Multistate reactivity of weak-field clusters at ambient temperatures

Abstract

Ambient-temperature reactivity in biological and industrially relevant reactions is typically attributed from the ground state as a sufficiently large energy gap between ground and excited states of reactants renders the thermal Boltzmann population of excited states as a minor perturbation. However, interactions between locally high-spin centers in polynuclear clusters can afford low-lying excited states with appreciable populations at ambient temperature and provide alternate reaction pathways. Consequently, a mechanistic understanding of the reactivity of such clusters presents challenges. In this perspective, we consider advances towards dissecting the effects of such low-lying states on reactivity.

Magnetic interactions between locally high-spin centers in polynuclear metal clusters can afford low-lying excited states which are populated at ambient temperature. Here, the authors consider advances towards dissecting the effects of such low-lying states on reactivity.

Introduction

The reactivity of a molecule is governed by its electronic state, which describes its spin state and molecular orbital population^1–4. Chemical transformations that involve a change in the spin state for the entire system (reactants and products) along a given reaction coordinate are forbidden because such a crossing between spin states violates the principle of conservation of angular momentum. Spin-orbit coupling (SOC), as is frequently observed in the heavier elements, provides an allowed pathway to access potential energy surfaces (PES) of different spin multiplicities, as dictated by the available thermal energy in a Boltzmann distribution. Seminal work by Armentrout and coworkers demonstrated the influence of the spin state on the reactivity of several gas-phase transition metal ions⁴. One notable example from those studies is the reaction between the Fe⁺ ion and H₂. The Fe⁺ (⁶D) ground state (3d⁶ 4s¹) is relatively unreactive towards H₂ with an estimated barrier of 2.35 eV (54.19 kcal/mol). Contrastingly, the Fe⁺ (⁴F) excited state (3d⁷ 4s⁰), which lies 0.25 eV (5.77 kcal/mol) above the ⁶D ground state, exhibits a 70-fold increase in the reaction rate, highlighting the pronounced difference in the activation energies as a function of the reactant spin state^5,6. The state-selective reactivity of Fe⁺ with H₂ is attributed to a combination of appropriate orbital population and spin-state of the Fe⁺ (⁴F) excited state. The vacant 4s orbital on Fe⁺ (⁴F) is a better acceptor for the H–H bond than the partially filled 4s of the ⁶D ground state. Additionally, the same multiplicity of the excited state and the intermediate eliminates the need for a change to the spin magnetic quantum number (m_s) values for one or more electrons (or spin-flips) in the reaction^7–10. SOC leads to appreciable mixing of the L and S quantum numbers to generate J states that can be mixtures of more than one pure S state^11–13. Consequently, appreciable SOC, as in the heavier elements, provides a mechanism for crossing between formally pure S states along the reaction coordinate.

A conceptual framework for understanding thermal (non-photoinduced) reactions involving spin inversion (crossing of spin PES) was provided by Schröder, Shaik, and Schwarz, who introduced the concept of Two-State Reactivity (TSR) to explain the kinetic anomalies observed in the gas-phase reaction of FeO⁺ and H₂¹⁴. In this model, TSR is defined as a thermal reaction mechanism involving spin crossover along the reaction coordinate from reactants to products, accompanied by product formation through an interplay of spin inversion and the respective barrier heights on both spin surfaces¹⁴. A representative reaction for this model is that of FeO⁺ with H₂ in the gas phase (Eq. 1). Despite the reaction being significantly exothermic (Δ_rxnH ~ –38 kcal/mol) and spin-allowed on the ground-state surface, the gas-phase collision efficiency from kinetic analysis using Transition State Theory and pseudo-first-order assumptions was only 0.6%, implying a substantial activation barrier for the overall reaction. Schröder, Shaik, and Schwarz proposed that the reaction on the sextet surface had a large barrier for the first step (8.4 kcal/mol), corresponding to H₂ cleavage to form [HFeOH]⁺. In contrast, a pathway on the quartet adiabatic surface is near barrierless for this first step (0.6 kcal/mol)¹⁵. As the reaction outcome is observed, all productive collisions were then proposed to involve spin crossover from the sextet to the quartet state to access the lower activation barrier to initiate the reaction. A recrossing event from the quartet to the sextet surface must also occur, given the experimentally observed product. This crossing is postulated to occur in the penultimate step, for which the intermediate on the sextet surface is lower in energy than the related transient on the quartet surface (Fig. 1). The effective lower activation barrier accessed through crossings between the sextet and quartet surfaces in this reaction, as compared to exclusively remaining on the sextet surface, is consistent with the experimentally determined kinetic isotope effect (KIE).

$$Fe{O}^{+}\left({}^6\Sigma ^{+}\right)+H_2\to {Fe}^{+}\left({}^{6}D\right)+H_{2}O$$ 1

Fig. 1. The adiabatic sextet and quartet surfaces for the reaction of FeO⁺ with H₂.

