ja00298a004 Seefeldt LC, Yang Z-Y, Lukoyanov DA, Harris DF, Dean DR, Raugei S, Hoffman BM (2020) Reduction of Substrates by Nitrogenases. Chem Rev 120(12):5082–5106. https://doi.org/10.1021/acs.chemrev.9b00556 Liu J, Chakraborty S, Hosseinzadeh P, Yu Y, Tian S, Petrik I, Bhagi A, Lu Y (2014) Metalloproteins Containing Cytochrome, Iron–Sulfur, or Copper Redox Centers. Chem Rev 114(8):4366–4469. https://doi.org/10.1021/cr400479b Beinert H, Holm RH, Munck E (1997) Iron-Sulfur Clusters: Nature’s Modular, Multipurpose Structures. Science 277:653–659. https://doi.org/10.1126/science.277.5326.653 Noodleman L, Peng CY, Case DA, Mouesca J-M (1995) Orbital Interactions, Electron Delocalization and Spin Coupling in Iron-Sulfur Clusters. Coord Chem Rev 144:199–244. https://doi.org/10.1016/0010-8545(95)07011-L Wang X-B, Niu S, Yang X, Ibrahim SK, Pickett CJ, Ichiye T, Wang L-S (2003) Probing the Intrinsic Electronic Structure of the Cubane [4Fe – 4S] Cluster: Nature’s Favorite Cluster for Electron Transfer and Storage. J Am Chem Soc 125(46):14072–14081. https://doi.org/10.1021/ja036831x Jafari S, Tavares Santos YA, Bergmann J, Irani M, Ryde U (2022) Benchmark Study of Redox Potential Calculations for Iron–Sulfur Clusters in Proteins. Inorg Chem 61(16):5991–6007. https://doi.org/10.1021/acs.inorgchem.1c03422 Min J, Ali F, Brooks BR, Bruce BD, Amin M (2025) Predicting Iron–Sulfur Cluster Redox Potentials: A Simple Model Derived from Protein Structures. ACS Omega 10(15):15790–15798. https://doi.org/10.1021/acsomega.5c01976 Dereli B, Baer MD, Peters JW, Raugei S (2025) The Properties That Allow Tuning the Reduction Potentials over a Volt Range in Biological Iron/Sulfur Clusters. J Phys Chem Lett 16(19):4602–4606. https://doi.org/10.1021/acs.jpclett.5c00616 Bruska MK, Stiebritz MT, Reiher M (2011) Regioselectivity of H Cluster Oxidation. J Am Chem Soc 133(50):20588–20603. https://doi.org/10.1021/ja209165r Burley SK, Bhatt R, Bhikadiya C, Bi C, Biester A, Biswas P, Bittrich S, Blaumann S, Brown R, Chao H, Chithari VR, Craig PA, Crichlow GV, Duarte JM, Dutta S, Feng Z, Flatt JW, Ghosh S, Goodsell DS, Green RK, Guranovic V, Henry J, Hudson BP, Joy M, Kaelber JT, Khokhriakov I, Lai J-S, Lawson CL, Liang Y, Myers-Turnbull D, Peisach E, Persikova I, Piehl DW, Pingale A, Rose Y, Sagendorf J, Sali A, Segura J, Sekharan M, Shao C, Smith J, Trumbull M, Vallat B, Voigt M, Webb B, Whetstone S, Wu-Wu A, Xing T, Young JY, Zalevsky A, Zardecki C (2025) Updated Resources for Exploring Experimentally-Determined PDB Structures and Computed Structure Models at the RCSB Protein Data Bank. Nucleic Acids Res 53(D1):D564–D574. https://doi.org/10.1093/nar/gkae1091 Eltis LD, Iwagami SG, Smith M (1994) Hyperexpression of a Synthetic Gene Encoding a High Potential Iron Sulfur Protein. Protein Eng 7(9):1145–1150. https://doi.org/10.1093/protein/7.9.1145 Takeda K, Kusumoto K, Hirano Y, Miki K (2010) Detailed Assessment of X-Ray Induced Structural Perturbation in a Crystalline State Protein. J Struct Biol 169(2):135–144. https://doi.org/10.1016/j.jsb.2009.09.012 Cowan JA, Lui SM (1998) Structure-Function Correlations in High-Potential IRON Proteins. Adv Inorg Chem 45:313–350. https://doi.org/10.1016/S0898-8838(08)60028-8 Hatchikian EC, Cammack R, Patil DS, Robinson AE, Richards AJM, George S, Thomson AJ (1984) Spectroscopic Characterization of Ferredoxins I and II from Desulfovibrio Africanus . Biochim Biophys Acta BBA - Protein Struct Mol Enzymol 784(1):40–47. https://doi.org/10.1016/0167-4838(84)90170-5 Iismaa SE, Vázquez AE, Jensen GM, Stephens PJ, Butt JN, Armstrong FA, Burgess BK (1991) Site-Directed Mutagenesis of Azotobacter Vinelandii Ferredoxin I. Changes in [4Fe-4S] Cluster Reduction Potential and Reactivity. J Biol Chem 266(32):21563–21571. https://doi.org/10.1016/S0021-9258(18)54675-5 Tan M-L, Perrin BS Jr., Niu S, Huang Q, Ichiye T (2016) Protein Dynamics and the All-Ferrous [Fe4S4] Cluster in the Nitrogenase Iron Protein. Protein Sci 25(1):12–18. https://doi.org/10.1002/pro.2772 Jolliffe IT, Cadima J (2016) Principal Component Analysis: A Review and Recent Developments. Philos Trans A 354:20150202. http://dx.doi.org/10.1098/rsta.2015.0202 Neese F, The ORCAP, System (2012) WIREs Comput Mol Sci 2(1):73–78. https://doi.org/10.1002/wcms.81 Torres RA, Lovell T, Noodleman L, Case DA (2003) Density Functional and Reduction Potential Calculations of Fe4S4 Clusters. J Am Chem Soc 125(7):1923–1936. https://doi.org/10.1021/ja0211104 Blank MA, Lee CC, Hu Y, Hodgson KO, Hedman B, Ribbe MW (2011) Structural Models of the [Fe4S4] Clusters of Homologous Nitrogenase Fe Proteins. Inorg Chem 50(15):7123–7128. https://doi.org/10.1021/ic200636k Venkateswara Rao P, Holm RH (2004) Synthetic Analogues of the Active Sites of Iron – Sulfur Proteins. Chem Rev 104(2):527–560. https://doi.org/10.1021/cr020615+ Noodleman L, Case DA, Aizman (1988) Arie. Broken Symmetry Analysis of Spin Coupling in Iron-Sulfur Clusters. J Am Chem Soc 110(4):1001–1005. https://doi.org/10.1021/ja00212a003 Noodleman L, Case DA (1992) Density-Functional Theory of Spin Polarization and Spin Coupling in Iron—Sulfur Clusters. Adv Inorg Chem 38:423–470. https://doi.org/10.1016/S0898-8838(08)60070-7 Caldeweyher E, Ehlert S, Hansen A, Neugebauer H, Spicher S, Bannwarth C, Grimme SA (2019) Generally Applicable Atomic-Charge Dependent London Dispersion Correction. J Chem Phys 150(15):154122. https://doi.org/10.1063/1.5090222 Caldeweyher E, Bannwarth C, Grimme S (2017) Extension of the D3 Dispersion Coefficient Model. J Chem Phys 147(3):034112. https://doi.org/10.1063/1.4993215 Gray M, Herbert JM (2022) Comprehensive Basis-Set Testing of Extended Symmetry-Adapted Perturbation Theory and Assessment of Mixed-Basis Combinations to Reduce Cost. J Chem Theory Comput 18(4):2308–2330. https://doi.org/10.1021/acs.jctc.1c01302 Becke AD (1988) Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys Rev A 38(6):3098–3100. https://doi.org/10.1103/PhysRevA.38.3098 Perdew JP, Yue W (1986) Accurate and Simple Density Functional for the Electronic Exchange Energy: Generalized Gradient Approximation. Phys Rev B 33(12):8800–8802. https://doi.org/10.1103/PhysRevB.33.8800 Perdew JP, Burke K, Ernzerhof M (1996) Generalized Gradient Approximation Made Simple. Phys Rev Lett 77(18):3865–3868. https://doi.org/10.1103/PhysRevLett.77.3865 Becke AD (1988) Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys Rev A 38(6):3098–3100. https://doi.org/10.1103/PhysRevA.38.3098 Lee C, Yang W, Parr RG (1988) Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys Rev B 37(2):785–789. https://doi.org/10.1103/PhysRevB.37.785 Perdew JP, Constantin LA (2007) Laplacian-Level Density Functionals for the Kinetic Energy Density and Exchange-Correlation Energy. Phys Rev B 75(15):155109. https://doi.org/10.1103/PhysRevB.75.155109 Perdew JP, Ruzsinszky A, Csonka GI, Constantin LA, Sun J (2009) Workhorse Semilocal Density Functional for Condensed Matter Physics and Quantum Chemistry. Phys Rev Lett 103(2):026403. https://doi.org/10.1103/PhysRevLett.103.026403 Furness JW, Kaplan AD, Ning J, Perdew JP, Sun J (2020) Accurate and Numerically Efficient r2SCAN Meta-Generalized Gradient Approximation. J Phys Chem Lett 11(19):8208–8215. https://doi.org/10.1021/acs.jpclett.0c02405 Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J Phys Chem 98(45):11623–11627. https://doi.org/10.1021/j100096a001 Becke AD (1993) Density-functional Thermochemistry. III. The Role of Exact Exchange. J Chem Phys 98(7):5648–5652. https://doi.org/10.1063/1.464913 Vosko SH, Wilk L, Nusair M (1980) Accurate Spin-Dependent Electron Liquid Correlation Energies for Local Spin Density Calculations: A Critical Analysis. Can J Phys 58:1200–1210. https://doi.org/10.1139/p80-159 Adamo C, Barone V (1999) Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J Chem Phys 110(13):6158–6170. https://doi.org/10.1063/1.478522 Staroverov VN, Scuseria GE, Tao J, Perdew JP (2003) Comparative Assessment of a New Nonempirical Density Functional: Molecules and Hydrogen-Bonded Complexes. J Chem Phys 119(23):12129–12137. https://doi.org/10.1063/1.1626543 Bursch M, Neugebauer H, Ehlert S, Grimme S (2022) Dispersion Corrected r2SCAN Based Global Hybrid Functionals: r2SCANh, r2SCAN0, and r2SCAN50. J Chem Phys 156(13):134105. https://doi.org/10.1063/5.0086040 Yanai T, Tew DP, Handy NC (2004) A New Hybrid Exchange–Correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP). Chem Phys Lett 393(1):51–57. https://doi.org/10.1016/j.cplett.2004.06.011 Chu S, Bovi D, Cappelluti F, Orellana AG, Martin H, Guidoni L (2017) Effects of Static Correlation between Spin Centers in Multicenter Transition Metal Complexes. J Chem Theory Comput 13(10):4675–4683. https://doi.org/10.1021/acs.jctc.7b00316 Tzeli D, Golub P, Brabec J, Matoušek M, Pernal K, Veis L, Raugei S, Xantheas SS (2024) Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe–2S] Systems: A Benchmark Study of the [Fe2S2(SCH3)4]2–,3–,4–, [Fe2S2(SCys)4]2–, [Fe2S2(S-p-Tol)4]2–, and [Fe2S2(S-o-Xyl)4]2– Complexes. J. Chem. Theory Comput. 20 (23), 10406–10423. https://doi.org/10.1021/acs.jctc.4c00781 Sharma S, Sivalingam K, Neese F, Chan GK-L (2014) Low-Energy Spectrum of Iron–Sulfur Clusters Directly from Many-Particle Quantum Mechanics. Nat Chem 6(10):927–933. https://doi.org/10.1038/nchem.2041 Mejuto-Zaera C, Tzeli D, Williams-Young D, Tubman NM, Matoušek M, Brabec J, Veis L, Xantheas SS, de Jong WA (2022) The Effect of Geometry, Spin, and Orbital Optimization in Achieving Accurate, Correlated Results for Iron–Sulfur Cubanes. J Chem Theory Comput 18(2):687–702. https://doi.org/10.1021/acs.jctc.1c00830 Tzeli D, Raugei S, Xantheas SS (2021) Quantitative Account of the Bonding Properties of a Rubredoxin Model Complex [Fe(SCH3)4]q, q = – 2, – 1, +2, + 3. J Chem Theory Comput 17(10):6080–6091. https://doi.org/10.1021/acs.jctc.1c00485 Mouesca J-M, Noodleman L, Case DA, Lamotte B (1995) Spin Densities and Spin Coupling in Iron-Sulfur Clusters: A New Analysis of Hyperfine Coupling Constants. Inorg Chem 34(17):4347–4359. https://doi.org/10.1021/ic00121a013 Noodleman L (1991) Exchange Coupling and Resonance Delocalization in Reduced Iron-Sulfur [Fe4S4] + and Iron-Selenium [Fe4Se4] + Clusters. 