Orbital interactions, electron delocalization and spin coupling in iron-sulfur clusters

Restricted Open-Shell Hartree-Fock Method for a General Configuration State Function Featuring Arbitrarily Complex Spin-Couplings

In this work, we present a general spin restricted open-shell Hartree-Fock (ROHF) implementation that is able to generate self-consistent field (SCF) wave functions for an arbitrary configuration state function (CSF). These CSFs can contain an arbitrary number of unpaired electrons in arbitrary spin-couplings. The resulting method is named CSF-ROHF. We demonstrate that starting from the ROHF energy expression, for example, the one given by Edwards and Zerner, it is possible to obtain the values of the ROHF vector-coupling coefficients by setting up an open-shell for each group of consecutive parallel-coupled spins dictated by the unique spin-coupling pattern of any given CSF. To achieve this important and nontrivial goal, we employ the machinery of the iterative configuration expansion configuration interaction (ICE-CI) method, which is able to tackle general CI problems on the basis of spin-adapted CSFs. This development allows for the efficient generation of SCF spin-eigenfunctions for systems with complex spin-coupling patterns, such as polymetallic chains and metal clusters, while maintaining SCF scaling with system size (quadratic or less, depending on the specific algorithm and approximations chosen).

Magnetic study and DFT analysis of a doubly carboxylato-bridged Co(II) derivative anchored with a 'scorpionate' precursor as a potential electrocatalyst for heterogeneous H2 evolution

A new doubly carboxylato-bridged Co(II) dinuclear complex, [Co(bdtbpza)(NCS)]2 (1), was obtained in a satisfactory yield by employing a 'scorpionate'-type precursor, bdtbpza {bis-(3,5-di-tert-butylpyrazol-1-yl)acetate}, and was then structurally characterized. Single-crystal X-ray diffraction analysis revealed that, in 1, each Co(II) is penta-coordinated, leading to a distorted trigonal-bipyramidal geometry within the coordination environment of N3O2. Weak antiferromagnetic coupling within the Co(II) ions in 1 was found based on the isotropic spin Hamiltonian H = -J(S1·S2) for the Si = 3/2 system. For evaluating the spin density distribution and the mechanism for the magnetic exchange coupling, DFT analysis was performed, with the calculated result agreeing the experimental magnetic data. A study into electrochemical H2 evolution, involving cyclic voltammetry (CV), controlled potential electrolysis (CPE), and gas chromatographic (GC) analyses of the graphite electrode modified with the cobalt complex in a neutral aqueous solution revealed the high catalytic activity of the complex with a low overpotential toward H2O reduction. The faradaic efficiency of the catalyst was found to be 83.7% and the di-cobalt catalyst-modified electrode displayed quite an interesting H2-evolution activity compared with that of bare electrodes. These results are encouraging for the future potential application of 1 in water splitting.

Ni(2,2':6',2''-terpyridine)2: a high-spin octahedral formal Ni(0) complex

We have synthesised and characterised the complex Ni(tpy)2 (tpy = 2,2':6',2''-terpyridine). This formally Ni(0) complex is paramagnetic both in the solid state and in solution (S = 2). The crystal structure shows an octahedral geometry, with molecules arranged in independent dimers involving π-stacking between pairs of complexes. Magnetic measurementes and DFT calculations suggest the existence of temperature-dependent intermolecular antiferromagnetic coupling in the solid state.

Initial Steps in Methanobactin Biosynthesis: Substrate Binding by the Mixed-Valent Diiron Enzyme MbnBC

The MbnBC enzyme complex converts cysteine residues in a peptide substrate, MbnA, to oxazolone/thioamide groups during the biosynthesis of copper chelator methanobactin (Mbn). MbnBC belongs to the mixed-valent diiron oxygenase (MVDO) family, of which members use an Fe(II)Fe(III) cofactor to react with dioxygen for substrate modification. Several crystal structures of the inactive Fe(III)Fe(III) form of MbnBC alone and in complex with MbnA have been reported, but a mechanistic understanding requires determination of the oxidation states of the crystallographically observed Fe ions in the catalytically active Fe(II)Fe(III) state, along with the site of MbnA binding. Here, we have used electron nuclear double resonance (ENDOR) spectroscopy to determine such structural and electronic properties of the active site, in particular, the mode of substrate binding to the MV state, information not accessible by X-ray crystallography alone. The oxidation states of the two Fe ions were determined by 15N ENDOR analysis. The presence and locations of both bridging and terminal exogenous solvent ligands were determined using 1H and 2H ENDOR. In addition, 2H ENDOR using an isotopically labeled MbnA substrate indicates that MbnA binds to the Fe(III) ion of the cluster via the sulfur atom of its N-terminal modifiable cysteine residue, with displacement of a coordinated solvent ligand as shown by complementary 1H ENDOR. These results, which underscore the utility of ENDOR in studying MVDOs, provide a molecular picture of the initial steps in Mbn biosynthesis.

Ligand Field Sensitive Spin Acceleration in the Iron-Catalyzed [2 + 2] Cycloaddition of Unactivated Alkenes and Dienes

Redox-active pyridine(diimine) (PDI) iron catalysts promote the reversible [2 + 2] cycloaddition of alkenes and dienes to cyclobutane derivatives that have applications ranging from fuels to chemically recyclable polymers. Metallacycles were identified as key intermediates, and spin crossover from the singlet to the triplet surface was calculated to facilitate the reductive coupling step responsible for the formation of the four-membered ring. In this work, a series of sterically and electronically differentiated PDI ligands was studied for the [2 + 2] cycloaddition of ethylene and butadiene to vinylcyclobutane. Kinetic studies revealed that the fastest and slowest turnover were observed with equally electron-deficient supporting ligands that either feature phenyl-substituted imine carbon atoms (MeBPDI) or a pyrazine core (MePZDI). While the oxidative cyclization was comparatively slow for both catalysts, the rate of reductive coupling─determined by stoichiometric 13C2H4 labeling studies─correlated with the turnover frequencies. Two-state density functional theory studies and the distinct electronic structures of related (iPrBPDI) and (iPrPZDI) iron methyl complexes revealed significantly different ligand field strengths due to either diminished ligand σ-donation (MeBPDI) or promoted metal π-backbonding (MePZDI). Spin acceleration, leading to fast reductive coupling and catalytic turnover, was promoted in the case of the weaker ligand field and depends on both the nature and position of the electron-withdrawing group. This study provides strong evidence for the role of two-state reactivity in C(sp3)-C(sp3) bond formation and insights on how ligand design either promotes or inhibits spin acceleration in earth-abundant metal catalysis.

The protein phosphorylation landscape in photosystem I of the desert algae Chlorella sp

The phosphorylation of photosystem II (PSII) and its antenna (LHCII) proteins has been studied, and its involvement in state transitions and PSII repair is known. Yet, little is known about the phosphorylation of photosystem I (PSI) and its antenna (LHCI) proteins. Here, we applied proteomics analysis to generate a map of the phosphorylation sites of the PSI-LHCI proteins in Chlorella ohadii cells that were grown under low or extreme high-light intensities (LL and HL). Furthermore, we analyzed the content of oxidized tryptophans and PSI-LHCI protein degradation products in these cells, to estimate the light-induced damage to PSI-LHCI. Our work revealed the phosphorylation of 17 of 22 PSI-LHCI subunits. The analyses detected the extensive phosphorylation of the LHCI subunits Lhca6 and Lhca7, which is modulated by growth light intensity. Other PSI-LHCI subunits were phosphorylated to a lesser extent, including PsaE, where molecular dynamic simulation proposed that a phosphoserine stabilizes ferredoxin binding. Additionally, we show that HL-grown cells accumulate less oxidative damage and degradation products of PSI-LHCI proteins, compared with LL-grown cells. The significant phosphorylation of Lhca6 and Lhca7 at the interface with other LHCI subunits suggests a physiological role during photosynthesis, possibly by altering light-harvesting characteristics and binding of other subunits.