P₁ and P₂ are the spin-state crossing points. Energies are not to scale. Used with permission of American Chemical Society, from Two-state reactivity as a new concept in organometallic chemistry, American Chemical Society, 33, 3,2000]; permission conveyed through Copyright Clearance Center, Inc.

The TSR concept has since been extended to consider more than two spin surfaces, which is termed as Multistate Reactivity (MSR) (Fig. 2) ^16–18.

Fig. 2. Adiabatic potential energy surfaces (PES) for a reaction undergoing multistate reactivity (MSR).

The reactants (A + B) have two excited states, S₁ and S₂, above the ground spin state, S₀. P₁ and P₂ are the spin state crossing points as the reaction proceeds through state crossings (S₀ → S₁ → S₂) to the intermediate (X) and products (C + D), respectively.

Two essential features of spin inversion in MSR are spin-surface intersection and spin-flip induced by SOC¹⁴. Hence, as has been observed, d- and f-block complexes are especially prone to TSR/MSR¹⁹. The predisposition for compounds of lanthanides and actinides to exhibit MSR is accentuated by the multiconfigurational ground states of the elements, allowing barrierless access to multiple PES^20–22. Collman first extended TSR to the condensed phase²³. Later, Harvey and Poli paved the way for quantitative inferences by advancing the concept of Minimum Energy Crossing Point, where the PES of different states intersect^16,24. As representative examples, TSR in spin-state crossings in solution-phase reaction coordinates was implicated in the mechanism for CO and O₂ binding to heme proteins, spin acceleration (lowering of activation barrier by spin inversion) in high-spin Fe complexes, and delayed CO-binding kinetics in high-spin complexes due to spin blocking (high barrier to spin inversion for reactions requiring a spin state change)^17,25–33. Collman proposed a high barrier for the formation of high-spin Cp₂ML-type species from low-spin Cp₂ML₂-type complexes due to the difference in multiplicities of the product and reactants.

This proposed state-selectivity has since been widely exploited in synthetic chemistry to control reaction kinetics. Changing the barrier height for reactions proceeding through spin inversion tunes the rate for transition metal-catalyzed C-H activation, [2+2] cycloaddition, and hydrosilylation reactions^33–35. Spin inversion is also invoked to rationalize the fast kinetics of formally spin-forbidden β-hydride elimination in high-spin metal hydrides^25,36. In photochemistry, state selectivity is exploited to achieve state-selective chromophore excitation ^37–39.

At this stage, it should be made clear that not all thermally accessible excited states participate in reactivity. Just like excited states offering a lower activation barrier than the ground state, the converse is also possible, where the activation barrier from the ground state is energetically more accessible than that of the excited state, despite the excited state possessing more total energy. Such systems have been observed and studied extensively in gas-phase ion chemistry ^4,9,10.

However, for reactions involving excited states with a low activation barrier, performed at operating temperatures typical for solution phase (−100 °C to 100 °C), the combination of MSR and Boltzmann population of states jointly implies that reactivity distinct from the ground state could arise from thermally populated low-lying excited spin states if ΔE_GS-_ES ≲ 300 cm⁻¹ (0.86 kcal/mol) (Fig. 2). The electronic configurations of weak-field ligated transition-metal centers are dictated by balancing the electron-exchange and molecular kinetic energy (kT) against the electron-pairing energy. The consequence of that balance will be thermally accessible low-lying spin-excited states. As such, greater opportunity exists for such MSR to be observed for open-shell molecules in which high- or intermediate-spin states can be readily accessed as compared to metal centers supported by strong-field ligands, which impose larger energy separations between ground and excited states ³⁶.

Unlike transition metals in a strong ligand field, in which pairing energy is less than the exchange stabilization and the energy difference between valence orbitals, this balance creates an opportunity to use ligand design or complex structure to fine-tune the strength of coupling between metal ions and the overall electronic structure. High- or intermediate-spin molecules further open the possibility of electron spin-flipping under external stimuli, such as an applied magnetic field or photoexcitation. The thermal population of excited states in such complexes is readily inferred from the deviation of the room-temperature magnetic moment from the ground-state magnetic moment ⁴⁰.