1. Basic Theory of Spin-State Energies and EPR and Hyperfine Properties. Inorg Chem 30(2):246–256. https://doi.org/10.1021/ic00002a019 Mouesca J-M, Chen JL, Noodleman L, Bashford D, Case DA (1994) Density Functional/Poisson-Boltzmann Calculations of Redox Potentials for Iron-Sulfur Clusters. J Am Chem Soc 116(26):11898–11914. https://doi.org/10.1021/ja00105a033 Gaughan SJH, Hirst JD, Croft AK, Jäger CM (2022) Effect of Oriented Electric Fields on Biologically Relevant Iron–Sulfur Clusters: Tuning Redox Reactivity for Catalysis. J Chem Inf Model 62(3):591–601. https://doi.org/10.1021/acs.jcim.1c00791 Li L, Li C, Zhang Z, Alexov E (2013) On the Dielectric Constant of Proteins: Smooth Dielectric Function for Macromolecular Modeling and Its Implementation in DelPhi. J Chem Theory Comput 9(4):2126–2136. https://doi.org/10.1021/ct400065j Cascella M, Magistrato A, Tavernelli I, Carloni P, Rothlisberger U (2006) Role of Protein Frame and Solvent for the Redox Properties of Azurin from Pseudomonas Aeruginosa. Proc. Natl. Acad. Sci. 103 (52), 19641–19646. https://doi.org/10.1073/pnas.0607890103 Sulpizi M, Raugei S, VandeVondele J, Carloni P, Sprik M (2007) Calculation of Redox Properties: Understanding Short- and Long-Range Effects in Rubredoxin. J Phys Chem B 111(15):3969–3976. https://doi.org/10.1021/jp067387y George A, Bilbao A, Agarwal K, Mejia-Rodriguez D, Samantray S, Kim H, Rice PS, Jacob B, Baer M, Raugei S, Cheung MS, Rigor P ADEPT: A Pedagogical Framework for Integrating Agentic AI with Deterministic Scientific Workflows Additional Declarations No competing interests reported. Supplementary Files riceSI20251107.pdf Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 10 Feb, 2026 Reviews received at journal 02 Feb, 2026 Reviews received at journal 30 Jan, 2026 Reviewers agreed at journal 22 Jan, 2026 Reviewers agreed at journal 22 Jan, 2026 Reviewers invited by journal 09 Jan, 2026 Editor assigned by journal 12 Nov, 2025 Submission checks completed at journal 12 Nov, 2025 First submitted to journal 07 Nov, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8059723","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":573166207,"identity":"08736c3a-5693-450d-b86d-4f7af4fdb8ea","order_by":0,"name":"Peter S. Rice","email":"","orcid":"","institution":"Pacific Northwest National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Peter","middleName":"S.","lastName":"Rice","suffix":""},{"id":573166219,"identity":"0dd691d7-07e7-4329-b1a3-04253c712acb","order_by":1,"name":"Bruno Jacob","email":"","orcid":"","institution":"Pacific Northwest National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Bruno","middleName":"","lastName":"Jacob","suffix":""},{"id":573166225,"identity":"3a2f184e-2f54-4b24-af0f-fff9732b4710","order_by":2,"name":"Khushbu Agarwal","email":"","orcid":"","institution":"Pacific Northwest National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Khushbu","middleName":"","lastName":"Agarwal","suffix":""},{"id":573166227,"identity":"14d1ad9a-d403-47e1-baa8-5ee6bfce7532","order_by":3,"name":"Marcel D. Baer","email":"","orcid":"","institution":"Pacific Northwest National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Marcel","middleName":"D.","lastName":"Baer","suffix":""},{"id":573166229,"identity":"e5e6d9f6-584a-4c20-9cdb-17e6fb85e7ac","order_by":4,"name":"Simone Raugei","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8UlEQVRIiWNgGAWjYDACZmROQgWQYCdNyxl0EYKAsY0ILfLt3ImPCyoY8vlnpF988HDenTxzZgbmFx/bcGsxOMy72XjGGQbLGTdyig0Stz0rtmxmYLOciU8LM+82ad42BgOGGzlpEonbDiduOMzAZsxzBo/DmkFa/jEYyN/ISf+ROIcILQyHQVoaGAwMbqQfY0hsAGthfsxTQcAvPMckDAzPvGGWSDj2DKiFsY1xBh4t8v1nNz7mqbExkDue/vDjj5o7iRuONx/+8MEAj8MgQAKIeUDKDjCAYkeCoAYIYH8A1cLA/IFILaNgFIyCUTAyAADznlHveAH8TQAAAABJRU5ErkJggg==","orcid":"","institution":"Pacific Northwest National Laboratory","correspondingAuthor":true,"prefix":"","firstName":"Simone","middleName":"","lastName":"Raugei","suffix":""}],"badges":[],"createdAt":"2025-11-07 19:08:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8059723/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8059723/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100147608,"identity":"87ddb9da-dbc2-460e-a9b4-aff2b017ba3a","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2086349,"visible":true,"origin":"","legend":"","description":"","filename":"rice20251111.docx","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/eeb233ac8121c098d1b29588.docx"},{"id":100368735,"identity":"78fbcba2-967f-4ebf-8728-6f15b832d183","added_by":"auto","created_at":"2026-01-16 07:58:18","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":6011,"visible":true,"origin":"","legend":"","description":"","filename":"9189693c39164be39ce06f3b24802953.json","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/207981bcb24dfdc8e786a1b4.json"},{"id":100147611,"identity":"b5e8f6bc-9713-4cd6-8328-1428f1130e32","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":282750,"visible":true,"origin":"","legend":"","description":"","filename":"riceSI20251107.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/1cd8237410529787783574b2.pdf"},{"id":100367940,"identity":"4cf42567-62da-46e5-aa38-71197ea51a8f","added_by":"auto","created_at":"2026-01-16 07:57:28","extension":"xml","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":155576,"visible":true,"origin":"","legend":"","description":"","filename":"9189693c39164be39ce06f3b248029531enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/054e2ae0a71dcf795a8fd3fe.xml"},{"id":100147616,"identity":"55a9b020-f446-4221-9c94-85da515b9249","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"jpeg","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":605792,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/bfb9b51f771025bcf57a7b36.jpeg"},{"id":100147624,"identity":"2aa89ba0-3a84-466a-aa0d-dad9febc36b8","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"jpeg","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1595009,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/ef5d39561d92cfc25ca54540.jpeg"},{"id":100147613,"identity":"5bbb7142-2cf2-43f3-ac6a-4e15638017fd","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"emf","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1232916,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage3.emf","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/4329a8c9382789c75567b984.emf"},{"id":100367585,"identity":"ac6ee621-feaf-46d3-a465-d29c7446ac24","added_by":"auto","created_at":"2026-01-16 07:57:08","extension":"jpeg","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":397696,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/163725d2bb0d9fc5439e4c2e.jpeg"},{"id":100367592,"identity":"fd1f7b1c-e5b0-46c3-9d5f-02c72c46441f","added_by":"auto","created_at":"2026-01-16 07:57:08","extension":"jpeg","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":412883,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/484b81897c038e30ba963fdc.jpeg"},{"id":100367658,"identity":"d90c0164-57fc-4026-8010-5e496150bc7f","added_by":"auto","created_at":"2026-01-16 07:57:13","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":110023,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/0c34e753b766918a8a113a7e.png"},{"id":100147620,"identity":"e2f7cd49-2457-4162-a3e3-bfee09fbdf06","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"png","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":209304,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/3c5d67dd48c2232838726546.png"},{"id":100368027,"identity":"e2bd63d8-da1f-4c42-bda8-0b55f88d2a54","added_by":"auto","created_at":"2026-01-16 07:57:31","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":9994,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/08146bc35ad448328c116ad5.png"},{"id":100147623,"identity":"a4b11897-427f-4315-8d66-f2f6d6aa4e05","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"png","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":93985,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/bfa3865d3118760c11c2fc24.png"},{"id":100367986,"identity":"38082c50-6449-4d20-b370-520c2f35a0df","added_by":"auto","created_at":"2026-01-16 07:57:30","extension":"png","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":119922,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/98d6044b7dfc89d9607c98e8.png"},{"id":100147618,"identity":"fac76b6a-50e9-43cb-92e3-0c9a7fcc4a34","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"xml","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":152628,"visible":true,"origin":"","legend":"","description":"","filename":"9189693c39164be39ce06f3b248029531structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/000467f8c468fb244c473ea9.xml"},{"id":100147621,"identity":"f7191fe5-7bc8-4b84-b296-5e66c878c618","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"html","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":167977,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/c8baa9fbecc83c61a388812c.html"},{"id":100147604,"identity":"c3a1c9ae-5664-44ee-be09-5112e596bf1d","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":249565,"visible":true,"origin":"","legend":"\u003cp\u003eBS-DFT optimized geometries of the most probable cysteine ligand configurations of [Fe\u003csub\u003e4\u003c/sub\u003eS\u003csub\u003e4\u003c/sub\u003e] clusters in the oxidized state. Initial structures were extracted from a statistical analysis of 1049 redox proteins taken from the PDB files.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/65c02804dc91e838fdd85879.png"},{"id":100147603,"identity":"ddba2c87-48b7-4459-913b-9302f0838bf0","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":127727,"visible":true,"origin":"","legend":"\u003cp\u003eViolin plot showing the calculated Adiabatic Electron Affinity (AEA\u003csub\u003eZPE\u003c/sub\u003e) for each of the five ferredoxin [4Fe-4S] clusters with commonly used exchange-correlation functionals (E\u003csub\u003eXC\u003c/sub\u003e). Violins with a larger vertical span have more variation between clusters. The violin thickness is related to the probability density (i.e., where AEA\u003csub\u003eZPE\u003c/sub\u003e values cluster), the wider the violin, the more points near that energy. White diamond markers with a black outline indicate the median AEA\u003csub\u003eZPE\u003c/sub\u003e for that functional. The dashed line at the median highlights the trend between various functional families. The color shading indicates functional families. These calculations include zero-point vibrational energy (ZPE) and van der Waals corrections. The raw data are shown in Table S1 (Supporting Information).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/985bb4be99028f5f3aff14e1.png"},{"id":100147605,"identity":"672427d8-659b-48f2-aa71-8de9dddfefbd","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":159702,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Extended broken symmetry DFT spin ladder for each of the five oxidized [4Fe-4S] clusters. (b) calculated stabilization energy for each oxidized cluster in the low-spin ground state (\u003cem\u003eS \u003c/em\u003e= 0). (c) Extended broken symmetry DFT spin ladder for each of the five reduced [4Fe-4S] clusters. in the low-spin two-layer model ground state (\u003cem\u003eS=1\u003c/em\u003e). (d) calculated stabilization energy for each reduced cluster. The number of Fe 3d-electrons and the unpaired d-electrons (UPE) is assigned to each of the four iron ion centers used in the construction of the model. The colors correspond to the clusters from Figure 1.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/4d9e250798839a9cdc7b03a7.png"},{"id":100147610,"identity":"1d05f1b5-0eb0-49d1-ac4f-c12ab518f783","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":223041,"visible":true,"origin":"","legend":"\u003cp\u003eAdiabatic electron affinity (AEA\u003csub\u003eZPE\u003c/sub\u003e) calculated as a function of the universal solvation model dielectric constant (\u003cem\u003eε\u003c/em\u003e) with both (a) broken-symmetry DFT and (b) extended broken symmetry DFT. (c) Difference in AEA\u003csub\u003eZPE\u003c/sub\u003e between EBS-DFT and BS-DFT for each cluster. (d) Plot showing the difference between clusters with the maximum and minimum AEA\u003csub\u003eZPE\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/00b689b0735e123c804934a6.png"},{"id":100147607,"identity":"ff7785e0-5d6b-430b-a1bb-e1aed8be0b0a","added_by":"auto","created_at":"2026-01-13 12:43:00","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":222361,"visible":true,"origin":"","legend":"\u003cp\u003e(a) The structure of the SPC/E water droplet structure taken after a 100 ns NVT molecular dynamics simulation, consisting of up to 5953 (\u003cem\u003er\u003c/em\u003e\u003csub\u003ecutoff\u003c/sub\u003e = 35 Å) water molecules with the \u003cem\u003eD\u003c/em\u003e\u003csub\u003e2d\u003c/sub\u003e-cluster 4 in the center. (b) Models used to systematically explore the influence of water on the vertical electron affinity (VEA). (c) Calculated VEA of the [4Fe-4S] cluster in water using: (i) QM DFT with all water molecules treated at the QM level; (ii) QM/MM with all water molecules treated as MM point charges; (iii) QM/MM with a growing subset of water molecules included in the QM region (\u0026gt; QM H\u003csub\u003e2\u003c/sub\u003eO); (iv) QM with implicit solvent (SMD, \u003cem\u003eε\u003c/em\u003e = 78); and (v) QM/MM with CPCM implicit solvent and an increasing number of QM water molecules (QM/MM + CPCM, \u0026gt; QM H\u003csub\u003e2\u003c/sub\u003eO).