Mechanism of N–N Bond Formation by Transition Metal–Nitrosyl

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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Mechanism of N−N Bond Formation by Transition Metal−Nitrosyl Complexes: Modeling Flavodiiron Nitric Oxide Reductases Casey Van Stappen*,‡ and Nicolai Lehnert* Department of Chemistry and Department of Biophysics, University of Michigan, 930 North University Avenue, Ann Arbor, Michigan 48109-1055, United States S Supporting Information *

ABSTRACT: Nitric oxide (NO) has a number of important biological functions, including nerve signaling transduction, blood pressure control, and, at higher concentrations, immune defense. A number of pathogenic bacteria have developed methods of degrading this toxic molecule through the use of flavodiiron nitric oxide reductases (FNORs), which utilize a nonheme diiron active site to reduce NO → N2O. The well-characterized diiron model complex [Fe2(BPMP)(OPr)(NO)2]2+ (BPMP− = 2,6-bis[(bis(2pyridylmethyl)amino)methyl]-4-methylphenolate), which mimics both the active site structure and reactivity of these enzymes, offers key insight into the mechanism of FNORs. Presently, we have used computational methods to elucidate a coherent reaction mechanism that shows how one and two-electron reduction of this complex induces N−N bond formation and N2O generation, while the parent complex remains stable. The initial formation of a N−N bond to generate hyponitrite (N2O22−) follows a radical-type coupling mechanism, which requires strong Fe−NO π-interactions to be overcome to effectively oxidize the iron centers. Hyponitrite formation provides the largest activation barrier with ΔG‡ = 7−8 kcal/mol (average of several functionals) in the two-electron, super-reduced mechanism. This is followed by the formation of a N2O22− complex with a novel binding mode for nonheme diiron systems, allowing for the facile release of N2O with the assistance of a carboxylate shift. This provides sufficient thermodynamic driving force for the reaction to proceed via N2O formation alone. Surprisingly, the oneelectron “semireduced” mechanism is predicted to be competitive with the super-reduced mechanism. This is due to the asymmetry imparted by the BPMP− ligand, allowing a one-electron reduction to overcome one of the primary Fe−NO πinteractions. Generally, mediation of N2O formation by high-spin [{M-NO−}]2 cores depends on the ease of oxidizing the M centers and breaking of the M−NO π-bonds to formally generate a “full” 3NO− unit, allowing for the critical step of N−N bond formation to proceed (via a radical-type coupling mechanism). 2NO + 2e− + 2H+ → N2O + H 2O

I. INTRODUCTION In recent decades, nitric oxide (NO) has become well-known for its variety of functions in biology.1−6 At nanomolar concentrations this diatomic serves as a signaling molecule in mammals and is involved in both blood pressure control in the cardiovascular system and nerve signal transduction in the brain.7−11 Macrophages also utilize higher concentrations of NO as an immune defense agent to kill invading pathogens.12 In addition, NO is an important metabolite in the biogeochemical nitrogen cycle and is produced by denitrifying bacteria and fungi as part of their respiration, where nitrate is stepwise reduced to N2 and N2O.13−15 Other processes that involve NO as a reactant or intermediate are the direct sixelectron reduction of nitrite to ammonia by assimilatory and dissimilatory nitrite reductases, as well as the production of nitrate by nitric oxide dioxygenases (NODs).15−19 The reductive coupling of two molecules of NO to produce N2O according to eq 1 is an important reaction in biology that is catalyzed by NO reductases (NORs).20 © XXXX American Chemical Society

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As mentioned above, this process is used on a large scale by denitrifying bacteria and fungi living in soil and seawater to degrade the toxic molecule (metabolite) NO under anaerobic conditions, utilizing enzymes such as NorBC and Cytrochrome P450nor.21−24 This reaction is therefore responsible for the generation of the greenhouse gas N2O at scale as a response to the overfertilization of agricultural soils.25 In addition, NORs are used by certain pathogenic bacteria as a means of protection against exposure to NO,26,27 which is produced in response to bacterial infections as a mammalian immune defense agent. This latter process is catalyzed by flavodiiron nitric oxide reductases (FNORs).26,28−33 Therefore, these enzymes are significant for bacterial pathogenesis, as they promote proliferation of pathogenic microbes within the human body, causing harmful infections. Hence, it is of particular interest to investigate the mechanism by which FNORs reduce NO to Received: September 10, 2017

A

DOI: 10.1021/acs.inorgchem.7b02333 Inorg. Chem. XXXX, XXX, XXX−XXX

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formation of a diferrous dinitrosyl intermediate, [{FeNO}7]2, prior to N2O generation.40,41 The identification of the [{FeNO}7]2 intermediate in T. maritima FNOR41 directly supports the di-{FeNO}7 mechanism shown in Scheme 2, ruling out the hyp mechanism which avoids the [{FeNO}7]2 intermediate. It is further proposed that the [{FeNO}7]2 intermediate is catalytically competent to undergo N−N bond formation and hyponitrite generation, followed by N2O release and water formation. In turn, FMNH2 acts to rereduce the ferric diiron active site following turnover. The superreduced (sr) pathway is a variant of the di-{FeNO} 7 mechanism, in which the neighboring flavin performs a twoelectron reduction to generate the [{FeNO}8]2 state prior to N2O production. Interestingly, it was reported recently by Kurtz and co-workers that, in the absence of the FMN cofactor, NO degradative reactivity is still possible;41 however, whether this is also the case under turnover is still a matter of debate in the literature. Previous investigations on mononuclear nonheme iron {FeNO}7 complexes (S = 3/2) have shown that these compounds are best described as consisting of a high-spin iron(III) center (S = 5/2) with a bound triplet NO− (nitroxyl) ligand (S = 1), where the spins are antiferromagnetically coupled to produce the experimentally observed S = 3/2 ground state.42−47 Here, the bound NO− ligand serves as a strong π-donor, leading to a strong and very covalent Fe−NO bond.47,48 Correspondingly, the formally NO− ligand does not chemically behave like a nitroxyl group and is generally not very reactive; that is, it cannot be protonated.49 On the basis of a recent study on [Fe(TMG3tren)(NO)]2+/1+, the one-electron reduced nonheme {FeNO}8 complex is best described as a high-spin Fe(II) with a bound triplet NO−, where the spins are again antiferromagnetically coupled to give an S = 1 ground state.49,50 This one-electron reduction leads to a distinct decrease in the covalency of the Fe−NO bond and a general activation of the Fe−NO unit for chemical reactivity. Although it seems counterintuitive that two NO− units, which should electrostatically repel one another, can couple to make a N−N bond, the experimental data on FNORs described above conclude that this is in fact the case (by either the di-{FeNO}7 or sr mechanism). In addition, studies on the functional model complex for FNORs, [Fe2(BPMP)(OPr)(NO)2]2+ (12+; see Scheme 1c), demonstrate the feasibility of the sr pathway.37 This complex contains an [{FeNO}7]2 core that is stable and shows no propensity for N−N bond formation. However, upon addition of 2 equiv of reductant, fast and efficient N2O formation is observed from complex 12+. Finally, Hayton and co-workers have demonstrated analogous Ni−NO chemistry, where two {NiNO}10 units, best described as Ni(II)−NO−, couple to generate N2O via a hyponitrite intermediate, which has been structurally characterized.51,52 Related chemistry has also been observed in a diruthenium dinitrosyl dimer.53 It is evident from these results that N−N coupling can very efficiently be mediated by two M(II)−NO− units; however, the detailed molecular mechanism of how two M(II)−NO− units can mediate N−N bond formation and N2O generation is not well understood. In this paper, we use density functional theory (DFT) calculations to obtain insight into this reaction. For this purpose, the wellcharacterized model complex 12+ is used as a representative example. As mentioned above, this model system is not able to mediate N2O formation directly from the 12+ form. In previous

N2O to better understand their functionality. FNORs belong to the flavodiiron protein (FDP) family, the active site of which is composed of a dinuclear nonheme iron center (see Scheme 1a) located at the N-terminus, which lies in close proximity to a redox-active flavin mononucleotide (FMN) cofactor on the Cterminus of the neighboring subunit.30−33 Scheme 1. Structural Comparison of the Active Site of M. thermoacetica FNOR (a) and the Model Complex [Fe2(BPMP)(OPr)]2+ (b)a

a

[Fe2(BPMP)(OPr)]2+ binds two molecules of NO to form (c), which has been structurally characterized.37 This complex generates N2O upon treatment with reductant to form product (d).

Scheme 2. Summary of the Proposed Reaction Mechanisms of FNORs20,30

The mechanism of FNORs has been the subject of intense investigation in recent years.34−39 Several proposals have been formulated based on a combination of experimental and theoretical work, as shown in Scheme 2.20,30 Note that, in the following, we will use the Enemark−Feltham notation, {MNO}n, to describe the overall oxidation state of the Fe− NO unit, where n is the number of valence electrons of the complex (= metal-d plus NO-π* electrons).39 For example, a complex formed between NO· and Fe(II) would be classified as {FeNO}7. This formalism accommodates the fact that NO is a redox-active (“noninnocent”) ligand, often making the electronic structures of transition metal−nitrosyl complexes complicated, and a priori assignments of the electron distribution is rarely possible (see below). Recent studies by Kurtz and co-workers have provided clear evidence for the B

DOI: 10.1021/acs.inorgchem.7b02333 Inorg. Chem. XXXX, XXX, XXX−XXX

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Additionally, two separate fragments were generated for the BPMP− and OPr− ligands, both with a charge of −1 and S = 0, bringing the total charge of the system to +2. This “initial guess” was then used as a starting point in single-point and optimization calculations. While the two {FeNO}7 units of 12+ are known to be antiferromagnetically coupled, it has been shown previously for similar iron−nitrosyl complexes that this coupling is often relatively weak.75 Thus, calculations were performed to optimize both the antiferro- and ferromagnetically coupled states of 12+ and 10 for all exchangecorrelation functionals to theoretically predict the exchange coupling constant J according to the operator H = −2J(SA·SB). Further calculations of the {FeNO}8 complexes 11+ and 10 and on following structures, which evolve along the reaction coordinate, utilized the same technique, assigning fragments and initial guesses for spin states as appropriate. For 10, this involves the use of S = 1 and a charge of +1 for either {FeNO}8 unit. In 20−50, each Fe is treated separately with S = 2 and a charge of +2, with hyponitrite treated as S = 0, charge = −2 in 20−40‡ and the bridging μ-oxo of 50 also with S = 0, charge = −2. For 11+, calculations were performed with the assignment of one Fe−NO unit as {FeNO}7 (with S = 3/2 and a charge of +2) and the other one as {FeNO}8 (with S = 1 and a charge of +1). As the two Fe−NO centers are nondegenerate, calculations were performed for both {Fe1NO1}7/{Fe2NO2}8 and {Fe1NO1}8/ {Fe2NO2}7. Subsequent structures of 21+−51+ were acquired using initial fragment guesses as described for 20−50, except that one of the Fe atoms is treated as S = 5/2 with a charge of +3. Naturally, the complements were also calculated (Fe12+/Fe23+ and Fe13+/Fe22+). All reaction coordinates were determined using relaxed potential energy surface scans, allowing for reoptimization of the geometry with each scan step. Transition states were determined using the QST2 and QST3 methods available in Gaussian 09.

work, addition of 2 equiv of reductant has been shown to mediate N2O generation, following the overall reaction: [Fe2(BPMP)(OPr)(NO)2 ]2 + + 2e− → [Fe2(BPMP)(OPr)(O)] + N2O

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To gain detailed molecular insight into the mechanism of this reaction, we investigated N2O formation from all three relevant oxidation states of the complex, [{FeNO}7]2 (12+), [{FeNO}7{FeNO}8] (11+), and [{FeNO}8]2 (10), according to the established direct and super-reduced mechanisms, as well as the scenario where the reaction starts from the one-electron reduced, mixed-valent form. Our work provides, for the first time, detailed insight into the general mechanism of N−N bond formation by coupling of two transition-metal nitroxyl (Mn+−NO−) species and the electronic-structural requirements for this process.

