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

Orbital Entanglement Analysis of Exchange-Coupled Systems

A new tool for the interpretation of multiconfigurational wave functions representing the spin states of exchange-coupled transition metal complexes is introduced. Based on orbital entanglement measures, herein derived from multiconfigurational density matrix renormalization group calculations, the complexity of the wave function is reduced, thus facilitating a connection with established concepts for the interpretation of magnetically coupled systems. We show that the entanglement of localized orbitals with a small basis set is a good representation of the magnetic coupling topology and that it is sensitive to chemical changes in homologous complexes. Furthermore, we introduce a measure for the magnetic relevance of orbitals in the active subspace and a concept for the quantitative comparison of different chemical species. The approach presented here will be easily applicable to higher nuclearity clusters, providing a direct insight into all states of the Heisenberg spin ladder for systems previously accessible only by single-configurational methods.

Localized Electronic Structure of Nitrogenase FeMoco Revealed by Selenium K-Edge High Resolution X-ray Absorption Spectroscopy

The size and complexity of Mo-dependent nitrogenase, a multicomponent enzyme capable of reducing dinitrogen to ammonia, have made a detailed understanding of the FeMo cofactor (FeMoco) active site electronic structure an ongoing challenge. Selective substitution of sulfur by selenium in FeMoco affords a unique probe wherein local Fe-Se interactions can be directly interrogated via high-energy resolution fluorescence detected X-ray absorption spectroscopic (HERFD XAS) and extended X-ray absorption fine structure (EXAFS) studies. These studies reveal a significant asymmetry in the electronic distribution of the FeMoco, suggesting a more localized electronic structure picture than is typically assumed for iron-sulfur clusters. Supported by experimental small molecule model data in combination with time dependent density functional theory (TDDFT) calculations, the HERFD XAS data is consistent with an assignment of Fe2/Fe6 as an antiferromagnetically coupled diferric pair. HERFD XAS and EXAFS have also been applied to Se-substituted CO-inhibited MoFe protein, demonstrating the ability of these methods to reveal electronic and structural changes that occur upon substrate binding. These results emphasize the utility of Se HERFD XAS and EXAFS for selectively probing the local electronic and geometric structure of FeMoco.

A Synthetic Model of Enzymatic [Fe4S4]-Alkyl Intermediates

Although alkyl complexes of [Fe₄S₄] clusters have been invoked as intermediates in a number of enzymatic reactions, obtaining a detailed understanding of their reactivity patterns and electronic structures has been difficult owing to their transient nature. To address this challenge, we herein report the synthesis and characterization of a 3:1 site-differentiated [Fe₄S₄]²⁺–alkyl cluster. Whereas [Fe₄S₄]²⁺ clusters typically exhibit pairwise delocalized electronic structures in which each Fe has a formal valence of 2.5+, Mössbauer spectroscopic and computational studies suggest that the highly electron-releasing alkyl group partially localizes the charge distribution within the cubane, an effect that has not been previously observed in tetrahedrally coordinated [Fe₄S₄] clusters.

Theoretical Investigation of the Electronic Structure and Magnetic Properties of Oxo-Bridged Uranyl(V) Dinuclear and Trinuclear Complexes

The uranyl(V) complexes [UO₂(dbm)₂K(18C6)]₂ (dbm = dibenzoylmethanate) and [UO₂(L)]₃(L = 2-(4-tolyl)-1,3-bis(quinolyl)malondiiminate), exhibiting diamond-shaped U₂O₂ and triangular-shaped U₃O₃ cores respectively with 5f¹-5f¹ and 5f¹-5f¹-5f¹ configurations, have been investigated using relativistic density functional theory (DFT). The bond order and QTAIM analyses reveal that the covalent contribution to the bonding within the oxo cores is slightly more important for U₃O₃ than for U₂O₂, in line with the shorter U-O distances existing in the trinuclear complex in comparison to those in the binuclear complex. Using the broken symmetry (BS) approach combined with the B3LYP functional for the calculation of the magnetic exchange coupling constants (J) between the magnetic centers, the antiferromagnetic (AF) character of these complexes was confirmed, the estimated J values being respectively equal to -24.1 and -7.2 cm^-1 for the dioxo and trioxo species. It was found that the magnetic exchange is more sensitive to small variations of the core geometry of the dioxo species in comparison to the trioxo species. Although the robust AF exchange coupling within the U_xO_x cores is generally maintained when small variations of the UOU angle are applied, a weak ferromagnetic character appears in the dioxo species when this angle is higher than 114°, its value for the actual structure being equal to 105.9°. The electronic factors driving the magnetic coupling are discussed.