When multiple such high-spin metal ions are positioned sufficiently close, as in a polynuclear complex or cluster, the frontier magnetic orbitals on each metal center interact directly (direct exchange) or are mediated by orbitals on a bridging ligand. The resultant ferromagnetic or antiferromagnetic coupling thus stabilizes the high- or low-spin state, respectively (Fig. 3). In addition to the exchange interaction between the high-spin ions, minor structural perturbations and SOC can effect zero-field splitting (ZFS), lifting the degeneracy of the m_s states of the polynuclear species⁴¹. ZFS parameters are typically of the order of ~10 cm⁻¹ (0.03 kcal/mol), of sufficient magnitude to influence the ordering of states when the exchange interaction is weak, and afford non-canonical (intermediate) spin ground states. In a dinuclear complex, the effective magnetic interactions between two high-spin ions of spin multiplicities ($\overrightarrow{S_1}$ and $\overrightarrow{S_2}$), with ZFS, mediated by a bridging ligand, are described by the classic Heisenberg-Dirac-van Vleck (HDvV) Hamiltonian,

$$\widehat{H}=2J\overrightarrow{S_1}\cdot \overrightarrow{S_2}+{\sum }_{i=1}^2\left[D_i\left(S_{iz}^2-\frac{1}{3}{S}_i\left(S_i+1\right)\right)+E_i\left(S_{ix}^2-S_{iy}^2\right)\right]$$ 2

where J is the exchange coupling constant between the two ions, D and E are the axial and rhombic ZFS parameters, and S_x, S_y, and S_z are the spin components along x, y, and z directions, respectively. Extending the theory to include electron delocalization in mixed valent dimers (double exchange) introduces an additional term in the Hamiltonian expression:

$${\widehat{H}}_{DE}=-B\sqrt{\left(1+\frac{S_1\cdot S_2}{S_1{S}_2}\right)}$$ 3

where B is the double exchange constant, resulting in the final Hamiltonian⁴²

$$\widehat{H}=2J\overrightarrow{S_1}\cdot \overrightarrow{S_2}+{\sum }_{i=1}^2\left[D_i\left(S_{iz}^2-\frac{1}{3}{S}_i\left(S_i+1\right)\right)+E_i\left(S_{ix}^2-S_{iy}^2\right)\right]-B\sqrt{\left(1+\frac{S_1\cdot S_2}{S_1{S}_2}\right)}$$ 4

Fig. 3. The increase in the density of states of a metal cluster as it grows in nuclearity.

Each orange sphere represents a paramagnetic metal ion. J represents the exchange coupling between the ions. J nomenclature and long-range coupling interactions are omitted in the rightmost figure for clarity.

The magnitude and sign of the exchange coupling between the two ions dictate the magnetic properties of the dinuclear complex. Strong antiferromagnetic coupling (J < −1000 cm⁻¹ or 2.86 kcal/mol) can be thought of as a (pseudo) metal-metal bond with an energetically well-isolated low-spin ground state^41,43. Strong ferromagnetic coupling (J > 1000 cm⁻¹) affords a well-isolated high-spin ground state, which is rare for transition metal complexes, and has been reported for triplet organic radicals with degenerate valence orbitals⁴¹. Weakly interacting coupled centers, by contrast to the two strongly coupled extrema, give rise to low-lying excited spin states (Fig. 4). The resulting dense spin manifold features the maximum spin ferromagnetic state to the low-spin antiferromagnetic state, whose energy is primarily dictated by J, with other molecule-specific factors (viz., double exchange, ZFS, and vibronic coupling) also influencing the ordering⁴¹. Indeed, the energy difference between spin states can be as low as 10 cm⁻¹ (0.03 kcal/mol) as observed in non-heme polynuclear metallocofactors and, thus, excited states are readily populated under ambient reaction conditions (T ~ 25 °C) since the available thermal energy (~0.6 kcal/mol or ~200 cm⁻¹) far exceeds the energy separation between states^44–46. As the type and strength of coupling relate to direct exchange or superexchange mediated by the orientation of metal and ligand orbitals, the synthetic chemist can in principle tune the magnitude and type of exchange interactions between locally high-spin metal ions to influence the energy separation between ground and excited states and to establish a necessary criterion for MSR. Moreover, one can then envision using cluster composition as a further chemical handle to influence electronic structure and reactivity.

Fig. 4. Energy level correlation diagram of a binuclear high-spin Fe (II) complex.

Exchange coupling and single-site zero-field splitting (ZFS) are included, plotted using Eq. 2. Zero field splitting constant, D, kept constant at 10 cm^-1 and E = 0. Labels in parentheses denote the total spin (S) and spin magnetic quantum number (M_s), respectively. Used with permission of American Chemical Society, from Circular Dichroism and Magnetic Circular Dichroism Studies of the Reduced Binuclear Non-Heme Iron Site of Stearoyl-ACP Δ9-Desaturase: Substrate Binding and Comparison to Ribonucleotide Reductase, American Chemical Society, 121, 12, 1999; permission conveyed through Copyright Clearance Center, Inc.

However, as mentioned above, not all low-lying excited states lead to productive chemistry, which is also contingent on the activation barrier for the corresponding excited state. Incorporating the Boltzmann population distribution and Transition State Theory into the kinetic expressions of a reaction involving a low-lying excited state allows us to develop a quantitative framework for visualizing the dependence.