Mechanisms of hydrogen evolution by six-coordinate cobalt complexes: a density functional study on the role of a redox-active pyridinyl-substituted diaminotriazine benzamidine ligand as a proton relay

The hydrogen evolution reaction is an important process for energy storage. The six-coordinate cobalt complex [CoIII(L1-)(LH)]2+ (LH = N-(4-amino-6-(pyridin-2-yl)-1,3,5-triazin-2-yl)benzamidine) was found to catalyze photocatalytic hydrogen evolution. In this work, we performed density functional calculations to obtain the reduction potentials and the proton-transfer free energy of possible intermediates to determine the preferred pathways for proton reduction. The mechanism involves the metal-based reduction of Co(III) to Co(II) before the protonation at the amidinate N on the pyridinyl-substituted diaminotriazine benzamidinate ligand L1- to form [CoII(LH)(LH)]2+. Essentially, the subsequent electron transfer is not metal-based reduction, but rather ligand-based reduction to form [CoII(LH)(LH˙1-)]1+. Through a proton-coupled electron transfer process, the cobalt hydride [CoIIH(LH)(LH2˙)]1+ is formed as the key intermediate for hydrogen evolution. As the cobalt hydride complex is coordinatively saturated, a structural change is required when the hydride on Co is coupled with the proton on pyridine. Notably, the redox-active nature of the ligand results in the low acidity of the protonated pyridine moiety of LH2˙, which impedes its function as a proton relay. Our findings suggest that separating the proton relay fragment from the electron reservoir fragment of the redox-active ligand is preferred for fully utilizing both features in catalytic H2 evolution.

What governs magnetic exchange couplings in radical-bridged dinuclear complexes?

Coupling transition metal or lanthanide ions through a radical bridging ligand is a promising route to increase performances in the area of single molecular magnets. A better understanding of the underlying physical mechanisms governing the magnetic exchange couplings is thus of valuable importance to design future compounds. Here, couplings in three series of metal-radical-metal compounds based on transition metal ions are investigated by means of the decomposition/recomposition methods. This work presents the generalisation and first application of the method to systems with an arbitrary number of magnetic centres featuring several unpaired electrons. Thanks to the decomposition into the three main contributions (direct exchange, kinetic exchange, and spin polarisation) as well as a description in terms of electron-electron interactions, we study the influence of the nature of the metal centre and the radical ligand on the couplings. We combine the energetic contributions extracted with orbital and charge population analysis to rationalise the results.

The cytochrome b6f complex: plastoquinol oxidation and regulation of electron transport in chloroplasts

In oxygenic photosynthetic systems, the cytochrome b6f (Cytb6f) complex (plastoquinol:plastocyanin oxidoreductase) is a heart of the hub that provides connectivity between photosystems (PS) II and I. In this review, the structure and function of the Cytb6f complex are briefly outlined, being focused on the mechanisms of a bifurcated (two-electron) oxidation of plastoquinol (PQH2). In plant chloroplasts, under a wide range of experimental conditions (pH and temperature), a diffusion of PQH2 from PSII to the Cytb6f does not limit the intersystem electron transport. The overall rate of PQH2 turnover is determined mainly by the first step of the bifurcated oxidation of PQH2 at the catalytic site Qo, i.e., the reaction of electron transfer from PQH2 to the Fe2S2 cluster of the high-potential Rieske iron-sulfur protein (ISP). This point has been supported by the quantum chemical analysis of PQH2 oxidation within the framework of a model system including the Fe2S2 cluster of the ISP and surrounding amino acids, the low-potential heme b6L, Glu78 and 2,3,5-trimethylbenzoquinol (the tail-less analog of PQH2). Other structure-function relationships and mechanisms of electron transport regulation of oxygenic photosynthesis associated with the Cytb6f complex are briefly outlined: pH-dependent control of the intersystem electron transport and the regulatory balance between the operation of linear and cyclic electron transfer chains.

The chimera of 2D- and 1D-graphene magnetization by hydrogenation or fluorination: critically revisiting old schemes and proposing new ones by ab initio methods

Graphene is an ideal candidate material for spintronics due to its layered structure and peculiar electronic structure. However, in its pristine state, the production of magnetic moments is not trivial. A very appealing approach is the chemical modification of pristine graphene. The main obstacle is the control of the geometrical features and the selectivity of functional groups. The lack of a periodic functionalization pattern of the graphene sheet prevents, therefore, the achievement of long-range magnetic order, thus limiting its use in spintronic devices. In such regards, the stability and the magnitude of the instilled magnetic moment depending on the size and shape of in silico designed graphane islands and ribbons embedded in graphene matrix will be computed and analysed. Our findings thus suggest that a novel and magneto-active graphene derivative nanostructure could become achievable more easily than extended graphone or nanoribbons, with a strong potential for future spintronics applications with a variable spin-current density.

Antiaromatic Molecules as Magnetic Couplers: A Computational Quest

In this study, we investigate a set of organic diradical structures in which two oxo-verdazyl radicals are selected as radical spin centers that are connected (coupled) via six coupler molecules (CM), resulting in various magnetic (ferromagnetic (FM) or antiferromagnetic (AFM)) characteristics, as reflected by their exchange coupling constants (J). We have designed 12 diradicals with 6-antiaromatic couplers coupled with bis-oxo-verdazyl diradicals with meta-meta (m-m) and para-meta (p-m) positional connectivities. The nature of the magnetic coupling (ferromagnetic, nonmagnetic, or antiferromagnetic) and the magnitude of the exchange constant J depend on the type of coupler, the connecting point between each radical center and CM, the degree of aromaticity of the coupler, and the length of the through-bond distance between radical centers. The computed magnetic exchange coupling constants J for these diradicals at the B3LYP/6-311++G(d,p) and MN12SX/6-311++G(d,p) levels of theory are large for many of these structures, indicating strong ferromagnetic coupling (with positive J values). In some cases, magnetic couplings are observed with J > 1000 cm-1 (B3LYP/6-311++G(d,p)) and strong antiferromagnetic coupling (with negative J values) with J < -1000 cm-1 (B3LYP/6-311++G(d,p)). Similarly, in some cases, magnetic couplings are observed with J > 289 cm-1 (MN12SX/6-311++G(d,p)) and strong antiferromagnetic coupling (with negative J values) with J < -568 cm-1 (MN12SX/6-311++G(d,p)). Furthermore, while numerous studies have reported that the degree of aromaticity of molecular couplers often favors strong ferromagnetic coupling, displaying the high-spin character of diradicals in their ground states, the couplers chosen in this study are characterized as antiaromatic or nonaromatic. The current investigation provides evidence that, remarkably, antiaromatic couplers are able to enhance stability by favoring electronic diradical structures with very strong ferromagnetic coupling when the length of the through-bond distance and connectivity pattern between radical centers are selected in such a way that the FM coupling is optimized. The findings in this study offer new strategies in the design of novel organic materials with interesting magnetic properties for practical applications.

