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Julie A Kovacs

Publications and source records attributed to Julie A Kovacs.

14 recordsLinked to original sources
PubMed2006

A functional model for the cysteinate-ligated non-heme iron enzyme superoxide reductase (SOR).

Superoxide reductases (SORs) are cysteine-ligated, non-heme iron enzymes that reduce toxic superoxide radicals (O2-). The functional role of the trans cysteinate, as well as the mechanism by which SOR reduces O2-, is unknown. Herein is described a rare example of a functional metalloenzyme analogue, which catalytically reduces superoxide in a proton-dependent mechanism, via a trans thiolate-ligated iron-peroxo intermediate, the first example of its type. Acetic-acid-promoted H2O2 release, followed by Cp2Co reduction, regenerates the active Fe(II) catalyst. The thiolate ligand and its trans positioning relative to the substrate are shown to contribute significantly to the catalyst's function, by lowering the redox potential, changing the spin state, and dramatically lowering the nuFe-O stretching frequency well-below that of any other reported iron-peroxo, while leaving nuO-O high, so as to favor superoxide reduction and Fe-O, as opposed to O-O, bond cleavage. Thus we provide critical insight into the relationship between the SOR structure and its function, as well as important benchmark parameters for characterizing highly unstable thiolate-ligated iron-peroxo intermediates.

Catalysis↗
PubMed2006

How does single oxygen atom addition affect the properties of an Fe-nitrile hydratase analogue? The compensatory role of the unmodified thiolate.

Nitrile hydratase (NHase) is one of a growing number of enzymes shown to contain post-translationally modified cysteine sulfenic acids (Cys-SOH). Cysteine sulfenic acids have been shown to play diverse roles in cellular processes, including transcriptional regulation, signal transduction, and the regulation of oxygen metabolism and oxidative stress responses. The function of the cysteine sulfenic acid coordinated to the iron active site of NHase is unknown. Herein we report the first example of a sulfenate-ligated iron complex, [Fe(III)(ADIT)(ADIT-O)](+) (5), and compare its electronic and magnetic properties with those of structurally related complexes in which the sulfur oxidation state and protonation state have been systematically altered. Oxygen atom addition was found to decrease the unmodified thiolate Fe-S bond length and blue-shift the ligand-to-metal charge-transfer band (without loss of intensity). S K-edge X-ray absorption spectroscopy and density functional theory calculations show that, although the modified RS-O(-) fragment is incapable of forming a pi bond with the Fe(III) center, the unmodified thiolate compensates for this loss of pi bonding by increasing its covalent bond strength. The redox potential shifts only slightly (75 mV), and the magnetic properties are not affected (the S = (1)/(2) spin state is maintained). The coordinated sulfenate S-O bond is activated and fairly polarized (S(+)-O(-)). Addition of strong acids at low temperatures results in the reversible protonation of sulfenate-ligated 5. An X-ray structure demonstrates that Zn(2+) binds to the sulfenate oxygen to afford [Fe(III)(ADIT)(ADIT-O-ZnCl(3))] (6). The coordination of ZnCl(3)(-) to the RS-O(-) unit causes the covalent overlap with the unmodified thiolate to increase further. A possible catalytic role for the unmodified NHase thiolate, involving its ability to "tune" the electronics in response to protonation of the sulfenate (RS-O(-)) oxygen and/or substrate binding, is discussed.

Hydro-Lyases↗
PubMed2006

Sulfur K-edge XAS and DFT calculations on nitrile hydratase: geometric and electronic structure of the non-heme iron active site.

The geometric and electronic structure of the active site of the non-heme iron enzyme nitrile hydratase (NHase) is studied using sulfur K-edge XAS and DFT calculations. Using thiolate (RS(-))-, sulfenate (RSO(-))-, and sulfinate (RSO(2)(-))-ligated model complexes to provide benchmark spectral parameters, the results show that the S K-edge XAS is sensitive to the oxidation state of S-containing ligands and that the spectrum of the RSO(-) species changes upon protonation as the S-O bond is elongated (by approximately 0.1 A). These signature features are used to identify the three cysteine residues coordinated to the low-spin Fe(III) in the active site of NHase as CysS(-), CysSOH, and CysSO(2)(-) both in the NO-bound inactive form and in the photolyzed active form. These results are correlated to geometry-optimized DFT calculations. The pre-edge region of the X-ray absorption spectrum is sensitive to the Z(eff) of the Fe and reveals that the Fe in [FeNO](6) NHase species has a Z(eff) very similar to that of its photolyzed Fe(III) counterpart. DFT calculations reveal that this results from the strong pi back-bonding into the pi antibonding orbital of NO, which shifts significant charge from the formally t(2)(6) low-spin metal to the coordinated NO.

