High-valent iron-oxo complexes dominate C-H bond activation chemistry, whereas analogous reactivity of nonoxo iron oxidants remains largely unexplored. Here, we report two structurally characterized FeIV-cyanide complexes supported by a bTAML ligand: [FeIV(CN)(bTAML)]- and [FeIV(CN)2(bTAML)]2-. Despite possessing a 150 mV more positive FeIV/III potential, the five-coordinated complex is ∼550-fold less reactive and incapable of C-H bond activation, whereas the six-coordinated analogue oxidizes both O-H and C-H bonds. Kinetic studies reveal no correlation with C-H bond dissociation energies but a strong dependence on substrate pKa, indicating asynchronous (basicity-controlled) H atom abstraction. Large KIEs, Hammett analysis, and asynchronicity parameter of the HAA reactions support a proton-transfer-dominated asynchronous PCET mechanism, which is corroborated by quantum-chemical calculations that reproduce the reactivity trends and identify the electronic origin of the lower barrier in the dicyano complex, including revealing the Fe-C≡N → Fe-N≡C isomerization, which enables the PCET event. These results demonstrate that coordination-induced modulation of basicity and linkage isomerization can govern PCET asynchronicity in nonoxo iron complexes, establishing Fe-cyanide species as a distinct class of hydrogen-atom abstractors and providing a design principle for tuning C-H activation reactivity beyond conventional redox paradigms.

ConspectusHydrogen atom abstraction (HAA) is one of the most pervasive radical reactions in biology and chemistry. It is central to enzymatic catalysis, respiration, and photosynthesis, and underpins modern synthetic strategies like selective C-H functionalization. Despite its ubiquity, predicting HAA reactivity and selectivity remains notoriously difficult: comparably strong X-H bonds (with X = C, O, N, ...) within the same molecule often display starkly contrasting reactivities that well-known linear free-energy relationships (LFERs) often fail to capture.In this Account, we describe how off-diagonal thermodynamics complements Hammond's view of transition states as early or late as a consequence of their diagonal thermodynamic driving force (ΔG0). It does so by gauging the effect of proton-transfer (PT) and electron-transfer (ET) states in the character of a concerted HAA reaction, that is, whether the charge distribution in transition state resembles more PT or ET instead of neutral HAA. Two key descriptors are presented, asynchronicity (η) and frustration (σ), which account for the effect of PT/ET states on HAA kinetics and, together with ΔG0, they formulate a three-component thermodynamic framework. Herein, we summarize and provide a unifying view of how this framework can be utilized to provide insight and quantification of reaction outcomes, e.g., through prediction of relative barriers and selectivity, tunneling contributions, polarity effects, and even judgement of the bias in post-HAA selectivity. Extending the concept of off-diagonal thermodynamics uncovers how H atom abstraction connects to broader radical-transfer chemistries, ultimately leading to the discovery of a newly described mechanism: hydride-coupled electron transfer (HCET). By integrating thermodynamic cycles, Marcus theory, and computational analyses, we propose that off-diagonal thermodynamics provide not only a unifying language in HAA and related radical chemistry, connecting quantum chemistry and experimental measurements, but also a practical predictive tool for chemists. Looking ahead, we outline how this framework can guide experimental design, bridge the gap between adiabatic and nonadiabatic regimes, and expand beyond HAA to an extended theory of radical reactivity.

Proton-coupled electron transfer (PCET) and hydrogen-atom transfer (HAT) reactions, collectively called H-atom abstraction (HAA) reactions, play critical roles in biological processes and modern organic synthesis. The kinetics of these processes can align with the principles described in the renowned Marcus cross relation (MCR), a framework initially formulated to describe electron transfer mechanisms. The MCR provides an outstanding link between the kinetics of HAA reactions involving two distinct reactants and two related auxiliary self-exchange reactions-each between a molecule of one of the reactants and its conjugated radical. In this study, we investigate the applicability and limitations of the canonical MCR across over 300 HAA reactions, providing a comprehensive theoretical analysis. Our findings reveal the need for an enhanced framework that incorporates "off-diagonal" thermodynamic factors-asynchronicity and frustration. Of these factors, asynchronicity, which quantifies the imbalance between the proton vs electron transfer components of the reaction, is identified as the dominant contributor to the improved predictive accuracy of the MCR. Notably, the incorporation of off-diagonal thermodynamics yields a more pronounced enhancement for HAT reactions than for PCET-like HAA reactions. As a corollary, the model also describes a so-called pseudoinverted region, in which more exergonic reactions feature higher free energy barriers even though the thermodynamic driving force is not so large as it is required for the proper inverted region well-known from the original Marcus theory. This advancement offers a refined theoretical basis for understanding H-atom abstraction mechanisms and underscores the importance of off-diagonal effects in HAA chemistry.