\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/645b28343441037f139550e4.png"},{"id":100382465,"identity":"78af29e2-ef82-49bc-b730-c2bf5241fdba","added_by":"auto","created_at":"2026-01-16 10:42:42","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1707307,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/726d4e48-3b6e-4b11-9742-07012e34950c.pdf"},{"id":100367682,"identity":"cd8319f0-da6e-4cd0-9448-280de9ed5b07","added_by":"auto","created_at":"2026-01-16 07:57:13","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":282750,"visible":true,"origin":"","legend":"","description":"","filename":"riceSI20251107.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8059723/v1/9e40888bcca4d804b30ceccb.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Geometry, Spin Coupling, and Dielectric Control of Redox Potentials in [4Fe–4S] Clusters","fulltext":[{"header":"Introduction","content":"\u003cp\u003eIron-sulfur (Fe-S) clusters are among the most ancient and versatile cofactors in biology,\u003csup\u003e1\u003c/sup\u003e supporting an extraordinary range of redox processes that underpin life itself. Their emergence is thought to predate enzymatic catalysis, with mineral Fe-S motifs likely serving as primitive electron mediators in early metabolic networks. Indeed, the chemical environment of alkaline hydrothermal vents (rich in Fe\u003csup\u003e2+\u003c/sup\u003e, sulfide, and CO\u003csub\u003e2\u003c/sub\u003e) has been hypothesized to provide ideal conditions for the self-assembly of such clusters, fostering the first energy-converting reactions at the origin of life.\u003csup\u003e\u003cspan additionalcitationids=\"CR3\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eOver billions of years of evolution, nature has retained and refined these motifs within proteins, embedding them in scaffolds that exquisitely tune their electronic properties. Fe-S clusters now appear in an enormous variety of biological contexts, from simple electron carriers such as rubredoxins and ferredoxins to complex catalytic centers such as the FeMo-cofactor of nitrogenase.\u003csup\u003e\u003cspan additionalcitationids=\"CR6\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e Among these, the cubane-type [4Fe-4S] cluster stands out as a paradigmatic redox module, mediating single-electron transfers over a potential range exceeding 1 V while maintaining a common inorganic core. This remarkable tunability arises from the interplay between intrinsic cluster geometry and the surrounding protein environment, including the nature of cysteine ligation, local hydrogen-bond networks, and long-range electrostatics.\u003csup\u003e\u003cspan additionalcitationids=\"CR9 CR10 CR11 CR12 CR13\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eDespite decades of structural, spectroscopic, and electrochemical investigations, a quantitative understanding of how these environmental factors modulate the redox potential of [4Fe-4S] clusters remains incomplete. Experimentally, potentials vary from approximately\u0026thinsp;+\u0026thinsp;0.40 V to -0.80 V vs. SHE across different proteins (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), suggesting that subtle geometric and electrostatic effects can dramatically shift the thermodynamics of electron transfer. However, disentangling the contributions from cluster distortions, spin coupling, and environmental polarization remains a formidable challenge for both theory and experiment.\u003c/p\u003e \u003cp\u003eTo address this question, we combine statistical analysis of Protein Data Bank\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e (PDB) structures with broken-symmetry and extended broken-symmetry density functional theory (BS-DFT and EBS-DFT). Our approach isolates the effect of ligand orientation and local dielectric screening on the redox energetics of representative [4Fe-4S] cores. By comparing more than one thousand unique cysteine-ligated clusters, we identify five dominant geometrical motifs and evaluate their adiabatic electron affinities using a wide range of exchange-correlation functionals. We further employ the Heisenberg\u0026ndash;Dirac\u0026ndash;van Vleck (HDvV) Hamiltonian framework to assess spin-coupling effects, providing a rigorous treatment of exchange interactions often neglected in single-determinant DFT. In doing so, we aim to quantify how much of the redox potential variability can be ascribed to intrinsic geometric differences versus environmental screening and electronic correlation. Our results contribute to this enduring question by providing computational insight into how local coordination and the dielectric environment collectively shape the bio-electrochemical behavior of Fe-S clusters.\u003c/p\u003e \u003cp\u003eThe remainder of this paper is organized as follows. We first describe the statistical analysis of Protein Data Bank structures used to identify representative cysteine-ligation motifs in ferredoxin-type [4Fe-4S] clusters. These geometries form the basis for a systematic series of broken-symmetry and extended broken-symmetry DFT (BS-DFT and EBS-DFT) calculations designed to quantify the influence of ligand orientation, exchange coupling, and electronic correlation on redox energetics. We then examine solvation and dielectric effects using both continuum and explicit models to assess the relative importance of environmental screening. Finally, we integrate these results to determine the extent to which geometry, electronic correlation, and electrostatics collectively modulate the redox properties of biological Fe-S clusters, drawing connections to experimental trends and to design principles underlying bio-inspired redox catalysts.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRedox properties of a select few bacteria containing [4Fe-4S] clusters, highlighting the large variation of E0.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOrganism\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eE\u003c/em\u003e\u0026deg; (V)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eA. vinosum\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e+\u0026thinsp;0.355\u003csup\u003e16\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eT. tepidum\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e+\u0026thinsp;0.323\u003csup\u003e17\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eB. thermoproteolyticus\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u0026ndash;0.280\u003csup\u003e18\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eD. africanus\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u0026ndash;0.385\u003csup\u003e19\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eA. vinelandii\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u0026ndash;0.650\u003csup\u003e20\u003c/sup\u003e, -0.790\u003csup\u003e21\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"Computational Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eDataset curation and structural clustering\u003c/h2\u003e \u003cp\u003eWe queried the Protein Data Bank (PDB) for proteins containing [4Fe-4S] clusters ligated by four cysteine residues. From more than 2000 entries, 1049 unique, non-redundant clusters were retained after removing mutants and duplicate proteins. Five recurrent ligand-orientation motifs were identified (Fig.\u0026nbsp;1); three dominate the population and cleanly separate in principal-component space\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e (Clusters 1, 2, and 4). These motifs occur broadly across oxidoreductases (\u003cem\u003ee.g.\u003c/em\u003e, ferredoxins, dehydrogenases, dehalogenases, sulfite/nitrate reductases).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAll broken-symmetry density-functional theory (BS-DFT) calculations were performed with ORCA 6.0\u003csup\u003e23\u003c/sup\u003e. To focus on primary coordination effects, the cysteine ligands (Fe-SCH\u003csub\u003e2\u003c/sub\u003e-R) were modeled as methyl thiolates (CH\u003csub\u003e3\u003c/sub\u003eS\u003csup\u003e\u0026minus;\u003c/sup\u003e).\u003csup\u003e24\u0026ndash;26\u003c/sup\u003e Oxidized [4Fe-4S]\u003csup\u003e2+\u003c/sup\u003e (\u003cem\u003eS\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0) and reduced [4Fe-4S]\u003csup\u003e+\u003c/sup\u003e (\u003cem\u003eS\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1) states were considered. For [4Fe-4S] \u003csup\u003e2+\u003c/sup\u003e, all relevant BS solutions were examined using a two-layer picture with ferromagnetically coupled Fe pairs within each [2Fe-2S] sublayer and antiferromagnetic coupling between sublayers.\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e Dispersion was included using Grimme\u0026rsquo;s D4 scheme,\u003csup\u003e29,30\u003c/sup\u003e and the ma-def2-TZVP\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e basis (with diffuse functions) was used for all atoms. Geometries taken from the statistical analysis of PDB structures were initially optimized with BP86\u003csup\u003e32\u003c/sup\u003e, with further geometry and energy refinements surveyed with a representative set of LDA/GGA/meta-GGA/hybrid and range-separated functionals (PWLDA\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e, BP86\u003csup\u003e32\u003c/sup\u003e, PBE\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e, BLYP\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e,\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e, TPSS\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e, revTPSS\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e, r2SCAN\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e, B3LYP (20% HF)\u003csup\u003e36,40\u0026ndash;42\u003c/sup\u003e, PBE0 (25% HF)\u003csup\u003e43\u003c/sup\u003e, TPSSh (10% HF)\u003csup\u003e44\u003c/sup\u003e, TPSS0 (25% HF)\u003csup\u003e44\u003c/sup\u003e, r\u003csup\u003e2\u003c/sup\u003eSCANh (10% HF)\u003csup\u003e45\u003c/sup\u003e and CAM-B3LYP\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e). Harmonic frequency analysis verified minima and provided zero-point vibrational energy (ZPE) corrections.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eRedox metrics: adiabatic and vertical electron affinities\u003c/h3\u003e\n\u003cp\u003eWe report adiabatic electron affinities with ZPE (AEA\u003csub\u003eZPE\u003c/sub\u003e) by optimizing both oxidation states and adding ZPE terms:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\text{Ox}+{e}^{-}\\to\\:\\text{Red},\\:{\\:\\text{A}\\text{E}\\text{A}}_{\\text{Z}\\text{P}\\text{E}}=\\left(E\\right(\\text{O}\\text{x})+\\text{Z}\\text{P}\\text{E}(\\text{O}\\text{x}\\left)\\right)-\\left(E\\right(\\text{R}\\text{e}\\text{d})+\\text{Z}\\text{P}\\text{E}(\\text{R}\\text{e}\\text{d}).