II. COMPUTATIONAL METHODS To investigate the properties of the reduced and super-reduced states 11+ and 10, a calibration of theoretical methods was necessary. Therefore, a rigorous study of 12+ was undertaken to determine the most appropriate method with which to proceed. While functional and basis set considerations for the treatment of diamagnetic transition metal complexes are generally standard, accurate calculations of the electronic properties of broken symmetric systems such as 12+ require a more intensive method calibration. Six exchange-correlation functionals were chosen, which span a range of Hartree−Fock exchange contributions. The initial structure of 12+ was obtained from crystallographic coordinates37 and optimized at the DFT level using the following exchange-correlation functionals: (a) Becke’s 1988 exchange functional54 and the gradient corrections of Perdew, along with his 1981 local correlation functional P8655 (BP86); (b) the hybrid-exchange functional of Tao, Perdew, Staroverov, and Scuseria TPSSH;56 (c) Becke’s three-parameter hybrid exchange functional57 and the gradient corrections provided by the Lee−Yang−Parr nonlocal correlation functional58 (B3LYP); and (d) the 1996 pure functional of Perdew, Burke, and Ernzerhof combined with the gradient-corrected correlation functional of Perdew, Burke, and Ernzerhof 59−61 (PBE1PBE). Additionally, (e) Handy’s OPTX modification of Becke’s exchange functional in conjuction with the Lee−Yang−Parr nonlocal correlation functional (OLYP)58,62,63 has been shown to reasonably treat some iron−nitrosyls,64 and hence, this method was employed as well. Finally, (f) the Minnesota 2006 local functional (M06-L) of Zhao and Truhlar was tested,65 as it has recently found success in the treatment of an FNOR active-site model.66 In all calculations, iron was treated using the triple-ζ polarized basis set of Ahlrich and co-workers (TZVP67,68). The smaller 6-311G(d) basis set60,69,70 was used for carbon, nitrogen, and oxygen, while 631G(d)71,72 was applied for hydrogen. To treat solvation properties, all calculations were performed using the polarizable continuum model (PCM) as implemented in Gaussian09 with dichloromethane selected as the solvent to imitate the previously reported reaction conditions.31 All calculations were performed with the Linux version of the Gaussian09 program.73 Mulliken orbital composition analyses for Gaussian09 single-point calculations were performed using the Linux version of QMForge.74 Despite being overall diamagnetic, the complex 12+ contains two high-spin {FeNO} 7 units with S = 3/2 spin, which are antiferromagnetically coupled via phenolate and propionate bridges to give a total spin of Stot = 0. Hence, the system must be treated using broken symmetry (BS) so as to ensure appropriate calculation of electron density and total energies of the complex.64 Thus, the unrestricted formalisms of all utilized exchange-correlation functionals were employed, and fragments were used to describe the BS state of the system. This was achieved in Gaussian09 by the generation of an “initial guess”, which involves the treatment of each {FeNO}7 unit as separate fragments, each with S = |3/2| and a charge of +2.

III. RESULTS III.1. Method Calibration for 12+. To identify the best method for further investigation of the reaction mechanism of 11+ and 10, a series of calculations was performed for 12+, and the results were compared with experimentally determined properties, such as the X-ray diffraction (XRD)-determined geometry and vibrational frequencies.37 As each iron is slightly inequivalent due to the inherent asymmetry introduced by the BPMP− ligand, the atomic numbering scheme for 12+/1+/0 presented in Scheme 1c is used to aid in the further discussion. Structural deviations of calculated geometries from the crystal structure of 12+ for a set of key coordinates are provided in Figure 1 and Table S1. For small inorganic molecules, deviations of ±0.03 Å in bond distances and ±1.0° in bond angles in DFT-calculated geometries are considered within excellent agreement with experiment.76 However, in larger systems such as 12+, these tolerances may be relaxed due to the

Figure 1. Bond deviations of the core [{FeNO}7]2 geometry of 12+. C

DOI: 10.1021/acs.inorgchem.7b02333 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry inherently greater degree of flexibility in the model and the unusually complicated electronic structure of this complex. Most important is the accurate calculation of key geometric parameters within the {FeNO}7-O(Ph)-{FeNO}7 core. There is an inherent asymmetry of the Fe sites generated within the BPMP− scaffold, which is evident from the trans-coordinated nitrogen ligand of NO. At the Fe1 center, the tert-amine group lies trans to NO, while the ligand trans to NO at Fe2 is an Ncoordinated pyridine. This asymmetry is reflected by the calculated geometries and the electronic structure of the {FeNO}7 units, where the tert-amine serves as a weaker trans ligand. This is easily seen in the asymmetric coordination of propionate, where the Fe1−O4 coordinate is 0.07 Å longer than that of Fe2−O5. This is also observed to a lesser degree in the Fe−NO coordinates, where the Fe1−N1 coordinate is 0.023 Å shorter than Fe2−N2. From Figure 1, it can be seen that all methods provide a reasonable treatment of the individual {FeNO}7 units, as evident from the calculated Fe− NO and NO bond distances. However, OLYP poorly estimates the distances within the Fe1−O3−Fe2 backbone, which are critical to the electronic coupling between the two {FeNO}7 units investigated here. This behavior has previously been observed in the treatment of {FeNO}x complexes with this functional.64 All exchange correlation functionals find difficulty in describing the interatomic distances between the respective NO units; interestingly, however, while most functionals generally underestimate these distances, they are overestimated by OLYP. The general trend for the key Fe−N− O distances and angles is in line with previous theoretical reports of {FeNO}7 systems, in which the Fe−N distance is mildly underestimated by BP86 and overestimated by hybrid functionals such as B3LYP, while the N−O distance is overestimated by both.77,78 Vibrational frequency calculations also serve as a complementing diagnostic for gauging the ability of a method to accurately predict electronic structure (see Figure 2 and Table

and antisymmetric NO stretching frequencies. It can be seen that the pure functionals generally predict the NO stretching frequencies more accurately, with BP86 underestimating and OLYP slightly overestimating the energies of these modes. However, OLYP is considerably poorer in calculating the Fe− NO stretching frequency, likely corresponding to the overestimation of the Fe−NO bond length. The M06-L functional, which contains a self-correlation correction, predicts considerably higher-energy NO stretching frequencies, similar to those of the hybrid functionals. Besides geometric and vibrational frequency considerations, calculation of the magnetic exchange coupling between the two {FeNO}7 units can be useful in understanding how well a functional treats the given system. Unfortunately, this quantity has not been measured for 12+; despite this, as the overall spin of the complex is S = 0, it is still interesting to calculate and compare the strength of coupling between the two {FeNO}7 units. The Heisenberg exchange Hamiltonian, which describes the magnetic exchange between two centers (A and B), may be written as H = −2J( S̲ A· S̲ B)

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where SA and SB are the spin operators of centers A and B. The exchange coupling constant J between the two centers may be estimated by the difference in energy between the high-spin (HS) and broken-symmetry (BS) states in the weak coupling limit using the Noodleman formalism64,79 J = (E BS − E HS)/(4SA·SB)

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where EHS and EBS are the energies of the high-spin and broken symmetry states, and SA and SB are the total spin of centers A and B. An alternative expression for describing spin coupling was derived by Yamaguchi and co-workers, which utilizes the spin expectation values, ⟨S2⟩, of the HS and BS states:80 J = (E BS − E HS)/( S2

HS

− S2

BS

)

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Here, the calculated exchange coupling constants are presented for both formalisms for comparison. Since it is known experimentally that the iron centers are antiferromagnetically coupled, fully optimized structures were first generated for the BS state of the complex. Second, the energies of the ferromagnetically coupled states were then calculated for each BS optimized geometry, both in the 12+ and 10 oxidation states. Approaches of how to treat this coupling have been established previously by Noodleman and co-workers.64 The spin exchange coupling constant J of the [{FeNO}7]2 dimer is calculated to be in a range between −65 and −110 cm−1 by either eq 4 or 5, varying by functional and method utilized, presenting an intermediate spin coupling (Table S1). These values are likely overestimated when compared to the known experimental values of similar systems; for example, the J value for the [{FeNO}7]2 complex [Fe2(Et-HPTB)(O2CPh)](BF4)2 (where Et-HPTB = N,N,N′,N′-tetrakis(N-ethyl-2-benzimidazolyl-methyl)-1,3-diaminopropane) has been determined to be −23 cm−1 (H = −2J·SA·SB) via magnetic susceptibility measurements.75 We expect 12+ to have a similar J value in the −10 to −20 cm−1 range, corresponding to weak exchange coupling between the two Fe−NO units. On the basis of these results in comparison to experimental observations, it can be concluded that while the employed hybrid-exchange correlation functionals provide reasonable geometries of the {FeNO}7-O-{FeNO}7 core and Fe−NO

Figure 2. Calculated vibrational frequencies for 12+ as a function of the exact exchange used in the listed functionals.