Binding Sites↗
PubMed2005

Spectroscopy of non-heme iron thiolate complexes: insight into the electronic structure of the low-spin active site of nitrile hydratase.

Detailed spectroscopic and computational studies of the low-spin iron complexes [Fe(III)(S2(Me2)N3 (Pr,Pr))(N3)] (1) and [Fe(III)(S2(Me2)N3 (Pr,Pr))]1+ (2) were performed to investigate the unique electronic features of these species and their relation to the low-spin ferric active sites of nitrile hydratases. Low-temperature UV/vis/NIR and MCD spectra of 1 and 2 reflect electronic structures that are dominated by antibonding interactions of the Fe 3d manifold and the equatorial thiolate S 3p orbitals. The six-coordinate complex 1 exhibits a low-energy S(pi) --> Fe 3d(xy) (approximately 13,000 cm(-1)) charge-transfer transition that results predominantly from the low energy of the singly occupied Fe 3d(xy) orbital, due to pure pi interactions between this acceptor orbital and both thiolate donor ligands in the equatorial plane. The 3d(pi) --> 3d(sigma) ligand-field transitions in this species occur at higher energies (>15,000 cm(-1)), reflecting its near-octahedral symmetry. The Fe 3d(xz,yz) --> Fe 3d(xy) (d(pi) --> d(pi)) transition occurs in the near-IR and probes the Fe(III)-S pi-donor bond; this transition reveals vibronic structure that reflects the strength of this bond (nu(e) approximately 340 cm(-1)). In contrast, the ligand-field transitions of the five-coordinate complex 2 are generally at low energy, and the S(pi) --> Fe charge-transfer transitions occur at much higher energies relative to those in 1. This reflects changes in thiolate bonding in the equatorial plane involving the Fe 3d(xy) and Fe 3d(x2-y2) orbitals. The spectroscopic data lead to a simple bonding model that focuses on the sigma and pi interactions between the ferric ion and the equatorial thiolate ligands, which depend on the S-Fe-S bond angle in each of the complexes. These electronic descriptions provide insight into the unusual S = 1/2 ground spin state of these complexes: the orientation of the thiolate ligands in these complexes restricts their pi-donor interactions to the equatorial plane and enforces a low-spin state. These anisotropic orbital considerations provide some intriguing insights into the possible electronic interactions at the active site of nitrile hydratases and form the foundation for further studies into these low-spin ferric enzymes.

Binding Sites↗
PubMed2005

Role of protons in superoxide reduction by a superoxide reductase analogue.

Superoxide reduction by thiolate-ligated [FeII(SMe2N4(tren))]+ (1) involves two proton-dependent steps and a single peroxide intermediate, [FeIII(SMe2N4(tren))(OOH)]+ (2). An external proton donor is required, ruling out mechanisms involving H+ or H-atom abstraction from the ligand N-H. The initial protonation step affording 2 occurs with fairly basic proton donors (EtOH, MeOH, NH4+) in THF. More acidic proton donors are required to cleave the Fe-O(peroxide) bond in MeOH, and this occurs via a dissociative mechanism. Reaction rates are dependent on the pKa of the proton donor, and a common [FeIII(SMe2N4(tren))(MeOH)]2+ (3) intermediate is involved. Acetic acid releases H2O2 from 2 under pseudo-first-order conditions ([HOAc] = 138 mM, [2] = 0.49 mM) with a rate constant of 8.2 x 10(-4) s(-1) at -78 degrees C in MeOH. Reduction of 3 with Cp2Co regenerates the active catalyst 1.

Hydrogen Peroxide↗
PubMed2004

Ligand oxidations in high-spin nickel thiolate complexes and zinc analogues.