[This corrects the article DOI: 10.1039/D4SC01507J.].

This study explores hydride-coupled electron transfer (HCET) as a fundamentally distinct mechanism alternative to proton-coupled electron transfer (PCET). HCET was identified in the reaction between a CuIII-OH complex and organic substrates, involving hydride transfer coupled with a reversed electron transfer from CuIII-OH to the substrate in a single-barrier step. First, we identified the connection between the thermodynamic cycles and reactivity and showed that the mechanism is dictated by the cycle with more favorable off-diagonal thermodynamics. As evidenced by electronic-structure-based descriptors, the transferred hydrogen atom in HCET gains electron density and volume at the transition state, indicating hydride character, while in PCET, it loses electron density and volume, signaling proton character. Second, intrinsic bond orbital analysis confirmed that HCET is a two-electron process: it involves the complete transfer of the proton and the C-H α-electron from the substrate to the Cu ion, while the β-electron undergoes a transient exchange, initially migrating alongside the α-electron to the Cu center before returning to substrate. An analogous HCET mechanism was identified in the reaction between a NiII-OH complex and TEMPOH, where two β-electrons are engaged in the process: one transiently and one completely transferred to a NiII-coordinating ligand.

This study investigates the factors modulating the reactivity of 5 '-deoxyadenosyl (5 ' dAdo(center dot)) radical, a potent hydrogen atom abstractor that forms in the active sites of radical SAM enzymes and that otherwise undergoes a rapid self-decay in aqueous solution. Here, we compare hydrogen atom abstraction (HAA) reactions between native substrates of radical SAM enzymes and 5 ' dAdo(center dot) in aqueous solution and in two enzymatic microenvironments. With that we reveal that HAA efficiency of 5 ' dAdo(center dot) is due to (i) the in situ formation of 5 ' dAdo(center dot) in a pre-ordered complex with a substrate, which attenuates the unfavorable effect of substrate:5 ' dAdo(center dot) complex formation, and (ii) the prevention of the conformational changes associated with self-decay by a tight active-site cavity. The enzymatic cavity, however, does not have a strong effect on the HAA activity of 5 ' dAdo(center dot). Thus, we performed an analysis of in-water HAA performed by 5 ' dAdo(center dot) based on a three-component thermodynamic model incorporating the diagonal effect of the free energy of reaction, and the off-diagonal effect of asynchronicity and frustration. To this aim, we took advantage of the straightforward relationship between the off-diagonal thermodynamic effects and the electronic-structure descriptor - the redistribution of charge between the reactants during the reaction. It allows to access HAA-competent redox and acidobasic properties of 5 ' dAdo(center dot) that are otherwise unavailable due to its instability upon one-electron reduction and protonation. The results show that all reactions feature a favourable thermodynamic driving force and tunneling, the latter of which lowers systematically barriers by similar to 2 kcal mol-1. In addition, most of the reactions experience a favourable off-diagonal thermodynamic contribution. In HAA reactions, 5 ' dAdo(center dot) acts as a weak oxidant as well as a base, also 5 ' dAdo(center dot)-promoted HAA reactions proceed with a quite low degree of asynchronicity of proton and electron transfer. Finally, the study elucidates the crucial and dual role of asynchronicity. It directly lowers the barrier as a part of the off-diagonal thermodynamic contribution, but also indirectly increases the non-thermodynamic part of the barrier by presumably controlling the adiabatic coupling between proton and electron transfer. The latter signals that the reaction proceeds as a hydrogen atom transfer rather than a proton-coupled electron transfer. SAM enzymes harness inherent HAA activity of 5 ' dAdo(center dot) via in situ formation of the radical and by hindering its self-decay reactions.