S2). Calculation of the Hessian provides insight into how well a method predicts the core {FeNO}7 electronic structure, since both the Fe−NO and NO vibrational frequencies are highly dependent on the nature of the Fe−NO interaction; additionally, in diiron dinitrosyl complexes, there are both symmetric and antisymmetric NO and Fe−NO stretching modes, adding a gauge for the electronic coupling between the two {FeNO}7 units. Figure 2 contains experimental and calculated frequencies for the Fe−NO stretches, as well as both symmetric D

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NO− → Fe(III) π-donation. Because of the antiferromagnetic coupling between Fe1 and Fe2, this bonding motif is flipped for Fe2 with respect to the α- and β-spin MOs, as indicated in Scheme 3; however, the overall Fe−NO bonding interactions are very similar. Combining the two {FeNO}7 units into one molecular orbital scheme thus produces two sets of d-π* MOs, that is, the respective NO in-plane (NO-ip) and out-of-plane (NO-oop) sets shown in Figure 3 (which are the bonding combinations of the Fe(d) and NO−(π*) orbitals), relative to the coplanar Fe2(NO)2 unit. The electronic structure of 12+ is discussed in greater detail in Figure S2. III.3. Reduction to the 10 State. In line with the superreduced mechanism first proposed for FNORs,31 we first investigated how two-electron reduction would affect the geometric and electronic structures of model complex 12+, and we determined how this activates the complex for NOR activity as previously proposed.37 Geometric Differences. The key geometric parameters of the [{FeNO}8]2 core of 10 are summarized in Table 2. Upon twoelectron reduction of 12+, the coordination environment of the two iron centers increases in asymmetry. For Fe1, there is a general contraction in the N1−N3−N4 facial plane and an expansion in the complementing O3−N5−O4 plane. Changes to the first coordination sphere of Fe2 are much less pronounced, where a mild expansion of almost all Fe2-ligand bond lengths is observed. These changes in bond distances are in agreement with a predominately iron-centered reduction when moving from to 12+→ 10. Overall, this causes a decrease in the orbital overlap of Fe1 with the propionate ligand, as well as a decrease in covalency between both irons and the BPMP− phenolate backbone, in turn decreasing the strength of the superexchange interaction between the two iron centers. In addition to changes in bond distances, several changes in the internal angles of the {FeNO} cores occur upon twoelectron reduction. In particular, a significant decrease of 15° is observed for the Fe2−N2−O2 bond angle. The torsion angle between the respective NO units increases significantly as well, moving from nearly planar (5°) to 40°; these geometric changes are noted across all functionals utilized here. On the basis of these observations, it would be expected that the electronic coupling between the two {FeNO} units decreases upon reduction to 10. This is indeed predicted by all methods used in the present study, where significantly decreased spinexchange coupling constants J are calculated (Table S4). However, for N−N bond formation to occur, the electron spins of the two {FeNO} units must remain antiferromagnetically coupled. In turn, this means that in the [{FeNO}8]2 dimer the catalytically relevant state should still be of broken-symmetry (S = 0) type. Electronic Differences. A molecular orbital diagram of 10 is shown in Figure 4. Upon two-electron reduction of the iron centers, it is anticipated from the previous analysis that the additional two electrons will pair with the existing electrons of the Fe-dxy orbitals at either iron center. Indeed, this has been found in previous studies on mononuclear {FeNO}8 complexes.44,49 Correspondingly, in the {Fe1NO1}8 unit, the βorbital of dxy becomes occupied. Interestingly, however, in the {Fe2NO2}8 unit, the antibonding in-plane α-Fe2-dxz/NO2(π*) orbital drops in energy below the unoccupied α-Fe2-dxy orbital and becomes the highest occupied molecular orbital (HOMO). This is in agreement with the expansion of both the Fe2−N2 and N2−O2 coordinates as described above and the decrease in the Fe2−N2−O2 bond angle from 143° to 129°; this implies a

stretching frequencies, all significantly overestimate the NO stretching frequencies. This is also true for M06-L. Meanwhile, OLYP provides excellent NO stretching frequencies but overestimates the internal Fe1−O3−Fe2 distances. Lastly, BP86 provides both a reasonable geometry and the second best estimate of the NO stretch (calc: 1733 cm−1, exp: 1758 cm−1). On this basis, we chose to employ BP86 for the further determination of the reaction pathway of 12+/1+/0. III.2. Electronic Structure of 12+. The frontier orbitals of the 12+ complex are composed of the two partially occupied Fe 3d shells in a pseudo-Oh environment along with partially occupied, mixed Fe(3d)−NO(π*) orbitals. The electronic structure of each individual {FeNO}7 unit is best described as a high-spin Fe(III) center (S = 5/2) with a bound triplet NO− ligand (S = 1), where the spins of these subunits are strongly antiferromagnetically coupled to yield a total spin of S = 3/2. This has been previously determined for similar, mononuclear {FeNO}7 complexes.42,43,45,47,48,81,82 From here, the two {FeNO}7 units are antiferromagnetically coupled to one another, resulting in a net diamagnetic complex.37 For the purpose of discussing electronic structure throughout the paper, the primary (z) axis of each Fe center is assigned to the Fe−N(O) vector. Thus, each Fe exhibits π-bonding between the Fe-dxz,yz (Fe-dπ) and the NO-π* orbitals, while the Fe-dxy orbital lies orthogonal to the Fe−NO unit. The BS ground state of 12+ is qualitatively outlined in Scheme 3 in a spinScheme 3. A General Scheme of the Broken-Symmetry Couplinga of the Two {FeNO}7 Units of 12+

Here, interaction of high-spin FeIII with 3NO− is shown for both {FeNO}7 units, which are antiferromagnetically coupled. a

unrestricted formalism. According to ligand field theory, each Fe-d manifold in an Oh field will split into the t2g and eg sets; while neither Fe is truly Oh in symmetry, the approximation will be made for the sake of discussion. From here, the dxz and dyz orbitals are capable of overlapping with the NO π* orbitals to form covalent d-π* interactions. Note that when using the unrestricted Kohn−Sham formalism, α and β spins are split into two sets of molecular orbitals. A summary of the electronic structure of 12+ along with corresponding molecular orbitals is provided in Figure 3, with MO contributions listed in Table 1. At Fe1, the five α-spin electrons predominantly occupy the Fe1-d orbitals, with little contribution from the NO π* orbitals. Hence, as described above, π-backbonding is negligible in highspin {FeNO}7 complexes.47,49,50,83 In contrast, a large degree of orbital mixing is observed between the occupied β−π* orbitals of NO− and the dxz/dyz orbitals of Fe1, corresponding to strong E

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Figure 3. Molecular orbital diagram of 12+ calculated using the BP86 method, utilizing fragments to describe the individual {FeNO}7 units, as well as the OPr− and BPMP− ligands. As a further note, the terms “NO1” and “NO2” refer to the NO groups bound to Fe1 and Fe2, respectively.

Table 1. Molecular Orbital Compositions and Spin Densities of 12+ molecular orbital compositiona (%) label

energy (eV)

a

spin density α-manifold 201-LUMO 200-HOMO 199 198 197 196 188 187 186 β-manifold 201-LUMO 200-HOMO 199 198 197 196 190 188 187

Fe1

NO1

Fe2

NO2

OPr

BPMP

3.00

−0.44

−2.97

0.39

−0.01

0.03

Fe2-dxy Fe1-dx2−y2 Fe1-dz2 Ph* NO2-oop NO2-ip Fe1-dyz Fe1-dxz Fe1-dxy

−4.714 −5.860 −5.868 −6.197 −6.446 −6.519 −7.802 −7.942 −8.044

1.4 29.9 36.2 12.3 4.9 4.7 28.2 29.8 43.1

0.1 15.1 8.3 0.5 0.7 1.9 4.5 2.5 3.2

75.3 6.0 3.3 16.0 32.4 33.5 2.4 4.0 4.5

0.2 0.3 1.9 16.8 28.8 34.9 2.5 0.5 0.2

5.6 0.3 11.3 6.3 5.6 2.8 28.0 15.3 14.9

17.4 48.4 39.0 48.0 27.7 22.3 34.4 48.0 34.1

Fe1-dxy Fe2-dx2−y2 Fe2-dz2 Ph* NO1-oop NO1-ip Fe2-dyz Fe2-dxz Fe2-dxy

−4.941 −5.675 −5.865 −6.286 −6.633 −6.689 −7.661 −7.749 −7.827

72.5 4.5 5.3 2.9 37.4 35.6 2.7 2.5 1.5

0.5 0.2 0.7 4.9 38.7 41.2 1.7 0.9 0.8

1.8 36.2 34.2 14.9 2.1 4.4 21.1 20.4 52.7

0.2 0.1 23.2 7.8 0.3 1.3 2.7 2.3 6.5

3.1 9.5 4.1 1.3 4.4 5.0 24.6 20.6 6.6

21.9 49.5 32.5 68.3 17.2 12.6 47.3 53.4 32.0

a

As calculated with BP86, using the PCM method with dichloromethane as solvent. Underestimated spin densities are well-known to occur when utilizing BP86 towards {FeNO}7 systems and arise from an overestimation of the covalency of the Fe−NO bond, reducing the spin-polarization between Fe and NO.82

decrease in the α-Fe2-dxz/NO2(π*) in-plane bonding interaction. This results in a weakening of the Fe2−N2 bond, activating the NO2 unit. This is further reflected by the differential spin densities calculated for the two NO ligands, as shown in Table 3, where the reduction of the {Fe1NO1} unit appears more iron-centered, and that of the {Fe2NO2} unit is more NO-centered. Correspondingly, a significant difference is

observed between the calculated stretching vibrational frequencies: rather than coupled symmetric and antisymmetric stretching modes as in the case of the [{FeNO}7]2 dimer, two largely uncoupled N−O vibrations appear, where νN1−O1 = 1564 cm−1 and νN2−O2 = 1487 cm−1. Alpha Manifold. The overall electronic structure of the αmanifold in 10 remains similar to that of the 12+ complex, with F

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Inorganic Chemistry Table 2. Selected Geometric Parameters of Broken-Symmetry Optimized Structures of 10 coordinate distance (Å) Fe1−Fe2 Fe1−O3 Fe2−O3 Fe1−N1 Fe2−N2 Fe1−O4 Fe2−O5 N1−O1 N2−O2 N1−N2 O1−O2 angle (deg) Fe1−O3−Fe2 Fe1−N1−O1 Fe2−N2−O2 N1−Fe1−Fe2−N2 O1−N1−N2−O2