Oxidations of a trigonal-bipyramidal, high-spin Ni(II) dithiolate complex of a pentadentate, N3S2-donor ligand, N1,N9-bis(imino-2-mercaptopropane)-1,5,9-triazanonane) nickel(II), and the structurally analogous Zn(II) complex, lead to oxidations of the ligand. Oxidation of the Ni(II) complex with I2 produces a novel Ni(II) macrocyclic cationic complex containing a monodentate disulfide ligand (2). Crystals of the I3- salt of the complex form in the triclinic space group P(1) with cell dimensions a=8.508(3) A, b=9.681(2) A, c=14.066(4) A, angles alpha=90.97(2) degrees , beta=91.61(3) degrees , gamma=90.83(2) degrees , and Z=2. The structure was refined to R=6.31% and Rw=16.63% (I > 2sigma(I)). Oxidation of the Ni(II) complex with O2 leads to the formation of a novel pentadentate bis-iminothiocarboxylate complex with trigonal-bipyramidal geometry (3). This neutral product crystallizes in the monoclinic space group P21/c with cell dimensions a=13.625(3) A, b=7.605(5) A, c=14.902(4) A, angles alpha=gamma=90 degrees, beta=102.81(2) degrees , and Z=4. The structure was refined to R=7.18% and Rw=17.86% (I > 2sigma(I)). Oxidation of the Zn(II) dithiolate analogue with O2 leads to the formation of the Zn(II) complex of the pentadentate bis-iminothiocarboxylate ligand. The neutral complex is isomorphous with the Ni(II) complex and crystallizes in the monoclinic space group P2(1)/c with cell dimensions a=13.8465(4) A, b=7.6453(2) A, c=15.0165(6) A, angles alpha=gamma=90 degrees , beta=103.2140(11) degrees , and Z=4. The structure was refined to R=3.96% and Rw=9.45% (I > 2sigma(I)). Details of the crystal structures are reported. Kinetics of the O2 reactions show that the reactions of the Ni(II) and Zn(II) dithiolates follow the rate law, Rate=k2[1][O2], with k2=1.81 M(-1) s(-1) for the Ni(II) complex and k2=1.93 x 10(-2) M(-1) s(-1) for the Zn(II) complex. The O2 oxidation of the high-spin Ni(II) thiolate complex was found to follow a similar oxidation mechanism to those of low-spin Ni(II) complexes, which form transient persulfoxide intermediates that yield S-oxidation products. In the case of the high-spin system reported here, the transient persulfoxide intermediate gives rise to an alternative ligand oxidation product, a bis-iminothiocarboxylate complex, because of the reactivity of the ligand, which contains a methylene with acidic H atoms alpha to the thiolate sulfur. The proposed mechanism is supported by studies of the analogous Zn dithiolate complex, which gives rise to the analogous bis-iminothiocarboxylate product (5).

Crystallography, X-Ray↗
PubMed2004

Steric and electronic control over the reactivity of a thiolate-ligated Fe(II) complex with dioxygen and superoxide: reversible mu-oxo dimer formation.

The reactivity between a thiolate-ligated five-coordinate complex [FeII(SMe2N4(tren))]+ (1) and dioxygen is examined in order to determine if O2 activation, resembling that of the metalloenzyme cytochrome P450, can be promoted even when O2 binds cis, as opposed to trans, to a thiolate. Previous work in our group showed that [FeII(SMe2N4(tren))]+ (1) reacts readily with superoxide (O2-) in the presence of a proton source to afford H2O2 via an Fe(III)-OOH intermediate, thus providing a biomimetic model for the metalloenzyme superoxide reductase (SOR). Addition of O2 to 1 affords binuclear mu-oxo-bridged [FeIII(SMe2N4(tren))]2(mu2-O)(PF6)2.3MeCN (3). At low temperatures, in protic solvents, an intermediate is detected, the details of which will be the subject of a separate paper. Although the thiolate ligand does not appear to perturb the metrical parameters of the unsupported mu-oxo bridge (Fe-O= 1.807(8) A, and Fe-O-Fe= 155.3(5) degrees fall in the usual range), it decreases the magnetic coupling between the irons (J=-28 cm(-1)) and creates a rather basic oxo site. Protonation of this oxo using strong (HBF4, HCl) or weak (HOAc, NH4PF6, LutNHCl) acids results in bridge cleavage to cleanly afford the corresponding monomeric anion-ligated (OAc- (6), or Cl- (7)) or solvent-ligated (MeCN (4)) derivatives. Addition of OH- converts [FeIII(SMe2N4(tren))(MeCN2+ (4) back to mu-oxo 3. Thus, mu-oxo bridge cleavage is reversible. The protonated mu-hydroxo-bridged intermediate is not observed. In an attempt to prevent mu-oxo dimer formation, and facilitate the observation of O2-bound intermediates, a bulkier tertiary amine ligand, tren-Et4= N-(2-amino-ethyl)-N-(2-diethylamino-ethyl)-N',N'-diethyl-ethane-1,2-diamine, and the corresponding [FeII(SMe2N4(tren-Et4))]+ (5) complex was synthesized and structurally characterized. Steric repulsive interactions create unusually long FeII-N(3,4) amine bonds in 5 (mean distance=2.219(1) A). The [(tren-Et4)N4SMe2]1- ligand is unable to accommodate iron in the +3 oxidation state, and consequently, in contrast to most thiolate-ligated Fe(II) complexes, [FeII(SMe2N4(tren-Et4))]+ (5) does not readily react with O2. Oxidation of 5 is irreversible, and the potential (Epa=+410 mV (vs SCE)) is anodically shifted relative to 1 (E1/2=-100 mV (vs SCE)).