Energy of off-diagonal states, associated with the thermodynamic cycle characterizing the mechanism, affects the barrier for radical ligand transfer and determines, which scenario, R − /electron transfer or R + /electron transfer, is the operative one.

Several manganese-dependent enzymes utilize MnIII-hydroxo units in concerted proton-electron transfer (CPET) reactions. We recently demonstrated that hydrogen bonding to the hydroxo ligand in the synthetic [MnIII(OH)(PaPy2N)]+ complex increased rates of CPET reactions compared to the [MnIII(OH)(PaPy2Q)]+ complex that lacks a hydrogen bond. In this work, we determine the effect of hydrogen bonding on the basicity of the hydroxo ligand and evaluate the corresponding effect on CPET reactions. Both [MnIII(OH)(PaPy2Q)]+ and [MnIII(OH)(PaPy2N)]+ react with strong acids to yield MnIII-aqua complexes [MnIII(OH2)(PaPy2Q)]2+ and [MnIII(OH2)(PaPy2N)]2+, for which we determined pKa values of 7.6 and 13.1, respectively. Reactions of the MnIII-aqua complexes with one-electron reductants yielded estimates of reduction potentials, which were combined with pKa values to give O-H bond dissociation free energies (BDFEs) of 77 and 85 kcal mol-1 for the MnII-aqua complexes [MnII(OH2)(PaPy2Q)]+ and [MnII(OH2)(PaPy2N)]+. Using these BDFEs, we performed an analysis of the thermodynamic driving force for phenol oxidation by these complexes and observed the unexpected result that slower rates are associated with more asynchronous CPET. In addition, reactions of acidic phenols with the MnIII-hydroxo complexes show rates that deviate from the thermodynamic trends, consistent with a change in mechanism from CPET to proton transfer.

Tyrosinase is a ubiquitous coupled binuclear copper enzyme that activates O2 toward the regioselective monooxygenation of monophenols to catechols via a mechanism that remains only partially defined. Here, we present new mechanistic insights into the initial steps of this monooxygenation reaction by employing a pre-steady-state, stopped-flow kinetics approach that allows for the direct measurement of the monooxygenation rates for a series of para-substituted monophenols by oxy-tyrosinase. The obtained biphasic Hammett plot and the associated solvent kinetic isotope effect values provide direct evidence for an initial H-transfer from the protonated phenolic substrate to the Cu2O2 core of oxy-tyrosinase. The correlation of these experimental results to quantum mechanics/molecular mechanics calculations provides a detailed mechanistic description of this H-transfer step. These new mechanistic insights revise and expand our fundamental understanding of Cu2O2 active sites in biology.

Methyl-coenzyme M reductase, responsible for the biological production of methane by catalyzing the reaction between coenzymes B (CoBS-H) and M (H3C-SCoM), hosts in its core an F430 cofactor with the low-valent Ni-I ion. The critical methanogenic step involves F430-assisted reductive cleavage of the H3C-S bond in coenzyme M, yielding the transient CH3 radical capable of hydrogen atom abstraction from the S-H bond in coenzyme B. Here, we computationally explored whether and why F430 is unique for methanogenesis in comparison to four identified precursors formed consecutively during its biosynthesis. Indeed, all precursors are less proficient than the native F430, and catalytic competence improves at each biosynthetic step toward F430. Against the expectation that F430 is tuned to be the strongest possible reductant to expedite the rate-determining reductive cleavage of H3C-S by Ni-I, we discovered the opposite. The unfavorable increase in reduction potential along the F430 biosynthetic pathway is outweighed by strengthening of the Ni-S bond formed upon reductive cleavage of the H3C-S bond. We found that F430 is the weakest electron donor, compared to its precursors, giving rise to the most covalent Ni-S bond, which stabilizes the transition state and hence reduces the rate-determining barrier. In addition, the transition state displays high pro-reactive motion of the transient CH3 fragment toward the H-S bond, superior to its biosynthetic ancestors and likely preventing the formation of a deleterious radical intermediate. Thus, we show a plausible view of how the evolutionary driving force shaped the biocatalytic proficiency of F430 toward CH4 formation.