DFT method uBP86 3.703 2.221 2.159 1.699 1.786 2.324 2.059 1.210 1.221 2.854 3.604 115.4 146.1 128.7 −16.78 41.50

uOLYP

uM06-L

uTPSSH

uB3LYP

3.878 2.286 2.290 1.735 1.826 2.476 2.078 1.119 1.208 3.118 3.853

3.537 2.189 2.126 1.794 1.901 2.202 2.055 1.194 1.212 2.706 3.236

3.602 2.166 2.141 1.794 1.894 2.245 2.062 1.206 1.223 2.910 3.642

3.633 2.183 2.173 1.856 1.947 2.251 2.078 1.214 1.225 3.117 4.085

115.85 152.44 129.75 −15.66 34.81

110.06 159.92 129.33 −21.77 26.47

113.45 154.07 129.27 −17.15 36.82

113.06 148.55 129.79 −16.59 40.16

uPBE1PBE 3.593 2.156 2.144 1.867 1.954 2.211 2.070 1.209 1.219 3.111 4.083 113.34 148.34 130.30 −17.31 40.41

S4). Interestingly, the HOMO−6, composed of the Ph* orbital, shows an increased contribution from Fe1 and appears responsible for the continued but very weak superexchange interaction. Moving to lower energy, the HOMO−2 corresponds to the bonding combination of Fe2-dyz and the NO2oop orbital. This MO is raised significantly in energy relative to the corresponding MO in 12+. The Fe1-dz2 orbital becomes the HOMO−3, which is in turn followed by the NO2-ip orbital as the HOMO−4. Additionally, the occupied t2g-type orbitals of Fe1 have raised significantly in energy to become the HOMO− 5 (Fe1-dxy), HOMO−7 (Fe1-dxz), and HOMO−8 (Fe1-dyz); this can be attributed to the decrease in effective nuclear charge of the iron centers upon reduction. In summary, the reduction of 12+ to 10 results in a significant decrease in the covalency of the Fe2−NO2 bond. Beta Manifold. The β-manifold rearranges in a similar fashion to that of the α-manifold, as anticipated. The HOMO is composed of Fe1-dxy as predicted from the {FeNO}7 electronic analysis. The Fe2-dx2−y2 and dz2 orbitals remain the highest occupied β-Fe2-d orbitals as the HOMO−1 and HOMO−2. Next, the NO1-ip orbital appears as the HOMO−3; it is interesting to note that this is opposite to the case of 12+, where the NO1-oop orbital appears higher in energy than NO1-ip. The Fe2-dyz and NO1-oop orbitals are located to lower energy as the HOMO−4 and HOMO−5. Below these orbitals lies Ph*, which, as mentioned above, shows a possible continuation of the superexchange pathway. Still lower in energy lie the Fe2dxy and dxz orbitals, which remain near degenerate. It is notable that the NO2-oop and NO2-ip orbitals both appear significantly higher in energy (and in turn less stabilized) than NO1-oop and NO1-ip. The differences may be summarized as an effective decrease in the covalency of the Fe2−NO2 bond, due to a decrease in the Fe2−NO2 in-plane π-interaction, which is caused by the occupation of the Fe−NO antibonding Fe2-dxz orbital upon reduction. This further indicates that the asymmetry of the two Fe sites, induced by BPMP−, increases in 10, leading to an activation of NO2. III.4. Mechanism of N2O Formation. With a thorough calibration and understanding of the electronic structures of 12+ and 10 in hand, it is possible to move forward to investigate the reactivity of 10. For 10 to produce N2O in the absence of a

Figure 4. Molecular orbital diagram of 10 calculated using the BP86 method, utilizing fragments to describe the individual {FeNO}8 units, as well as the OPr− and BPMP− ligands. Orbital surfaces were generated with an isosurface value of 0.04.

some minor rearrangements. As noted above, the HOMO consists of the Fe2-dxz rather than the expected Fe2-dxy orbital, implying an activation of NO2 with a weaker Fe2−NO2 bond and increased spin density on NO2; this trend of increased spin-polarization between Fe2 and NO2 is observed for all functionals (Table S3). The HOMO−1 is composed of Fe1dx2−y2; however, it may be noted that the interaction of the dx2−y2 orbital with the backbone phenolate O3 p-orbital appears decreased. This is reflected in the calculated exchange-coupling constant J, which decreases significantly relative to 12+ with a calculated value of only ca. −1 cm−1 (from BP86; see Table G

DOI: 10.1021/acs.inorgchem.7b02333 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 3. Molecular Orbital Compositions and Spin Densities of 10 molecular orbital compositiona (%) label

energy (eV)

a

spin density α-manifold 201-HOMO 200 199 198 197 196 195 194 193 β-manifold 201-HOMO 200 199 198 197 196 195 194 193 a

Fe1

NO1

Fe2

NO2

OPr

BPMP

2.44

−0.42

−2.80

0.77

−0.02

0.03

Fe2-dxz Fe1-dx2−y2 NO2-oop Fe1-dz2 NO2-ip Fe1-dxy Ph* Fe1-dxz Fe1-dyz

−2.795 −3.541 −3.631 −3.779 −4.066 −4.388 −4.768 −5.328 −5.547

2.5 47.7 9.9 30.5 12.4 70.0 13.9 46.5 59.9

1.9 1.3 1.7 19.2 4.2 0.1 0.1 16.4 17.2

44.7 6.8 23.1 9.7 24.8 1.3 1.8 2.0 0.5

13.5 5.2 47.2 9.8 32.3 1.4 1.3 0.3 0.3

1.7 5.1 2.2 5.2 3.6 2.2 3.2 1.6 15.4

35.4 33.9 16.0 25.7 22.7 25.0 79.8 33.1 6.6

Fe1-dxy Fe2-dx2−y2 Fe2-dz2 NO1-ip Fe2-dyz NO1-oop Ph* Fe2-dxy Fe2-dxz

−3.119 −3.534 −3.757 −4.422 −4.533 −4.555 −4.783 −5.214 −5.235

55.2 2.2 1.1 23.7 7.1 30.6 10.5 2.7 0.6

0.6 0.3 0.3 36.4 9.8 40.3 12.5 2.1 0.3

1.5 47.4 45.0 7.6 56.1 5.0 22.1 57.7 58.5

0.2 5.6 22.8 1.8 3.6 0.3 2.7 5.1 6.8

1.8 5.0 6.5 2.8 2.2 2.9 3.6 13.3 11.4

40.8 39.5 24.4 27.6 21.3 21.0 48.6 19.1 22.4

As calculated with BP86, using the PCM method with dichloromethane as solvent.

Scheme 4. Proposed Primary Reaction Pathwaya for N2O Generation from [Fe2BPMP(OPr)(NO)2] (10)

a

Calculated using the BP86 method.

release of N2O from 10. These results are particularly interesting, since it has been previously hypothesized that the primary driving force for N2O production in FNORs is the formation of H2O as a byproduct;30 here, we see that the formation and release of N2O alone is capable of providing a substantial driving force for the reaction to proceed. This is in agreement with recent computational studies using the M06-L functional on a minimized model of the active site of Moorella thermoacetica FNOR, where a driving force of 26.5 kcal/mol was found.66 Following the requirements for the reaction as stated above, a survey of reaction coordinate scans was performed to elucidate the intermediates and transition states for the release of N2O from 10. A summary of the obtained reaction profile is shown in Scheme 4. Step 1: N1−N2 Bond Formation. The formation of a N−N bond, generating hyponitrite, is the first logical step for the

proton source, two key steps must be accomplished. First, and most fundamental, a new N−N bond must be formed between the two nitric oxide units to generate hyponitrite (N2O22−). Second, nitrous oxide must be released through the cleavage of an N−O bond. Additionally, experimental data indicate that the final product contains a μ-oxo bridged FeII core ([Fe2BPMP(OPr)O]2+ (50), as seen in Scheme 1d. This allows for a third requirement to be postulated, namely, the formation of a μ-oxo bridge, which will be present in the final product. To ensure that this product is feasible, the μ-oxo complex was modeled and optimized. The energy of this complex, along with the N2O product, is indeed calculated to be 7.8 kcal/mol lower in energy than the starting material; additionally, the release of N2O provides an additional −9.6 kcal/mol in free energy (predominantly from the entropic component), providing a total driving force of −17.4 kcal/mol for the formation and H

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transition state 10‡ occurs at the critical point in which the Fe− NO π-interactions are significantly weakened. This reduction in covalency of the Fe−NO bonds leads to a localization of the two π-bonding electrons of each NO− ligand on the newly formed hyponitrite (N2O22−) unit that is now bound to the iron centers. These changes are reflected by an increase in spin density at either Fe center, as listed in Table 4, accompanied by a decrease in spin density on the (closed shell) hyponitrite ligand. Upon complete formation of N2O22− (20), it is clear that N1 and N2 have converted to approximate sp2 hybridization, resulting in a completely conjugated O−N−N−O2− unit from the formation of N−N σ- and π-bonds from the NO-ip(π*) and NO-oop(π*) orbitals, respectively. These orbital transformations are summarized in Figure 5. At this point (structure 20), the hyponitrite ligand has fully formed and is bound to two HS ferrous iron centers via its N atoms (Scheme 4). For the following considerations, the valence orbitals of the newly formed hyponitrite ligand, shown in Figure 6, are considered. The HOMO and HOMO−2 of

reaction to proceed. Because of the coordinative saturation of both iron centers, alternative pathways involving the rearrangement of the coordinated NO ligands would require dissociation of one of the NO ligands. However, as the reaction does not require an NO headspace to keep NO bound and generate quantitative amounts of N2O, it is very unlikely that the reaction proceeds in this way. To investigate the energetic barrier for the formation of hyponitrite, the N1−N2 coordinate was reduced in a stepwise fashion utilizing a relaxed potential energy surface scan. In this manner, the N1−N2 coordinate was scanned, starting from the initial N1−N2 distance of 2.855 Å, while all other coordinates were reoptimized at each interval. A local minimum was found at a N−N distance of 1.355 Å; reoptimization of this N-bound hyponitrite structure led to a final N−N distance of 1.371 Å, resulting in complex 20 (Scheme 4). In this structure, the N1− O1 and N2−O2 bond distances are increased from 1.210 and 1.221 Å in 10 to 1.294 and 1.281 Å in 20, respectively. Accordingly, the Fe1−N1 and Fe2−N2 distances increase significantly, from 1.699 and 1.786 Å in 10 to 2.018 and 2.117 Å in 20, respectively. The corresponding transition state (structure 10‡) is observed at a N−N distance of 1.661 Å, resulting in a barrier of 13.7 kcal/mol for the generation of 20. The overall (thermodynamic) change in free energy in going from 10 to 20 is calculated to be 12.6 kcal/mol. As the N−N distance decreases along the reaction coordinate, significant changes in the electronic structure of the complex are observed. It can be seen from Figure 5 that the

Figure 6. Labeling diagram of the N2O22− frontier orbitals that originate from bonding and antibonding combinations of the π* orbitals of NO1 and NO2, calculated using the BP86 method. Orbital surfaces were generated with an isosurface value of 0.04. Orbital labels were made based on their order of appearance in complex 40. Note that the σ1 and σ2 orbitals should be considered oxygen lone pairs, since they have greater than 70% O contribution.