Crystallography, X-Ray↗
PubMed2003

A chloride ion contained in a cobalt 'claw': [Co3(DADIT)3]Cl(PF6)2.

A trimeric compound containing Co(II) is described, namely tris[mu-2-[3-(dimethylamino)propylimino]propane-1-thiolato]tricobalt(II) chloride bis(hexafluorophosphate), [Co(3)(C(10)H(21)N(2)S)(3)]Cl(PF(6))(2). Each Co atom is ligated by one 2-[3-(dimethylamino)propylimino]propane-1-thiolate ligand, an amine group and an imine group. The thiolate groups bridge the Co atoms, forming a six-membered ring that encloses the chloride ion in a well defined binding pocket.

Chlorides↗
PubMed2003

How does cyanide inhibit superoxide reductase? Insight from synthetic FeIIIN4S model complexes.

Superoxide reductases (SORs) are nonheme iron-containing enzymes that reduce HO(2) to H(2)O(2). Exogenous substrates such as N(3)(-) and CN(-) have been shown to bind to the catalytic iron site of SOR, and cyanide acts as an inhibitor. To understand how these exogenous ligands alter the physical and reactivity properties of the SOR iron site, acetate-, azide-, and cyanide-ligated synthetic models of SOR have been prepared. The x-ray crystal structures of azide-ligated [Fe(III)(S(Me2)N(4)(tren))(N(3))](+) (3), dimeric cyanide-bridged ([Fe(III)(S(Me2)N(4)(tren))](2)-mu-CN)(3+) (5), and acetate-ligated [Fe(III)(S(Me2)N(4)(tren))(OAc)](+) (6) are described, in addition to x-ray absorption spectrum-derived and preliminary crystallographic structures of cyanide-ligated [Fe(III)(S(Me2)N(4)(tren))(CN)](+) (4). Cyanide coordination to our model (4) causes the redox potential to shift anodically by 470 mV relative to acetate-ligated 6 and 395 mV relative to azide-ligated 3. If cyanide coordination were to cause a similar shift in redox potential with SOR, then the reduction potential of the catalytically active Fe(3+) center would fall well below that of its biological reductants. These results suggest therefore that cyanide inhibits SOR activity by making the Fe(2+) state inaccessible and thus preventing the enzyme from turning over. Cyanide inhibits activity in the metalloenzyme superoxide dismutase via a similar mechanism. The reduced five-coordinate precursor to 3, 4, and 6 [Fe(II)(S(Me2)N(4)(tren))](+) (1) was previously shown by us to react with superoxide to afford H(2)O(2) via an [Fe(III)(S(Me2)N(4)(tren))(OOH)](+) intermediate. Cyanide and azide do not bind to 1 and do not prevent 1 from reducing superoxide.

Azides↗
PubMed2002

Synthetic models for the cysteinate-ligated non-heme iron enzyme superoxide reductase: observation and structural characterization by XAS of an Fe(III)-OOH intermediate.

