Reactivity principles based on orbital overlap and bonding/antibonding interactions are well established to describe the reactivity of organic species, and atomic structures are typically predicted by Hund's rules to have maximum single-electron occupancy of degenerate orbitals in the ground state. Here, we extend the role of exchange to transition states and discuss how, for reactions and kinetics of bioinorganic species, the analogue of Hund's rules is exchange-controlled reactivity. Pathways that increase the number of unpaired and spin-identical electrons on a metal centre will be favoured by exchange stabilization. Such exchange-enhanced reactivity endows transition states with a stereochemistry different from that observed in cases that are not exchange-enhanced, and is in good agreement with the reactivity observed for iron-based enzymes and synthetic analogues. We discuss the interplay between orbital- and exchange-controlled principles, and how this depends on the identity of the transition metal, its oxidation number and its coordination sphere.

Over the past decades metalloenzymes and their synthetic models have emerged as an area of increasing research interest. The metalloenzymes and their synthetic models oxidize organic molecules using oxometal complexes (OMCs), especially oxoiron(IV)-based ones. Theoretical studies have helped researchers to characterize the active species and to resolve mechanistic issues. This activity has generated massive amounts of data on the relationship between the reactivity of OMCs and the transition metal's identity, oxidation state, ligand sphere, and spin state. Theoretical studies have also produced information on transition state (TS) structures, reaction intermediates, barriers, and rate-equilibrium relationships. For example, the experimental-theoretical interplay has revealed that nonheme enzymes carry out H-abstraction from strong C-H bonds using high-spin (S = 2) oxoiron(IV) species with four unpaired electrons on the iron center. However, other reagents with higher spin states and more unpaired electrons on the metal are not as reactive. Still other reagents carry out these transformations using lower spin states with fewer unpaired electrons on the metal. The TS structures for these reactions exhibit structural selectivity depending on the reactive spin states. The barriers and thermodynamic driving forces of the reactions also depend on the spin state. H-Abstraction is preferred over the thermodynamically more favorable concerted insertion into C-H bonds. Currently, there is no unified theoretical framework that explains the totality of these fascinating trends. This Account aims to unify this rich chemistry and understand the role of unpaired electrons on chemical reactivity. We show that during an oxidative step the d-orbital block of the transition metal is enriched by one electron through proton-coupled electron transfer (PCET). That single electron elicits variable exchange interactions on the metal, which in turn depend critically on the number of unpaired electrons on the metal center. Thus, we introduce the exchange-enhanced reactivity (EER) principle, which predicts the preferred spin state during oxidation reactions, the dependence of the barrier on the number of unpaired electrons in the TS, and the dependence of the deformation energy of the reactants on the spin state. We complement EER with orbital-selection rules, which predict the structure of the preferred TS and provide a handy theory of bioinorganic oxidative reactions. These rules show how EER provides a Hund's Rule for chemical reactivity: EER controls the reactivity landscape for a great variety of transition-metal complexes and substrates. Among many reactivity patterns explained, EER rationalizes the abundance of high-spin oxoiron(IV) complexes in enzymes that carry out bond activation of the strongest bonds. The concepts used in this Account might also be applicable in other areas such as in f-block chemistry and excited-state reactivity of 4d and 5d OMCs.

This article addresses the intriguing hydrogen-abstraction (H-abstraction) and oxygen-transfer (O-transfer) reactivity of a series of nonheme [Fe(IV)(O)(TMC)(Lax)](z+) complexes, with a tetramethyl cyclam ligand and a variable axial ligand (Lax), toward three substrates: 1,4-cyclohexadiene, 9,10-dihydroanthracene, and triphenyl phosphine. Experimentally, O-transfer-reactivity follows the relative electrophilicity of the complexes, whereas the corresponding H-abstraction-reactivity generally increases as the axial ligand becomes a better electron donor, hence exhibiting an antielectrophilic trend. Our theoretical results show that the antielectrophilic trend in H-abstraction is affected by tunneling contributions. Room-temperature tunneling increases with increase of the electron donation power of the axial-ligand, and this reverses the natural electrophilic trend, as revealed through calculations without tunneling, and leads to the observed antielectrophilic trend. By contrast, O-transfer-reactivity, not being subject to tunneling, retains an electrophilic-dependent reactivity trend, as revealed experimentally and computationally. Tunneling-corrected kinetic-isotope effect (KIE) calculations matched the experimental KIE values only if all of the H-abstraction reactions proceeded on the quintet state (S = 2) surface. As such, the present results corroborate the initially predicted two-state reactivity (TSR) scenario for these reactions. The increase of tunneling with the electron-releasing power of the axial ligand, and the reversal of the "natural" reactivity pattern, support the "tunneling control" hypothesis (Schreiner et al., ref 19). Should these predictions be corroborated, the entire field of C-H bond activation in bioinorganic chemistry would lay open to reinvestigation.