Development of molecular cluster models to probe pyrite surface reactivity

The recent discovery that anaerobic methanogens can reductively dissolve pyrite and utilize dissolution products as a source of iron and sulfur to meet their biosynthetic demands for these elements prompted the development of atomic-scale nanoparticle models, as maquettes of reactive surface sites, for describing the fundamental redox steps that take place at the mineral surface during reduction. The given report describes our computational approach for modeling n(FeS2 ) nanoparticles originated from mineral bulk structure. These maquettes contain a comprehensive set of coordinatively unsaturated Fe(II) sites that are connected via a range of persulfide (S2 2- ) ligation. In addition to the specific maquettes with n = 8, 18, and 32 FeS2 units, we established guidelines for obtaining low-energy structures by considering the pattern of ionic, covalent, and magnetic interactions among the metal and ligand sites. The developed models serve as computational nano-reactors that can be used to describe the reductive dissolution mechanism of pyrite to better understand the reactive sites on the mineral, where microbial extracellular electron-transfer reactions can occur.

Kinetic and thermodynamic control of C(sp2)-H activation enables site-selective borylation

Catalysts that distinguish between electronically distinct carbon-hydrogen (C-H) bonds without relying on steric effects or directing groups are challenging to design. In this work, cobalt precatalysts supported by N-alkyl-imidazole-substituted pyridine dicarbene (ACNC) pincer ligands are described that enable undirected, remote borylation of fluoroaromatics and expansion of scope to include electron-rich arenes, pyridines, and tri- and difluoromethoxylated arenes, thereby addressing one of the major limitations of first-row transition metal C-H functionalization catalysts. Mechanistic studies established a kinetic preference for C-H bond activation at the meta-position despite cobalt-aryl complexes resulting from ortho C-H activation being thermodynamically preferred. Switchable site selectivity in C-H borylation as a function of the boron reagent was thereby preliminarily demonstrated using a single precatalyst.

Expression of clMagR/clCry4 protein in mBMSCs provides T2-contrast enhancement of MRI

Here, we propose for the first time the evaluation of magnetosensitive clMagR/clCry4 as a magnetic resonance imaging (MRI) reporter gene that imparts sensitivity to endogenous contrast in eukaryotic organisms. Using a lentiviral vector, we introduced clMagR/clCry4 into C57BL/6 mice-derived bone marrow mesenchymal stem cells (mBMSCs), which could specifically bind with iron, significantly affected MRI transverse relaxation, and generated readily detectable contrast without adverse effects in vivo. Specifically, clMagR/clCry4 makes mBMSCs beneficial for enhancing the sensitivity of MRI-R2 for iron-bearing granules, in which cells recruit exogenous iron and convert these stores into an MRI-detectable contrast; this is not achievable with control cells. Additionally, Prussian blue staining was performed together with ultrathin cell slices to provide direct evidence of natural iron-bearing granules being detectable on MRI. Hence, it was inferred that the sensitivity of MRI detection should be correlated with clMagR/clCry4 and exogenous iron. Taken together, the clMagR/clCry4 has great potential as an MRI reporter gene. STATEMENT OF SIGNIFICANCE: In this study, we propose the evaluation of magnetosensitive clMagR/clCry4 as an MRI reporter gene, imparting detection sensitivity to eukaryotic mBMSCs for endogenous contrast. At this point, the clMagR and clCry4 were located within the cytoplasm and possibly influence each other. The clMagR/clCry4 makes mBMSCs beneficial for enhancing the sensitivity of MRI-R2 for iron-bearing granules, in which protein could specifically bind with iron and convert these stores into MRI-detectable contrast; this is not achieved by control cells. The viewpoint was speculated that the clMagR/clCry4 and exogenous iron were complementary to each other. Additionally, Prussian blue staining was performed together with TEM observations to provide direct evidence that the iron-bearing granules were sensitive to MRI.

Multifunctional Roles of Clathrate Hydrate Nanoreactors for CO2 Reduction

In this study, we explore a possible platform for the CO2 reduction (CO2 R) in one of water's solid phases, namely clathrate hydrates (CHs), by ab initio molecular dynamics and well-tempered metadynamics simulations with periodic boundary conditions. We found that the stacked H2 O nanocages in CHs help to initialize CO2 R by increasing the electron-binding ability of CO2 . The substantial CO2 R processes are further influenced by the hydrogen bond networks in CHs. The first intermediate CO2 - in this process can be stabilized through cage structure reorganization into the H-bonded [CO2 - ⋅⋅⋅H-OHcage ] complex. Further cooperative structural dynamics enables the complex to convert into a vital transient [CO2 2- ⋅⋅⋅H-OHcage ] intermediate in a low-barrier disproportionation-like process. Such a highly reactive intermediate spontaneously triggers subsequent double proton transfer along its tethering H-bonds, finally converting it into HCOOH. These hydrogen-bonded nanoreactors feature multiple functions in facilitating CO2 R such as confining, tethering, H-bond catalyzing and proton pumping. Our findings have a general interest and extend the knowledge of CO2 R into porous aqueous systems.

Systematic determination of coupling constants in spin clusters from broken-symmetry mean-field solutions

Quantum-chemical calculations aimed at deriving magnetic coupling constants in exchange-coupled spin clusters commonly utilize a broken-symmetry (BS) approach. This involves calculating several distinct collinear spin configurations, predominantly by density-functional theory. The energies of these configurations are interpreted in terms of the Heisenberg model, H̃=∑i Collapse

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Shadan Ghassemi Tabrizi Department of Chemistry, University of Potsdam, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam-Golm, Germany

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The Nature of the Chemical Bonds of High-Valent Transition-Metal Oxo (M=O) and Peroxo (MOO) Compounds: A Historical Perspective of the Metal Oxyl-Radical Character by the Classical to Quantum Computations

This review article describes a historical perspective of elucidation of the nature of the chemical bonds of the high-valent transition metal oxo (M=O) and peroxo (M-O-O) compounds in chemistry and biology. The basic concepts and theoretical backgrounds of the broken-symmetry (BS) method are revisited to explain orbital symmetry conservation and orbital symmetry breaking for the theoretical characterization of four different mechanisms of chemical reactions. Beyond BS methods using the natural orbitals (UNO) of the BS solutions, such as UNO CI (CC), are also revisited for the elucidation of the scope and applicability of the BS methods. Several chemical indices have been derived as the conceptual bridges between the BS and beyond BS methods. The BS molecular orbital models have been employed to explain the metal oxyl-radical character of the M=O and M-O-O bonds, which respond to their radical reactivity. The isolobal and isospin analogy between carbonyl oxide R2C-O-O and metal peroxide LFe-O-O has been applied to understand and explain the chameleonic chemical reactivity of these compounds. The isolobal and isospin analogy among Fe=O, O=O, and O have also provided the triplet atomic oxygen (3O) model for non-heme Fe(IV)=O species with strong radical reactivity. The chameleonic reactivity of the compounds I (Cpd I) and II (Cpd II) is also explained by this analogy. The early proposals obtained by these theoretical models have been examined based on recent computational results by hybrid DFT (UHDFT), DLPNO CCSD(T0), CASPT2, and UNO CI (CC) methods and quantum computing (QC).