Superoxide reductases (SORs) belong to a new class of metalloenzymes that degrade superoxide by reducing it to hydrogen peroxide. These enzymes contain a catalytic iron site that cycles between the Fe(II) and Fe(III) states during catalysis. A key step in the reduction of superoxide has been suggested to involve HO(2) binding to Fe(II), followed by innersphere electron transfer to afford an Fe(III)-OO(H) intermediate. In this paper, the mechanism of the superoxide-induced oxidation of a synthetic ferrous SOR model ([Fe(II)(S(Me2)N(4)(tren))](+) (1)) to afford [Fe(III)(S(Me2)N(4)(tren)(solv))](2+) (2-solv) is reported. The XANES spectrum shows that 1 remains five-coordinate in methanolic solution. Upon reaction of 1 with KO(2) in MeOH at -90 degrees C, an intermediate (3) is formed, which is characterized by a LMCT band centered at 452(2780) nm, and a low-spin state (S = 1/2), based on its axial EPR spectrum (g(perpendicular) = 2.14; g(parallel) = 1.97). Hydrogen peroxide is detected in this reaction, using both (1)H NMR spectroscopy and a catalase assay. Intermediate 3 is photolabile, so, in lieu of a Raman spectrum, IR was used to obtain vibrational data for 3. At low temperatures, a nu(O-O) Fermi doublet is observed in the IR at 788(2) and 781(2) cm(-)(1), which collapses into a single peak at 784 cm(-1) upon the addition of D(2)O. This vibrational peak diminishes in intensity over time and essentially disappears after 140 s. When 3 is generated using an (18)O-labeled isotopic mixture of K(18)O(2)/K(16)O(2) (23.28%), the vibration centered at 784 cm(-1) shifts to 753 cm(-1). This new vibrational peak is close to that predicted (740 cm(-1)) for a diatomic (18)O-(18)O stretch. In addition, a nu(O-O) vibrational peak assigned to free hydrogen peroxide is also observed (nu(O-O) = 854 cm(-1)) throughout the course of the reaction between Fe(II)-1 and superoxide and is strongest after 100 s. XAS studies indicate that 3 possesses one sulfur scatterer at 2.33(2) A and four nitrogen scatterers at 2.01(1) A. Addition of two Fe-O shells, each containing one oxygen, one at 1.86(3) A and one at 2.78(3) A, improved the EXAFS fits, suggesting that 3 is an end-on peroxo or hydroperoxo complex, [Fe(III)(S(Me2)N(4)(tren))(OO(H))](+). Upon warming above -50 degrees C, 3 is converted to 2-MeOH. In methanol and methanol:THF (THF = tetrahydrofuran) solvent mixtures, 2-MeOH is characterized by a LMCT band at lambda(max) = 511(1765) nm, an intermediate spin-state (S = 3/2), and, on the basis of EXAFS, a relatively short Fe-O bond (assigned to a coordinated methanol or methoxide) at 1.94(10) A. Kinetic measurements in 9:1 THF:MeOH at 25 degrees C indicate that 3 is formed near the diffusion limit upon addition of HO(2) to 1 and converts to 2-MeOH at a rate of 65(1) s(-1), which is consistent with kinetic studies involving superoxide oxidation of the SOR iron site.

Ferric Compounds↗
PubMed2002

The first example of a nitrile hydratase model complex that reversibly binds nitriles.