Assuming a single low-lying excited state (ΔE_GS-ES < RT) (Fig. S1) for a reactant following first-order kinetics yields the following equation connecting the observed rate constant ($k_{obs}$), rate constant with single state reactivity ($k_{SSR}$), and the difference in activation barrier between the excited and ground states ($\mathrm{\Delta }{G}_{GS}^{‡}-\mathrm{\Delta }{G}_{ES}^{‡}$) (Calculation in Supplementary Information).

$$k_{obs}=k_{SSR}\left[1+\frac{{\kappa }_{ES}}{2{\kappa }_{GS}}\exp \left(\frac{\mathrm{\Delta }{G}_{GS}^{‡}-\mathrm{\Delta }{G}_{ES}^{‡}}{RT}\right)\right]$$ 5

Where κ_ES and κ_GS are the transmission coefficients (defined by the Eyring equation) of the excited and ground states, respectively. The non-productive excited states have a higher activation barrier than the ground state ($\left(\mathrm{\Delta }{G}_{GS}^{‡}-\mathrm{\Delta }{G}_{ES}^{‡}\right)<0$) and the reaction essentially proceeds via the ground state surface. Plotting the equation for three different reaction temperatures (Fig. 5) illustrates the exponential relationship between $k_{obs}$ and $\left(\mathrm{\Delta }{G}_{GS}^{‡}-\mathrm{\Delta }{G}_{ES}^{‡}\right)$, especially when the available thermal energy is low. Consequently, the rate amplification is more pronounced at low temperatures, potentially leading to contrasting mechanistic inferences when performed at different temperatures (vide infra).

Fig. 5. Plot of the $\frac{k_{obs}}{k_{SSR}}$ versus $\left(\mathrm{\Delta }{G}_{GS}^{‡}-\mathrm{\Delta }{G}_{ES}^{‡}\right)$ for a reaction involving a single low-lying excited state.

Plots assume three different reaction temperatures (100 K, 298 K, and 500 K). Ratio of transmission coefficients is taken to be unity.

Thermally accessible low-lying excited state clusters in proteins

The coordination environment plays a significant role in controlling the electronic structure and, consequently, access to lying excited states for metal clusters. Examples of this influence are readily apparent in metalloproteins, where amino acid residues (e.g., cysteine and histidine) are weak-field donors in enzyme active sites. In addition to their weak-field nature, amino acid residues provide a dynamic coordination environment (e.g., carboxylate shift in dinuclear metalloenzymes), enabling tuning of their reactivity^47–50. Combined with the presence of low-lying excited states, the dynamic, weak-field coordination environment facilitates multifunctionality in these multimetallic metalloenzymes (vide infra). This electronic malleability of metallocofactors is referenced as a factor that affords a wide variety of functions with minimal overall structural change for comparable cofactors⁵¹. The functional versatility of enzymatic clusters is epitomized by iron-sulfur (Fe-S) metallocofactors, which effect electron transfer, small molecule activation, radical generation, and energy storage in enzymes with minimal changes to the primary coordination sphere ⁵².

The structural complexity of proteins that harbor metal cofactors can complicate correlating cofactor structure with the electronic states that dictate the observed reactivities, with site-directed mutagenesis and spectroscopy of freeze-quenched samples during catalysis or single turnover being the predominantly used techniques. Site-directed mutagenesis allows the roles of specific amino acid residues to be demonstrated, inter alia, in cofactor maturation and in the transport of protons, water, and substrates to and from the active site^53,54. Leveraging the presence of unpaired electrons in metal cofactors and their interaction with substrates and amino acids, various electron paramagnetic resonance methods (e.g., ENDOR, ESEEM, HYSCORE) have yielded key structural and electronic information of the turnover intermediates^55,56. However, the line broadening of the signals at higher temperatures renders paramagnetic spectroscopic methods less informative at physiological temperatures. For metallocofactor clusters with thermally accessible low-lying excited states, the electronic (and structural) properties at the active site under physiological conditions will differ from those at low temperatures. Hence, the reactivity at physiological temperatures differs from that inferred from low-temperature spectroscopy measurements.

A notable finding demonstrating the state-specificity of enzyme reactivity is the 15-fold decrease in electron-transfer kinetics upon site-directed mutagenesis at the binuclear CuA metallocofactor found in both cytochrome c oxidase and nitrous oxide reductase. The Cu₂S₂ site exhibits a low-lying excited state, σ_u* (200 cm⁻¹–900 cm⁻¹ or 0.57 kcal/mol–2.57 kcal/mol), which is structurally distinguished from the ground state (π_u) by an increase in Cu-Cu distance of 0.57 Å. Minor changes to the secondary coordination sphere of the active site can alter the energies of the ground and excited states, even inverting the energy ordering and altering the direction of electron transfer at the active site^57–59. The kinetic control of electron transfer by the primary coordination sphere of the cofactor hints at the mechanisms enzymes employ for gating electron transfer.