Structural Analysis of a Nitrogenase Iron Protein from Methanosarcina acetivorans: Implications for CO2 Capture by a Surface-Exposed [Fe4S4] Cluster

This work reports the crystal structure of a previously uncharacterized Fe protein from a methanogenic organism, which provides important insights into the structural properties of the less-characterized, yet highly interesting archaeal nitrogenase enzymes. Moreover, the structure-derived implications for CO₂ capture by a surface-exposed [Fe₄S₄] cluster point to the possibility of developing novel strategies for CO₂ sequestration while providing the initial insights into the unique mechanism of FeS-based CO₂ activation.

Nitrogenase iron (Fe) proteins reduce CO₂ to CO and/or hydrocarbons under ambient conditions. Here, we report a 2.4-Å crystal structure of the Fe protein from Methanosarcina acetivorans (MaNifH), which is generated in the presence of a reductant, dithionite, and an alternative CO₂ source, bicarbonate. Structural analysis of this methanogen Fe protein species suggests that CO₂ is possibly captured in an unactivated, linear conformation near the [Fe₄S₄] cluster of MaNifH by a conserved arginine (Arg) pair in a concerted and, possibly, asymmetric manner. Density functional theory calculations and mutational analyses provide further support for the capture of CO₂ on MaNifH while suggesting a possible role of Arg in the initial coordination of CO₂ via hydrogen bonding and electrostatic interactions. These results provide a useful framework for further mechanistic investigations of CO₂ activation by a surface-exposed [Fe₄S₄] cluster, which may facilitate future development of FeS catalysts for ambient conversion of CO₂ into valuable chemical commodities.

Concerted Two-Electron Reduction of Ubiquinone in Respiratory Complex I

Respiratory complex I catalyzes two-electron/two-proton reduction of a ubiquinone (Q) substrate bound at its Q-binding pocket; upon reduction, ubiquinole carries electrons further down the electron transport chain. The mechanism of this two-electron transfer reaction is poorly understood. Here we consider a hypothetical scheme in which two electrons transfer together with two protons in a concerted fashion. On one side, a coupled electron/proton transfer occurs from the reduced N2 FeS cluster and protonated His38 residue, respectively, while on the other side a hydrogen atom transfer occurs from the neutral Tyr87 residue, generating a tyrosyl radical. A method to evaluate the coupling matrix element that corresponds to a concerted tunneling of two electrons was developed. Overall, our calculations indicate that the concerted reaction is feasible, in which case a transient tyrosyl radical is formed during the catalytic cycle of the enzyme.

Regio- and Diastereoselective Iron-Catalyzed [4+4]-Cycloaddition of 1,3-Dienes

A family of single-component iron precatalysts for the [4+4]-cyclodimerization and intermolecular cross-[4+4]-cycloaddition of monosubstituted 1,3-dienes is described. Cyclooctadiene products were obtained with high regioselectivity, and catalyst-controlled access to either cis- or trans-diastereomers was achieved using 4-substituted diene substrates. Reactions conducted either with single-component precatalysts or with iron dihalide complexes activated in situ proved compatible with common organic functional groups and were applied on multigram scale (up to >100 g). Catalytically relevant, S = 1 iron complexes bearing 2-(imino)pyridine ligands, (^RPI)FeL₂ (^RPI = [2-(2,6-R₂-C₆H₃-N═CMe)-C₅H₄N] where R = ⁱPr or Me, L₂ = bis-olefin), were characterized by single-crystal X-ray diffraction, Mößbauer spectroscopy, magnetic measurements, and DFT calculations. The structural and spectroscopic parameters are consistent with an electronic structure description comprised of a high spin iron(I) center ( S_Fe = 3/2) engaged in antiferromagnetically coupling with a ligand radical anion ( S_PI = -1/2). Mechanistic studies conducted with these single-component precatalysts, including kinetic analyses, ¹²C/¹³C isotope effect measurements, and in situ Mößbauer spectroscopy, support a mechanism involving oxidative cyclization of two dienes that determines regio- and diastereoselectivity. Topographic steric maps derived from crystallographic data provided insights into the basis for the catalyst control through stereoselective oxidative cyclization and subsequent, stereospecific allyl-isomerization and C-C bond-forming reductive elimination.