N2O22− arise from N−N bonding interactions, generating the N2O22−-π1 and N2O22−-σ2 orbitals. Close in energy lies N2O22−σ1, which is weakly N−N antibonding. Note that both N2O22−σ1 and N2O22−-σ2 have greater than 70% O character and should therefore be considered lone pairs of the oxygens. Furthermore, the term “π” in N2O22−-π1 is used to denote the out-of-plane N−N bonding orbital, while σ is used to denote orbitals that lie within the O1−N1−N2−O2 plane. As seen in Figure 5, the α-NO2-oop and β-NO1-oop orbitals of 10 couple to form a new N2O22−-π bond, while the α-NO2-ip and βNO1-ip orbitals couple to form the N2O22−-σ orbitals. Despite

Figure 5. Formation of N2O22− from 10 as calculated using the BP86 method, utilizing fragments to describe the individual {FeNO}8 units, as well as the OPr− and BPMP− ligands in 10. An initial guess for 10 utilizes individual fragments for each {FeNO}8 unit, while the initial guess for 20 utilizes separate fragments describing each individual Fe, as well as N2O22−. Orbital surfaces were generated with an isosurface value of 0.04.

Table 4. Spin Densities of 10, 10‡, and 20 As Calculated Using the BP86 Method spin densities of N−N coupling spin densities

Fe1

N1

O1

Fe2

N2

O2

OPr

BPMP

10 10‡ 20

2.44 3.45 3.65

−0.22 −0.20 −0.03

−0.20 −0.20 −0.05

−2.80 −3.45 −3.68

0.45 0.24 0.06

0.32 0.23 0.13

−0.02 −0.03 −0.04

0.03 −0.04 −0.03

I

DOI: 10.1021/acs.inorgchem.7b02333 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry being effectively closed shell, a skewing of the energies of the spin−orbitals of hyponitrite is observed, due to spin-polarization induced by interaction with the high-spin iron centers. Particularly, the N2O22−-σ2 orbital forms a σ-bond with the Fedz2 orbitals of both iron centers as shown in Figure 5. Additionally, the N2O22−-σ1 orbital is close in energy to the N2O22−-σ2 and N2O22−-π1 orbitals and, thus, is also available to participate in bonding interactions with either iron center. Step 2: Conformational Flexibility of the Hyponitrite Ligand. Following formation of the N-bound hyponitrite intermediate 20, it is necessary for at least one oxygen atom to coordinate to one of the iron centers to proceed toward the formation and release of N2O from hyponitrite. In addition, it is also expected that the Fe(II) centers will have a greater affinity toward binding of the negatively charged oxygen atoms of N2O22− rather than the nitrogens, and hence, isomerization of the hyponitrite ligand to an O-bound form should also be energetically advantageous. This idea is supported by recent crystallographic data for Ni(II) and Fe(III) hyponitrite complexes, which show O-coordination of this ligand.51,84−86 Correspondingly, we investigated possible rearrangement pathways for the hyponitrite ligand next. Numerous coordinates can be chosen to accomplish this task, and an inherently high degree of freedom exists in rotating the hyponitrite unit. Multiple coordinates involving atomic distances, angles, and torsion angles were investigated; all results converged to a “side-on” coordinated hyponitrite, in which hyponitrite coordinates in an Fe1−O1−N1−Fe2 fashion, referred to as complex 30 (see Scheme 4). This side-on coordination mode of hyponitrite in 30 is 4.7 kcal/mol lower in free energy than the N−N coordinated structure 20. The N1−O1 distance increases to 1.393 Å, and the N1−N2 bond length decreases to 1.314 Å, whereas the N2−O2 distance experiences virtually no change at 1.278 Å. The optimized transition state, 20‡, is found at a free energy of ∼5 kcal/mol relative to 20; this relatively small free energy barrier implies that rotation occurs facilely (Scheme 4). In 20, the N2O22−-π1 orbital undergoes a weak π-donor interaction with the unoccupied Fe-dyz spin orbital of each iron center, while the N2O22−-σ2 orbital is found to undergo a σbond with the unoccupied dz2 spin orbitals of each iron(II). To lower energy, N2O22−-σ1 interacts with the partially occupied Fe-dxz orbitals of both iron centers. These interactions alter upon rotation of the hyponitrite ligand to side-on, as seen by the change in energy of these orbitals in Figure 7. Tables S6− S8 summarize the compositions and energies of the relevant MOs. Moving from 20 to 20‡, the bonding interactions between the nitrogen atoms in N2O22−-σ1 and the respective unoccupied Fedxz spin orbitals break, while a small π-type stabilizing interaction is formed between O1 and the unoccupied Fe1dyz spin orbital. Similarly, the relatively strong σ-interactions between the nitrogen atoms in N2O22−-σ2 and Fe-dz2 of both iron centers break, leaving only a small degree of σ-bonding between N2 and Fe2-dz2. Finally, the weak π-bond between N2O22−-π1 and the partially occupied Fe-dyz orbitals of both iron centers breaks, while the rotation of the N2O22− ligand opens several new (minor) σ-interactions between N2O22−-π1 and Fe1-dz2 and Fe2-dz2, respectively. Moving from 20‡ to 30, the Fe−N2O22− bonds are re-established through the formation of σ-interactions between Fe1-dz2 and Fe2-dz2 and the O1 and N1 atoms in N2O22−-σ2, as well as the formation of a π-bond between the O1 and N1 atoms of N2O22−-π1 and Fe-dyz of either iron center.

Figure 7. Energies of orbitals involved in hyponitrite bonding from intermediates 20 to 40. (top) Energies of orbitals undergoing one bonding/one antibonding interaction between N2O22− and the Fe centers. (bottom) Energies of orbitals undergoing fully bonding interaction between N2O22− and both Fe centers. All energies were calculated using the BP86 method.

Step 3: A Novel Binding Mode of Hyponitrite. Moving forward from complex 30, three requirements in the mechanism that still remain are (a) hyponitrite N−O bond cleavage, (b) μoxo formation, (c) and N2O release. The direct cleavage of the N1−O1 bond from 30 was first investigated; however, a highenergy transition state corresponding to a free energy barrier of 25.8 kcal/mol relative to 30 was calculated, making this pathway unrealistic in terms of the experimentally observed reactivity of 1. A similar N−O bond cleavage step has recently been proposed in a computational study on the super-reduced mechanism using an FNOR active-site model.66 In this study, a side-on binding motif of N2O22−, similar to 30, was also observed. The proposed direct release of N2O from this intermediate requires the system to overcome a large energy barrier of 21.5 kcal/mol. While such a barrier is not completely unreasonable when errors within the calculations themselves are considered, it still appears rather large considering the fast kinetics of N2O formation in both the model complex and FNOR enzymes.38 Therefore, the potential energy surface (PES) of our hyponitrite complex 30 was further explored to identify alternative binding modes of hyponitrite that could allow for a more facile N−O bond cleavage step. It has previously been observed by Hayton and co-workers that hyponitrite is capable of forming a κ2-O2N22− complex, in which the two oxygens of hyponitrite coordinate a single metal center in a bidentate fashion.51 Blomberg and Siegbahn have also recently proposed such a binding mode as an intermediate in the reduction of nitric oxide in cytochrome c dependent nitric oxide reductases (cNORs).87 Indeed, scanning the O3− N2−O2 angle of complex 30 shifts hyponitrite from a side-on N−O coordination mode to a new μ-oxo structure, where hyponitrite coordinates Fe1 in a bidentate fashion to form complex 40 (see Scheme 4 and Figure 8). In this new coordination mode, O1 bridges Fe1 and Fe2, while O2 coordinates solely to Fe1. Importantly, this coordination mode of hyponitrite is enabled by the f lexible binding mode of propionate, which is capable of either mono- or bidentate coordination (see Scheme 5). This mimics the “carboxylate shift” originally described by Lippard et al. known to occur in nonheme diiron enzymes such as methane monooxygenase, allowing both iron centers to maintain their coordination numbers while stabilizing intermediates and facilitating μ-oxo formation.88 The formation of this new intermediate 40 is favored by −6.4 J

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In moving from 30 → 40, the complex must pass through a transition state (30‡) that appears very similar to 20‡ in terms of both energy and geometric structure. Correspondingly, the electronic structure of 30‡ appears very similar to that of 20‡, where the π-bond between N2O22−-π1 and the partially occupied Fe-dyz orbitals is lost, and a new σ-interaction with the Fe-dz2 orbitals of both iron centers is formed. Additionally, the σ-interaction between the O1 atom in N2O22−-σ2 and Fe1dz2 breaks, and a weak π-interaction between the O2 atom and Fe1-dyz is formed. In relaxing from 30‡ to 40 (exo), N2O22−-π1 forms a π-bond between Fe1-dyz and the O2 atom, while the O1 atom undergoes a new σ-interaction with Fe2-dz2. In addition, the N2O22−-σ2 orbital forms a strong σ-bond through the O1 and O2 atoms with Fe1-dz2, and N2O22−-σ1 engages in a σ-interaction with Fe1-dx2−y2. Note that the formation of these bonds establishes O1 as part of a second superexchange pathway between the two iron centers. These interactions strongly perturb the orbitals of the N2O22− ligand. This is reflected by the removal of the near degeneracy of the α- and βspin orbitals of the coordinated N2O22− unit in 40. A diagram of the electronic structure of 40 and the ensuing release of N2O is provided in Figure 8. Step 4: Release of N2O. Excitingly, the thermodynamic free energy barrier for N2O release from complex 40 via the optimized transition state 40‡ is only 5.6 kcal/mol. Here, the propionate group recoordinates Fe1, facilitating the release of N2O. The overall free energy of formation of complex 50 and release of N2O is −19.0 kcal/mol relative to 40, with an enthalpic contribution of −8.25 kcal/mol (−8 kcal/mol relative to 10) and an entropic contribution of −10.7 kcal/mol (−9.4 kcal/mol relative to 10) due predominately to the release of N2O. Overall, this corresponds to a total driving force for the reaction from 10 to 50 and N2O of −17.4 kcal/mol. This result further supports the notion that N2O formation provides a sufficient driving force for the reaction to proceed in the absence of a proton source, and therefore, without the formation of water. The structure of transition state 40‡ lies heavily toward the reactant (40) side: once the Fe1−O2 coordination is lost, the release of N2O is facile. The loss of coordination of O2 occurs synchronously with the recoordination of O4 of the propionate ligand to Fe1. At 40‡, the Fe1−O4 distance has decreased from 4.18 to 2.85 Å, with only a nominal increase of 0.03 Å in the Fe1−O2 coordinate. Consequentially, few differences are observed between the electronic structures of 40 and 40‡. The progression of the electronic structure from 40 → 50 is illustrated in Figure 8. The final product (50) is composed of two antiferromagnetically coupled high-spin FeII centers that are exchange-coupled through a μ-oxo group and the backbone phenolate bridge (illustrated in Scheme S2). The new μ-oxo group is derived from O1 in 40 and allows for the formation of three new superexchange pathways through bonding/antibonding combinations with either iron center. These new pathways involve the dz2, dxz, and dyz orbitals of either iron center, interacting with the three available p orbitals of oxygen. Three unique combinations of orbitals occur between the two iron centers and the newly formed μ-oxo group; these are (1) {Fe1dz2/O-px/Fe2-dxz}, (2) {Fe1-dxz/O-py/Fe2-dz2}, and (3) {Fe1dyz/O-pz/Fe2-dyz} (Scheme S2). Each of these combinations is split into two spin orbitals, the phase of which manifests itself as an antibonding interaction between the “occupied” metal orbital and the respective O-p orbital and a bonding interaction between the unoccupied metal orbital and O-p. An additional