When oxidants favour cleaving a strong C-H bond at the expense of weaker ones, which are otherwise inherently preferred due to their favourable reaction energy, reactivity factors such as the polarity match effect are often invoked. Polarity match follows the intuition of electrophilic (nucleophilic) oxidants reacting faster with nucleophilic (electrophilic) C-H bonds. Nevertheless, this concept is purely qualitative and is best suited for a posteriori rationalization of experimental observations. Here, we propose and inspect two methods to quantify polar effects in C-H cleavage reactions, one by computation via the difference of atomic charges (Δq) of reacting atoms, and one amenable to experimental measurement through asynchronicity factors, η. By their application to three case studies, we observe that both Δq and η faithfully capture the notion of polarity match. The polarity match model, however, proves insufficient as a predictor of H-atom abstraction reactivity and we discourage its use as a standalone variable in reaction design. Besides this caveat, η and Δq (through its mapping on η) allow the implementation of polarity match into a Marcus-type model of reactivity, alleviating its shortcomings and making reaction planning feasible.

Hydrogen atom abstraction (HAA) is central to life, and its importance in synthetic chemistry continues to grow. Enzymes rely on HAA to trigger life-sustaining reaction cascades, and greener synthetic routes are attainable by in situ capture of the carbon-centered radicals generated by HAA. Despite the potential of HAA for the diversification of molecular complexity and the late-stage functionalization of bioactive compounds, readily applicable and reliable models translating experimentally or computationally accessible thermodynamic quantities into relative free energy barriers are missing. In this work, we discovered a complete thermodynamic basis for the description of HAA reactivity, which consists of three components. Besides, the traditional linear free energy relationship and the recently introduced factor of asynchronicity (Srnec et al., PNAS 2018, 115, E10287-E10294), we present the third thermodynamic component of H atom abstraction reactions: the factor of frustration that arises from the dissimilarity of the species competing over a hydrogen atom in their overall ability to acquire an electron and proton. Incorporating these nonclassical descriptors into a Marcus-type model, the approach herein presented allows nearly quantitative prediction of relative barriers in six sets of metal-oxo-mediated HAA reactions, outperforming existing methods even in a stringent test with >200 computational HAA reactions.

Recently, the analysis of single-orbital entropy and mutual information has been introduced as a tool for the investigation of contributions to the exchange (J) coupling between open-shell metal ions [Stein et al. J. Phys. Chem. Lett. 2019, 10, 6762-6770]. Here, we show that this analysis may lead to an incorrect interpretation of the J-coupling mechanism. Instead, we propose an orbital-entanglement analysis that is based on the two-electron density and that provides a coherent picture of the contributing exchange pathways, which seems fully consistent with the available J values. For this purpose, we used a prototypical bis-μ-oxo binuclear manganese complex ([Mn2O2(NH3)8]4+) and demonstrated that its antiferromagnetism (J < 0), calculated by using the active space composed of all valence pO and dMn orbitals, correlates well with the largest elements in the differential low-spin vs high-spin entanglement map. These elements correspond to interactions between the pairs of dMn orbitals mediated by the oxo-bridging out-of-plane p orbitals, representing the π superexchange pathway. We also show that the reduction of active space to manifold of the singly occupied magnetic orbitals does not lead to discrepancy between the calculated J values and entanglement maps. This contrasts to analysis of mutual information, which suggests the "direct" dMn-dMn interactions to play a dominant role for the J coupling, irrespective of the size of active space as well as of the antiferromagnetism expected. The failure is attributed to the large contribution of spin entanglement contained in the mutual information of the low-spin state, which may be regarded as the origin of the different complexity of its wave function and electron density.