Hubbard Trimer with Spin-Orbit Coupling: Hartree-Fock Solutions, (Non)Collinearity, and Anisotropic Spin Hamiltonian

We present unrestricted and generalized Hartree-Fock solutions (UHF and GHF, respectively) for the single-band Hubbard model of an equilateral triangle. Spin-orbit coupling (SOC) is treated self-consistently, and HF stability and properties of different spin structures are studied in detail. The GHF solution switches from noncollinear to collinear when crossing a high-symmetry point in parameter space (spanned by the amplitudes of spin-conserving and spin-dependent hopping, i.e., kinetic energy and SOC, respectively). The collinear GHF solution represents a simple example to disprove the notion that a collinear vector spin density in a Slater determinant necessarily entails a defined spin projection. Spin Hamiltonian parameters for the anisotropic interaction between three spin-1/2 centers are extracted from HF energies and subsequently compared to exact results from effective Hamiltonian theory. This provides an unambiguous benchmark for interpreting broken-symmetry mean-field solutions in terms of spin configurations and puts this semiclassical approach (frequently applied in broken-symmetry density functional theory) on a firmer basis.

Site-Specific Oxidation State Assignments of the Iron Atoms in the [4Fe:4S]2+/1+/0 States of the Nitrogenase Fe-Protein

The nitrogenase iron protein (Fe-protein) contains an unusual [4Fe:4S] iron-sulphur cluster that is stable in three oxidation states: 2+, 1+, and 0. Here, we use spatially resolved anomalous dispersion (SpReAD) refinement to determine oxidation assignments for the individual irons for each state. Additionally, we report the 1.13-Å resolution structure for the ADP bound Fe-protein, the highest resolution Fe-protein structure presently determined. In the dithionite-reduced [4Fe:4S]1+ state, our analysis identifies a solvent exposed, delocalized Fe2.5+ pair and a buried Fe2+ pair. We propose that ATP binding by the Fe-protein promotes an internal redox rearrangement such that the solvent-exposed Fe pair becomes reduced, thereby facilitating electron transfer to the nitrogenase molybdenum iron-protein. In the [4Fe:4S]0 and [4Fe:4S]2+ states, the SpReAD analysis supports oxidation states assignments for all irons in these clusters of Fe2+ and valence delocalized Fe2.5+ , respectively.

Spin, Valence, and Structural Isomerism in the S3 State of the Oxygen-Evolving Complex of Photosystem II as a Manifestation of Multimetallic Cooperativity

Photosynthetic water oxidation is catalyzed by a Mn₄CaO₅-cluster in photosystem II through an S-state cycle. Understanding the roles of heterogeneity in each S-state, as identified recently by the EPR spectroscopy, is very important to gain a complete description of the catalytic mechanism. We performed herein hybrid DFT calculations within the broken-symmetry formalism and associated analyses of Heisenberg spin models to study the electronic and spin structures of various isomeric structural motifs (hydroxo-oxo, oxyl-oxo, peroxo, and superoxo species) in the S₃ state. Our extensive study reveals several factors that affect the spin ground state: (1) (formal) Mn oxidation state; (2) metal-ligand covalency; (3) coordination geometry; and (4) structural change of the Mn cluster induced by alternations in Mn···Mn distances. Some combination of these effects could selectively stabilize/destabilize some spin states. We found that the high spin state ( S_total = 6) of the oxyl-oxo species can be causative for catalytic function, which manifests through mixing of the metal-ligand character in magnetic orbitals at relatively short O5···O6 distances (<2.0 Å) and long Mn_A···O5 distances (>2.0 Å). These results will serve as a basis to conceptually identify and rationalize the physicochemical synergisms that can be evoked by the unique "distorted chair" topology of the cluster through cooperative Jahn-Teller effects on multimetallic centers.