Computational Description of Alkylated Iron-Sulfur Organometallic Clusters

The radical S-adenosyl methionine (SAM) enzyme superfamily has widespread roles in hydrogen atom abstraction reactions of crucial biological importance. In these enzymes, reductive cleavage of SAM bound to a [4Fe-4S]1+ cluster generates the 5'-deoxyadenosyl radical (5'-dAdo•) which ultimately abstracts an H atom from the substrate. However, overwhelming experimental evidence has surprisingly revealed an obligatory organometallic intermediate Ω exhibiting an Fe-C5'-adenosyl bond, whose properties are the target of this theoretical investigation. We report a readily applied, two-configuration version of broken symmetry DFT, denoted 2C-DFT, designed to allow the accurate description of the hyperfine coupling constants and g-tensors of an alkyl group bound to a multimetallic iron-sulfur cluster. This approach has been validated by the excellent agreement of its results both with those of multiconfigurational complete active space self-consistent field computations for a series of model complexes and with the results from electron nuclear double-resonance/electron paramagnetic resonance spectroscopic studies for the crystallographically characterized complex, M-CH3, a [4Fe-4S] cluster with a Fe-CH3 bond. The likewise excellent agreement between spectroscopic results and 2C-DFT computations for Ω confirm its identity as an organometallic complex with a bond between an Fe of the [4Fe-4S] cluster and C5' of the deoxyadenosyl moiety, as first proposed.

Magnetic coupling modulation in meta-nitroxide-functionalized isoalloxazine magnets with redox-active units as efficient side-modulators

Magnetic conversion can be accomplished in a variety of ways, as organic molecules with switchable magnetic characteristics offer numerous technological applications. It is crucial to find magnetism-switchable systems because, in the field of organic magnetic materials, the redox-induced magnetic reversal is very simple to achieve and shows significant applications. Herein, we computationally design isoalloxazine-based diradicals through oxidizing N10 and adding a nitroxide to C8 as the spin source (i.e. 8-nitroxide-isoalloxazine 10-oxide, an m-phenylene-like nitroxide diradical expanded with a redox unit as a side-modulator) and its N1/N5-hydrogenated/protonated diradical derivatives and introducing substituents (-OH, -NH₂, and -NO₂) to C6. We demonstrate that the basically modified structure exhibits ferromagnetic (FM) characteristics with a magnetic coupling constant (J) of 561.3 cm^-1 calculated at the B3LYP/6-311+G(d,p) level, obeying the meta-phenylene-mediated diradical character, and dihydrogenation can lead to an AFM diradical with considerably large J (-976.1 cm^-1). Surprisingly, protonation at N1 or N5 can lead to distinctly different magnetic variations (561.3 → -1602.9 cm^-1 at N1 versus 561.3 → 379.1 cm^-1 at N5). Analyses indicate that small singlet-triplet energy gaps and small energy gaps between the highest occupied and lowest unoccupied molecular orbitals (HOMO, LUMO) of the closed shell singlet state are the key features of these isoalloxazine diradicals, and aromaticity variations, significant spin delocalization from the π-conjugated structure and spin polarization from the non-Kekule structure induced by modification are responsible for the magnetic conversion. Furthermore, the spin alternation rule, the singly occupied molecular orbital (SOMO) effect, and the SOMO-SOMO energy splitting of the triplet state are used to analyze these distinct variations. This work provides a novel understanding of the structures and characteristics of modified isoalloxazine diradicals, as well as essential details for the intricate design and characterization of new isoalloxazine-based potential organic magnetic switches.

Evidence of Atypical Structural Flexibility of the Active Site Surrounding of an [FeFe] Hydrogenase from Clostridium beijerinkii

[FeFe] hydrogenase from Clostridium beijerinkii (CbHydA1) is an unusual hydrogenase in that it can withstand prolonged exposure to O₂ by reversibly converting into an O₂-protected, inactive state (H_inact). It has been indicated in the past that an atypical conformation of the "SC₃₆₇CP" loop near the [2Fe]_H portion of the six-iron active site (H-cluster) allows the Cys367 residue to adopt an "off-H⁺-pathway" orientation, promoting a facile transition of the cofactor to H_inact. Here, we investigated the electronic structure of the H-cluster in the oxidized state (H_ox) that directly converts to H_inact under oxidizing conditions and the related CO-inhibited state (H_ox-CO). We demonstrate that both states exhibit two distinct forms in electron paramagnetic resonance (EPR) spectroscopy. The ratio between the two forms is pH-dependent but also sensitive to the buffer choice. Our IR and EPR analyses illustrate that the spectral heterogeneity is due to a perturbation of the coordination environment of the H-cluster's [4Fe4S]_H subcluster without affecting the [2Fe]_H subcluster. Overall, we conclude that the observation of two spectral components per state is evidence of heterogeneity of the environment of the H-cluster likely associated with conformational mobility of the SCCP loop. Such flexibility may allow Cys367 to switch rapidly between off- and on-H⁺-pathway rotamers. Consequently, we believe such structural mobility may be the key to maintaining high enzymatic activity while allowing a facile transition to the O₂-protected state.

Revisiting magnetic exchange couplings in heterodinuclear complexes through the decomposition method in KS-DFT

Providing tools to understand the physical mechanisms governing magnetic properties in transition metal-based compounds is still of great interest. Here, the magnetic exchange coupling in a series of heterodinuclear complexes is investigated by means of the decomposition method. This work presents the first application of the decomposition method to systems where magnetic centres may bear more than one unpaired electron. By decomposing the coupling into three physical contributions (direct exchange, kinetic exchange, and spin polarisation), we provide numerical arguments to confirm or infirm the rationalisation allowed by the conceptual analysis of the magnetic d orbitals. We also take advantage of the recently proposed generalisation of the method [David et al., J. Chem. Theory Comput., 2023, 19, 157] to get more insights into the underlying mechanisms by disentangling the coupling between centres into its electron-electron interactions.

Exploiting Molecular Symmetry to Quantitatively Map the Excited-State Landscape of Iron-Sulfur Clusters

Cuboidal [Fe4S4] clusters are ubiquitous cofactors in biological redox chemistry. In the [Fe4S4]1+ state, pairwise spin coupling gives rise to six arrangements of the Fe valences ("valence isomers") among the four Fe centers. Because of the magnetic complexity of these systems, it has been challenging to understand how a protein's active site dictates both the arrangement of the valences in the ground state as well as the population of excited-state valence isomers. Here, we show that the ground-state valence isomer landscape can be simplified from a six-level system in an asymmetric protein environment to a two-level system by studying the problem in synthetic [Fe4S4]1+ clusters with solution C3v symmetry. This simplification allows for the energy differences between valence isomers to be quantified (in some cases with a resolution of <0.1 kcal/mol) by simultaneously fitting the VT NMR and solution magnetic moment data. Using this fitting protocol, we map the excited-state landscape for a range of clusters of the form [(SIMes)3Fe4S4-X/L]n, (SIMes = 1,3-dimesityl-imidazol-4,5-dihydro-2-ylidene; n = 0 for anionic, X-type ligands and n = +1 for neutral, L-type ligands) and find that a single ligand substitution can alter the relative ground-state energies of valence isomers by at least 103 cm-1. On this basis, we suggest that one result of "non-canonical" amino acid ligation in Fe-S proteins is the redistribution of the valence electrons in the manifold of thermally populated excited states.