It is shown that H-abstraction reactivity by oxoiron(IV) complexes with a quintet ground state is highly enhanced due to exchange-stabilization endowed by the increased number of the exchange Correspondence to: Lawrence Que, Jr, larryque@umn.edu; Sason Shaik, sason@yfaat.ch.huji.ac.il. One of us, [6] has recently prepared two such S=2 reagents and compared their H-abstraction activities to those of the synthetic complexes that possess the more common S=1 ground state. These results generated however, a bag full of surprises, which are addressed herein by means of DFT calculations. Shown in Figure 1 are DFT calculated iron(IV)-oxo complexes along with their key geometric features, and spin state information. The isolated complex with an S=2 ground state is TMG 3 trenFe(IV)O 2+ (1),[6a] which possesses a trigonal bipyramidal iron coordination, typified by two-below-two-below-one d-orbital block, [3b] and hence a quintet ground state, well below the S=1 state. Surprisingly, however, 1 exhibited a rather sluggish H-abstraction reactivity even towards the weak C-H bonds of 1,4-cyclohexadiene (CHD). Thus, 1 was slightly less reactive than N4PyFe(IV)O 2+ 2 and five times more reactive than TMC(AN)Fe(IV)O 2+ , 3;[6b] both of which are thought to react via TSR. NIH Public Access[4] To add to the puzzle, the putative Tp(OBz)Fe(IV)O, 4, which was proposed to form upon oxygenation of Tp(benzoylformate)Fe(II) as a model for TauD, was found to be highly reactive and capable of activating even the strong C-H bond of cyclopentane (BDE = 96.3 kcal mol −1 ).[6b] Note that in the S=2 state, 5 4, Fe loses one of the benzoate arms and becomes a pentacoordinated square pyramid with a basal Fe(IV)-oxo moiety (Fig. 1). Thus, it is this weaker ligand field that stabilizes S=2 relative to the hexacoordinated S=1. Indeed, as can be seen from Figure 1, 4 is computed to involve degenerate S=1 and S=2 states.[7] So, in 4 a competition is expected between the two spin states to effect C-H activation; which state dominates? In summation, the experimental relative reactivities of the four Fe=O reagents order in a puzzling sequence:What is the origin of this reactivity pattern, and what are the electronic and steric factors that shape this trend? Answering this question is important for establishing rules of design of effective catalysts for C-H activation.To answer these questions we studied the reactivities of 1-4 towards H-abstraction from CHD. The geometries of all the critical species along the H-abstraction paths of 1-3, which are di-positively charged, were optimized at the B3LYP/B1(CH 3 CN) (B1 is LACVP) level at the reaction solvent, to minimize self-interaction errors which cause artificial electron transfer in some of these systems.[8] For 4, which is neutral and hence less subject to these particular errors, [8] we used B3LYP/B1. All energies were subsequently estimated using a NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript larger basis set, B2 (B2 is LACV3P+*), and solvent corrections, using th...

b S Supporting Information T here is a surge of interest in synthetic models of mononuclear nonheme iron enzymes, 1À6 which perform CÀH activation and lead to the formation of alcohols and alkenes. Both the enzymes 1 and the synthetic models utilize high-valent iron-(IV)-oxo complexes as the active species. 2À5 One of the potent synthetic complexes is [N4PyFe IV O] 2+ (N4Py: N,N-bis (2-pyridylmethyl)-bis(2-pyridyl) methylamine), which is depicted in Scheme 1 and which is capable of activating even cyclohexane. 6,7 However, unlike the enzymatic complexes that have high-spin quintet (S = 2) ground states, the synthetic variants are generally characterized by triplet ground states (S = 1) 4 and low-lying quintet excited states (S = 2) and as such have a more complex reactivity behavior. Density functional theory (DFT) has contributed to the understanding of this reactivity, which was characterized as two-state reactivity (TSR), 8 wherein the S = 2 state cuts through the larger S = 1 barrier and mediates the reaction. 9À13 However, because most of the synthetic complexes carry a high positive charge, usually 2+, the gas-phase calculations have resulted in some nonphysical anomalies, such as barrier-free S = 2 surfaces, 10,11 electron transfer processes, artificial charge delocalization, 14 formation of charged organic intermediates due to hydride abstractions instead of the experimentally observed hydrogen atom abstraction (HAT), 6 and discontinuities in the potential energy profiles. 10,15 These anomalies were invincibly shown 14,16,17 to originate in the self-interaction error inherent in DFT. As such, an important class of these bioinorganic reactions cannot be confidently studied with DFT unless these anomalies can be evaded. Siegbahn et al. 14,16 have suggested that the anomalies can be muted by masking the charge of the iron oxo reagent, for example, by using counterions. 14 In this Letter, we report the boon of incorporating counterions in the UB3LYP calculations of the reactions, depicted in Scheme 1, of the synthetic complex 6 [N4PyFe IV O] 2+ with cyclohexadiene, with which all of the above anomalies manifest with the bare oxidant (model 1), and cyclohexane, for which the anomalies appear after the first HAT, in the follow-up steps in Scheme 1a. As shall be shown, adding the two ClO 4À counterions (model 2) as in the [N4PyFe II (CH 3 CN)](ClO 4 ) 2 crystal structure 18 removes the anomalies and creates smooth energy profiles that enable one to study the entire stepwise processes in Scheme 1a, explore various reaction trajectories (σ/π) 9b,19À21 of the rate-limiting HAT step, offer unequivocal characterization of the reaction intermediates, assess and derive coherent reactivity Scheme 1. (a) Reactions Studied Using (b) Oxidant Models 1, 1-solv, and 2 (1-solv Signifies That All Species Are Optimized in the Solvent) and (c) Two Substrates a a Reb and 2H are abbreviated processes.