Oxidative Addition of Dihydrogen, Boron Compounds, and Aryl Halides to a Cobalt(I) Cation Supported by a Strong-Field Pincer Ligand

Cationic cobalt(I) dinitrogen complexes with a strong-field tridentate pincer ligand were prepared and the oxidative addition of polar and non-polar bonds was studied. Addition of H₂ to [(^iPrPNP)Co(N₂)]⁺ (^iPrPNP = 2,6-bis((diisopropylphosphaneyl)methyl)pyridine) in THF-d8 resulted in rapid oxidative addition and formation of the cis-Co(III) dihydride complex, cis-[(^iPrPNP)Co(H)₂L]⁺ where L = THF or N₂. The addition of H₂ was reversible as evidenced by the dynamics observed by variable temperature ¹H NMR spectroscopy and the regeneration of [(^iPrPNP)Co(N₂)]⁺ upon exposure to dinitrogen. In contrast, addition of HBPin, (Pin = pinacolato) B₂Pin₂ and aryl halides resulted in the formation of net one-electron oxidation products: cationic Co(II)-boryl and Co(II)-halide/aryl complexes, respectively. All products were structurally characterized by X-ray crystallography and the electronic structures were determined by a combination of magnetic moment measurements, EPR spectroscopy and DFT calculations. Monitoring the addition of HBPin to [(^iPrPNP)Co(N₂)]⁺ provided evidence for a transient Co(III) oxidative addition product that likely undergoes comproportionation with the cobalt(I) starting material to generate the observed Co(II) products.

DFT Investigations of the Magnetic Properties of Actinide Complexes

Over the past 25 years, magnetic actinide complexes have been the object of considerable attention, not only at the experimental level, but also at the theoretical one. Such systems are of great interest, owing to the well-known larger spin–orbit coupling for actinide ions, and could exhibit slow relaxation of the magnetization, arising from a large anisotropy barrier, and magnetic hysteresis of purely molecular origin below a given blocking temperature. Furthermore, more diffuse 5f orbitals than lanthanide 4f ones (more covalency) could lead to stronger magnetic super-exchange. On the other hand, the extraordinary experimental challenges of actinide complexes chemistry, because of their rarity and toxicity, afford computational chemistry a particularly valuable role. However, for such a purpose, the use of a multiconfigurational post-Hartree-Fock approach is required, but such an approach is computationally demanding for polymetallic systems—notably for actinide ones—and usually simplified models are considered instead of the actual systems. Thus, Density Functional Theory (DFT) appears as an alternative tool to compute magnetic exchange coupling and to explore the electronic structure and magnetic properties of actinide-containing molecules, especially when the considered systems are very large. In this paper, relevant achievements regarding DFT investigations of the magnetic properties of actinide complexes are surveyed, with particular emphasis on some representative examples that illustrate the subject, including actinides in Single Molecular Magnets (SMMs) and systems featuring metal-metal super-exchange coupling interactions. Examples are drawn from studies that are either entirely computational or are combined experimental/computational investigations in which the latter play a significant role.

Design, synthesis and isolation of a new 1,2,5-selenadiazolidyl and structural and magnetic characterization of its alkali-metal salts

A new electron acceptor is synthesized and reduced into its radical-anion isolated in the form of two salts with different structures and magnetic properties.

Field-induced single-ion magnet behaviour of a hexacoordinated Co(ii) complex with easy-axis-type magnetic anisotropy

This study presents the novel hexacoordinated Co(ii) mononuclear complex with SIM behavior.

Computational Methods for Modeling Metalloproteins

Metalloproteins are challenging objects if we want to investigate their chemical reactivity with theoretical approaches such as density functional theory (DFT). The complexity of these biomolecules often requires us to find a compromise between accuracy and feasibility, one that is tailored to the questions we set out to answer. In this chapter, we discuss computational approaches to studying chemical reactions in metalloproteins and how to utilize the information hidden in homologous proteins.

Binding for endohedral-metallofullerene superatoms induced by magnetic coupling

To design new materials based on artificial superatoms, clarifying their involved interaction is particularly important. In this study, we discuss first-principle calculations to show that the interaction between endohedral metallofullerenes (EMFs) of U@C28 can lead to different chemical and physical adsorption structures. Especially, these structures are derived from different magnetic coupling resonances, and they can transform by changing the distance between U@C28 superatoms. These findings will promote the future development for bottom-up assembling of new functional materials and even devices.