Low-lying excited states have been spectroscopically observed in a variety of metallocofactors, including the Native Intermediate (NI) of the tricopper active site of multicopper oxidase (MCO). The three antiferromagnetically coupled Cu(II) ions with canted spins result in a spin-frustrated topology with low-lying excited states (ΔE_GS-_ES = 150 cm⁻¹ or 0.43 kcal/mol)⁶⁰. Our group has reported a Cu₃(µ₃-E) cluster (E=S and Se) bearing structural resemblance to the Cu₃(µ₃-O) core of NI (Fig. 6)⁶¹. Notably, the Cu₃(µ₃-E) clusters (E=S and Se) exhibited charge polarization at the Cu sites induced by long-range non-covalent interactions, hinting at the sensitivity of the electronic structure of such polynuclear copper chalcogenide clusters to minor structural perturbations in the secondary coordination sphere ^62,63.

Fig. 6. Cu₃ cores exhibiting low-lying excited states in synthetic and enzymatic systems.

A Geometry optimized Cu₃(µ₃-O) core of the Native Intermediate (NI) in multicopper oxidase (MCO) (Used with permission of American Chemical Society, from Mechanism of the Reduction of the Native Intermediate in the Multicopper Oxidases: Insights into Rapid Intramolecular Electron Transfer in Turnover, American Chemical Society, 136, 51 2014; permission conveyed through Copyright Clearance Center, Inc.). B Cu₃(µ₃-S) core of a synthetic complex supported on β-diketiminate ligand. (Used with permission of American Chemical Society, from Electronic Desymmetrization of Cu₃(μ₃‑E) Clusters (E = S, Se) Induced by Edge-to-Face π‑Stacking Interactions in the Second Coordination Sphere, American Chemical Society, 63, 52 2024; permission conveyed through Copyright Clearance Center, Inc.).

Despite substantial structural similarities of the active site and similar amino acid sequence, the diiron metalloenzymes, reduced rubredoxin (RR), methane monooxygenase (MMO), and stearoyl-acyl carrier protein Δ⁹-desaturase (Δ⁹D) exhibit a wide range of oxidation reactivity, with rates spanning 30 min⁻¹ to 0.001 min^−164–67. This wide difference in reactivity has been attributed to coordination-induced spin-state changes⁶⁸. Dictated by the ZFS at individual iron centers and the exchange coupling between them, the diiron core of the enzyme has a dense spin manifold with low-lying excited states (Fig. 4)⁴⁶. The influence of excited states on the reactivity of this enzyme class at ambient temperature is then likely important to any broad mechanistic understanding ⁶⁸.

Low-lying excited states have also been observed in the non-heme iron in oxidized rubredoxin (ΔE_GS-_ES = 14 cm⁻¹ or 0.04 kcal/mol), 4Fe4S cluster active sites in ferredoxins, and several other protein active sites^45,63,69,70. The excited states of lower nuclearity 2Fe2S clusters are reported to be populated at temperatures as low as 80 K ^71,72.

Thermally accessible excited states in molecular systems

A central theme in molecular chemistry is understanding complex enzymatic and catalytic transformations by drawing insights from simpler synthetic models. Advances in supporting ligand synthesis and, particularly, those that template polynuclear metal complexes supported by weak-field donors, enable access to synthetic models of protein active sites that can approximate the electronic structures of metalloproteins. The excited states in these clusters, which exhibit distinct magnetic and electronic properties, are readily observed in magnetometry and paramagnetic spectroscopy.

Synthetic models of the water-oxidizing complex (WOC) in Photosystem II (PSII), reported by Agapie and coworkers, feature Mn₃Ca cubanes with low-lying excited states (5.5–350 cm⁻¹ or 0.02–1.00 kcal/mol). The triangular magnetic interactions between the three Mn(IV) are best modeled with two distinct overall coupling constants, one ferromagnetic and one antiferromagnetic, with their ratio determining the ground state. Upon desymmetrization of the pseudo C₃ symmetric parent complex (S_GS = 9/2), by substituting two acetate ligands with a bis-oxime, the spin state energies reorder, resulting in a new ground spin state (S_GS = 5/2) with low-lying exited states at 210 ± 50 cm⁻¹ (S_ES1 = 3/2) and 350 ± 50 cm⁻¹ (S_ES2 = 7/2). The destabilization of the S = 9/2 state beyond the second excited state in the low-symmetry product reveals the power of molecular symmetry and the influence of minor perturbations on spin-state energetics. Given the ongoing debate on the spin of the S₂ state in WOC and the sensitivity of the EPR spectrum to measurement conditions, the changes to the spin manifold by subtle coordination sphere changes underscore the need to move beyond ground-state mechanistic explorations^73,74. The conversion of H₂O to O₂ at WOC in PSII at physiological temperatures, with rapid motion of water and carboxylate residues around the active site, suggests that crossing between spin-states is aided by both temperature and the symmetry of the intermediates ⁷⁵.