$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe results are summarized in \u003cb\u003eFig.\u0026nbsp;2\u003c/b\u003e and \u003cb\u003eTable \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/b\u003e (Supporting Information). In the final section, we also evaluated the vertical electron affinities (VEA).\u003c/p\u003e\n\u003ch3\u003eEBS-DFT and Heisenberg–Dirac–van Vleck (HDvV) Hamiltonian\u003c/h3\u003e\n\u003cp\u003eGiven that BS-DFT is single-determinant in nature, the resulting electronic states are not true spin eigenfunctions but linear combinations of determinants with different \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003eS\u003c/em\u003e\u003c/sub\u003e projections (\u003cem\u003ee.g.\u003c/em\u003e, mixtures of \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003eS\u003c/em\u003e\u003c/sub\u003e = 1/2 or 0 components). Consequently, the computed energies correspond to spin-contaminated states whose ordering and splitting can deviate from those of the proper pure-spin states. This limitation is particularly significant for low-spin configurations of Fe-S clusters, where near-degeneracy and spin frustration are common.\u003c/p\u003e \u003cp\u003eTo obtain physically meaningful spin energies and exchange couplings, the BS-DFT results were mapped onto a Heisenberg\u0026ndash;Dirac\u0026ndash;van Vleck (HDvV) Hamiltonian using the Extended Broken-Symmetry DFT (EBS-DFT) formalism.\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e This procedure reconstructs the spin ladder by comparing the energies of high-spin and broken-symmetry solutions to extract pairwise exchange constants \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{J}_{ij}\\)\u003c/span\u003e\u003c/span\u003e between Fe centers, followed by diagonalization of the Hamiltonian:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:\\widehat{H}=-2\\sum\\:_{i\u0026lt;j}{J}_{ij}{\\widehat{s}}_{i}\\bullet\\:{\\widehat{s}}_{j}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{s}}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the spin operator on the spin site \u003cem\u003ei\u003c/em\u003e, yielding spin eigenstates and total-spin energies consistent with a multideterminant description.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eContinuum solvation: dielectric-response scans\u003c/h3\u003e\n\u003cp\u003eEnvironmental screening was modeled using the SMD continuum, scanning dielectric constants from \u003cem\u003ee\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1 (vacuum) to \u003cem\u003ee\u003c/em\u003e\u0026thinsp;=\u0026thinsp;80 (\u0026sim;water). Both BS-DFT and EBS-DFT show rapid AEA\u003csub\u003eZPE\u003c/sub\u003e stabilization at low \u003cem\u003ee\u003c/em\u003e, approaching a plateau near \u003cem\u003ee\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;15, consistent with protein-like interiors; the across-cluster spread remains small (~\u0026thinsp;0.1 eV) relative to solvent shifts.\u003c/p\u003e\n\u003ch3\u003eExplicit solvation and hybrid QM/MM protocols\u003c/h3\u003e\n\u003cp\u003eTo capture first-shell specificity, we constructed an SPC/E water droplet (up to 5953 water molecules) and equilibrated it for 100 ns in the canonical (NVT) ensemble, with the \u003cem\u003eD\u003c/em\u003e\u003csub\u003e2d\u003c/sub\u003e-like Cluster 4 at the center. We evaluated VEA using: (i) all-QM water (QM is calculated at the BP86-D4/ma-def2-TZVP level of theory), (ii) hybrid QM/MM with waters as point charges, (iii) QM/MM(+\u0026thinsp;QM H\u003csub\u003e2\u003c/sub\u003eO) by progressively promoting waters within radial cutoffs (3\u0026ndash;15 \u0026Aring;) into the QM region, (iv) QM\u0026thinsp;+\u0026thinsp;SMD (\u003cem\u003ee\u003c/em\u003e\u0026thinsp;=\u0026thinsp;78), and (v) QM/MM\u0026thinsp;+\u0026thinsp;CPCM(+\u0026thinsp;QM H\u003csub\u003e2\u003c/sub\u003eO) hybrid treatments.\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eOverview\u003c/h2\u003e \u003cp\u003eThe electronic structure and redox properties of [4Fe-4S] clusters were examined using the five representative ligand configurations derived from statistical analysis of ferredoxin-type proteins. For each configuration, BS-DFT and EBS-DFT calculations were performed in both oxidized ([4Fe-4S]\u003csup\u003e2+\u003c/sup\u003e, \u003cem\u003eS\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0) and reduced ([4Fe\u0026ndash;4S]\u003csup\u003e+\u003c/sup\u003e, \u003cem\u003eS\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1) states. The adiabatic electron affinities with zero-point correction (AEA\u003csub\u003eZPE\u003c/sub\u003e) were computed using a range of exchange-correlation functionals, and additional dielectric and solvation models were used to probe environmental screening effects.\u003c/p\u003e \u003cp\u003eThis multi-tiered approach allows for a systematic comparison of how intrinsic geometric features, spin coupling, and medium polarization collectively modulate the redox thermodynamics of Fe-S clusters.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eStructural Diversity in Biological [4Fe-4S] Clusters\u003c/h3\u003e\n\u003cp\u003eA comprehensive survey of the Protein Data Bank identified more than two thousand Fe-S-containing proteins, of which 1049 unique [4Fe-4S] cores were selected after removing redundant and mutant entries. Principal component analysis (PCA) of the cysteine-ligation vectors revealed five distinct geometric motifs, differing primarily in the orientation of the C\u0026ndash;S\u0026ndash;Fe bonds relative to the cubane core (Fig.\u0026nbsp;1). Among these, three configurations account for the majority of observed structures and correspond to ligand orientations that recur across diverse enzyme families, including ferredoxins, dehydrogenases, and reductases.\u003c/p\u003e \u003cp\u003eDespite subtle geometric differences, all clusters preserve the [4Fe-4S] cubane core framework with average Fe\u0026ndash;Fe distances of 2.70\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05 \u0026Aring; and Fe-S distances of 2.28\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03 \u0026Aring;. Variations in cysteine orientation primarily affect the outer-sphere topology and, consequently, the directionality of potential hydrogen-bond networks and local electrostatics. These structural descriptors, therefore, provide a physically grounded set of models for assessing the effects of geometry on intrinsic redox energetics.\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eProbing the influence of the ligation environment with BS-DFT\u003c/h2\u003e \u003cp\u003eThe electronic structure of [4Fe-4S] clusters is characterized by the presence of Fe(II) and Fe(III) ions that are anti-ferromagnetically coupled through bonding to S\u003csup\u003e2\u0026minus;\u003c/sup\u003e ions. Broken-symmetry DFT (BS-DFT) is widely used to treat these strongly correlated species. To assess how the methyl thiolate ligand orientation influences the redox properties of the five [4Fe-4S] clusters (Fig.\u0026nbsp;1), we have computed the adiabatic electron affinity with zero-point energy corrections (AEA\u003csub\u003eZPE\u003c/sub\u003e) for several commonly used exchange-correlation functionals. From \u003cb\u003eFig.\u0026nbsp;2\u003c/b\u003e, it is found that the absolute AEA\u003csub\u003eZPE\u003c/sub\u003e is highly sensitive to the choice of functional. For any given cluster, the range across the different functionals is calculated to be between 1.19 eV and 1.38 eV (maximum for cluster 4), indicating that functional choice dominates the absolute scale.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eElectronic Structure and Redox Energetics\u003c/h2\u003e \u003cp\u003eBroken-symmetry DFT (BS-DFT) and extended broken-symmetry DFT (EBS-DFT) calculations were performed on each of the five representative ligand configurations to assess how geometric variation and spin coupling affect the intrinsic redox energetics of the [4Fe\u0026ndash;4S]\u003csup\u003e2+/+\u003c/sup\u003e couple. Figure\u0026nbsp;2 and \u003cb\u003eTable \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/b\u003e summarize the computed adiabatic electron affinities with zero-point correction (AEA\u003csub\u003eZPE\u003c/sub\u003e) obtained using a series of exchange-correlation functionals spanning local, semi-local, hybrid, and range-separated levels of theory.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn general, semi-local functionals (LDA/GGA/meta-GGA) yield AEA\u003csub\u003eZPE\u003c/sub\u003e values\u0026thinsp;~\u0026thinsp;0.70 eV more negative than hybrid functionals. This observation is consistent with delocalization/self‑interaction error artificially stabilizing anionic species for semi-local functionals. In contrast, hybrid functionals reduce this stabilization and are known to under-bind excess electrons (reduced states) in systems containing delocalized electrons. In such clusters with strong screening effects, unscreened HF exchange can significantly widen HOMO-LUMO gaps and minimize diffuse charge states.\u003c/p\u003e \u003cp\u003eAcross all functionals, the absolute AEA\u003csub\u003eZPE\u003c/sub\u003e values fall within the range of -3.2 eV / -4.3 eV, consistent with previous gas-phase estimates for cubane-type clusters.\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e The spread (\u0026#120590;) among functionals is substantial (up to about 0.5 eV), reflecting the expected sensitivity to exchange mixing and self-interaction error. In contrast, the geometric dependence is minimal: the variation in AEA\u003csub\u003eZPE\u003c/sub\u003e between the five ligand orientations is less than 0.1 eV. This finding demonstrates that while the cysteine-ligand geometry contributes a measurable but secondary effect, the dominant factors governing the redox energy are the intrinsic Fe-S electronic structure and the broader electrostatic environment. Such modest geometric modulation nevertheless provides a possible mechanism for fine-tuning redox potentials within a protein fold, consistently with the empirical observation that site-specific mutations can induce small but reproducible potential shifts.\u003c/p\u003e \u003cp\u003eThe spin-coupling analysis reinforces this picture, as shown by the calculated spin-ladders for all clusters (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003e). For both oxidation states, all clusters exhibit a low-spin ground state arising from antiferromagnetic coupling between two ferromagnetically aligned [2Fe-2S] subunits.\u003csup\u003e\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e,\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e The energy separation between adjacent spin states follows a linear trend with total spin quantum number \u003cem\u003eS\u003c/em\u003e(\u003cem\u003eS\u003c/em\u003e\u0026thinsp;+\u0026thinsp;1), well described by an isotropic Heisenberg model with the exchange constants of approximately\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003eJ\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e = 193\u0026ndash;208 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and \u0026minus;\u0026thinsp;\u003cem\u003eJ\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e = 109\u0026ndash;113 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e (\u003cb\u003eFigure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/b\u003e), which is within the range of previous literature reports.