Electronic Structure and Magneto-Structural Correlations Study of Cu2UL Trinuclear Schiff Base Complexes: A 3d-5f-3d Case

The magnetic properties of trinuclear Schiff base complexes M₂AnLⁱ (M^II = Zn, Cu; An^IV = Th, U; Lⁱ = Schiff base; i = 1-4, 6, 7, 9), exhibiting the [M(μ-O)₂]₂U core structure with adjacent M1···U and M2···U and next-adjacent M1···M2 interactions, featuring 3d-5f-3d subsystems, have been investigated theoretically using relativistic ZORA/B3LYP computations combined with the broken symmetry (BS) approach. Bond order and natural population analyses reveal that the covalent contribution to the bonding within the Cu-O-U coordination is important thus favoring superexchange coupling between the transition metal and the uranium magnetic centers. The calculated coupling constants J_CuU between the Cu and U atoms, agree with the observed shift from the antiferromagnetic (AF) character of the L^1,2,3,4 complexes to the ferromagnetic (ferro) of the L^6,7,9 ones. The structural parameters, i.e., the Cu···U distances and the Cu-O-U angles, as well as the electronic factors driving the magnetic couplings are discussed. The analyses are supported by the study of the mixed ZnCuULⁱ and Cu₂ThLⁱ systems, where in the first complex the Cu^II (3d⁹) ion is replaced by the diamagnetic Zn^II (3d¹⁰) one, whereas in the second complex the U^IV (5f²) paramagnetic center is replaced by the diamagnetic Th^IV (5f⁰) one.

First crystal structure of an Fe(III) anionic complex based on a pyruvic acid thiosemicarbazone ligand with Li+: synthesis, features of magnetic behavior and theoretical analysis

The iron(III) anionic complex based on a pyruvic acid thiosemicarbazone ligand with the lithium cation Li[Fe^III(thpy)₂]·3H₂O (1) has been synthesized and characterized by FTIR spectroscopy, powder and single crystal X-ray diffraction, direct current magnetic susceptibility measurements, and ⁵⁷Fe Mössbauer spectroscopy. Moreover, the molecular structure of the [Fe(thpy)₂]^- anion has been determined for the first time. The [Fe(thpy)₂]^- units in the triclinic P1̄ lattice of 1 are assembled into layers parallel to the bc plane. The Li⁺ cations and water molecules are located between the layers and the structure is stabilized by hydrogen bonding. The [Fe(thpy)₂]^- anions form interconnected dimer pairs through hydrogen bonds and short contacts with Fe⋯Fe separation of 6.7861(4) Å. According to dc magnetic measurements, compound 1 demonstrates an incipient spin-crossover transition from the LS (S = 1/2) to the HS (S = 5/2) state above 250 K. The Bleaney-Bowers equation for a model of an isolated LS dimer with a mean-field correction was applied to fit the experimental data of magnetic susceptibility dependence on temperature in the temperature range of 2-250 K. The intra-dimer J₁ = -1.79(1) K and inter-dimer J₂ = -0.24(3) K antiferromagnetic coupling constants were defined. The analysis of the ⁵⁷Fe Mössbauer spectra at 80 K and 296 K confirms the presence of the shortened distances between the iron nuclei. Moreover, the influence of the lithium cation on the stabilization of the LS state was shown for the [Fe(thpy)₂]^- anion. BS-DFT calculations for the optimized structure of two isolated [Fe(thpy)₂]^- anions also correctly predict a weak exchange J₁(calc) = -0.92 K. DFT calculations revealed the OPBE (GGA-type) functional that correctly predicts the spin-crossover transition for the iron(III) thpy compounds. Besides, the effect of the N₂O₄, N₂S₂O₂, and N₂Se₂O₂ coordination environments on the energy stabilization of the LS state of iron(III) anionic thpy complexes was noted as well.

Characterization of the Geometrical and Electronic Structures of the Active Site and Its Effects on the Surrounding Environment in Reduced High-Potential Iron-Sulfur Proteins Investigated by the Density Functional Theory Approach

The high-potential iron-sulfur protein (HiPIP) is an electron-transporting protein that functions in the photosynthetic electron-transfer system and possesses a cubane-type [4Fe-4S] cluster in the active center. Characterization of the geometrical and electronic structures of the [4Fe-4S] cluster leads to an understanding of the functions in HiPIP, which are expected to be influenced by the environment surrounding the [4Fe-4S] cluster. This work characterized the geometrical and electronic structures of the [4Fe-4S] cluster in the reduced HiPIP and evaluated their effects on the protein environment using the density functional theory (DFT) approach. DFT calculations showed that the structural asymmetry and spin delocalization between iron atoms allowed for the acquisition of a unique stable geometrical and electronic structure in the open-shell singlet. In addition, the formation of an Fe-Fe bond accompanying the spin delocalization was found to depend on the interatomic distance. A comparison of the calculated stable structures with and without consideration of the amino acids around the [4Fe-4S] cluster demonstrated that the surrounding amino acids stabilized the unique geometrical and electronic structure of the [4Fe-4S] cluster in HiPIP.

Valence Localization in Alkyne and Alkene Adducts of Synthetic [Fe4S4]+ Clusters

Reported herein are alkyne and alkene adducts of synthetic [Fe₄S₄]⁺ clusters that model intermediates and inhibitor-bound states in enzymes involved in isoprenoid biosynthesis. Treatment of the N-heterocyclic carbene-ligated cluster [(IMes)₃Fe₄S₄(OEt₂)][BAr^F₄] (IMes = 1,3-dimesitylimidazol-2-ylidene; [BAr^F₄]^- = tetrakis(3,5-bis(trifluoromethyl)phenyl)borate) with phenylacetylene (PhCCH) or cis-cyclooctene (COE) results in displacement of the Et₂O ligand to yield the corresponding π complexes, [(IMes)₃Fe₄S₄(PhCCH)][BAr^F₄] and [(IMes)₃Fe₄S₄(COE)][BAr^F₄]. EPR spectroscopic analysis demonstrates that both clusters are doublets with g_iso > 2 and thus are spectroscopically faithful models of the analogous species characterized in the isoprenoid biosynthetic enzymes IspG and IspH. Structural and Mössbauer spectroscopic analysis reveals that both complexes are best described as [Fe₄S₄]⁺ clusters in which the unique Fe site engages in modest back-bonding to the π-acidic ligand. Paramagnetic NMR studies show that, even at room temperature, the alkyne/alkene-bound Fe centers harbor minority spin and therefore adopt an Fe²⁺ valence. We propose that such valence localization could likewise occur in Fe-S enzymes that interact with π-acidic molecules.

Consistent Evaluation of Magnetic Exchange Couplings in Multicenter Compounds in KS-DFT: The Recomposition Method

The use of broken-symmetry calculations in Kohn-Sham density functional theory has offered an affordable route to study magnetic exchange couplings in transition-metal-based compounds. However, computing this property in compounds exhibiting several couplings is still challenging and especially due to the difficulties to overcome the well-known problem of spin contamination. Here, we present a new and general method to compute magnetic exchange couplings in systems featuring several spin sites. To provide a consistent spin decontamination of J values, our strategy exploits the decomposition method of the magnetic exchange coupling proposed by Coulaud et al. and generalizes our previous work on diradical compounds where the overall magnetic exchange coupling is defined as the sum of its three main and properly extracted physical contributions (direct exchange, kinetic exchange, and spin polarization). In this aim, the generalized extraction of all contributions is presented to systems with multiple spin sites bearing one unpaired electron. This is done by proposing a new paradigm to treat the kinetic exchange contribution, which proceeds through monorelaxations of the magnetic orbitals. This method, so-called the recomposition method, is applied to a compound featuring three Cu(II) ions with a linear arrangement and to a recently synthesized complex containing a Cu₄O₄ cubane unit presenting an unusual magnetic behavior.

