Kinetics of the oxidation of octacyanomolybdate(IV) by periodate in aqueous acid

Summary The kinetics of oxidation of [Mo(CN)₈]^4– by IO ₄ ^– in aqueous acid is described by the equation: d[{Mo(CN)₈}^3–]/ dt=2k₃[{Mo(CN)₈}^4–][IO ₄ ^– ][H⁺]. Unlike IO ₄ ^– oxidations of [Fe(CN)₆]^4– and [W(CN)₈]^4–, no [H⁺] independent term exists in the [Mo(CN)₈]^4– reaction, which indicates that, in neutral and alkaline solutions, oxidation of [Mo(CN)₈]^4– is thermodynamically unfavourable. An inner-sphere mechanism, consistent with the rate law, is proposed. This conclusion is based, in the absence of direct evidence, on the observed behaviour of IO ₄ ^– as an inner-sphere oxidant.     

Kinetics and mechanism of pentacyanohydroxoferrate(III) formation from the reaction of cyanide ion with [Fe2L(OH)2]2− (L=triethylenetetraaminehexaacetate)

Summary The kinetics and mechanism of the reaction between [Fe₂L(OH)₂]^2– and cyanide ion (L = TTHA, triethylenetetraaminehexaacetate) have been studied spectrophotometrically atpH=11.0±0.1,I=0.1 M(NaClO₄) and T = 25±0.1 °C. The overall reaction consists of three distinct, observable stages. The first stage involves the dissociation of the binuclear complex into a mononuclear complex [FeL(OH)]^4– which then reacts with cyanide to form [Fe(CN)₅OH]^3–. The species [Fe(CN)₅OH]^3– reacts further with an excess of cyanide and forms [Fe(CN)₆]^3– in the second stage of reaction. The last stage involves the reduction of [Fe(CN)₆]^3– formed in the second stage by the TTHA^6– released in the first stage of reaction. The formation of [Fe(CN)₅OH]^3– in the first stage is firstorder in [Fe₂L(OH)₂]^2– and third-order in cyanide over a large range of cyanide concentrations but becomes zero-order in cyanide at [CN^–] < 4×10^–2M.These observations enable us to suggest the presence of a slow step in which [Fe₂L(OH)₂]^2– dissociates into [FeL(OH)]^4– and [FeOH]²⁺ at low cyanide concentrations and a cyanide assisted rapid dissociation of [Fe₂L(OH)₂]^2– to [FeL(OH)(CN)]^5– at higher cyanide concentrations. The species [FeL(OH)(CN)]^5– reacts further with an excess of cyanide to produce [Fe(CN)₅OH]^3– finally.The reverse reaction between [Fe(CN)₅OH]^3– and TTHA^6– follows first-order dependence in each of [Fe(CN)₅OH]^3– and TTHA^6– and inverse first-order dependence on cyanide concentration. A six-step mechanism has been proposed for the first stage of reaction in which the fifth has been identified as the rate-determining step.     

Kinetics and mechanism of pentacyanohydroxoferrate(III) formation from mono(aminocarboxylato)iron(III) complexes

Summary The kinetics and mechanism of the system: [FeL(OH)]^2–n + 5 CN^– [Fe(CN)₅(OH)]^3– + L^n–, where L=DTPA or HEDTA, have been investigated at pH= 10.5±0.2, I=0.25 M and t=25±0.1 C.As in the reaction of [FeEDTA(OH)]^2–, the formation of [Fe(CN)₅(OH)]^3– through the formation of mixed ligand complex intermediates of the type [FeL(OH)(CN)_x]^2–n–x, is proposed. The reactions were found to consist of three observable stages. The first involves the formation of [Fe(CN)₅(OH)]^3–, the second is the conversion of [Fe(CN)₅(OH)]^3– into [Fe(CN)₆]^3– and the third is the reduction of [Fe(CN)₆]^3– to [Fe(CN)₆]^4– by oxidation of L^n– The first reaction exhibits a variable order dependence on the concentration of cyanide, ranging from one at high cyanide concentration to three at low concentration. The transition between [FeL(OH)]^2–n and [Fe(CN)₅(OH)]^3– is kinetically controlled by the presence of four cyanide ions around the central iron atom in the rate determining step. The second reaction shows first order dependence on the concentration of [Fe(CN)₅(OH)]^3– as well as on cyanide, while the third reaction follows overall second order kinetics; first order each in [Fe(CN)₆]^3– and L^n–, released in the reaction. The reaction rate is highly dependent on hydroxide ion concentration.The reverse reaction between [Fe(CN)₅(OH)]^3– and L^n– showed an inverse first order dependence on cyanide concentration along with first order dependence each on [Fe(CN)_5– (OH)]^3– and L^n–. A five step mechanism is proposed for the first stage of the above two systems.     