The symmetrically dinuclear title compounds were isolated as diamagnetic [(bpy)2Ru(mu-H2L)Ru(bpy)2](ClO4)2 (1-(ClO4)2) and as paramagnetic [(acac)2Ru(mu-H2L)Ru(acac)2] (2) complexes (bpy=2,2'-bipyridine; acac- = acetylacetonate = 2,4-pentanedionato; H2L = 2,5-dioxido-1,4-benzoquinonediimine). The crystal structure of 22 H2O reveals an intricate hydrogen-bonding network: Two symmetry-related molecules 2 are closely connected through two NH(H2L2-)O(acac-) interactions, while the oxygen atoms of H2L2- of two such pairs are bridged by an (H2O)8 cluster at half-occupancy. The cluster consists of cyclic (H2O)6 arrangements with the remaining two exo-H2O molecules connecting two opposite sides of the cyclo-(H2O)6 cluster, and oxido oxygen atoms forming hydrogen bonds with the molecules of 2. Weak antiferromagnetic coupling of the two ruthenium(III) centers in 2 was established by using SQUID magnetometry and EPR spectroscopy. Geometry optimization by means of DFT calculations was carried out for 1(2+) and 2 in their singlet and triplet ground states, respectively. The nature of low-energy electronic transitions was explored by using time-dependent DFT methods. Five redox states were reversibly accessible for each of the complexes; all odd-electron intermediates exhibit comproportionation constants K(c)>10(8). UV-visible-NIR spectroelectrochemistry and EPR spectroscopy of the electrogenerated paramagnetic intermediates were used to ascertain the oxidation-state distribution. In general, the complexes 1n+ prefer the ruthenium(II) configuration with electron transfer occurring largely at the bridging ligand (mu-H2Ln-), as evident from radical-type EPR spectra for 13+ and (+. Higher metal oxidation states (iii, iv) appear to be favored by the complexes 2m; intense long-wavelength absorption bands and RuIII-type EPR signals suggest mixed-valent dimetal configurations of the paramagnetic intermediates 2+ and 2-.

Oxidative C–H bond activation is a transformation of fundamental and practical interest, particularly if it can be carried out with high regio- and enantioselectivity. With nonheme iron oxygenases as inspiration (e.g., the Rieske oxygenases), a family of biomimetic nonheme iron complexes has been found to catalyze hydrocarbon oxidations by H2O2 via a postulated FeV(O)(OH) oxidant. Of particular interest is the Fe(S,S-PDP) catalyst discovered by White that, in the presence of acetic acid as an additive, performs selective C–H bond activation, even in complex organic molecules. The corresponding FeV(O)(OAc) species has been suggested as the key oxidant. We have carried out DFT studies to assess the viability of such an oxidant and discovered an alternative formulation. Theory reveals that the barrier for the formation of the putative FeV(O)(OAc) oxidant is too high for it to be feasible. Instead, a much lower barrier is found for the formation of a [(S,S-PDP)FeIII(κ2-peracetate)] species. In the course of C–H activation, this complex undergoes O–O bond homolysis to become a transient [(S,S-PDP)FeIV(O)(AcO·)] species that performs the efficient hydroxylation of alkanes. Thus, the acetic acid additive alters completely the nature of the high-valent oxidant, which remains disguised in the cyclic structure. This new mechanism can rationalize the many experimental observations associated with the oxidant formed in the presence of acetic acid, including the S = 1/2 EPR signal associated with the oxidant. These results further underscore the rich multioxidant scenario found in the mechanistic landscape for nonheme iron catalysts.

This theoretical work addresses the mechanistic switch between hydroxylase (alcohol formation) and desaturase (olefin formation) activities during alkane oxidation by two non-heme high-valent oxoiron reagents, the enzyme taurine:α-ketoglutarase dioxygenase (TauD) and the synthetic shape-selective catalyst (TpOBzFe), toward cyclohexadiene, cyclohexane, cyclopentane, and ethane. As we show, the desaturase/hydroxylase steps obey unique orbital selection rules, and the mechanistic switch is determined by intrinsic reactivity factors that depend on the ligand-sphere flexibility of the oxoiron species, the substrate, and the spin states of the reaction pathways. Testable predictions are outlined.