Spin-Coupled Electron Densities of Iron-Sulfur Cluster Imaged by In Situ Serial Laue Diffraction

Iron-sulfur clusters are inorganic cofactors found in many proteins involved in fundamental biological processes including DNA processing. The prokaryotic DNA repair enzyme PhrB, a member of the protein family of cryptochromes and photolyases, carries a four-iron-four-sulfur cluster [4Fe4S] in addition to the catalytic cofactor flavin adenine dinucleotide (FAD) and a second pigment 6,7-dimethyl-8-ribityllumazine (DMRL). The light-induced redox reactions of this multi-cofactor protein complex were recently shown as two interdependent photoreductions of FAD and DMRL mediated by the [4Fe4S] cluster functioning as an electron cache to hold a fine balance of electrons. Here, we apply the more traditional temperature-scan cryo-trapping technique in protein crystallography and the newly developed technology of in situ serial Laue diffraction at room temperature. These diffraction methods in dynamic crystallography enable us to capture strong signals of electron density changes in the [4Fe4S] cluster that depict quantized electronic movements. The mixed valence layers of the [4Fe4S] cluster due to spin coupling and their dynamic responses to light illumination are observed directly in our difference maps between its redox states. These direct observations of the quantum effects in a protein bound iron-sulfur cluster have thus opened a window into the mechanistic understanding of metal clusters in biological systems.

A Theoretical Account of the Coupling between Metal- and Ligand-centred Spins

This study addresses the magnetic interaction between paramagnetic metal ions and the radical ligands taking the [Cu^II (hfac)₂ (imVDZ)] and [M^II (hfac)₂ (pyDTDA)] (imVDZ=1,5-dimethyl-3-(1-methyl-2-imidazolyl)-6-oxoverdazyl; hfac=(1,1,1,5,5,5)hexafluroacetylacetonate; pyDTDA=4-(2'-pyridyl)-1,2,3,5-dithiadiazolyl), (M=Cu, Ni, Co, Fe, Mn) compounds as reference systems. The coupling between the metal and ligand spins is quantified in terms of the exchange coupling constant (J) in the platform of density functional theory (DFT) and the wave function-based complete active space self-consistent field (CASSCF) method. Application of DFT and broken symmetry (BS) formalism results ferromagnetic coupling for all the transition metal complexes except the Mn(II) complex. This DFT-BS prediction of magnetic nature matches with the experimental finding for all the complexes other than the Fe(II)-pyDTDA complex, for which an antiferromagnetic coupling between high spin iron and the thiazyl ligand has been reported. However, evaluation of spin state energetics through the multiconfigurational wave function-based method produces the S=3/2 ground spin state for the iron-thiazyl in parity with experiment. Electronic structure analyses find the overlap between the metal- and ligand-based singly occupied molecular orbitals (SOMOs) to be one of the major reasons attributing to different extent of exchange coupling in the systems under investigation.

The Elusive Mononitrosylated [Fe4 S4 ] Cluster in Three Redox States

Iron-sulfur clusters are well-established targets in biological nitric oxide (NO) chemistry, but the key intermediate in these processes-a mononitrosylated [Fe4 S4 ] cluster-has not been fully characterized in a protein or a synthetic model thereof. Here, we report the synthesis of a three-member redox series of isostructural mononitrosylated [Fe4 S4 ] clusters. Mononitrosylation was achieved by binding NO to a 3 : 1 site-differentiated [Fe4 S4 ]+ cluster; subsequent oxidation and reduction afforded the other members of the series. All three clusters feature a local high-spin Fe3+ center antiferromagnetically coupled to 3 [NO]- . The observation of an anionic NO ligand suggests that NO binding is accompanied by formal electron transfer from the cluster to NO. Preliminary reactivity studies with the monocationic cluster demonstrate that exposure to excess NO degrades the cluster, supporting the intermediacy of mononitrosylated intermediates in NO sensing/signaling.

Terminal N2 Dissociation in [(PNN)Fe(N2 )]2 (μ-N2 ) Leads to Local Spin-State Changes and Augmented Bridging N2 Activation

Nitrogen fixation at iron centres is a fundamental catalytic step for N₂ utilisation, relevant to biological (nitrogenase) and industrial (Haber-Bosch) processes. This step is coupled with important electronic structure changes which are currently poorly understood. We show here for the first time that terminal dinitrogen dissociation from iron complexes that coordinate N₂ in a terminal and bridging fashion leaves the Fe-N₂ -Fe unit intact but significantly enhances the degree of N₂ activation (Δν≈180 cm^-1 , Raman spectroscopy) through charge redistribution. The transformation proceeds with local spin state change at the iron centre (S= 1 / 2 ${{ 1/2 }}$ →S=³ /₂ ). Further dissociation of the bridging N₂ can be induced under thermolytic conditions, triggering a disproportionation reaction, from which the tetrahedral (PNN)₂ Fe could be isolated. This work shows that dinitrogen activation can be induced in the absence of external chemical stimuli such as reducing agents or Lewis acids.

Series of Fluorinated Benzimidazole-Substituted Nitronyl Nitroxides: Synthesis, Structure, Acidity, Redox Properties, and Magnetostructural Correlations

A special series of nitronyl nitroxides was synthesized: 2-(benzimidazol-2'-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyls mono-, di-, tri-, or tetrafluorinated on the benzene ring. The structure of all paramagnets was unambiguously confirmed by single-crystal X-ray diffraction. It was found that in crystals, the radicals are assembled into chains due to intermolecular H-bonds between the benzimidazole moiety (H-bond donor) and the nitronyl nitroxide group or benzimidazole ring (H-bond acceptor). The magnetic properties of nitronyl nitroxides depend on the type of binding of radicals by H-bonds. The magnetic motif of 4-fluoro-, 5-fluoro-, 4,6-difluoro-, 4,5,6-trifluoro-, 4,5,7-trifluoro-, and 4,5,6,7-tetrafluoro-derivatives, as well as the nonfluorinated compound, consists of ferromagnetic chains (J/k_B ≈ 20-40 K) formed by the McConnell type I mechanism. In the 5,6-difluoro- and 4,5-difluoro-derivatives, the distances between the paramagnetic centers are large, as a result of which the exchange interactions are weak. According to cyclic voltammetry, paramagnets are oxidized reversibly, while their reduction is a quasi-reversible electron transfer (EC mechanism); experimental redox potentials of radicals correlate well with the calculated values. Quantum chemical assessment of the acidity of benzimidazolyl-substituted nitronyl nitroxides revealed that the introduction of fluorine atoms into the benzene ring enhances the acidity of the paramagnets by more than 5 orders of magnitude.