Dinuclear complexes with a μ-cyano ligand. Part XI(1). Synthesis and characterization of several derivatives ofcis-[Co(NH3)(en)2(H2O)]3+

Summary The new complex double saltscw-[Co(NH₃)(en)₂(H₂O)]₂ [M(CN)₄]₃ (en = ethylenediamine; M = Ni, Pd or Pt),cis-[Co(NH₃(en)₂(H₂O)]₂[FeNO(CN)₅]₃ andcis-[Co(NH₃)(en)₂(H₂O)][Co(CN)₆] have been synthesized and by anation in the solid state the corresponding new dinuclear complexes with a cyano bridgecis- ortrans-[(NH₃)(en)₂Co-NC-M(CN)₃]₂ [M(CN)₄] (M = Ni, Pd or Pt);cis-, trans-[(NH₃)(en)₂Co-NC-FeNO(CN)₄]₂[FeNO(CN)₅] andcis-[(NH₃)(en)₂Co-NC-Co(CN)₅ have been prepared. The complexes have been characterized by chemical analysis, t.g. measurements, and by i.r. and electronic spectroscopy. With [Ni(CN)₄][^2– and [Co(CN)in]₆ ^3– only thecis-isomer is produced; with [Pd(CN)₄]^2–, [Pt(CN)₄]^2– and [FeNO(CN)₅]^2– thetrans- isomer is the dominant species. The dinuclear complex derived from [Pt(CN)₄]^2– shows strong Pt-Pt interactions both in the solid state and in solution.     

Kinetic and mechanism of pentacyanohydroxoferrate(III) formation from the reaction of [Fe2HPDTA(OH)2] with cyanide ions

Summary The kinetics and mechanism of exchange of HPDTA in [Fe₂HPDTA(OH)₂] with cyanide ion (HPDTA=2-hydroxytrimethylenediaminetetraacetic acid) was investigated spectrophotometrically by monitoring the peak at 395 nm ( _max of [Fe(CN)₅OH]^3– at pH=11.0±0.02,I=0.25m (NaClO₄) at ±0.1°C).Three distinct observable stages were identified; the first is the formation of [Fe(CN)₅OH]^3–, the second the formation of [Fe(CN)₆]^3– from it and the third the reduction of [Fe(CN)₆]^3– to [Fe(CN)₆]^4– by HPDTA^4– released in the first stage.The first stage follows first-order kinetics in [Fe₂HPDTA(OH)₂] and second-order in [CN^–] over a wide range of [CN^–], but becomes zero order at [CN^–]<5×10^–2 m. We suggest a cyanide-independent dissociation of [Fe₂HPDTA)(OH)₂] into [FeHPDTA(OH)] and [Fe(OH)]²⁺ at low cyanide concentrations and a cyanide-assisted rapid dissociation of [Fe₂HPDTA(OH)₂] to [FeHPDTA(OH)(CN)]^3– and [Fe(OH)]²⁺ at higher cyanide concentrations. The excess of cyanide reacts further with [FeHPDTA(OH)(CN)]^3– finally to form [Fe(CN)₅OH]^3–.The reverse reaction between [Fe(CN)₅OH]^3– and HPDTA^4– is first-order in [Fe(CN)₅OH]^3– and HPDTA^4–, and exhibits inverse first-order dependence on cyanide concentration.A six-step mechanism is proposed for the first stage of reaction, with the fifth step as rate determining.     