Figure 8. Detailed orbital pathway and energies for the release of N2O from 40, resulting in the formation of 50. Because of the nature of the N2O22− interaction with the diiron complex, orbitals overlap to create four possible bonding/antibonding combinations, two of which are occupied and two of which are virtual. These include the bonding orbital between both Fe and N2O22− (occupied, shown), two sets of orbitals in which one Fe is bonding and the other antibonding (one set occupied, shown here, and the other set virtual, not shown), and one in which both Fe are antibonding to N2O22− (virtual, not shown). Here, the notation “*” is used to differentiate the occupied partially antibonding orbitals from the fully bonding MOs. All energies and orbitals were calculated using the BP86 method. Orbital surfaces were generated with an isosurface value of 0.04.

Scheme 5. Depiction of the Carboxylate Shifta When Going from 30 to 40‡

a

For clarity, only μ-O3 of the BPMP− ligand is shown.

kcal/mol relative to 30, with a free energy barrier of 7.2 kcal/ mol for the transition state 30‡. Interestingly, there are two possible conformations of 40, one of which must be initially formed from 30 and a second more thermodynamically favorable isomer; however, the barrier to isomerization is greater than that for N2O release, and therefore, the reaction likely proceeds through the less stable intermediate. This is illustrated in greater detail in Scheme S1. K

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N−N bond. At the near-equilibrium N−N bond distance of 1.35 Å, there is still no observed transition state or intermediate, as mentioned above. Clearly, the ability of the two molecules of NO to couple is critically dependent on the electron density provided by the two iron centers. Upon reduction of 12+ to 10, each iron center is first reduced by one electron, leading to the occupation of the Fe1-dxy and Fe2-dxz orbitals. This leads to both an increase in electron density at either iron center and a weakening of both Fe−NO π-bonds (especially the Fe2−NO2 π-interaction), allowing the two molecules of NO to couple to form N2O22−. Formation of the hyponitrite ligand carries the energetic punishment of losing both of the strong Fe−NO π-bonds. A plausible explanation for the lack of reactivity of the [{FeNO}7]2 state is therefore that, in this case, the Fe−NO bonds are simply too strong, and N−N bond formation does not provide enough energy to break these interactions (see Figure 9). In contrast, in the super-reduced state (10) the Fe− NO π-bonds are distinctively weakened, allowing N−N bond formation to proceed via a radical-type coupling between the two triplet NO− ligands (although the process is still overall endothermic; see Scheme 4). III.6. Investigation of the Partially Reduced Species 11+. On the basis of the previously described results, that is, the successful formation of N2O from the doubly reduced complex 10 and the failure of the starting complex 12+ to undergo N−N bond formation, the question arises whether N2O generation is capable of proceeding following one-electron reduction of 12+. Clearly, formation of the N−N bond of hyponitrite requires sufficient electron density on the nitroxyl (NO−) ligands, so one would expect a priori that the “mixed-valent” [{FeNO}7{FeNO}8] case 11+ represents an intermediate between 12+ and 10. Because of the asymmetry of the Fe−NO units in the dimer and the absence of experimental data regarding the mixed-valent state of complex 1, it is necessary to investigate the initial localization of the unpaired electron in the [{FeNO}7{FeNO}8] complex 11+ first. To ensure congruence, structures of the mixed-valent state were optimized first by considering both the [{Fe1NO1} 7 {Fe2NO2} 8 ] and [{Fe1NO1}8{Fe2NO2}7] forms of the complex. From a practical point of view, starting geometry optimizations were set up by either adding an antiferromagnetically coupled electron to 12+ and/or removing an antiferromagnetically coupled electron from 10. All of these calculations delivered consistent results and provided one starting structure for each of the two possible mixed-valent forms of the dimer. An illustration of the electronic structure of 11+ is found in Figure 10. Notably, they closely resemble combinations of the electronic structures of 12+ and 10 presented before; here, as in 10 the addition of an electron to {Fe2NO2}7 results in occupation of the α-Fe2-dxz orbital, leading to a drastic decrease in the in-plane Fe2−NO2 bonding interaction. In contrast, reduction of Fe1 leads to occupation of the β-Fe1-dxy orbital. Both forms are found to be relatively close in terms of free energy, with the [{Fe1NO1}8{Fe2NO2}7] complex being more stable by 6.8 kcal/mol as calculated using BP86. The final N1− N2 distance in [{Fe1NO1}8{Fe2NO2}7] was found to be 2.56 Å, smaller than that observed previously for either 12+ or 10. With this relatively small barrier and the assumed conformational flexibility of the ligand, one would anticipate that [{Fe1NO1}8{Fe2NO2}7] and [{Fe1NO1}7{Fe2NO2}8] are capable of facile interconversion (Class II mixed-valent state).

superexchange pathway involves the dx2−y2 orbital of either iron center and the O3-pπ orbital of the phenolate backbone. III.5. N−N Coupling from the [{FeNO}7]2 State. As mentioned in the Introduction, recent work from the Kurtz group indicates that, in FNORs, N2O formation can occur, albeit slowly, from the [{FeNO}7]2 state (the di-{FeNO}7 mechanism).40,41 This is not the case for model systems, which are generally stable in the {FeNO} 7 (monomer) or [{FeNO}7]2 (dimer) state.37,48,75 It is therefore interesting to investigate why N−N coupling and N2O formation is not observed from the [{FeNO}7]2 state of the model complex (12+). To accomplish this, structures of 22+, 32+, and 42+ were optimized starting from the already determined structures 20, 30, and 40, respectively. While both 32+ and 42+ remain stable, albeit rather unfavorable (Figure S6), unrestricted optimization of 22+ resulted in spontaneous dissociation of the N−N bond to reform 12+. Therefore, we further investigated the N−N coupling step by performing a relaxed scan of the N1−N2 coordinate. As evident from Figure 9a, our calculations

Figure 9. Differences between 12+ and 10 along the N1−N2 reaction coordinate. (a) Change in total energies of 12+ (blue) and 10 (red). Energies of the NO-centered orbitals of (b) 12+ and (c) 10. All energies and orbitals were calculated using the BP86 method.

correctly predict that this first step cannot occur due to unfavorable energetics, which render the [{FeNO}7]2 state stable. Upon decreasing the N−N bond distance, the free energy of the complex steadily increases to 25 kcal/mol (at 1.35 Å) without ever reaching a stable minimum, that is, the potential energy surface is clearly dissociative with respect to N−N bond formation. Hence, the N2O22− intermediate cannot form under ambient conditions. Figure 9 provides further detail with respect to changes in relative energies of the key NO-ip and NO-oop orbitals in both the α- and β-manifolds (for Fe1 and Fe2, respectively) along the N1−N2 bond-forming reaction coordinate. Little variation is observed in either of these orbital sets upon decrease of the N1−N2 coordinate, with both rising slightly in energy until ∼2.0 Å in N−N distance, then decreasing slightly. The NO-ip set decreases further in energy and loses degeneracy with the NO-oop set due to constructive overlap; however, these orbitals remain localized on their respective Fe−NO units rather than forming a new L

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kcal/mol of one another (again with G[{Fe1NO1} 8 {Fe2NO2}7] < G[{Fe1NO1}7{Fe2NO2}8]), and it is therefore likely that the 6.8 kcal/mol difference obtained by BP86 is an overestimate. To overcome this tendency of BP86 to converge to the CS solution and to identify the BS pathway, several restrictions were applied; in particular, the Fe-ligand distances that were observed to contract strongly upon conversion from 11+ to 21+ were frozen when scanning along the N−N coordinate. This entails freezing of the Fe1−O4/Fe2-O5, Fe1−N4/Fe2−N8, and Fe1−O3/Fe2-O3 coordinates. Doing so, a transition state 11+‡ was found at an N1−N2 distance of 1.62 Å and a free energy of 14 kcal/mol, which relaxes to intermediate 21+ with a free energy of 13 kcal/mol and a final N1−N2 distance of 1.38 Å. This is surprisingly close to the energetic barrier calculated for 20; in reality, the distance restrictions imposed likely inflate these energies somewhat, and the barrier to forming 21+ is likely even lower. Further completely unrestricted optimizations of the one-electron reduced forms of the previously determined intermediates and the end point (31+, 41+, and 51+) all result in BS solutions with reasonable energies to promote formation of N2O (summarized in Figure 11 and Figure S9). Additionally, all

Figure 10. Molecular orbital diagram of 11+, with electronic configurations of (a) {Fe1NO1}8/{Fe2NO2}7 and (b) {Fe1NO1}7/ {Fe2NO2}8. All energies were calculated using the BP86 method.