Super-Excimer: Anomalous Bonding in a Metastable Excited-State Dimer of Superatomic Dimers

A new type of excimer formation was reported, which stems from an unexpected discovery of a short-lived excited-state dimer of superatomic dimers. In theoretical investigation of the dimer formation, it was found that the physical adsorption states maintain the closed-shell properties of the dimeric units via van der Waals interaction, while the chemical adsorption excited state is a broken-symmetry (BS) state, having a higher energy of about 0.5 eV. Potential energy surface calculations indicate that the short-lived metastable chemical bonding state can transform into energetically lower physical adsorption states by crossing a shallow energy barrier and eventually disintegrate into two ground-state dimers. Since the basic unit is a superatomic cluster, the chemical adsorption state discovered may be called "super-excimer", which opens up a new avenue for the discovery of tailorable excimer materials.

Evidence for Low-Valent Electronic Configurations in Iron-Sulfur Clusters

Although biological iron-sulfur (Fe-S) clusters perform some of the most difficult redox reactions in nature, they are thought to be composed exclusively of Fe²⁺ and Fe³⁺ ions, as well as mixed-valent pairs with average oxidation states of Fe^2.5+. We herein show that Fe-S clusters formally composed of these valences can access a wider range of electronic configurations─in particular, those featuring low-valent Fe¹⁺ centers. We demonstrate that CO binding to a synthetic [Fe₄S₄]⁰ cluster supported by N-heterocyclic carbene ligands induces the generation of Fe¹⁺ centers via intracluster electron transfer, wherein a neighboring pair of Fe²⁺ sites reduces the CO-bound site to a low-valent Fe¹⁺ state. Similarly, CO binding to an [Fe₄S₄]⁺ cluster induces electron delocalization with a neighboring Fe site to form a mixed-valent Fe^1.5+Fe^2.5+ pair in which the CO-bound site adopts partial low-valent character. These low-valent configurations engender remarkable C-O bond activation without having to traverse highly negative and physiologically inaccessible [Fe₄S₄]⁰/[Fe₄S₄]^- redox couples.

Structural Characterization of Nanocellulose/Fe3O4 Hybrid Nanomaterials

The rise of innovation in the electrical industry is driven by the controlled design of new materials. The hybrid materials based on magnetite/nanocellulose are highly interesting due to their various applications in medicine, ecology, catalysis and electronics. In this study, the structure and morphology of nanocellulose/magnetite hybrid nanomaterials were investigated. The effect of nanocellulose loading on the crystal structure of synthesized composites was investigated by XRD and FTIR methods. The presented study reveals that the interaction between the cellulose and magnetic nanoparticles depends on the nanocellulose content. Further, a transition from cellulose II to cellulose I allomorph is observed. SEM and EDS are employed to determine the variation in morphology with changes in component concentrations. By the calculation of magnetic interactions between adjacent Fe³⁺ and Fe²⁺ ions within composites, it is determined that ferromagnetic coupling predominates.

Spin Alternation Rule in USCF for Through-Bond Magnetic Coupling─A New Look: Why and When Does It Arise and How To See It

This work takes a new look at the spin alternation rule in unrestricted self-consistent-field (USCF) calculations in terms of structural characteristics such as periodicity, impurity location, and Coulomb exchange. For clarity, the systems considered are biradicals produced from linear conjugated hydrocarbons. Both site-parametrized Hamiltonian models for theoretical analysis and spin unrestricted density functional theory (DFT) calculations are used. Theoretical analysis leads to the following conclusions: (1) The diradical state is an excited state of a linear chain of N conjugated carbon atoms (when N is about ≤ 10). Spin alternation is a consequence of the (truncated) periodic symmetry combined with filling each closed-shell pi orbital with two electrons and each singly occupied molecular orbital (SOMO) with one electron. Spin polarization is evident in triplet (T) and broken symmetry (BS) solutions for an odd N and only in the T solution for an even N. Spin alternation is visible in the BS for an odd N and always remains muted in the calculated T. (2) For a doped chain with two radical centers, spin alternation is generally visible in the BS for an odd N. The sign of spin population on the radical centers in the BS indicates the stable spin. For radical centers separated by an odd (even) number of p_z electrons, spin alternation favors T (S) state with FM (AFM) interaction. Spin oscillation remains less transparent for an even N without exchange. (3) In an unrestricted treatment with exchange, spin alternation becomes observable. Without SCF iterations, the more stable state can be identified from a clear spin oscillation in the BS. An irregular oscillation indicates a possible singlet ground state. These observations are supported by density functional calculations using the B3LYP functional and the 6-311+g(d,p) basis set on linear decapentaene diradicals with nitronyl nitroxide moieties substituted on two sets of conjugated atoms, (3,9) and (3,10). Because of the SCF procedure, one finds spin alternation in the T (BS) solution and erratic oscillation in the BS (T) solution of the 3,9 (3,10) diradical in respective equilibrium geometries. The ground state is T (S). DFT adiabatic coupling constants, SOMO energies, spin population plots, and SOMO lobe diagrams compare well with molecular electronic characteristics from theoretical analysis using Hamiltonian parameters.

Study of Self-Interaction Errors in Density Functional Calculations of Magnetic Exchange Coupling Constants Using Three Self-Interaction Correction Methods

We examine the role of self-interaction error (SIE) removal on the evaluation of magnetic exchange coupling constants. In particular, we analyze the effect of scaling down the self-interaction correction (SIC) for three nonempirical density functional approximations (DFAs) namely, the local spin density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, and the recent SCAN family of meta-GGA functionals. To this end, we employ three one-electron SIC methods: Perdew-Zunger SIC [Perdew, J. P.; Zunger, A. Phys. Rev. B, 1981, 23, 5048.], the orbitalwise scaled SIC method [Vydrov, O. A. et al. J. Chem. Phys. 2006, 124, 094108.], and the recent local scaling method [Zope, R. R. et al. J. Chem. Phys. 2019, 151, 214108.]. We compute the magnetic exchange coupling constants using the spin projection and nonprojection approaches for sets of molecules composed of dinuclear and polynuclear H···He models, organic radical molecules, and chlorocuprate and compare these results against accurate theories and experiment. Our results show that for the systems that mainly consist of single-electron regions, PZSIC performs well, but for more complex organic systems and the chlorocuprates, an overcorrecting tendency of PZSIC combined with the DFAs utilized in this work is more pronounced, and in such cases, LSIC with kinetic energy density ratio performs better than PZSIC. Analysis of the results in terms of SIC corrections to the density and to the total energy shows that both density and energy correction are required to obtain an improved prediction of magnetic exchange couplings.