Ligand Radicals as Modular Organic Electron Spin Qubits

The intrinsic redox activity of the dithiolene ligand is presented here as the novel spin host in the design of a prototype molecular electron spin qubit, where the traditional roles of the metal and ligand components in coordination complexes are inverted. A series of paramagnetic bis(dithiolene) complexes with group 10 metals-nickel, palladium, platinum-provides a backdrop to investigate the spin dynamics of the organic ligand radical using pulsed EPR spectroscopy. The temperature dependence of the phase memory time (T_M ) is shown to be dependent on the identity of the diamagnetic metal ion, with the short times recorded for platinum a consequence of a diminishing spin-lattice (T₁ ) relaxation time driven by spin-orbit coupling. The utility of the radical ligand spin center is confirmed when it delivers one of the longest phase memory times ever recorded for a molecular two-qubit prototype.

Fe-V sulfur clusters studied through photoelectron spectroscopy and density functional theory

Iron-vanadium sulfur cluster anions are studied by photoelectron spectroscopy (PES) at 3.492 eV (355 nm) and 4.661 eV (266 nm) photon energies, and by density functional theory (DFT) calculations. The structural properties, relative energies of different structural isomers, and the calculated first vertical detachment energies (VDEs) of different structural isomers for cluster anions FeVS1-3- and FemVnSm+n- (m + n = 3, 4; m > 0, n > 0) are investigated at a BPW91/TZVP theory level. The experimental first VDEs for these Fe-V sulfur clusters are reported. The most probable ground state structures and spin multiplicities for these clusters are tentatively assigned by comparing their theoretical and experiment first VDE values. For FeVS1-3- clusters, their first VDEs are generally observed to increase with the number of sulfur atoms from 1.45 eV to 2.86 eV. The NBO/HOMOs of the ground state of FeVS1-3- clusters are localized in a p orbital on a S atom; the partial charge distribution on the NBO/HOMO localized site of each cluster anion is responsible for the trend of their first VDEs. A less negative localized charge distribution is correlated with a higher first VDE. Structure and steric effect differences for FemVnSm+n- (m + n = 3, m > 0, n > 0) clusters are suggested to be responsible for their different first VDEs and properties. Two types of structural isomers are identified for FemVnSm+n- (m + n = 4, m > 0, n > 0) clusters: a tower structure isomer and a cubic structure isomer. The first VDEs for tower like isomers are generally higher than those for cubic like isomers of FemVnSm+n- (m + n = 4, m > 0, n > 0) clusters. Their first VDEs are can be understood through: (1) NBO/HOMO distributions, (2) structures (steric effects), and (3) partial charge numbers on the NBO/HOMO's localized sites. EBEs for excited state transitions for all Fe-V sulfur clusters are calculated employing OVGF and TDDFT approaches at the TZVP level. The OVGF approach for these Fe/V/S cluster anions is better for the higher transition energies than the TDDTF approach. The experimental and theoretical results for these Fe/V/S cluster anions are compared with their related pure iron sulfur cluster anions. Properties of the NBO/HOMO are essential for understanding and estimating the different first VDEs for Fe/V/S, and comparing them to those of the pure Fe/S cluster anions.

A Dimeric η1 ,η5 -Germole Dianion Bridged Titanium(III) Complex with a Multicenter Ti-Ge-Ge-Ti Bond

Dimeric germole dianion bridged Ti^III and Zr^IV complexes have been synthesized. In these complexes, the germole dianion adopts a formal η¹ ,η⁵ coordination to the two metal centers. The bonding situation in these bridged dimers is dominated by a covalent Ge-Ge interaction that results, for example, in a strong antiferromagnetic coupling of the d¹ Ti centers.

Understanding titanium-catalysed radical-radical reactions: a DFT study unravels the complex kinetics of ketone-nitrile couplings

The computational investigation of a titanium-catalysed reductive radical-radical coupling is reported. The results match the conclusions from an earlier experimental study and enable a further interpretation of the previously observed complex reaction kinetics. Furthermore, the interplay between neutral and cationic reaction pathways in titanium(iii)-catalysed reactions is investigated for the first time. The results show that hydrochloride additives and reaction byproducts play an important role in the respective equilibria. A full reaction profile is assembled and the computed activation barrier is found to be in reasonable agreement with the experiment. The conclusions are of fundamental importance to the field of low-valent titanium catalysis and the understanding of related catalytic radical-radical coupling reactions.