Kinetics and mechanism of pentacyanohydroxoferrate(III) formation from [FeL(OH)2]− complex, (L=N-(2-hydroxyethyl) iminodiacetate anion

Summary The kinetics and mechanism of the system [FeHIDA-(OH)₂]^–+5CN^–[Fe(CN)₅OH^–+HIDA^2–+OH^– (HIDA=N-(2-hydroxyethyl) (iminodiacetate) at pH=9.5±0.02, I=0.1 M and at 25±0.1°C have been studied spectrophotometrically at 395 nm ( _max of [Fe(CN)₅OH]^3–]. The reaction has three distinguishable stages; the first is formation of [Fe(CN)₅OH]^3–, the second is conversion of [Fe(CN)₅OH]^3– into [Fe(CN)₆]^3–, and last is the reduction of [Fe(CN)₆]^3– to [Fe(CN)₆]^4– by the HIDA^2– released in the first stage. The first stage shows variable-order dependence on cyanide concentration, unity at high cyanide concentration and zero at low cyanide concentration. The second stage exhibits first-order dependence on the concentration of [Fe(CN)₅OH]^3– as well as on cyanide. The reverse reaction between [Fe(CN)₅OH]^3– and HIDA^2– is first-order in each of these species and inverse first-order in cyanide. On the basis of forward and reverse rate studies, a five-step mechanism has been proposed for the first stage. The first step involves a slow loss of one OH^–, by a cyanide-independent path.     

Synthesis,protonation and substitution behaviour of K3[ReO2(CN)4]

Summary The preparation and characterization of salts of the [ReO₂(CN)₄]^3–, [ReO(OH)(CN)₄]^2–, [ReO(H₂O)(CN)₄]^–, [Re₂O₃(CN)₈]^4– and [ReO(NCS)(CN)₄]^2– species are described. The nature of the protonation reactions of [ReO₂(CN)₄]^3– was established by the successful isolation of these salts.     

Halogen-und Pseudohalogenkomplexe von Kobalt(II) in Nitromethan

Zusammenfassung Die neutralen Halogenide und Pseudohalogenide von Kobalt(II) sind in Nitromethan kaum dissoziiert. Bei Zusatz entsprechender Anionen zu Kobalt(II)-perchloratlösungen werden in Nitromethan folgende Koordinationsformen leicht gebildet: CoCl₂, CoCl₃ ^–, CoCl₄ ^2–, CoBr₂, CoBr₃ ^–, CoBr₄ ^2–, CoJ₂, CoJ₃ ^–, CoJ₄ ^2–, Co[N₃]₂, [Co(N₃)₄]^2–, Co[NCS]₂, [Co(NCS)₄]^2–, Co[CN]₂ [Co(CN)₄]^2– und [Co(CN)₅]^3–.

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The neutral halides and pseudohalides of cobalt(II) are nearly undissociated in nitromethane. On addition of the appropriate anion to a solution of cobalt(II)-perchlorate in nitromethane the following coordination forms are easily produced: CoCl₂, CoCl₃ ^–, CoCl₄ ^2–, CoBr₂, CoBr₃ ^–, CoBr₄ ^2–, CoJ₂, CoJ₃ ^–, CoJ₄ ^2–, Co[N₃]₂, [Co(N₃)₄]^2–, Co[NCS]₂, [Co(NCS)₄]^2–, Co[CN]₂, [Co(CN)₄]^2– and [Co(CN)₅]^3–.

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Mit 10 Abbildungen     

Kinetic study of the reaction betweentrans-tetracyanodioxomolybdate(IV) and fluoride ions

Summary The kinetics of the reaction between [MoO₂(CN)₄]^4– and F^– have been studied in the pH range 8 to 11. The results indicated that the diprotonated form, [MoO(OH₂)(CN)₄]^2–, is the only reactive species and that the aqua-ligand is substituted by the F^– ion according to the following reaction. The k₁ and k_–1 values are 8.8(2) M^–1 s^–1 and 0.6(1)s^–1, respectively, at 15°C. A dissociative substitution process is proposed.     

Azido-, Rhodano-, Cyano- und Fluorokomplexe des Fe(III)-Ions in Dimethylsulfoxid

Zusammenfassung Auf Grund spektrophotometrischer und konduktometrischer Messungen wurden folgende Koordinationsformen des Eisen(III)-ions mit Azid-, Rhodanid-, Cyanid- und Fluoridionen in Dimethylsulfoxid festgestellt: [Fe(N₃)₄]^–, [Fe(SCN)₆]^3–, [Fe(CN)₂]⁺, Fe(CN)₃, [Fe(CN)₄]^–, [FeF₂]⁺, [FeF₄]^–.