For odd-electron clusters, the fine balance between the conflicting phenomena of double exchange and superexchange interactions that influence the spin-state energies of metal clusters is exemplified in the [2Fe2S]¹⁺ enzyme active sites and model complexes^76–83. A precondition for double exchange is the near-degeneracy of the coupling ions, to favor valence delocalization between the two metal centers rather than a valence-localized electronic structure. Amino acid residues that coordinate weakly to the mixed-valent cluster in the active site can control the extent of double exchange and, hence, the energy ordering of states by altering the local geometry around the paramagnetic ion. Considering only the primary coordination spheres, no significant structural changes are observed across multiple complexes that distinguish complexes with the S = 9/2 versus the S = 1/2 ground state in [2Fe2S]¹⁺ clusters^78–83. The presence of low-lying excited states in 2Fe2S complexes and intrinsic errors associated with X-ray diffraction measurements conducted at liquid nitrogen temperature (~80 K) limit such an analysis ^71,72,78.

In addition to the symmetry of the ligand environment around each high-spin ion, the role of the bridging ligand in manipulating the spin manifold was revealed in a recent study that modeled reduced 2Fe2S enzymatic clusters. The antiferromagnetically coupled [Fe₂S₂]¹⁺ (S_GS = 1/2), has low lying excited states at ~100 cm⁻¹ or 0.29 kcal/mol (S_ES1 = 3/2) and ~300 cm⁻¹ or 0.86 kcal/mol(S_ES2 = 5/2). Switching the bridging ligand to Se^2- compresses the spin ladder with ground states and the first three excited states (S = 3/2, 5/2, and 7/2, respectively) lying within 100 cm⁻¹ or 0.29 kcal/mol. Furthermore, substituting for Te^2-, S = 3/2 becomes the new ground state, thereby raising the energy of S = ½. The authors attribute spin-state energetic rearrangements to the influence of the chalcogenide on vibronic coupling⁸⁴. A similar phenomenon of Se^2- stabilizing high-spin states in enzymatic systems is observed in the selenium-substituted [4Fe-4Se] ferredoxin in Photosystem I (PSI), which adopts an S_GS = 7/2 with accessible excited states, whereas the wild-type ferredoxin displays S_GS = 3/2^85,86. The reversible interconversion between S = 9/2 and S = ½ as a function of pH in the reduced forms of C56S and C60S variants of the Clostridium pasteurianum ferredoxin, also bears resemblance to the observations in the synthetic system⁷⁷. Extending to oxygen-atom bridged systems, the tuning of the spin ladder by means of bridging ligand orientation is commonly observed for peroxide complexes. The two degenerate low-lying orthogonal π* orbitals can influence the magnitude and sign of the exchange coupling by adjusting the overlap and orientation of the π* orbitals with the magnetic orbitals of the metals^87,88. However, most reported O₂^2- complexes have metals in a strong-field environment, with high-energy excited states⁸⁹. Finally, transitioning to hydride donors, a recent report observes that the dynamic motion of the bridging hydrides in an iron(II) hydride dimer above 160 K influences the local spin state at each Fe(II) center. The dynamic motion of the µ-hydrides causes the two Fe(II) centers to interconvert between two local geometries and two individual ion spin states (square planar (s = 1) and tetrahedral (s = 2)). The complex undergoes this transformation without a spin change; however, the SOC of the three low-lying (S = 3) excited states (ΔE_GS-_ES = 390 cm⁻¹ (1.12 kcal/mol), 770 cm⁻¹ (2.20 kcal/mol), and 1250 cm⁻¹ (3.57 kcal/mol)) with the GS, as observed in the contribution of the excited states to the ZFS parameter, suggests the role of these excited states in bringing about the structural change ⁹⁰.

Hence, although much work remains to be done in mechanistic elucidation techniques for synthetic clusters featuring low-lying excited states, progress in the field toward achieving structural and electronic similarity to enzymatic active sites promises the field’s potential to unravel enzymatic pathways.