Noncollinear Two-Component Quasirelativistic Description of Spin Interactions in Exchange-Coupled Systems. Mapping Generalized Broken-Symmetry States to Effective Spin Hamiltonians

We provide a consistent mapping of noncollinear two-component quasirelativistic DFT energies with appropriate orientations of localized spinor quantization axes for multinuclear exchange-coupled transition-metal complexes onto an uncoupled anisotropic effective spin Hamiltonian. This provides access to the full exchange interaction tensor between the centers of spin-coupled systems in a consistent way. The proposed methodology may be best viewed as a generalized broken-symmetry density functional theory approach (gBS-DFT). While the calculations provided are limited to trinuclear systems ([M₃O(OOCH)₆(H₂O)₃]⁺, where M = Cr(III), Mn(III), Fe(III)) with C₃ symmetry, the method provides a general framework that is extendable to arbitrary systems. It offers an alternative to previous approaches to single-ion zero-field splittings, and it provides access to the less often examined antisymmetric Dzyaloshinskii-Moriya exchange interaction. Spin-orbit coupling is included self-consistently. This will be of particular importance for complexes involving 4d or 5d transition metal centers or possibly also for f-block elements, where a perturbational treatment of spin-orbit coupling may not be valid anymore. While a comparison with experimental data was indirect due to simplifications in the chosen model structures, the agreement obtained indicates the essential soundness of the presented approach.

Design and Assembly of Covalently Functionalised Polyoxofluorovanadate Molecular Hybrids

Mixed-valent polyoxometalate (POM) clusters are one of the most interesting host species, showing a wide range of structural features and properties. The facile preparation and functionalisation of a mixed-valent polyoxofluorovanadates is reported, where two electrons are trapped to antipodal sites of the clusters. The first members of this family of clusters with the general formula, [V^V₁₂ V^IV₂ O₁₆ (μ-O)₁₀ (μ₃ -O)₁₀ (μ₃ -F)₂ (L)₂ ]^6- , where L: py=pyridine (1); pyr=pyrazine (2); im=imidazole (3), are unique organic-inorganic hybrids with the addition of a N-donor ligand at either end of the polyoxofluorovanadate. The composition and connectivity of 1-3 were characterised by single-crystal X-ray diffraction and electrospray ionisation mass spectrometry. Electron paramagnetic resonance spectroscopy revealed that the two well-separated V^IV ions in each cluster are fully uncoupled with J=0, giving a degenerate singlet-triplet ground state. This attenuation of the exchange interaction is probed with density functional theoretical calculations that reveal that the inclusion of the fluoride ion in the cluster produces a bond pathway biased toward destructive interference between competing ferromagnetic and antiferromagnetic interactions. These robust molecular materials are the ideal combination of desirable electronic properties, with an organic handle with which they can be integrated into spintronic circuitry for molecular devices.

Insight into the reaction mechanism of lipoyl synthase: a QM/MM study

Lipoyl synthase (LipA) catalyses the final step of the biosynthesis of the lipoyl cofactor by insertion of two sulfur atoms at the C6 and C8 atoms of the protein-bound octanoyl substrate. In this reaction, two [4Fe4S] clusters and two molecules of S-adenosyl-L-methionine are used. One of the two FeS clusters is responsible for the generation of a powerful oxidant, the 5'-deoxyadenosyl radical (5'-dA•). The other (the auxiliary cluster) is the source of both sulfur atoms that are inserted into the substrate. In this paper, the spin state of the FeS clusters and the reaction mechanism is investigated by the combined quantum mechanical and molecular mechanics approach. The calculations show that the ground state of the two FeS clusters, both in the [4Fe4S]2+ oxidation state, is a singlet state with antiferromagnetically coupled high-spin Fe ions and that there is quite a large variation of the energies of the various broken-symmetry states, up to 40 kJ/mol. For the two S-insertion reactions, the highest energy barrier is found for the hydrogen-atom abstraction from the octanoyl substrate by 5'-dA•. The formation of 5'-dA• is very facile for LipA, with an energy barrier of 6 kJ/mol for the first S-insertion reaction and without any barrier for the second S-insertion reaction. In addition, the first S ion attack on the C6 radical of octanoyl was found to take place directly by the transfer of the H6 from the substrate to 5'-dA•, whereas for the second S-insertion reaction, a C8 radical intermediate was formed with a rate-limiting barrier of 71 kJ/mol.