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By means of spectrophotometric and conductometric measurements the following coordination forms of iron(III) with azide-, thiocyanate-, cyanide- and fluoride ions were found in dimethyl sulfoxide: [Fe(N₃)₄]^–, [Fe(SCN)₆]^3–, [Fe(CN)₂]⁺, Fe(CN)₃, [Fe(CN)₄]^–, [FeF₂]⁺, [FeF₄]^–.

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Mit 4 Abbildungen     

Photochemical reactions of molybdenum and tungsten octacyanometallates(IV) in acidic aqueous media containing 2,2′-bipyridyl or 1,10-phenanthroline

Summary The reaction scheme of acidic photolysis of [M(CN)₈]^4– (M = Mo or W) in the presence of 2,2-bipyridyl (bipy) or 1,10-phenanthroline (phen) based on previous reports, and the present results, is given. In this scheme the formation of [M(CN)₆(N-N)]^2– (M = Mo or W), postulated in the literature to be a main product of photoexcitation of [M(CN)₈]^4– in the presence of bipy or phen, has definitively been excluded. The main cyano-polypyridyl species formed are [MO(CN)₃(N-N)]^– ions which, in acidic solution, undergo further reactions. A new product, [MoO(CN)₂(N-N)₂], resulting from thermal replacement of the cyanide ligand by polypyridyl, has been detected.Author to whom all correspondence should be directed.     

The kinetics and mechanism of reaction between ethylenediaminetetraacetomanganate(III) and cyanide ion

Summary The title reaction has been followed spectrophotometrically at 325 nm (_max of [Mn(CN)₆]^3–) under pseudo-first order conditions with cyanide in a large excess at pH=10.0, I=0.1M (NaClO₄) and 25°C. The reaction follows first-order kinetics in [MnEDTA(OH)]^2– and exhibits variable-order dependence in [CN^–] one at high cyanide concentration, and two at low cyanide concentration. The product of above reaction has been identified as [Mn(CN)₆]^3–.The kinetics of the reverse reaction,i.e., the reaction of [Mn(CN)₆]^3- with EDTA^4– have also been followed spectrophotometrically. This reactions is first-order with respect to both [Mn(CN) ₆ ^3– ] and [EDTA^4–] and exhibits an inverse first-order dependence on [CN^–]. A six-step mechanism has been proposed in which the penultimate step is rate-determining. The activation parameters have been obtained and support the postulated mechanism.     

Syntheses,crystal structures and magnetic properties of two cyano-bridged two-dimensional assemblies [Fe(salpn)]2 [Fe(CN)5NO] and [Fe(salpn)]2[Ni(CN)4]

Two cyano-bridged assemblies, [Fe^III(salpn)]₂[Fe^II(CN)₅NO] (1) and [Fe^III (salpn)]₂[Ni^II(CN)₄] (2) [salpn = N, N-1,2-propylenebis(salicylideneiminato)dianion], have been prepared and structurally and magnetically characterized. In each complex, [Fe(CN)₅NO]^2– or [Ni(CN)₄]^2– coordinates with four [Fe(salpn)]⁺ cations using four co-planar CN^– ligands, whereas each [Fe(salpn)]⁺ links two [Fe(CN)₅NO]^2– or [Ni(CN)₄]^2– ions in the trans form, which results in a two-dimensional (2D) network consisting of pillow-like octanuclear [—M^II—CN—Fe^III—NC—]₄ units (M = Fe or Ni). In complex (1), the NO group of [Fe(CN)₅NO]^2– remains monodentate and the bond angle of Fe^II—N—O is 180.0°. The variable temperature magnetic susceptibilities, measured in the 5–300 K range, show weak intralayer antiferromagnetic interactions in both complexes with the intramolecular iron(III)iron(III) exchange integrals of –0.017 cm^–1 for (1) and –0.020 cm^–1 for (2), respectively.     

Oxo-tricyano complexes of molybdenum(IV) and tungsten(IV) with bidentate Schiff bases

Summary The reaction of [M(CN)₄O(OH₂)]^2– (M = Mo or W) with 2-acetylpyridine and methyl-or butyl-amine in a water-MeOH mixture gave [M(CN)₃O(L-L)]^- (L-L= Schiff base ligand), isolated as [AsPh₄]⁺ salts. The complexes have been characterized by elemental analysis, and electronic, i.r. and¹H-n.m.r. spectroscopy. The Schiff base ligands complex in a bidentate manner through the two nitrogen atoms giving mixed-ligand compounds similarly to 2,2-bipyridyl or 1,10-phenanthroline.On leave from the Faculty of Chemistry, Jagiellonian University, Kraków.     