Analysis of the Geometric and Electronic Structure of Spin-Coupled Iron-Sulfur Dimers with Broken-Symmetry DFT: Implications for FeMoco

The open-shell electronic structure of iron–sulfur clusters presents considerable challenges to quantum chemistry, with the complex iron–molybdenum cofactor (FeMoco) of nitrogenase representing perhaps the ultimate challenge for either wavefunction or density functional theory. While broken-symmetry density functional theory has seen some success in describing the electronic structure of such cofactors, there is a large exchange–correlation functional dependence in calculations that is not fully understood. In this work, we present a geometric benchmarking test set, FeMoD11, of synthetic spin-coupled Fe–Fe and Mo–Fe dimers, with relevance to the molecular and electronic structure of the Mo-nitrogenase FeMo cofactor. The reference data consists of high-resolution crystal structures of metal dimer compounds in different oxidation states. Multiple density functionals are tested on their ability to reproduce the local geometry, specifically the Fe–Fe/Mo–Fe distance, for both antiferromagnetically coupled and ferromagnetically coupled dimers via the broken-symmetry approach. The metal–metal distance is revealed not only to be highly sensitive to the amount of exact exchange in the functional but also to the specific exchange and correlation functionals. For the antiferromagnetically coupled dimers, the calculated metal–metal distance correlates well with the covalency of the bridging metal–ligand bonds, as revealed via the corresponding orbital analysis, Hirshfeld S/Fe charges, and Fe–S Mayer bond order. Superexchange via bridging ligands is expected to be the dominant interaction in these dimers, and our results suggest that functionals that predict accurate Fe–Fe and Mo–Fe distances describe the overall metal–ligand covalency more accurately and in turn the superexchange of these systems. The best performing density functionals of the 16 tested for the FeMoD11 test set are revealed to be either the nonhybrid functionals r²SCAN and B97-D3 or hybrid functionals with 10–15% exact exchange: TPSSh and B3LYP*. These same four functionals are furthermore found to reproduce the high-resolution X-ray structure of FeMoco well according to quantum mechanics/molecular mechanics (QM/MM) calculations. Almost all nonhybrid functionals systematically underestimate Fe–Fe and Mo–Fe distances (with r²SCAN and B97-D3 being the sole exceptions), while hybrid functionals with >15% exact exchange (including range-separated hybrid functionals) overestimate them. The results overall suggest r²SCAN, B97-D3, TPSSh, and B3LYP* as accurate density functionals for describing the electronic structure of iron–sulfur clusters in general, including the complex FeMoco cluster of nitrogenase.

Broken-Symmetry Density Functional Theory Analysis of the Ω Intermediate in Radical S-Adenosyl-l-methionine Enzymes: Evidence for a Near-Attack Conformer over an Organometallic Species

Radical S-adenosyl-l-methionine (SAM) enzymes are found in all domains of life and catalyze a wide range of biochemical reactions. Recently, an organometallic intermediate, Ω, has been experimentally implicated in the 5'-deoxyadenosyl radical generation mechanism of the radical SAM superfamily. In this work, we employ broken-symmetry density functional theory to evaluate several structural models of Ω. The results show that the calculated hyperfine coupling constants (HFCCs) for the proposed organometallic structure of Ω are inconsistent with the experiment. In contrast, a near-attack conformer of SAM bound to the catalytic [4Fe-4S] cluster, in which the distance between the unique iron and SAM sulfur is ∼3 Å, yields HFCCs that are all within 1 MHz of the experimental values. These results clarify the structure of the ubiquitous Ω intermediate and suggest a paradigm shift reversal regarding the mechanism of SAM cleavage by members of the radical SAM superfamily.

Stabilization of intermediate spin states in mixed-valent diiron dichalcogenide complexes

The electronic structure and ground spin states, S, observed for mixed-valent iron–sulfur dimers (Fe^II-Fe^III) are typically determined by the Heisenberg exchange interaction, J, that couples the magnetic interaction of the two metal centres either ferromagnetically (J > 0, S = 9/2) or antiferromagnetically (J < 0, S = 1/2). In the case of antiferromagnetically coupled iron centres, stabilization of the high-spin S = 9/2 ground state is also feasible through a Heisenberg double-exchange interaction, B, which lifts the degeneracy of the Heisenberg spin states. This theorem also predicts intermediate spin states for mixed-valent dimers, but those have so far remained elusive. Herein, we describe the structural, electron paramagnetic resonance and Mössbauer spectroscopic, and magnetic characterization of a series of mixed-valent complexes featuring [Fe₂Q₂]⁺ (Q = S^2–, Se^2–, Te^2–), where the Se and Te complexes favour S = 3/2 spin states. The incorporation of heavier chalcogenides in this series reveals a delicate balance of antiferromagnetic coupling, Heisenberg double-exchange and vibronic coupling.

Despite extensive investigations of mixed-valence complexes, molecules with intermediate spin states have remained elusive. Now, selenium- and tellurium-bridged mixed-valent iron dimers have been prepared in which a balance of Heisenberg exchange and double-exchange coupling of the unpaired electron, combined with moderate vibronic contributions, stabilizes S = 3/2 ground spin states.

Effect of Oriented Electric Fields on Biologically Relevant Iron-Sulfur Clusters: Tuning Redox Reactivity for Catalysis

Enzyme-based iron-sulfur clusters, exemplified in families such as hydrogenases, nitrogenases, and radical S-adenosylmethionine enzymes, feature in many essential biological processes. The functionality of biological iron-sulfur clusters extends beyond simple electron transfer, relying primarily on the redox activity of the clusters, with a remarkable diversity for different enzymes. The active-site structure and the electrostatic environment in which the cluster resides direct this redox reactivity. Oriented electric fields in enzymatic active sites can be significantly strong, and understanding the extent of their effect on iron-sulfur cluster reactivity can inform first steps toward rationally engineering their reactivity. An extensive systematic density functional theory-based screening approach using OPBE/TZP has afforded a simple electric field-effect representation. The results demonstrate that the orientation of an external electric field of strength 28.8 MV cm^-1 at the center of the cluster can have a significant effect on its relative stability in the order of 35 kJ mol^-1. This shows clear implications for the reactivity of iron-sulfur clusters in enzymes. The results also demonstrate that the orientation of the electric field can alter the most stable broken-symmetry state, which further has implications on the directionality of initiated electron-transfer reactions. These insights open the path for manipulating the enzymatic redox reactivity of iron-sulfur cluster-containing enzymes by rationally engineering oriented electric fields within the enzymes.

Comparisons of bond valences and distances for CO- and N2-bound clusters of FeMo-cofactors

By comparisons of N2 and isoelectronic substrate CO bound FeMo-cofactors (FeMo-cos) in nitrogenases, we have used a classical bond valence method to calculate the oxidation states of the iron and molybdenum atoms in FeMo-cos.

Statistical analysis of PN clusters in Mo/VFe protein crystals using a bond valence method toward their electronic structures

Iron valences of 129 P-clusters from FeMo/V proteins were analyzed using a bond valence method, supposing the existence of Fe3+ in a generally considered all-ferrous PN cluster in solution with excess reducing agent.

The Density Functional Theory Account of Interplaying Long-Range Exchange and Dispersion Effects in Supramolecular Assemblies of Aromatic Hydrocarbons with Spin

Aromatic hydrocarbons with fused benzene rings and regular triangular shapes, called n-triangulenes according to the number of rings on one edge, form groundstates with n-1 unpaired spins because of topological reasons. Here, we focus on methodological aspects emerging from the density functional theory (DFT) treatments of dimer models of the n = 2 triangulene (called also phenalenyl), observing that it poses interesting new problems to the issue of long-range corrections. Namely, the interaction comprises simultaneous spincoupling and van der Waals effects, i.e., a technical conjuncture not considered explicitly in the benchmarks calibrating long-range corrections for the DFT account of supramolecular systems. The academic side of considering dimer models for calculations and related analysis is well mirrored in experimental aspects, and synthetic literature revealed many compounds consisting of stacked phenalenyl cores, with intriguing properties, assignable to their long-range spin coupling. Thus, one may speculate that a thorough study assessing the performance of state-of-the-art DFT procedures has relevance for potential applications in spintronics based on organic compounds.