Complexes with two or more magnetically coupled metal ions have attracted considerable attention as catalysts of many vital processes, single-molecule magnets, or spin-crossover compounds. Elucidation of their electronic structures is essential for understanding their catalytic and magnetic properties. Here, we provide an unprecedented insight into exchange-coupling mechanisms between the magnetic centers in six prototypical bis-μ-oxo bimetallic M2O2 complexes, including two biologically relevant models of non-heme iron enzymes. Employing multiconfigurational/multireference methods and related orbital entanglement analysis, we revealed the essential and counterintuitive role of predominantly unoccupied valence metal d orbitals in their strong antiferromagnetic coupling. We found that the participation of these orbitals is twofold. First, they enhance the superexchange between the singly occupied d orbitals. Second, they become substantially occupied and thus directly magnetically active, which we perceive as a new mechanism of the exchange interaction between the magnetic transition metal centers.

Bifurcating reactions yield two different products emerging from one single transition state and are therefore archetypal examples of reactions that cannot be described within the framework of the traditional Eyring's transition state theory (TST). With the growing number and importance of these reactions in organic and biosynthetic chemistry, there is also an increasing demand for a theoretical tool that would allow for the accurate quantification of reaction outcome at low cost. Here, we introduce such an approach that fulfils these criteria, by evaluating bifurcation selectivity through the energy distribution within the reactive mode of the key transition state. The presented method yields an excellent agreement with experimentally reported product ratios and predicts the correct selectivity for 89% of nearly 50 various cases, covering pericyclic reactions, rearrangements, fragmentations and metal-catalyzed processes as well as a series of trifurcating reactions. With 71% of product ratios determined within the error of less than 20%, we also found that the methodology outperforms three other tested protocols introduced recently in the literature. Given its predictive power, the procedure makes reaction design feasible even in the presence of complex non-TST chemical steps.

The selective functionalization of C-H bonds is one of the Grails of synthetic chemistry. In this work, we demonstrate that the selectivity toward fast hydroxylation or radical diffusion (known as the OH-rebound and dissociation mechanisms) following H-atom abstraction (HAA) from a substrate C-H bond by high-valent iron-oxo oxidants is already encoded in the HAA step when the post-HAA barriers are much lower than the preceding one. By applying the reactive mode composition factor (RMCF) analysis, which quantifies the kinetic energy distribution (KED) at the reactive mode (RM) of transition states, we show that reactions following the OH-rebound coordinate concentrate the RM kinetic energy on the motion of the reacting oxygen atom and the nascent substrate radical, whereas reactions following the dissociation channel localize most of their kinetic energy in H-atom motion. These motion signatures serve to predict the post-HAA selectivity, and since KED is affected by the free energy of reaction and asynchronicity (factor eta) of HAA, we show that bimolecular HAA reactions in solution that are electron transfer-driven and highly exergonic have the lowest fraction of KED on the transferred H-atom and the highest chance to follow rebound hydroxylation. Finally, the RMCF analysis predicts that the HID primary kinetic isotope effect can serve as a probe for these mechanisms, as confirmed in virtually all reported examples in the literature.

Iron porphyrin carbenes (IPCs) are important reaction intermediates in engineered carbene transferase enzymes and homogeneous catalysis. However, discrepancies between theory and experiment complicate the understanding of IPC electronic structure (i.e., open- vs. closed-shell singlet (OSS vs. CSS)). Here we investigate the structurally dependent ground and excited spin state energetics of a free carbene and its IPC analogs. Only multireference ab initio wave function methods are consistent with experiment and predict a CSS ground state (Fe(II)←{:C(X)Y} 0 ), contrary to density functional theory (DFT). The OSS is a high-lying metal-to-ligand charge transfer (MLCT) excited state that is sensitive to the nature of the axial ligand. Furthermore, potential energy surfaces (PESs) along the Fe–C bond elongation coordinate exhibit strong mixings between CSS/OSS characters, which can be an important feature for describing reaction mechanisms. Future studies on IPC reaction coordinates should evaluate contributions from ground and excited state multireference character.