Photoexcitation of octacyano complexes of molybdenum(IV) and tungsten(IV) with ethylene diamine. Kinetics and reaction mechanism

Summary The kinetics of thermal reactions of photochemically generated aquaheptacyano Mo^IV and W^IV complexes and their protonated and deprotonated forms have been studied spectrophotometrically in buffer solutions at pH 5.0–10.0, and ionic strength, 8×10^–2 M at 25°C. A reaction scheme for the photochemical and thermal reactions of the Mo^IV and W^IV octacyano complexes with ethylene diamine is proposed. Rate constants and quantum yields for these systems are maximal at pH 8.0. At pH>8.0, the reverse reaction, generating octacyano complexes from heptacyano species, is faster; at low pH the ligand is protonated and is less reactive. Quantum yields are higher for Mo than for W owing to the shorter life time of excited state species. This is because physical deactivation is expected to be more rapid in the heavier element due to enhanced spin-orbit coupling. Furthermore Mo-induced splitting is larger in [W(CN)₈]^4– as compared to [Mo(CN)₈]^4– which results in greater bond strength for tungsten.     

Electronic structure of octacyanides of molybdenum IV and V according to the SCCC MO method

The SCCC MO method has been used to calculate the electronic structure and spectrum of Mo(CN) ₈ ^4– and Mo(CN) ₈ ^3– ions of a D _4d symmetry. All metal-ligand and ligand-ligand interactions and all overlap integrals (over products of HF atomic orbitals) have been included within the SCCC MO scheme. Basing on these calculations a new assignment of some absorption bands is proposed. The overall agreement between the calculated and observed electronic spectrum is satisfactory.

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Zusammenfassung Elektronenstruktur und Spektrum der [Mo(CN)₈]^–4- und [Mo(CN)₈]^–3-Ionen in D _4d -Symmetrie wurden mit der SCCC-MO-Methode berechnet. Alle Metall-Ligand- und Ligand-Ligand-Wechsel-wirkungen und Überlappungsintegrale wurden berücksichtigt. Die Bandenzuordnung wurde neu vorgenommen. Die Übereinstimmung der berechneten und gemessenen Spektren ist befriedigend.

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Résumé Application à Mo(CN) ₈ ^4– et Mo(CN) ₈ ^3– de la méthode SCCC MO basée sur des orbitales atomiques HF approchées, en tenant compte du recouvrement et de toutes les interactions ligand-ligand. Dans la partie I on discute le cas de la symétrie D _4d . L'accord global avec l'expérience est satisfaisant en ce qui concerne les spectres. On montre aussi que toutes les attributions antérieures basées sur la théorie du champ cristallin semblent inadéquates.

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The authors are grateful to Prof. W. Jakób, Dr. Z. Stasicka and Dr. A. Samotus for many interesting discussions, to Prof. J. Chojnacki for providing us with new X-ray results before publication and to Dr. A. J. Sadlej for a help in dealing with the computer.     

Thermal and photochemical interaction of octacyanometallates(IV), [M(CN)8]4− (M = Mo or W) in the presence of pyrazine

The interactions between [M(CN)₈]^4– (M = Mo or W) and pyrazine (pz) in the solid state and in aqueous solutions have been analysed. In strongly acidic solutions {pzH⁺, [M(CN)₈]^4–} ion pair formation is observed; the pyrazinium salts (pzH)₂(H₃O)₂[Mo(CN)₈]·0.5pz·3H₂O and (pzH)₂K(H₃O)[W(CN)₈]·H₂O have been isolated. The X-ray crystal structure of the latter, and the spectroscopic properties of both, are described. The [W(CN)₈]^4– anion is approximately square antiprismatic (D_4d), with different H-bond environments around the N atoms. The ligand-field photolysis of [M(CN)₈]^4– in the presence of pyrazine in neutral and alkaline solution results in the formation of tetracyanooxometallates(IV) in equilibrium with pentacyanooxometallates(IV) through the [M(CN)₇(pz)]^3– anions as intermediates. The formation of the [M(CN)₆(pz)₂]^2– ion, postulated in the literature to be the final product of the alkaline photolysis, has definitively been excluded.     