Nitrile hydratase (NHase) is an iron-containing metalloenzyme that converts nitriles to amides. The mechanism by which this biochemical reaction occurs is unknown. One mechanism that has been proposed involves nucleophilic attack of an Fe-bound nitrile by water (or hydroxide). Reported herein is a five-coordinate model compound ([Fe(III)(S(2)(Me2)N(3)(Et,Pr))](+)) containing Fe(III) in an environment resembling that of NHase, which reversibly binds a variety of nitriles, alcohols, amines, and thiocyanate. XAS shows that five-coordinate [Fe(III)(S(2)(Me2)N(3)(Et,Pr))](+) reacts with both methanol and acetonitrile to afford a six-coordinate solvent-bound complex. Competitive binding studies demonstrate that MeCN preferentially binds over ROH, suggesting that nitriles would be capable of displacing the H(2)O coordinated to the iron site of NHase. Thermodynamic parameters were determined for acetonitrile (DeltaH = -6.2(+/-0.2) kcal/mol, DeltaS = -29.4(+/-0.8) eu), benzonitrile (-4.2(+/-0.6) kcal/mol, DeltaS = -18(+/-3) eu), and pyridine (DeltaH = -8(+/-1) kcal/mol, DeltaS = -41(+/-6) eu) binding to [Fe(III)(S(2)(Me2)N(3)(Et,Pr))](+) using variable-temperature electronic absorption spectroscopy. Ligand exchange kinetics were examined for acetonitrile, iso-propylnitrile, benzonitrile, and 4-tert-butylpyridine using (13)C NMR line-broadening analysis, at a variety of temperatures. Activation parameters for ligand exchange were determined to be DeltaH(+ +) = 7.1(+/-0.8) kcal/mol, DeltaS(+ +) = -10(+/-1) eu (acetonitrile), DeltaH(+ +) = 5.4(+/-0.6) kcal/mol, DeltaS(+ +) = -17(+/-2) eu (iso-propionitrile), DeltaH(+ +) = 4.9(+/-0.8) kcal/mol, DeltaS(+ +) = -20(+/-3) eu (benzonitrile), and DeltaH(+ +) = 4.7(+/-1.4) kcal/mol DeltaS(+ +) = -18(+/-2) eu (4-tert-butylpyridine). The thermodynamic parameters for pyridine binding to a related complex, [Fe(III)(S(2)(Me2)N(3)(Pr,Pr))](+) (DeltaH = -5.9(+/-0.8) kcal/mol, DeltaS = -24(+/-3) eu), are also reported, as well as kinetic parameters for 4-tert-butylpyridine exchange (DeltaH(+ +) = 3.1(+/-0.8) kcal/mol, DeltaS(+ +) = -25(+/-3) eu). These data show for the first time that, when it is contained in a ligand environment similar to that of NHase, Fe(III) is capable of forming a stable complex with nitriles. Also, the rates of ligand exchange demonstrate that low-spin Fe(III) in this ligand environment is more labile than expected. Furthermore, comparison of [Fe(III)(S(2)(Me2)N(3)(Et,Pr))](+) and [Fe(III)(S(2)(Me2)N(3)(Pr,Pr))](+) demonstrates how minor distortions induced by ligand constraints can dramatically alter the reactivity of a metal complex.

Crystallography, X-Ray↗
PubMed2002

Enhancing reactivity via structural distortion.

To examine how small structural changes influence the reactivity and magnetic properties of biologically relevant metal complexes, the reactivity and magnetic properties of two structurally related five-coordinate Fe(III) thiolate compounds are compared. (Et,Pr)-ligated [Fe(III)(S(2)(Me2)N(3)(Et,Pr))]PF(6) (3) is synthesized via the abstraction of a sulfur from alkyl persulfide ligated [Fe(III)(S(2)(Me2)N(3)(Et,Pr))-S(pers)]PF(6) (2) using PEt(3). (Et,Pr)-3 is structurally related to (Pr,Pr)-ligated [Fe(III)(S(2)(Me2)N(3)(Pr,Pr))]PF(6) (1), a nitrile hydratase model compound previously reported by our group, except it contains one fewer methylene unit in its ligand backbone. Removal of this methylene distorts the geometry, opens a S-Fe-N angle by approximately 10 degrees, alters the magnetic properties by stabilizing the S = 1/2 state relative to the S = 3/2 state, and increases reactivity. Reactivity differences between 3 and 1 were assessed by comparing the thermodynamics and kinetics of azide binding. Azide binds reversibly to both (Et,Pr)-3 and (Pr,Pr)-1 in MeOH solutions. The ambient temperature K(eq) describing the equilibrium between five-coordinate 1 or 3 and azide-bound 1-N(3) or 3-N(3) in MeOH is approximately 10 times larger for the (Et,Pr) system. In CH(2)Cl(2), azide binds approximately 3 times faster to 3 relative to 1, and in MeOH, azide dissociates 1 order of magnitude slower from 3-N(3) relative to 1-N(3). The increased on rates are most likely a consequence of the decreased structural rearrangement required to convert 3 to an approximately octahedral structure, or they reflect differences in the LUMO (vs SOMO) orbital population (i.e., spin-state differences). Dissociation rates from both 3-N(3) and 1-N(3) are much faster than one would expect for low-spin Fe(III). Most likely this is due to the labilizing effect of the thiolate sulfur that is trans to azide in these structures.

Algorithms↗