\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e,\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e,\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e The ratio of these two states, \u003cem\u003eJ\u003c/em\u003e\u003csub\u003eOx\u003c/sub\u003e/\u003cem\u003eJ\u003c/em\u003e\u003csub\u003eRed\u003c/sub\u003e \u0026asymp; 1.71, indicates that the coupling is significantly stronger in the oxidized state than in the reduced state for all clusters,\u003csup\u003e23,51,52\u003c/sup\u003e consistent with greater Fe(III)\u0026ndash;Fe(III) coupling. In the reduced state, the spin levels are closer in energy than in the oxidized state, indicating a smaller spin gap and a weaker effective antiferromagnetic exchange. The small variation of the \u003cem\u003eJ\u003c/em\u003e (\u0026lt;\u0026thinsp;0.002 eV) across the five geometries confirms that local ligand orientation exerts only a minor perturbation on the electronic coupling within the [4Fe-4S] core. These results validate the use of the HDvV framework as an effective phenomenological description of exchange interactions, while highlighting that true spin-state energetics are primarily governed by the delocalized Fe\u0026ndash;S network rather than by any specific Fe\u0026ndash;S\u0026ndash;C orientation.\u003c/p\u003e \u003cp\u003eThe EBS-DFT and BS-DFT are compared in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. As can be seen, the explicit consideration of spin-coupling effects makes the absolute AEA\u003csub\u003eZPE\u003c/sub\u003e more negative (average over all clusters = -4.387 eV) for all clusters relative to BS-DFT (average over all clusters = -4.217 eV).\u003c/p\u003e \u003cp\u003eOverall, the DFT results reveal a clear hierarchy of influences on redox energetics: (1) the choice of exchange\u0026ndash;correlation functional and treatment of electronic correlation have the largest quantitative impact; (2) environmental screening and solvation (addressed below) provide the next-most significant modulation; and (3) ligand geometry contributes a smaller, yet non-negligible, fine-tuning effect within approximately 0.1 V. This hierarchy establishes the baseline for evaluating how the surrounding protein matrix further tunes redox properties through electrostatic polarization and hydrogen-bond interactions.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCalculated adiabatic electron affinity (AEAZPE) calculated using broken symmetry DFT (BS-DFT) and extended broken symmetry DFT (EBS-DFT) for all five [4Fe-4S] clusters using BP86-D4/ma-def2-TZVP.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e \u003cp\u003eAEA\u003csub\u003eZPE\u003c/sub\u003e / eV\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eMethod\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e#1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e#2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e#3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e#4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e#5\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eΔ(Max-Min)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBS-DFT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-4.239\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-4.187\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-4.188\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-4.270\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-4.203\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.082\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEBS-DFT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-4.439\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-4.341\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-4.378\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-4.430\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-4.346\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.098\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eDielectric and Solvation Effects\u003c/h2\u003e \u003cp\u003eTo quantify the influence of environmental polarization on redox energetics, we examined the variation in the adiabatic electron affinity (AEA\u003csub\u003eZPE\u003c/sub\u003e) as a function of the surrounding dielectric constant (\u003cem\u003ee\u003c/em\u003e) using the SMD continuum model, complemented by explicit and hybrid QM/MM simulations. These calculations reveal that the solvent and protein environment play a far more substantial role in modulating the redox properties of [4Fe-4S] clusters than variations in ligand geometry.\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e,\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e,\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eContinuum dielectric response\u003c/h2\u003e \u003cp\u003eIn the continuum SMD model, the AEA\u003csub\u003eZPE\u003c/sub\u003e increases monotonically with \u003cem\u003ee\u003c/em\u003e, reflecting progressive stabilization of the reduced state through dielectric screening. As shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003ea and \u003cb\u003eb\u003c/b\u003e, the AEA\u003csub\u003eZPE\u003c/sub\u003e rises sharply from vacuum (\u003cem\u003ee\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1) to \u003cem\u003ee\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;10\u0026ndash;15, after which it approaches a plateau. This plateau corresponds to the effective dielectric constant of a protein interior (\u003cem\u003ee\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;15), suggesting that most of the environmental polarization responsible for redox tuning originates from the immediate protein shell rather than from bulk solvent. The total stabilization between \u003cem\u003ee\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1 and \u003cem\u003ee\u003c/em\u003e\u0026thinsp;=\u0026thinsp;80 amounts to roughly 0.4 eV \u0026minus;\u0026thinsp;0.5 eV, an order of magnitude larger than the geometry-driven shift discussed above. This stabilization corresponds closely to the 0.4\u0026ndash;0.8 V redox window observed across ferredoxins, suggesting that dielectric screening alone can explain most of the biological tuning range. Thus, electrostatic screening represents the dominant physical lever controlling the thermodynamics of the [4Fe-4S]\u003csup\u003e2+/+\u003c/sup\u003e couple.\u003c/p\u003e \u003cp\u003eThe difference between the two methods is largest for \u003cem\u003ee\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;10 and decreases at higher ε (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003ec\u003cb\u003e)\u003c/b\u003e. This observation can be explained by the fact that BS‑DFT over‑delocalizes the added electron more than EBS‑DFT, generating a more anisotropic charge density distribution. The dielectric interacts differently with these changes in charge density and stabilizes them unevenly across orientations, hence the larger low ε spread for BS‑DFT. Increasing \u003cem\u003ee\u003c/em\u003e effectively screens delocalized charges, while EBS‑DFT already mitigates spurious anion over‑stabilization in vacuum, leaving less for the dielectric to screen.\u003c/p\u003e \u003cp\u003eFrom Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003ed, several interesting observations can be made regarding the response to changes in the dielectric medium. Small increases in \u003cem\u003ee\u003c/em\u003e from vacuum produce disproportionately large stabilization, accentuating differences between orientations with varying effective charge density distributions after reduction. This is one possible explanation why the max-min plots show the largest discrepancy at low \u003cem\u003eε\u003c/em\u003e and then collapse quickly as ε increases. In these plots, the small bump near very low \u003cem\u003ee\u003c/em\u003e for both BS-DFT and EBS-DFT is caused by a crossover in which a given cluster configuration is the most or least stabilized. When two AEA\u003csub\u003eZPE\u003c/sub\u003e curves cross, the max-min develops a local extremum. Across all \u003cem\u003ee\u003c/em\u003e, the cluster orientation ranking is preserved, and the across‑cluster spread remains small (on the order of 0.1 eV), i.e., this is much smaller than the solvent‑induced shift going from vacuum.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eExplicit and hybrid solvation models\u003c/h2\u003e \u003cp\u003eTo capture local hydrogen‑bonding effects beyond a continuum description, we computed the vertical electron affinity (VEA) of the \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e2d\u003c/em\u003e\u003c/sub\u003e‑like [4Fe-4S] cluster (Cluster 4) in an equilibrated SPC/E water droplet, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The VEA values were evaluated using a series of increasingly sophisticated models as a function of an increased water droplet radial cutoff (\u003cem\u003er\u003c/em\u003e\u003csub\u003ecutoff\u003c/sub\u003e): (i) full QM treatment of all water molecules (at the BP86-D4/ma-def2-TZVP level of theory); (ii) QM/MM with water represented as point charges (q(O) = -0.82 \u003cem\u003ee\u003c/em\u003e and q(H)\u0026thinsp;=\u0026thinsp;+\u0026thinsp;0.41 \u003cem\u003ee\u003c/em\u003e); (iii) QM/MM with an increasing number of QM water molecules (\u0026gt;\u0026thinsp;QM H\u003csub\u003e2\u003c/sub\u003eO) within 3\u0026ndash;15 \u0026Aring; of the cluster; (iv) QM with SMD implicit solvent (\u003cem\u003eε\u003c/em\u003e\u0026thinsp;=\u0026thinsp;78); and (v) QM/MM\u0026thinsp;+\u0026thinsp;CPCM with increased number of QM waters (\u0026gt;\u0026thinsp;QM H\u003csub\u003e2\u003c/sub\u003eO) representing a hybrid explicit-implicit model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e, all approaches exhibit the same general trend wherein the VEA increases as more water molecules are treated at the QM level. A QM/MM model that represents water only as point charges underestimates this stabilization because it lacks short‑range polarization and charge transfer. Adding CPCM to QM/MM supplies the long‑range reaction field and reaches the large cutoff‑radius limit with fewer QM waters. The implicit SMD model provides a bulk‑screened value close to, but generally below, the converged explicit result because it does not capture directional hydrogen bonding. Including explicit QM waters that hydrogen‑bond to exposed sulfur sites yields a modest additional stabilization, beyond a solvation radius of roughly 12 \u0026Aring;. Further, QM waters have a negligible impact, indicating that first‑shell and near‑surface interactions dominate. Overall, QM/MM\u0026thinsp;+\u0026thinsp;CPCM reproduces the cutoff‑radius plateau and gives slightly higher VEAs than the purely implicit model, consistent with cooperative hydrogen bonding and local polarization.