The role of computational chemistry in mechanistic elucidation

Due to the lack of clear spin-crossover signatures, experimental evidence for spin-crossover during a reaction is at best suggestive⁹¹. As such, computational methods are critical to advancing the concept of TSR^14,91. In particular, reaction trajectory calculations on different spin state surfaces report on the role of excited states in dictating reactivity at ambient temperatures when compared with experimental values of the rate constants. The straightforward approach to this problem is to first calculate the initial energies of the thermally populated electronic states of the reactant, then track the energies of the intermediates arising from each state as the substrate approaches. This process must be repeated for each thermally accessible excited state, which results in substantial computational expense. However, for weak-field clusters with low-lying (almost degenerate) excited states for reactants and intermediates, accurate energy calculations are needed, incurring more computational cost.

Two major approaches to calculating electronic state energies are wave-function theory (WFT) based methods and density functional theory (DFT). WFT methods solve the Schrödinger equation using approximate wave functions that capture the relevant features of the electronic structure (viz., valence-shell electronic interactions) with minimal parametrization of low-impact features (viz., core-shell electronic interactions). DFT methods derive the energy of states from the electronic density (a 3-dimensional quantity), bypassing the need to solve for the wavefunction (a 3N-dimensional quantity, where N is the number of atoms), and are a cheaper yet reasonably accurate computational method for calculating electronic state energies.

Significant advances in multireference wavefunction methods have led to an array of theories with various extensions aimed at improving performance across different use cases. Methods like Full Configuration Interaction (FCI), Complete Active Space Self-Consistent Field (CAS-SCF), Diagonal Matrix Renormalization Group (DMRG), Multireference Configuration Interaction (MRCI), and Multireference Coupled Cluster (MRCC), when coupled with extensions that improve accuracy and performance, should, in theory, help track spin manifold energies along a reaction pathway^92,93. Notable recent advances in using WFT approaches to compute the excited state energies of polynuclear metal clusters include the calculation of low-lying excited states and the spectra of Fe₄S₄ clusters and the Mn₄CaO₅ cluster in PSII using DMRG methods^94–97. Although other methods have been used to compute the energies of excited states of other biologically relevant multinuclear clusters and to probe the multiconfigurational ground state of lanthanides and actinides, the computational expense limits their use to benchmarking other methods^20,98,99. However, aside from the computational cost, a recurring theme in successfully implementing WFT calculations is the experiential knowledge in the selection of the active space^100–103. This prerequisite, along with the high computational cost and high level of theory, renders the cornucopia of WFT methods a significant bottleneck for experimental chemists seeking to track the ambient-temperature mechanism of clusters with low-lying excited states^104,105. The effect of this bottleneck is evident in the vast gap between reports on theory development and reports using these methods to compute reaction pathways of high-spin clusters^92,106. Unlike WFT methods, which perform well at capturing the strong correlation in electronic states, DFT methods, although affordable, due to their inherent single-determinant nature, struggle to accurately capture electron correlation, especially static correlation energy^107–110. The functional dependency of DFT and the corresponding errors involved further undermine the ability of DFT to accurately calculate energies of low-lying excited states ^111–113.

Consequently, ab initio mechanistic explorations that consider only ground states have led to mechanistic conclusions that differ from those proposed by experiments, complementing the inference illustrated in Fig. 5. A mechanistic elucidation study of the dehydrogenation of indolines by a diferric MMO mimic proposed that it proceeds via a μ-1,2-(hydro)peroxo intermediate, corroborated by resonance Raman (rR) spectroscopy¹¹⁴. Later, a DFT mechanistic exploration proposed an alternate pathway proceeding through a μ-1,1-(hydro)peroxo intermediate, contradicting the spectroscopic conclusion. However, to the merit of the ab initio methods, the calculated KIE and stereochemical selectivity match the experimental values ¹¹⁵.

A case of inconsistency encompassing spectroscopic and ab initio calculations is of the structurally related diiron active site of N-oxygenases, CmII and AurF enzymes, which has been proposed to go through a peroxy-level diferric P’ intermediate. The structure of P’ is disputed owing to different spectroscopic and ab initio calculation results. Results from nuclear resonance vibrational spectroscopy (NRVS) measured at He(I)-cooled cryostat conditions, supported by DFT (BP86-HF/6-31G*) calculations, indicate a μ-1,2-hydroperoxide structure¹¹⁶. A subsequent report, using DFT (B3LYP*-D3/LANL2TZ(f)) calculations, proposed a μ-η²:η² peroxo-bridged structure for P’¹¹⁷. A later spectroscopic report using extended X-ray absorption fine structure (EXAFS) measured at ∼10 K and rR spectroscopy measured at 4 °C proposed a μ-1,1-peroxide bridge¹¹⁸. The most recent study featuring NRVS at 60–80 K, supported by DFT (BP86-HF/6-31 G*), agrees with the prior NRVS report and supports a (μ-1,2-hydroxoperoxo)ferric site with a second hydroxide bridge¹¹⁹. Although other factors, such as sample preparation methods and conditions, might influence spectroscopic results, the presence of low-lying ground states of analogous active sites and the spectroscopic measurements performed at different temperatures can vary state populations that the ground state DFT calculations also struggle to capture ⁴⁶.