Investigating the N−N coordinate, decreasing the N1−N2 distance in the complex [{Fe1NO1}7{Fe2NO2}8] led to the barrierless formation of the Fe1III−N2O22−−Fe2II hyponitrite species 21+. This is analogous to the previously described intermediate 20 but with an N1−N2 distance of 1.51 Å, implying the formation of a single N−N bond. In contrast, an initial relaxed scan along the N1−N2 coordinate for the more energetically favorable (by −6.8 kcal/mol) [{Fe1NO1}8{Fe2NO2}7] state showed an energy barrier of just 5.5 kcal/ mol for the formation of a N1−N2 single bond and generation of 21+, again with a final N1−N2 distance of 1.51 Å. Importantly, this nearly spontaneous N−N bond formation is accompanied by a collapse of the unpaired spins of both Fe centers and the delocalization of the “extra” electron between the two iron centers via the out-of-plane π-bonding orbital of N2O22−. In Robin−Day classification, this delocalization implies that the system no longer acts as a Class II mixed-valent species but rather as a Class III system in which the extra electron is quantum-mechanically delocalized.89 As a result, the Fe1III/II− N2O22−−Fe2II/III product would be better described as Fe12.25+−N2O21.5−−Fe22.25+. Such a collapse may arise from either the conversion of the Fe centers from high-spin (HS) to low-spin (LS), or from a dramatic increase in coupling between the two Fe centers. Mössbauer studies of the closely related mixed-valent [FeIIFeIII(BPMP)(OPr)2](BPh4)2 complex by Que and co-workers have shown both iron centers to be HS;84 as N2O22− should be a relatively weak ligand, it would therefore be highly unlikely for the iron centers of 21+ to become LS experimentally. Analysis of the electronic structure of 21+ did indeed present a low-spin state at either Fe center in the calculations. Since it is known that pure functionals (such as BP86) often favor low-spin states,90−92 it was necessary to ensure that the observed spin collapse was not an artifact resulting from the use of the BP86 functional. To do so, calculations were performed for 11+ and 21+ using the B3LYP functional to test whether the addition of a Hartree−Fock exchange contribution to the energy would result in a separation of distinct spins at either Fe center. Indeed, optimization of 11+ and 21+ with B3LYP results in structures favoring the BS state. Therefore, based both upon previous experimental work and comparisons with B3LYP, we conclude that conversion to the collapsed spin (CS) solution in the BP86 optimized structure 21+ is an artifact, resulting from a shift of the Fe centers to the LS state. Additionally, the two valence tautomers of 11+ calculated by B3LYP lie within 1.3

Figure 11. Comparison of the primary reaction pathways for N2O generation from 11+ (one-electron reduced pathway) and 10 (superreduced pathway), calculated using the BP86 method. Note that for 11+, the free energies of the transition states were not calculated (except for 11+‡). Free energies of 11+‡ and 21+ were calculated using a partially constrained geometry as described in the text, and therefore, these are approximate energies. Additionally, energies of the transition state 11+‡ and intermediates 21+−51+ for the {Fe1NO1}8/{Fe2NO2}7 electronic configuration are omitted, as all lie within less than 1 kcal/ mol of those depicted for the {Fe1NO1}7/{Fe2NO2}8 system. Lastly, the free energy difference of the valence tautomers of 1+ is likely overestimated (with B3LYP, these lie within 1.3 kcal/mol of one another). The reaction will therefore proceed from the tautomer with the lower activation energy.

intermediates (2−4) appear as Class II mixed-valent systems, where localization of the single unpaired electron is favored at one of the iron centers, but only by less than 1 kcal/mol, meaning the extra electron is not trapped. These results are further corroborated by equivalent calculations using B3LYP, summarized in Figure S9. Therefore, in a surprising result, both the BP86 and B3LYP calculations predict that (a) N2O formation should occur upon one-electron reduction of 12+, proceeding from the [{Fe1NO1}7{Fe2NO2}8] state, and (b) that this reaction should proceed with a similar energetic barrier compared to the two-electron reduction. This ability appears to M

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2Fen + 2NO → 2Fen + 1−NO− → 2Fen + 1 + N2O2 2 −

be directly correlated with a significant decrease of the in-plane π-bonding interaction of Fe2−NO2 upon reduction (via occupation of the Fe2-dxz orbital, which corresponds to the antibonding combination of Fe2-dxz and NO2(π*)-ip).

However, one should not forget that the Fen+1−NO− bond is generally very covalent,47 meaning that for N−N coupling and hyponitrite formation to occur, a significant energetic price must be paid for breaking the two strong Fe−NO bonds. Or, in other words, the two unpaired electrons of the NO− ligand are strongly stabilized by donation to the Fe(III) centers, rendering the NO− ligands unreactive. In this sense, the iron centers must be partially oxidized to accomplish N−N bond formation; that is, the charge donated from the NO− ligands to the metal centers must be formally “moved back” to the NO groups during N−N bond formation. Whether this is energetically feasible will therefore strongly depend on the redox potentials of the iron centers and the covalency of the Fe−NO bonds. Our previous experimental work on nonheme {FeNO}7 complexes has shown that these two quantities are directly related. First of all, in the presence of a more strongly donating coligand set, the covalency and strength of the Fe−NO bond is reduced, which is directly evident from a drop in the N−O and Fe−NO stretching frequencies.47 Second, upon one-electron reduction of {FeNO}7 to {FeNO}8, the covalency of the Fe− NO bond is again strongly reduced.49 These findings are in agreement with our computational results for the complexes 12+ and 10. On the basis of these considerations, complex 10 should be more reactive toward N−N bond formation than 12+, since in the latter case the energetic penalty for breaking the Fe−NO bonds and partially oxidizing the iron centers is much higher. This is fully supported by our computational results. In addition, no monomeric {FeNO}7 or dimeric [{FeNO}7]2 model complex has been reported, to the best of our knowledge, which is able to spontaneously form a N−N bond and generate hyponitrite. In the [{FeNO}8]2 dimer 10, the N−O stretching frequencies are predicted to occur below 1600 cm−1, indicating that this is the right range of Fe−NO bond strength for N−N coupling to occur. Curiously, this is in agreement with the above-mentioned {NiNO}10 systems reported by Hayton and co-workers, where the threecoordinate complex [Ni(bipy)(NO)]+ with ν(N−O) = 1869 cm−1 does not induce N−N coupling, whereas the analogous five-coordinate complex [Ni(bipy)2(NO)]+ with ν(N−O) = 1567 cm−1 is able to facilitate hyponitrite formation.51 Our in-depth calculations on model complex 10 further provide a detailed reaction mechanism for N2O formation from a dimeric nonheme iron complex. After formation of a new N− N bond between the coordinated nitroxyl ligands (the step with the largest activation energy at ΔG‡(BP86) = 13.7 kcal/mol), rotation of the hyponitrite ligand occurs to form the more thermodynamically stable O-bound isomer. The first one of these rotations involves the formation of a side-on Fe−O−N− Fe binding motif; further rotation results in the formation of a κ2-O2N22− coordinated intermediate, which can only be accommodated by a change in the denticity of the propionate ligand. This binding mode is perfectly positioned to release N2O and form the product [Fe2BPMP(OPr)(O)]0, which is accomplished by a synchronous recoordination of the propionate group to again bridge the two iron centers. The resulting net gain in free energy of the process is ΔG = −17.4 kcal/mol. As a further check of reaction barriers, intermediates of the two-electron reduced system were reoptimized using several additional exchange correlation functionals and compared with those determined by BP86 (Figure 12). Surprisingly, all

IV. DISCUSSION In this paper, we investigated the electronic structures of the complexes [Fe2BPMP(OPr)(NO)2]2+ (12+), Fe2BPMP(OPr)(NO)2]1+ (11+), and [Fe2BPMP(OPr)(NO)2]0 (10) in detail, and we evaluated the ability, and lack thereof, of these complexes to couple the two NO ligands and generate nitrous oxide (N2O), using detailed computational studies. Experimentally, it is known that flavodiiron nitric oxide reductases (FNORs) use this process to detoxify NO and that the model complex 12+ has been shown to model this reaction by quantitatively producing N2O upon reduction. In fact, this reaction, that is, the reductive coupling of two NO units by two metal centers, constitutes a paradigm of how NO can be degraded in nature and in other synthetic model complexes such as the Ni-nitrosyl complexes reported by Hayton’s group. From the most general point of view, the critical first step of the reaction, N−N bond formation to generate a hyponitrite intermediate, follows the general redox reaction: 2Mn + + 2NO → 2M(n + 1) + + N2O2 2 −

(7)

(6)

In this paper, we investigated the detailed requirements for transition metal centers to catalyze this reaction. Nonheme iron centers in biology usually contain a combination of His, carboxylate (Asp/Glu), Tyr, and water/ hydroxide ligands, resulting in a high-spin state of the iron centers. In these cases, NO usually binds as a triplet nitroxyl (NO−) ligand via oxidation of the metal center, forming two strong π-bonds between the singly occupied π* orbitals of NO− and the dπ orbitals (e.g., dxz and dyz with the Fe−N(O) vector corresponding to the z axis) of the oxidized metal center.48 This electronic structure is reflected by relatively linear Fe−N− O units (which also depends on the coligands) and strong, isotropic Fe−NO bonds. This is exemplified by the fivecoordinate high-spin Fe(TMG3tren) platform, where the formally Fe(I), Fe(II), and Fe(III) complexes form nitrosyl adducts with Fe(II)−NO−, Fe(III)−NO−, Fe(IV)−NO− types of electronic structures.50 Similarly, formally Ni(I) and Co(I) complexes with NO show Ni(II)−NO− and Co(II)−NO− types of electronic structures, respectively.93−95 In all of these cases, the triplet form of the NO− ligand is energetically favorable, allowing for optimal π-donation into the partially filled d-orbitals of the high-spin metal center. In principle, this electronic structure is also favorable for N−N bond formation via the overlap of the singly occupied π* orbitals to form a new N−N bond, which represents a radical-type N−N coupling mechanism. Importantly, however, this also requires that, in a dimeric complex, the spins of the two Fe−NO units are antiferromagnetically coupled (or the antiferromagnetically coupled state is thermally accessible, at least at room temperature) to allow for N−N bond formation to occur. Since the exchange coupling between the two Fe−NO units in a diiron complex is usually weak, this requirement is generally fulfilled. In addition to this, eq 6 also requires an oxidation of the metal centers for hyponitrite formation to occur. As mentioned above, this oxidation already occurs in high-spin systems upon NO binding and formation of the nitroxyl complex: N

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given the consistent trend in relative energies of intermediates 20−40 for all functionals), then k2 > k−1, and now N−N bond formation (10 → 20) becomes rate-limiting. This step is also proposed to be rate-limiting in native FNORs. In summary, formation of N 2 O provides sufficient thermodynamic driving force for the NO reduction reaction to proceed. The largest kinetic barrier for the 2e− reduction of NO is N−N bond formation, which cannot be accomplished by the [{FeNO}7]2 dimer 12+. Since the thermodynamics of the reaction 2NO + 2e− → N2O22− is always the same, independent of the particular complex investigated, the difference in (free) reaction energy for eqn 7 for different nitrosyl complexes simply relates to the difference in energy required to oxidize the metal−NO units. In the case of iron, this would either be from {FeNO}7 to FeIII + NO− as in the diFeNO mechanism or from {FeNO}8 to FeII + NO− as in the super-reduced mechanism. Hence, which state the reaction may proceed from depends critically on the redox potential of the diiron active site and, related to this, the strength of the Fe− NO bonds.