By employing the computational protocol for calculation of reduction potentials of the Fe4 S4 -containing species validated using a representative series of well-defined synthetic complexes, we focused on redox properties of two prototypical radical SAM enzymes to reveal how they transform SAM into the reactive 5'-deoxyadenosyl radical, and how they tune this radical for its proper biological function. We found the reduction potential of SAM is indeed elevated by 0.3-0.4 V upon coordination to Fe4 S4 , which was previously speculated in the literature. This makes a generation of 5'-deoxyadenosyl radical from SAM less endergonic (by ca. 7-9 kcal mol-1 ) and hence more feasible in both enzymes as compared to the identical process in water. Furthermore, our calculations indicate that the enzyme-bound 5'-deoxyadenosyl radical has a significantly lower reduction potential than in referential aqueous solution, which may help the enzymes to suppress potential side redox reactions and simultaneously elevate its proton-philic character, which may, in turn, promote the radical hydrogen-atom abstraction ability.

The α-ketoglutarate (αKG)-dependent oxygenases catalyze a diverse range of chemical reactions using a common high-spin FeIV═O intermediate that, in most reactions, abstract a hydrogen atom from the substrate. Previously, the FeIV═O intermediate in the αKG-dependent halogenase SyrB2 was characterized by nuclear resonance vibrational spectroscopy (NRVS) and density functional theory (DFT) calculations, which demonstrated that it has a trigonal-pyramidal geometry with the scissile C-H bond of the substrate calculated to be perpendicular to the Fe-O bond. Here, we have used NRVS and DFT calculations to show that the FeIV═O complex in taurine dioxygenase (TauD), the αKG-dependent hydroxylase in which this intermediate was first characterized, also has a trigonal bipyramidal geometry but with an aspartate residue replacing the equatorial halide of the SyrB2 intermediate. Computational analysis of hydrogen atom abstraction by square pyramidal, trigonal bipyramidal, and six-coordinate FeIV═O complexes in two different substrate orientations (one more along [σ channel] and another more perpendicular [π channel] to the Fe-O bond) reveals similar activation barriers. Thus, both substrate approaches to all three geometries are competent in hydrogen atom abstraction. The equivalence in reactivity between the two substrate orientations arises from compensation of the promotion energy (electronic excitation within the d manifold) required to access the π channel by the significantly larger oxyl character present in the pπ orbital oriented toward the substrate, which leads to an earlier transition state along the C-H coordinate.

The α-ketoglutarate (αKG)-dependent oxygenases catalyze a diverse range of chemical reactions using a common high-spin FeIV=O intermediate and, in most reactions, abstracts a hydrogen atom from the substrate. Previously, the FeIV=O intermediate in the αKG-dependent halogenase SyrB2 was characterized by nuclear resonance vibrational spectroscopy (NRVS) and density functional theory (DFT) calculations, which demonstrated that it has a trigonal-pyramidal geometry with the scissile C-H bond of the substrate calculated to be perpendicular to the Fe-O bond. Here, we have used NRVS and DFT calculations to show that the FeIV=O complex in taurine dioxygenase (TauD), the αKG-dependent hydroxylase in which this intermediate was first characterized, also has a trigonal bipyramidal geometry, but with an aspartate residue replacing the equatorial halide of the SyrB2 intermediate. Computational analysis of hydrogen atom abstraction by square pyramidal, trigonal bipyramidal, and six-coordinate FeIV=O complexes in two different substrate orientations (one more along [σ channel] and another more perpendicular [π channel] to the Fe-O bond) reveals similar activation barriers. Thus, both substrate approaches to all three geometries are competent in hydrogen atom abstraction. The equivalence in reactivity between the two substrate orientations arises from compensation of the promotion energy (electronic excitation within the d manifold) required to access the π channel by the significantly larger oxyl character Corresponding Authors: solomone@stanford.edu. $Contributed equally Supporting Information. The supplementary section contains the Mössbauer spectrum of the NRVS sample, details on the processing of the NRVS data, the simulations for all the NRVS structural models and tables and figures relevant to the reaction coordinate calculations. This material is available free of charge via the Internet at http://pubs.acs.org. HHS Public Access Author manuscript J Am Chem Soc. Author manuscript; available in PMC 2020 November 05. Published in final edited form as: J Am Chem Soc. 2020 November 04; 142(44): 18886–18896. doi:10.1021/jacs.0c08903. A uhor M anscript