In their current form, ab initio methods cannot serve as routine tools for investigating the participation of thermally populated low-lying excited states. However, two promising advances in the field of ab initio method development that broaden accessibility to more accurate Hamiltonian solutions for excited states for computationally inexperienced experimentalists are automated active space selection and machine-learned functionals. Rather than applying the conventional trial-and-error method of selecting active spaces, systematic approaches such as those based on orbital entanglement entropy—a measure of electron correlation in the selected active space—(viz., AutoCAS and approximate pair coefficient (APC)), construction of active spaces with knowledge of which atomic orbitals contribute most to the strong correlation effects (viz., automatic valence active space (AVAS)), and several others^{100,102,120,121}. The automated active space selection methods have demonstrated promise, with the current state-of-the-art methods being able to predict excitation energies of mononuclear transition metals^100,122. On a parallel front, system-specific trained functionals, which have optimized weights for energy corrections to be used in energy estimations for the corresponding systems, are also gaining traction^123–125. A notable advance in machine-learned functionals has been the calculated incorporation of the Hartree-Fock exchange correction into the PBE or SCAN functional to calculate the spin-splitting energy (E_HS-E_LS) for mononuclear transition metals ¹²⁶.

Despite advances in electronic structure methods on classical computers, the holy grail of ab initio methods lies in the confluence of implementing quantum chemistry on quantum computers^127,128. The multistate qubits alleviate the scalability bottleneck that binary bits pose. Variational quantum algorithms (viz., variational quantum eigensolver or quantum phase estimation) implemented on quantum computers scale ~10⁹ and ~10³ less than Full CI or CI/DMRG methods, respectively, on classical computers^129,130. Newer modified quantum algorithms have reported cost scaling comparable to that of DFT, promising the routine use of quantum computers for excited-state energy calculations in the future^131–133. However, due to the absence of any practical test case scenarios and the nascent nature of the field, the extent of future applications remains speculative but optimistic.

Outlook

A general theme of functional versatility is emerging as more probes into biochemical processes are conducted, as exemplified by findings on enzyme promiscuity¹³⁴. A potential pathway by which this versatility is realized in weak-field ligated metal clusters is the existence of low-lying spin states due to the magnetic interaction between the open-shell ions. The thermal population of these low-lying excited states, in combination with the clusters’ low reorganization energy, provides access to multiple PES, engendering versatile reactivity. With respect to exploring the mechanism of the transformations, these thermally populated excited states lead to irregularities in structural, kinetic, and spectroscopic observations conducted across a range of temperatures. Although the ideal solution to this problem is to conduct all mechanistic studies at a single temperature, preferably at the temperatures at which these transformations occur in nature, the limitations imposed by spectroscopic techniques and the fast reaction rates undermine its practicality. An alternative approach to mechanistic investigations involves utilizing ab initio methods to elucidate the excited states pertinent to the reactivity. This approach necessitates methods capable of accurately determining the energies of reactants and intermediates. However, the double-edged sword of strong electron correlation in these systems limits the effectiveness of conventional single-reference DFT methods and necessitates the use of computationally more demanding wave-function methods. Hence, the accurate determination of the mechanism of multimetallic enzymes depends on making WFT calculations affordable without sacrificing accuracy. Although the use of WFT calculations on quantum computers is seen as a potential solution to this problem, the field’s nascent state renders any projections tentative.

Synthetic high-spin clusters, which can give rise to low-lying excited states while emulating a protein-like coordination sphere, are another potential solution that can inform the mechanism of enzyme active sites. The development of such model complexes is primarily fueled by advances in the synthesis of supporting ligand architectures. The compatibility of these clusters with a wider range of spectroscopic techniques than those available for active sites embedded in protein scaffolds provides more handles for elucidating mechanisms. Although mechanistic inferences drawn from these molecular systems can be complemented by ab initio methods to inform on enzyme active-site reactivity, the problems faced by active-site clusters are pertinent here as well. However, the experiential knowledge required for ab initio calculations in certain systems can be a beneficial artifact for molecular systems, where optimizing functionals or methods (e.g., for DFT) or selecting active spaces (e.g., for WFT methods) on similar model systems can prove useful in performing calculations for complex reactivity mechanisms, including elucidation, in those cases. Advances in theory development, such as automated active space selection or learned functional selection, promise better accuracy while alleviating the high entry-level barrier to computational calculations for experimentalists.

Author contributions

T.S.J. wrote the original draft and contributed to editing & reviewing. L.J.M. conceptualized the study and contributed to writing, editing, & reviewing. Both authors agree with the final version of the manuscript.

Peer review

Peer review information

Nature Communications thanks Nia Rodney-Pollard and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-78033-7.