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eImplications for biological environments\u003c/h2\u003e \u003cp\u003eThese results establish that the surrounding medium can tune the [4Fe-4S] redox potential by several tenths of a volt, an effect far exceeding that of local geometric distortion. The protein matrix effectively acts as an electrostatic dielectric, screening charge localization upon reduction and thereby stabilizing the Fe-S core. Variations in the local polarity, hydrogen-bond networks, or proximity to charged residues are thus expected to provide powerful yet reversible mechanisms for modulating electron-transfer thermodynamics within ferredoxins and related enzymes. The small sensitivity of the Fe-S cubane to ligand orientation, coupled with its pronounced responsiveness to the dielectric environment, may explain why nature employs this scaffold as a robust yet tunable redox module across a broad potential range. In multi-center enzymes such as hydrogenases and nitrogenases, where electron flow is coupled to proton translocation or substrate activation, such dielectric gating likely dictates both directionality and rate.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThe results presented here establish a clear quantitative hierarchy among the factors that modulate the redox energetics of [4Fe-4S] clusters in ferredoxin-type proteins. The systematic combination of statistical structural analysis, broken-symmetry (BS-DFT), and extended broken-symmetry DFT (EBS-DFT), and dielectric modeling allows each contribution (geometric, electronic, and environmental) to be evaluated on the same energetic scale. This workflow can be automated, enabling systematic, reproducible multi-state electronic-structure studies of Fe-S redox landscapes across various motifs and environments with minimal manual intervention.\u003csup\u003e\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003ePrincipal component analysis of 1049 unique [4Fe-4S] clusters from the Protein Data Bank identified five recurrent ligand-orientation motifs, three of which dominate natural occurrences. Despite differences in the orientation of the cysteine C\u0026ndash;S\u0026ndash;Fe vectors, the intrinsic [4Fe-4S] core geometry remains remarkably invariant. When these five representative motifs were optimized at the BS-DFT level, the resulting adiabatic electron affinities (AEA\u003csub\u003eZPE\u003c/sub\u003e) differed by less than 0.1 eV, a variation an order of magnitude smaller than the experimentally observed potential range among ferredoxins. This small but finite effect quantifies the extent to which ligand orientation can fine-tune redox potentials within an otherwise electronically rigid cubane scaffold.\u003c/p\u003e \u003cp\u003eThe spin-coupling analysis confirms that all clusters share the same qualitative magnetic topology: two ferromagnetically coupled [2Fe-2S] subunits that interact antiferromagnetically to produce an overall low-spin ground state. The extracted exchange constants, \u0026minus;\u003cem\u003eJ\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e = 193\u0026ndash;208 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e for [4Fe-4S]\u003csup\u003e2+\u003c/sup\u003e and \u0026minus;\u0026thinsp;\u003cem\u003eJ\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e = 109\u0026ndash;113 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e for [4Fe-4S]\u003csup\u003e2+\u003c/sup\u003e, differ by less than 0.002 eV across the five motifs. Thus, both the magnetic exchange pattern and the overall spin ladder are insensitive to the local cysteine geometry, underscoring the inherent electronic resilience of the Fe-S framework. This finding supports the notion that, within proteins, ligand orientation primarily serves as a fine-tuning variable rather than a determinant of redox-state stability.\u003c/p\u003e \u003cp\u003eIn contrast, the surrounding dielectric environment exerts a far more substantial influence on the redox energetics. Continuum SMD calculations (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003e) show that increasing the dielectric constant from \u003cem\u003ee\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1 to \u003cem\u003ee\u003c/em\u003e\u0026thinsp;=\u0026thinsp;80 stabilizes the reduced state by 0.4 eV \u0026minus;\u0026thinsp;0.5 eV. The stabilization rises steeply at low \u003cem\u003ee\u003c/em\u003e and plateaus at \u003cem\u003ee\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;15, corresponding to the upper range of effective permittivity of a protein interior.\u003csup\u003e\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e This behavior indicates that most of the polarization responsible for tuning the redox potential originates from the first few solvation shells and the local protein matrix, rather than from bulk solvent.\u003c/p\u003e \u003cp\u003eExplicit-solvent and QM/MM(+\u0026thinsp;QM H\u003csub\u003e2\u003c/sub\u003eO) calculations refine this picture by capturing the microscopic origins of the dielectric response. Inclusion of hydrogen-bonding interactions from water molecules or polar residues near the cluster further stabilizes the reduced state relative to the continuum model. Beyond a solvation radius of ~\u0026thinsp;12 \u0026Aring;, the incremental effect becomes negligible, demonstrating that first-shell and near-surface polarization dominate the environmental contribution. Together, these results suggest that small variations in the local dielectric constant, driven by changes in side-chain charge, hydration, or backbone orientation, can readily account for the 0.5\u0026ndash;1.0 V redox span observed experimentally across biological [4Fe-4S] centers.\u003c/p\u003e \u003cp\u003eCombining these analyses yields a physically transparent model for redox tuning in Fe-S proteins.\u003c/p\u003e \u003cp\u003eThe intrinsic cubane core defines a narrow energetic baseline determined primarily by Fe-S covalency and spin exchange. Ligand geometry introduces a secondary modulation (~\u0026thinsp;0.1 V), likely exploited by proteins to align the redox potentials of adjacent cofactors for efficient electron transfer. Environmental polarization, through dielectric screening\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e,\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e,\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e and local hydrogen-bond networks,\u003csup\u003e57,58\u003c/sup\u003e provides the dominant energetic control, enabling shifts of several tenths of a volt without altering the inorganic core. The protein scaffold thus functions as an electrostatic gate, stabilizing or destabilizing charge localization and thereby controlling both thermodynamics and kinetics of electron transfer.\u003c/p\u003e \u003cp\u003eThe quantitative hierarchy electronic rigidity\u0026thinsp;\u0026lt;\u0026thinsp;geometric fine-tuning\u0026thinsp;\u0026lt;\u0026thinsp;environmental control rationalizes why ferredoxins, hydrogenases, and nitrogenases can employ the same Fe-S cubane framework to span redox potentials from +\u0026thinsp;0.3 V to -0.8 V versus SHE. It also clarifies the apparent dichotomy between structural conservation and functional diversity in Fe-S enzymes: the cubane core provides stability and electronic continuity. In contrast, the protein matrix provides tunability through electrostatics and solvation.\u003c/p\u003e \u003cp\u003eIn summary, the present results delineate the physical factors that enable proteins to exploit the intrinsic resilience of Fe-S clusters while tailoring their redox properties through environmental polarization. This interplay between structure, electronic coupling, and electrostatics remains a guiding principle for the bio-inspired design of electrocatalysts and electrochemical materials.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eP.S.R, M.D.B, and S.R. designed the research. P.S.R, B.J., K.A., M.D.B, and S.R. conducted the study. P.S.R., M.D.B, and S.R. wrote the paper. All authors reviewed the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research was supported by the Generative AI (GenAI) for Science, Energy, and Security Science \u0026amp; Technology Investment under the Laboratory Directed Research and Development (LDRD) Program at Pacific Northwest National Laboratory (PNNL) and the U.S. DOE, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, Physical Biosciences Program under awards FWP 66476 (S.R. and M.B.).\u0026nbsp;A portion of the research was performed using resources available through Research Computing at PNNL. PNNL is a multiprogram national laboratory operated by Battelle for the Department of Energy under Contract No. DE-AC05-76RLO 1830.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data supporting the findings of this study are available within the paper and its Supplementary Information.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical approval\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to participate\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to publish\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eJohnson DC, Dean DR, Smith AD, Johnson MK, STRUCTURE, FUNCTION, AND FORMATION OF BIOLOGICAL IRON-SULFUR CLUSTERS (2005). \u003cem\u003eAnnu. Rev. Biochem. 74\u003c/em\u003e (Volume 74, 2005), 247\u0026ndash;281. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1146/annurev.biochem.74.082803.133518\u003c/span\u003e\u003cspan address=\"10.1146/annurev.biochem.74.082803.133518\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMartin W, Baross J, Kelley D, Russell MJ (2008) Hydrothermal Vents and the Origin of Life. Nat Rev Microbiol 6(11):805\u0026ndash;814. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/nrmicro1991\u003c/span\u003e\u003cspan address=\"10.1038/nrmicro1991\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMansy SS, Cowan JA (2004) Iron\u0026thinsp;\u0026ndash;\u0026thinsp;Sulfur Cluster Biosynthesis: Toward an Understanding of Cellular Machinery and Molecular Mechanism | Accounts of Chemical Research. Acc Chem Res 37(9):719\u0026ndash;725. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ar0301781\u003c/span\u003e\u003cspan address=\"10.1021/ar0301781\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFontecave M, Ollagnier-de-Choudens S (2008) Iron\u0026ndash;Sulfur Cluster Biosynthesis in Bacteria: Mechanisms of Cluster Assembly and Transfer. Arch Biochem Biophys 474(2):226\u0026ndash;237. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.abb.2007.12.014\u003c/span\u003e\u003cspan address=\"10.1016/j.abb.2007.12.014\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNoodleman L, Norman JG, Osborne JH, Aizman A, Case DA (1985) Models for Ferredoxins: Electronic Structures of Iron-Sulfur Clusters with One, Two, and Four Iron Atoms. J Am Chem Soc 107(12):3418\u0026ndash;3426. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ja00298a004\u003c/span\u003e\u003cspan address=\"10.1021/ja00298a004\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSeefeldt LC, Yang Z-Y, Lukoyanov DA, Harris DF, Dean DR, Raugei S, Hoffman BM (2020) Reduction of Substrates by Nitrogenases. Chem Rev 120(12):5082\u0026ndash;5106. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/acs.chemrev.9b00556\u003c/span\u003e\u003cspan address=\"10.1021/acs.chemrev.9b00556\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu J, Chakraborty S, Hosseinzadeh P, Yu Y, Tian S, Petrik I, Bhagi A, Lu Y (2014) Metalloproteins Containing Cytochrome, Iron\u0026ndash;Sulfur, or Copper Redox Centers. Chem Rev 114(8):4366\u0026ndash;4469. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/cr400479b\u003c/span\u003e\u003cspan address=\"10.1021/cr400479b\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBeinert H, Holm RH, Munck E (1997) Iron-Sulfur Clusters: Nature\u0026rsquo;s Modular, Multipurpose Structures. Science 277:653\u0026ndash;659. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1126/science.277.5326.653\u003c/span\u003e\u003cspan address=\"10.1126/science.277.5326.653\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNoodleman L, Peng CY, Case DA, Mouesca J-M (1995) Orbital Interactions, Electron Delocalization and Spin Coupling in Iron-Sulfur Clusters. Coord Chem Rev 144:199\u0026ndash;244. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/0010-8545(95)07011-L\u003c/span\u003e\u003cspan address=\"10.1016/0010-8545(95)07011-L\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang X-B, Niu S, Yang X, Ibrahim SK, Pickett CJ, Ichiye T, Wang L-S (2003) Probing the Intrinsic Electronic Structure of the Cubane [4Fe\u0026thinsp;\u0026ndash;\u0026thinsp;4S] Cluster: Nature\u0026rsquo;s Favorite Cluster for Electron Transfer and Storage. J Am Chem Soc 125(46):14072\u0026ndash;14081. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ja036831x\u003c/span\u003e\u003cspan address=\"10.1021/ja036831x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJafari S, Tavares Santos YA, Bergmann J, Irani M, Ryde U (2022) Benchmark Study of Redox Potential Calculations for Iron\u0026ndash;Sulfur Clusters in Proteins. Inorg Chem 61(16):5991\u0026ndash;6007. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/acs.inorgchem.1c03422\u003c/span\u003e\u003cspan address=\"10.1021/acs.inorgchem.1c03422\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMin J, Ali F, Brooks BR, Bruce BD, Amin M (2025) Predicting Iron\u0026ndash;Sulfur Cluster Redox Potentials: A Simple Model Derived from Protein Structures. ACS Omega 10(15):15790\u0026ndash;15798. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/acsomega.5c01976\u003c/span\u003e\u003cspan address=\"10.1021/acsomega.5c01976\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDereli B, Baer MD, Peters JW, Raugei S (2025) The Properties That Allow Tuning the Reduction Potentials over a Volt Range in Biological Iron/Sulfur Clusters. J Phys Chem Lett 16(19):4602\u0026ndash;4606. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/acs.jpclett.5c00616\u003c/span\u003e\u003cspan address=\"10.1021/acs.jpclett.5c00616\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBruska MK, Stiebritz MT, Reiher M (2011) Regioselectivity of H Cluster Oxidation. J Am Chem Soc 133(50):20588\u0026ndash;20603. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ja209165r\u003c/span\u003e\u003cspan address=\"10.1021/ja209165r\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBurley SK, Bhatt R, Bhikadiya C, Bi C, Biester A, Biswas P, Bittrich S, Blaumann S, Brown R, Chao H, Chithari VR, Craig PA, Crichlow GV, Duarte JM, Dutta S, Feng Z, Flatt JW, Ghosh S, Goodsell DS, Green RK, Guranovic V, Henry J, Hudson BP, Joy M, Kaelber JT, Khokhriakov I, Lai J-S, Lawson CL, Liang Y, Myers-Turnbull D, Peisach E, Persikova I, Piehl DW, Pingale A, Rose Y, Sagendorf J, Sali A, Segura J, Sekharan M, Shao C, Smith J, Trumbull M, Vallat B, Voigt M, Webb B, Whetstone S, Wu-Wu A, Xing T, Young JY, Zalevsky A, Zardecki C (2025) Updated Resources for Exploring Experimentally-Determined PDB Structures and Computed Structure Models at the RCSB Protein Data Bank. Nucleic Acids Res 53(D1):D564\u0026ndash;D574. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1093/nar/gkae1091\u003c/span\u003e\u003cspan address=\"10.1093/nar/gkae1091\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEltis LD, Iwagami SG, Smith M (1994) Hyperexpression of a Synthetic Gene Encoding a High Potential Iron Sulfur Protein. Protein Eng 7(9):1145\u0026ndash;1150. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1093/protein/7.9.1145\u003c/span\u003e\u003cspan address=\"10.1093/protein/7.9.1145\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTakeda K, Kusumoto K, Hirano Y, Miki K (2010) Detailed Assessment of X-Ray Induced Structural Perturbation in a Crystalline State Protein. J Struct Biol 169(2):135\u0026ndash;144. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jsb.2009.09.012\u003c/span\u003e\u003cspan address=\"10.1016/j.jsb.2009.09.012\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCowan JA, Lui SM (1998) Structure-Function Correlations in High-Potential IRON Proteins. Adv Inorg Chem 45:313\u0026ndash;350. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S0898-8838(08)60028-8\u003c/span\u003e\u003cspan address=\"10.1016/S0898-8838(08)60028-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHatchikian EC, Cammack R, Patil DS, Robinson AE, Richards AJM, George S, Thomson AJ (1984) Spectroscopic Characterization of Ferredoxins I and II from \u003cem\u003eDesulfovibrio Africanus\u003c/em\u003e. Biochim Biophys Acta BBA - Protein Struct Mol Enzymol 784(1):40\u0026ndash;47. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/0167-4838(84)90170-5\u003c/span\u003e\u003cspan address=\"10.1016/0167-4838(84)90170-5\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIismaa SE, V\u0026aacute;zquez AE, Jensen GM, Stephens PJ, Butt JN, Armstrong FA, Burgess BK (1991) Site-Directed Mutagenesis of Azotobacter Vinelandii Ferredoxin I. Changes in [4Fe-4S] Cluster Reduction Potential and Reactivity. J Biol Chem 266(32):21563\u0026ndash;21571. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S0021-9258(18)54675-5\u003c/span\u003e\u003cspan address=\"10.1016/S0021-9258(18)54675-5\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTan M-L, Perrin BS Jr., Niu S, Huang Q, Ichiye T (2016) Protein Dynamics and the All-Ferrous [Fe4S4] Cluster in the Nitrogenase Iron Protein. Protein Sci 25(1):12\u0026ndash;18. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/pro.2772\u003c/span\u003e\u003cspan address=\"10.1002/pro.2772\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJolliffe IT, Cadima J (2016) Principal Component Analysis: A Review and Recent Developments. Philos Trans A 354:20150202. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://dx.doi.org/10.1098/rsta.2015.0202\u003c/span\u003e\u003cspan address=\"10.1098/rsta.2015.0202\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNeese F, The ORCAP, System (2012) WIREs Comput Mol Sci 2(1):73\u0026ndash;78. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/wcms.81\u003c/span\u003e\u003cspan address=\"10.1002/wcms.81\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTorres RA, Lovell T, Noodleman L, Case DA (2003) Density Functional and Reduction Potential Calculations of Fe4S4 Clusters. J Am Chem Soc 125(7):1923\u0026ndash;1936. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ja0211104\u003c/span\u003e\u003cspan address=\"10.1021/ja0211104\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBlank MA, Lee CC, Hu Y, Hodgson KO, Hedman B, Ribbe MW (2011) Structural Models of the [Fe4S4] Clusters of Homologous Nitrogenase Fe Proteins. Inorg Chem 50(15):7123\u0026ndash;7128. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ic200636k\u003c/span\u003e\u003cspan address=\"10.1021/ic200636k\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVenkateswara Rao P, Holm RH (2004) Synthetic Analogues of the Active Sites of Iron\u0026thinsp;\u0026ndash;\u0026thinsp;Sulfur Proteins. Chem Rev 104(2):527\u0026ndash;560. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/cr020615+\u003c/span\u003e\u003cspan address=\"10.1021/cr020615+\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNoodleman L, Case DA, Aizman (1988) Arie. Broken Symmetry Analysis of Spin Coupling in Iron-Sulfur Clusters. J Am Chem Soc 110(4):1001\u0026ndash;1005. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ja00212a003\u003c/span\u003e\u003cspan address=\"10.1021/ja00212a003\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNoodleman L, Case DA (1992) Density-Functional Theory of Spin Polarization and Spin Coupling in Iron\u0026mdash;Sulfur Clusters. Adv Inorg Chem 38:423\u0026ndash;470. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S0898-8838(08)60070-7\u003c/span\u003e\u003cspan address=\"10.1016/S0898-8838(08)60070-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCaldeweyher E, Ehlert S, Hansen A, Neugebauer H, Spicher S, Bannwarth C, Grimme SA (2019) Generally Applicable Atomic-Charge Dependent London Dispersion Correction. J Chem Phys 150(15):154122. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1063/1.5090222\u003c/span\u003e\u003cspan address=\"10.1063/1.5090222\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCaldeweyher E, Bannwarth C, Grimme S (2017) Extension of the D3 Dispersion Coefficient Model. J Chem Phys 147(3):034112. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1063/1.4993215\u003c/span\u003e\u003cspan address=\"10.1063/1.4993215\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGray M, Herbert JM (2022) Comprehensive Basis-Set Testing of Extended Symmetry-Adapted Perturbation Theory and Assessment of Mixed-Basis Combinations to Reduce Cost. J Chem Theory Comput 18(4):2308\u0026ndash;2330. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/acs.jctc.1c01302\u003c/span\u003e\u003cspan address=\"10.1021/acs.jctc.1c01302\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBecke AD (1988) Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys Rev A 38(6):3098\u0026ndash;3100. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevA.38.3098\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevA.38.3098\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePerdew JP, Yue W (1986) Accurate and Simple Density Functional for the Electronic Exchange Energy: Generalized Gradient Approximation. Phys Rev B 33(12):8800\u0026ndash;8802. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevB.33.8800\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevB.33.8800\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePerdew JP, Burke K, Ernzerhof M (1996) Generalized Gradient Approximation Made Simple. Phys Rev Lett 77(18):3865\u0026ndash;3868. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevLett.77.3865\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevLett.77.3865\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBecke AD (1988) Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys Rev A 38(6):3098\u0026ndash;3100. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevA.38.3098\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevA.38.3098\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLee C, Yang W, Parr RG (1988) Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys Rev B 37(2):785\u0026ndash;789. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevB.37.785\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevB.37.785\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePerdew JP, Constantin LA (2007) Laplacian-Level Density Functionals for the Kinetic Energy Density and Exchange-Correlation Energy. Phys Rev B 75(15):155109. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevB.75.155109\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevB.75.155109\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePerdew JP, Ruzsinszky A, Csonka GI, Constantin LA, Sun J (2009) Workhorse Semilocal Density Functional for Condensed Matter Physics and Quantum Chemistry. Phys Rev Lett 103(2):026403. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevLett.103.026403\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevLett.103.026403\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFurness JW, Kaplan AD, Ning J, Perdew JP, Sun J (2020) Accurate and Numerically Efficient r2SCAN Meta-Generalized Gradient Approximation. J Phys Chem Lett 11(19):8208\u0026ndash;8215. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/acs.jpclett.0c02405\u003c/span\u003e\u003cspan address=\"10.1021/acs.jpclett.0c02405\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eStephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J Phys Chem 98(45):11623\u0026ndash;11627. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/j100096a001\u003c/span\u003e\u003cspan address=\"10.1021/j100096a001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBecke AD (1993) Density-functional Thermochemistry. III. The Role of Exact Exchange. J Chem Phys 98(7):5648\u0026ndash;5652. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1063/1.464913\u003c/span\u003e\u003cspan address=\"10.1063/1.464913\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVosko SH, Wilk L, Nusair M (1980) Accurate Spin-Dependent Electron Liquid Correlation Energies for Local Spin Density Calculations: A Critical Analysis. Can J Phys 58:1200\u0026ndash;1210. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1139/p80-159\u003c/span\u003e\u003cspan address=\"10.1139/p80-159\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAdamo C, Barone V (1999) Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J Chem Phys 110(13):6158\u0026ndash;6170. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1063/1.478522\u003c/span\u003e\u003cspan address=\"10.1063/1.478522\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eStaroverov VN, Scuseria GE, Tao J, Perdew JP (2003) Comparative Assessment of a New Nonempirical Density Functional: Molecules and Hydrogen-Bonded Complexes. J Chem Phys 119(23):12129\u0026ndash;12137. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1063/1.1626543\u003c/span\u003e\u003cspan address=\"10.1063/1.1626543\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBursch M, Neugebauer H, Ehlert S, Grimme S (2022) Dispersion Corrected r2SCAN Based Global Hybrid Functionals: r2SCANh, r2SCAN0, and r2SCAN50. J Chem Phys 156(13):134105. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1063/5.0086040\u003c/span\u003e\u003cspan address=\"10.1063/5.0086040\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYanai T, Tew DP, Handy NC (2004) A New Hybrid Exchange\u0026ndash;Correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP). Chem Phys Lett 393(1):51\u0026ndash;57. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.cplett.2004.06.011\u003c/span\u003e\u003cspan address=\"10.1016/j.cplett.2004.06.011\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChu S, Bovi D, Cappelluti F, Orellana AG, Martin H, Guidoni L (2017) Effects of Static Correlation between Spin Centers in Multicenter Transition Metal Complexes. J Chem Theory Comput 13(10):4675\u0026ndash;4683. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/acs.jctc.7b00316\u003c/span\u003e\u003cspan address=\"10.1021/acs.jctc.7b00316\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTzeli D, Golub P, Brabec J, Matoušek M, Pernal K, Veis L, Raugei S, Xantheas SS (2024) Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe\u0026ndash;2S] Systems: A Benchmark Study of the [Fe2S2(SCH3)4]2\u0026ndash;,3\u0026ndash;,4\u0026ndash;, [Fe2S2(SCys)4]2\u0026ndash;, [Fe2S2(S-p-Tol)4]2\u0026ndash;, and [Fe2S2(S-o-Xyl)4]2\u0026ndash; Complexes. \u003cem\u003eJ. Chem. Theory Comput. 20\u003c/em\u003e (23), 10406\u0026ndash;10423. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/acs.jctc.4c00781\u003c/span\u003e\u003cspan address=\"10.1021/acs.jctc.4c00781\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSharma S, Sivalingam K, Neese F, Chan GK-L (2014) Low-Energy Spectrum of Iron\u0026ndash;Sulfur Clusters Directly from Many-Particle Quantum Mechanics. Nat Chem 6(10):927\u0026ndash;933. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/nchem.2041\u003c/span\u003e\u003cspan address=\"10.1038/nchem.2041\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMejuto-Zaera C, Tzeli D, Williams-Young D, Tubman NM, Matoušek M, Brabec J, Veis L, Xantheas SS, de Jong WA (2022) The Effect of Geometry, Spin, and Orbital Optimization in Achieving Accurate, Correlated Results for Iron\u0026ndash;Sulfur Cubanes. J Chem Theory Comput 18(2):687\u0026ndash;702. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/acs.jctc.1c00830\u003c/span\u003e\u003cspan address=\"10.1021/acs.jctc.1c00830\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTzeli D, Raugei S, Xantheas SS (2021) Quantitative Account of the Bonding Properties of a Rubredoxin Model Complex [Fe(SCH3)4]q, q\u0026thinsp;=\u0026thinsp;\u0026ndash;\u0026thinsp;2, \u0026ndash;\u0026thinsp;1, +2, +\u0026thinsp;3. J Chem Theory Comput 17(10):6080\u0026ndash;6091. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/acs.jctc.1c00485\u003c/span\u003e\u003cspan address=\"10.1021/acs.jctc.1c00485\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMouesca J-M, Noodleman L, Case DA, Lamotte B (1995) Spin Densities and Spin Coupling in Iron-Sulfur Clusters: A New Analysis of Hyperfine Coupling Constants. Inorg Chem 34(17):4347\u0026ndash;4359. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ic00121a013\u003c/span\u003e\u003cspan address=\"10.1021/ic00121a013\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNoodleman L (1991) Exchange Coupling and Resonance Delocalization in Reduced Iron-Sulfur [Fe4S4]\u0026thinsp;+\u0026thinsp;and Iron-Selenium [Fe4Se4]\u0026thinsp;+\u0026thinsp;Clusters. 1. Basic Theory of Spin-State Energies and EPR and Hyperfine Properties. Inorg Chem 30(2):246\u0026ndash;256. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ic00002a019\u003c/span\u003e\u003cspan address=\"10.1021/ic00002a019\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMouesca J-M, Chen JL, Noodleman L, Bashford D, Case DA (1994) Density Functional/Poisson-Boltzmann Calculations of Redox Potentials for Iron-Sulfur Clusters. J Am Chem Soc 116(26):11898\u0026ndash;11914. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ja00105a033\u003c/span\u003e\u003cspan address=\"10.1021/ja00105a033\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGaughan SJH, Hirst JD, Croft AK, J\u0026auml;ger CM (2022) Effect of Oriented Electric Fields on Biologically Relevant Iron\u0026ndash;Sulfur Clusters: Tuning Redox Reactivity for Catalysis. J Chem Inf Model 62(3):591\u0026ndash;601. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/acs.jcim.1c00791\u003c/span\u003e\u003cspan address=\"10.1021/acs.jcim.1c00791\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi L, Li C, Zhang Z, Alexov E (2013) On the Dielectric Constant of Proteins: Smooth Dielectric Function for Macromolecular Modeling and Its Implementation in DelPhi. J Chem Theory Comput 9(4):2126\u0026ndash;2136. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ct400065j\u003c/span\u003e\u003cspan address=\"10.1021/ct400065j\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCascella M, Magistrato A, Tavernelli I, Carloni P, Rothlisberger U (2006) Role of Protein Frame and Solvent for the Redox Properties of Azurin from Pseudomonas Aeruginosa. \u003cem\u003eProc. Natl. Acad. Sci. 103\u003c/em\u003e (52), 19641\u0026ndash;19646. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1073/pnas.0607890103\u003c/span\u003e\u003cspan address=\"10.1073/pnas.0607890103\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSulpizi M, Raugei S, VandeVondele J, Carloni P, Sprik M (2007) Calculation of Redox Properties: Understanding Short- and Long-Range Effects in Rubredoxin. J Phys Chem B 111(15):3969\u0026ndash;3976. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/jp067387y\u003c/span\u003e\u003cspan address=\"10.1021/jp067387y\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGeorge A, Bilbao A, Agarwal K, Mejia-Rodriguez D, Samantray S, Kim H, Rice PS, Jacob B, Baer M, Raugei S, Cheung MS, Rigor P ADEPT: A Pedagogical Framework for Integrating Agentic AI with Deterministic Scientific Workflows\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"jbic-journal-of-biological-inorganic-chemistry","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [JBIC Journal of Biological Inorganic Chemistry](https://link.springer.com/journal/775)","snPcode":"775","submissionUrl":"https://submission.springernature.com/new-submission/775/3","title":"JBIC Journal of Biological Inorganic Chemistry","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8059723/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8059723/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIron\u0026ndash;sulfur (Fe\u0026ndash;S) clusters are common biological cofactors that facilitate vital redox reactions. Despite extensive research, the molecular basis of redox potential tuning in ferredoxin-like proteins remains a topic of ongoing debate. In this study, we combine statistical analysis of over one thousand [4Fe\u0026ndash;4S]-containing protein structures from the Protein Data Bank (PDB) with broken-symmetry and extended broken-symmetry density functional theory to examine how cysteine ligand orientations and environmental screening affect cluster redox energies. We identified five main ligand configurations, three of which are predominant in natural structures. Among these, the adiabatic electron affinity differs by less than 0.1 V, indicating that, while geometry plays a secondary role, it allows localized fine-tuning of redox properties. In contrast, electrostatic and solvation effects primarily determine the overall potential range.\u003c/p\u003e","manuscriptTitle":"Geometry, Spin Coupling, and Dielectric Control of Redox Potentials in [4Fe–4S] Clusters","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-13 12:42:55","doi":"10.21203/rs.3.rs-8059723/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-02-10T14:17:00+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-03T04:26:31+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-30T16:08:20+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"199271466463948847232880558338769554921","date":"2026-01-22T20:32:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"230235771380866354387410583305979665386","date":"2026-01-22T18:52:37+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-01-09T14:35:02+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-12T05:51:38+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-12T05:50:26+00:00","index":"","fulltext":""},{"type":"submitted","content":"JBIC Journal of Biological Inorganic Chemistry","date":"2025-11-07T18:59:25+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"jbic-journal-of-biological-inorganic-chemistry","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [JBIC Journal of Biological Inorganic Chemistry](https://link.springer.com/journal/775)","snPcode":"775","submissionUrl":"https://submission.springernature.com/new-submission/775/3","title":"JBIC Journal of Biological Inorganic Chemistry","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"4adf59f8-93ff-4f91-a651-5a092884d693","owner":[],"postedDate":"January 13th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-25T13:23:29+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-13 12:42:55","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8059723","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8059723","identity":"rs-8059723","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}