Supramolecular cis-“Bis(Chelation)” of [M(CN)6]3− (M = CrIII,FeIII, CoIII) by Phloroglucinol (H3PG)

Studies on molecular co-crystal type materials are important in the design and preparation of easy-to-absorb drugs, non-centrosymmetric, and chiral crystals for optical performance, liquid crystals, or plastic phases. From a fundamental point of view, such studies also provide useful information on various supramolecular synthons and molecular ordering, including metric parameters, molecular matching, energetical hierarchy, and combinatorial potential, appealing to the rational design of functional materials through structure–properties–application schemes. Co-crystal salts involving anionic d-metallate coordination complexes are moderately explored (compared to the generality of co-crystals), and in this context, we present a new series of isomorphous co-crystalline salts (PPh₄)₃[M(CN)₆](H₃PG)₂·2MeCN (M = Cr, 1; Fe, 2; Co 3; H₃PG = phloroglucinol, 1,3,5-trihydroxobenzene). In this study, 1–3 were characterized experimentally using SC XRD, Hirshfeld analysis, ESI-MS spectrometry, vibrational IR and Raman, ⁵⁷Fe Mössbauer, electronic absorption UV-Vis-NIR, and photoluminescence spectroscopies, and theoretically with density functional theory calculations. The two-dimensional square grid-like hydrogen-bond {[M(CN)₆]³⁻;(H₃PG)₂}_∞ network features original {[M(CN)₆]³⁻;(H₃PG)₄} supramolecular cis-bis(chelate) motifs involving: (i) two double cyclic hydrogen bond synthons M(-CN⋅⋅⋅HO-)₂Ar, {[M(CN)₆]³⁻;H₂PGH}, between cis-oriented cyanido ligands of [M(CN)₆]³⁻ and resorcinol-like face of H₃PG, and (ii) two single hydrogen bonds M-CN⋅⋅⋅HO-Ar, {[M(CN)₆]³⁻;HPGH₂}, involving the remaining two cyanide ligands. The occurrence of the above tectonic motif is discussed with regard to the relevant data existing in the CCDC database, including the multisite H-bond binding of [M(CN)₆]³⁻ by organic species, mononuclear coordination complexes, and polynuclear complexes. The physicochemical and computational characterization discloses notable spectral modifications under the regime of an extended hydrogen bond network.     

Kinetics and mechanism of metal ion catalysis. Part III. Osmium(VIII) catalysed oxidation of m-hydroxybenzaldehyde by Fe(CN)6 3− in alkaline medium

Os^VIII-catalysed oxidation of m-hydroxybenzaldehyde by alkaline Fe(CN)₆ ^3– has been studied in the 0.01–0.05 M [OH^–] range. Higher [OH^–] concentrations were not possible as the substrate turned yellow at [OH^–] > 0.05 M. The very low solubility of the substrate in H₂O restricted the kinetic study to [OH^–] < 0.01 M. A mechanism, consistent with the results is proposed.     

Mechanistic aspects of the reduction of ruthenium(III) catalyzed

The kinetics of Ru_III catalyzed reduction of hexacyanoferrate(III) [Fe(CN)₆]^3–, by atenolol in alkaline medium at constant ionic strength (0.80 mol dm^–3) has been studied spectrophotometrically, using a rapid kinetic accessory. The reaction between atenolol and [Fe(CN)₆]^3– in alkaline medium exhibits 1:2 stoichiometry [atenolol:Fe(CN)₆ ^3–]. The reaction showed first order kinetics in [Fe(CN)₆]^3– concentration and apparent less than unit order dependence, each in atenolol and alkali concentrations. Effect of added products, ionic strength and dielectric constant of the reaction medium have been investigated. A retarding effect was observed by one of the products i.e., hexacyanoferrate(II). The main products were identified by i.r., n.m.r., fluorimetric and mass spectral studies. A mechanism involving the formation of a complex between the atenolol and the hydroxylated species of ruthenium(III) has been proposed. The active species of oxidant and catalyst were [Fe(CN)₆]^3–and [Ru (H₂O)₅OH]²⁺, respectively. The reaction constants involved in the mechanism were evaluated. The activation parameters were computed with respect to the slow step of the mechanism, and discussed.