Figure 12. Comparison of calculated free energies for intermediates along the proposed N2O reaction pathway of 10 for a variety of exchange-correlation functionals. The structures of all species were fully optimized with the given method (starting from the BP86optimized structures).

functionals strongly favor this reaction, with all intermediates (2−4) appearing lower in energy than those determined via BP86. Therefore, it is highly likely that the reaction barriers predicted by BP86 are overestimated and that the reaction proceeds very rapidly with a barrier of only 7−8 kcal/mol. With this in mind, it was worthwhile to further check the free energy barrier for the NO reduction reaction from the one-electron reduced complex 11+. With the B3LYP functional, the resulting barrier to N−N bond formation was found to be 10 kcal/mol, nominally higher by 2 kcal/mol than that found for the twoelectron reduced complex 10, with formation of 21+ favored by 6 kcal/mol. Therefore, surprisingly, both BP86 and B3LYP predict the barrier for N−N bond formation upon one-electron reduction to be only 1−2 kcal/mol larger than that predicted for two-electron reduction of the complex. Typically, the largest activation barrier of a reaction is associated with the rate-limiting step. However, it has been demonstrated by Kozuch and co-workers that this definition often breaks down.96 To elucidate the rate-determining factors of our complex reaction pathway, we can translate the BP86 calculated free energies of the 10 pathway to rate constants using eq 8: ki =

kBT −ΔGi‡ / RT e h

V. CONCLUSION In this work, we have achieved a deeper understanding of the requirements for efficient NO reduction by high-spin iron dimers and other high-spin transition metal−nitrosyl complexes. For this purpose, we investigated the electronic structure and reactivity of the [Fe2(BPMP)(OPr)(NO)2]2+ (12+) model complex toward NO reduction and N2O formation. The reaction pathway following either one- or two-electron reduction of 12+ has been evaluated, showing that formation of the initial N−N bond results in the largest activation barrier of the reaction. In agreement with experiment, it has been found that, without the addition of any electrons, the complex fails to couple the two NO ligands to form hyponitrite and is therefore unable to produce N2O. Our results show that the formation of the N−N bond faces two closely related barriers: breaking of the Fe−NO π-interactions along with an effective (partial) electron transfer from the metal to the NO to generate a “full” triplet NO− unit. Naturally, the process is expected to be most facile for the two-electron reduced form 10: since electron transfer is largely accomplished in this case, only the barrier of breaking the Fe−NO πinteraction, which is weakest for this complex, remains. In turn, the barrier to N−N bond formation for the one-electron reduced complex 11+ should be higher, and for 12+ it should be higher still. Surprisingly, the formation of hyponitrite from the one-electron reduced state is energetically comparable to the two-electron reduced state, which is explained by a significant decrease in the Fe2−NO2 in-plane π-bonding interaction upon reduction of [Fe2(BPMP)(OPr)(NO)2]2+ (via occupation of an Fe2−NO2 antibonding orbital) and, hence, an activation of the Fe2−NO2 unit. In contrast, reduction of {Fe1NO1}7 results in the occupation of the nonbonding Fe1-dxy orbital. On the basis of these results, we conclude that N2O formation will proceed rapidly following addition of either one or two reducing equivalents to [Fe2(BPMP)(OPr)(NO)2]2+. Finally, our results show that the “right” binding mode of hyponitrite is crucial for facile N2O release.

(8)

where kB is the Boltzmann constant, R is the gas constant, and h is Planck’s constant. Doing so, we find that the first step of the reaction has the smallest rate constant of the forward reaction. If we focus on the first two steps of the reaction, considering k2 ≫ k−2, we can write the rate equation for the formation of 30 as r=

k 2 · k1 [10 ] k −1 + k 2

(9)

Since k2 < k−1, the rate of decomposition of 2 → 1 occurs faster than the rate of the forward reaction (20 proceeding to 30); thus, an equilibrium will form between 10 and 20, making the second step (20 → 30) of the BP86 calculated reaction profile rate-limiting! However, when we compare this to the results of the other functionals (M06-L, B3LYP, or PBE1PBE; see Figure 12), we now find that k1 > k−1. If we assume similar relative transition-state energies (which is not unreasonable 0

0

O

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Guilard, R., Eds.; World Scientific: New Jersey, 2011; Vol. 14, pp 1− 247. (11) Hunt, A. P.; Lehnert, N. Heme-Nitrosyls: Electronic Structure Implications for Function in Biology. Acc. Chem. Res. 2015, 48, 2117− 2125. (12) Stuehr, D. J.; Gross, S. S.; Sakuma, I.; Levi, R.; Nathan, C. F. Activated murine macrophages secrete a metabolite of arginine with the bioactivity of endothelium-derived relaxing factor and the chemical reactivity of nitric oxide. J. Exp. Med. 1989, 169, 1011−1020. (13) Ferguson, S. J. Nitrogen Cycle Enzymology. Curr. Opin. Chem. Biol. 1998, 2, 182−193. (14) Richardson, D. J.; Watmough, N. J. Inorganic nitrogen metabolism in bacteria. Curr. Opin. Chem. Biol. 1999, 3, 207−219. (15) Maia, L. B.; Moura, J. J. G. How Biology Handles Nitrite. Chem. Rev. 2014, 114, 5273−5357. (16) Bykov, D.; Neese, F. Six-Electron Reduction of Nitrite to Ammonia by Cytochrome c Nitrite Reductase: Insights from Density Functional Theory Studies. Inorg. Chem. 2015, 54, 9303−9316. (17) Gardner, P. R.; Gardner, A. M.; Martin, L. A.; Salzman, A. L. Nitric oxide dioxygenase: an enzymic function for flavohemoglobin. Proc. Natl. Acad. Sci. U. S. A. 1998, 95, 10378−10383. (18) Hausladen, A.; Gow, A. J.; Stamler, J. S. Nitrosative stress: metabolic pathway involving the flavohemoglobin. Proc. Natl. Acad. Sci. U. S. A. 1998, 95, 14100−14105. (19) Crawford, M. J.; Goldberg, D. E. Role for the Salmonella flavohemoglobin in protection from nitric oxide. J. Biol. Chem. 1998, 273, 12543−12547. (20) Speelman, A.; Lehnert, N. Heme versus Non-Heme IronNitroxyl {FeN(H)O}8 Complexes: Electronic Structure and Biologically Relevant Reactivity. Acc. Chem. Res. 2014, 47, 1106−1116. (21) Daiber, A.; Shoun, H.; Ullrich, V. Nitric Oxide Reductase (P450nor) From Fusarium Oxysporum. J. Inorg. Biochem. 2005, 99, 185−193. (22) Zumft, W. G. Nitric Oxide Reductases of Prokaryotes With Emphasis on the Respiratory, Heme−copper Oxidase Type. J. Inorg. Biochem. 2005, 99, 194−215. (23) McQuarters, A. B.; Wirgau, N. E.; Lehnert, N. Model Complexes of Key Intermediates in Fungal Cytochrome P450 Nitric Oxide Reductase (P450nor). Curr. Opin. Chem. Biol. 2014, 19, 82−89. (24) Shiro, Y. Structure and Function of Bacterial Nitric Oxide Reductases. Biochim. Biophys. Acta, Bioenerg. 2012, 1817, 1907−1913. (25) Lehnert, N.; Coruzzi, G.; Hegg, E.; Seefeldt, L.; Stein, L. NSF Workshop Report: Feeding the World in the 21st Century: Grand Challenges in the Nitrogen Cycle; National Science Foundation: Arlington, VA, 2016. (26) Gardner, A. M.; Helmick, R. A.; Gardner, P. R. Flavorubredoxin, an Inducible Catalyst for Nitric Oxide Reduction and Detoxification in Escherichia coli. J. Biol. Chem. 2002, 277, 8172−8177. (27) Gardner, A. M.; Gessner, C. R.; Gardner, P. R. Regulation of the Nitric Oxide Reduction Operon (norRVW) in Escherichia coli. Role of NorR and σ54 in the Nitric Oxide Stress Response. J. Biol. Chem. 2003, 278, 10081−10086. (28) Missall, T. A.; Lodge, J. K.; McEwen, J. E. Mechanisms of Resistance to Oxidative and Nitrosative Stress: Implications for Fungal Survival in Mammalian Hosts. Eukaryotic Cell 2004, 3, 835−846. (29) Sarti, P.; Fiori, P. L.; Forte, E.; Rappelli, P.; Teixeira, M.; Mastronicola, D.; Sanciu, G.; Giuffré, A.; Brunori, M. Trichomonas vaginalis degrades nitric oxide and expresses a flavorubredoxin-like protein: a new pathogenic mechanism? Cell. Mol. Life Sci. 2004, 61, 618−623. (30) Kurtz, D. M., Jr. Flavo-diiron enzymes: nitric oxide or dioxygen reductases? Dalton Trans. 2007, 4115−4121. (31) Khatua, S.; Majumdar, A. Flavodiiron Nitric Oxide Reductases: Recent Developments in the Mechanistic Study and Model Chemistry for the Catalytic Reduction of NO. J. Inorg. Biochem. 2015, 142, 145− 153. (32) Baek, S.-H.; Rajashekara, G.; Splitter, G. A.; Shapleigh, J. P. Phenotypic and genotypic characterization of Brucella neotomae identifies it as a partial denitrifier. J. Bacteriol. 2004, 186, 6025−6031.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b02333. MO charge contributions, enlarged choice figures, and coupling constants J (PDF) Molecular coordinates of optimized structures (ZIP)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (C.V.S.) *E-mail: [email protected]. (N.L.) ORCID

Casey Van Stappen: 0000-0002-1770-2231 Nicolai Lehnert: 0000-0002-5221-5498 Present Address ‡

Max-Planck Institute for Chemical Energy Conversion, Stiftstrasse 34−36, 45470 Mülheim an der Ruhr, NRW, Germany. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation (CHE-1608331 to N.L.). Financial support (to N.L.) for this work from the Univ. of Michigan, Associate Professor Support Fund, is gratefully acknowledged. C.V.S. also dearly thanks V. Nemykin (current: Univ. of Manitoba, Winnipeg; formerly: Univ. of Minnesota, Duluth) for generously allowing the authors to perform sections of this work using his computational resources.

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