Effect of conformational constraints on gated electron-transfer kinetics. 3. Copper(II/I) complexes with cis- and trans-cyclopentanediyl-1,4,8,11-tetrathiacyclotetradecane

Previous kinetic and electrochemical studies of copper complexes with macrocyclic tetrathiaethers-such as 1,4,8,11-tetrathiacyclotetradecane ([14]aneS4)-have indicated that electron transfer and the accompanying conformational change occur sequentially to give rise to a dual-pathway mechanism. Under appropriate conditions, the conformational change itself may become rate-limiting, a condition known as "gated" electron transfer. We have recently hypothesized that the controlling conformational change involves inversion of two donor atoms, which suggests that "gated" behavior should be affected by appropriate steric constraints. In the current work, two derivatives of [14]aneS4 have been synthesized in which one of the ethylene bridges has been replaced by either cis- or trans-1,2-cyclopentane. The resulting copper systems have been characterized in terms of their Cu(II/I)L potentials, the stabilities of their oxidized and reduced complexes, and their crystal structures. The electron self-exchange rate constants have been determined both by NMR line-broadening and by kinetic measurements of their rates of reduction and oxidation with six or seven counter reagents. All studies have been carried out at 25 degrees C, mu = 0.10 M (NaClO4 and/or Cu(ClO4)2), in aqueous solution. Both Cu(II/I) systems show evidence of a dual-pathway mechanism, and the electron self-exchange rate constants representative of both mechanistic pathways have been determined. The first-order rate constant for gated behavior has also been resolved for the Cu(I)(trans-cyclopentane-[14]aneS4) complex, but only a limiting value can be established for the corresponding cis-cyclopentane system. The rate constants for both systems investigated in this work are compared to values previously determined for the Cu(II/I) systems with the parent [14]aneS4 macrocycle and its derivatives involving phenylene and cis- or trans-cyclohexane substituents. The results are discussed in terms of the influence of the fused rings on the probable conformational changes accompanying the electron-transfer process.     

X-ray determination of the mean amplitudes of vibration and debye temperatures of some rare earth monochalcogenides

The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 Å (TmSe), 155 ± 7°K, 0·244 ± 0·012 Å (SmS), 153 ± 14°K, 0·221 ± 0·020 Å (SmSe) and 151 ± 20°K, 0·204 ± 0·027 Å (SmTe).     

Electron-transfer kinetics of copper(II/I) tripodal ligand complexes

The electron-transfer kinetics for each of three copper(II/I) tripodal ligand complexes reacting with multiple reducing and oxidizing counter reagents have been examined in aqueous solution at 25 degrees C, mu = 0.10 M. For all of the ligands studied, an amine nitrogen serves as the bridgehead atom. Two of the ligands (PMMEA and PEMEA) contain two thioether sulfurs and one pyridyl nitrogen as donor atoms on the appended legs while the third ligand (BPEMEA) has two pyridyl nitrogens and one thioether sulfur. Very limited kinetic studies were also conducted on two additional closely related tripodal ligand complexes. The results are compared to our previous kinetic study on a Cu(II/I) system involving a tripodal ligand (TMMEA) with thioether sulfur donor atoms on all three legs. In all systems, the Cu(II/I) electron self-exchange rate constants (k(11)) are surprisingly small, ranging approximately 0.03-50 M(-)(1) s(-)(1). The results are consistent with earlier studies reported by Yandell involving the reduction of Cu(II) complexes with four similar tripodal ligand systems, and it is concluded that the dominant reaction pathway involves a metastable Cu(II)L intermediate species (designated as pathway B). Since crystal structures suggest that the ligand reorganization accompanying electron transfer is relatively small compared to our earlier studies on macrocyclic ligand complexes of Cu(II/I), it is unclear why the k(11) values for the tripodal ligand systems are of such small magnitude.     

Direct evidence for a geometrically constrained "entatic state" effect on copper(II/I) electron-transfer kinetics as manifested in metastable intermediates

The absolute magnitude of an "entatic" (constrained) state effect has never been quantitatively demonstrated. In the current study, we have examined the electron-transfer kinetics for five closely related copper(II/I) complexes formed with all possible diastereomers of [14]aneS(4) (1,4,8,11-tetrathiacyclotetradecane) in which both ethylene bridges have been replaced by cis- or trans-1,2-cyclohexane. The crystal structures of all five Cu(II) complexes and a representative Cu(I) complex have been established by X-ray diffraction. For each complex, the cross-reaction rate constants have been determined with six different oxidants and reductants in aqueous solution at 25 degrees C, mu = 0.10 M. The value of the electron self-exchange rate constant (k(11)) has then been calculated from each cross reaction rate constant using the Marcus cross relation. All five Cu(II/I) systems show evidence of a dual-pathway square scheme mechanism for which the two individual k(11) values have been evaluated. In combination with similar values previously determined for the parent complex, Cu(II/I)([14]aneS(4)), and corresponding complexes with the two related monocyclohexanediyl derivatives, we now have evaluated a total of 16 self-exchange rate constants which span nearly 6 orders of magnitude for these 8 closely related Cu(II/I) systems. Application of the stability constants for the formation of the corresponding 16 metastable intermediates--as previously determined by rapid-scan cyclic voltammetry--makes it possible to calculate the specific electron self-exchange rate constants representing the reaction of each of the strained intermediate species exchanging electrons with their stable redox partners--the first time that calculations of this type have been possible. All but three of these 16 specific self-exchange rate constants fall within--or very close to--the range of 10(5)-10(6) M(-1) s(-1), values which are characteristic of the most labile Cu(II/I) systems previously reported, including the blue copper proteins. The results of the current investigation provide the first unequivocal demonstration of the efficacy of the entatic state concept as applied to Cu(II/I) systems.     

Analysis of coefficient identification problems associated to the inverse Euler-Bernoulli beam theory

A rigorous investigation of the identification of a heterogeneousflexural rigidity coefficient in the Euler-Bernoulli steady-statebeam theory in the presence of a prescribed load is presented.Mathematically, this study is an extension to higher-order differentialequations of the coefficient identification problem analysedby Marcellini (1982) for the one-dimensional Poisson equation.In addition, various types of boundary conditions are discussed.Conditions for the well-posedness of these inverse problemsare established and, furthermore, numerical results obtainedusing a regularization algorithm are presented.     

A critical investigation of the effects of the radio frequency potential on the trapping of externally injected ions in ion trap mass spectrometry

The sensitivity of all ion trap mass spectrometry (ITMS) methods is dependent on the trapping efficiency of the instrument. For ITMS instruments utilizing external ion sources, such as laser desorption, trapping efficiency is known to depend on the phase and amplitude of the radio frequency (RF) potential applied to the ring electrode at the time of ion introduction. It is remarkable that, in a considerable body of literature, no consensus exists regarding the effects of these parameters on the efficacy of trapping externally generated ions. In this paper, a summary of the literature is presented in order to highlight significant discrepancies. New laser desorption ion trap mass spectrometry (LD-ITMS) data are also presented, from which conclusions are drawn in our effort to clarify some of the confusion. Copyright 1999 John Wiley & Sons, Ltd.     

Kinetics and mechanism of copper(II) complex formation with tripodal aminopolythiaether and aminopolypyridyl ligands in aqueous solution

The complex formation kinetics of aquated copper(II) ion reacting with 12 related tripodal ligands have been studied in aqueous solution at 25 degrees C, mu = 0.10 M (NaClO4). For most of the ligands studied, specific formation rate constants have been resolved for both the unprotonated and monoprotonated ligand species. All of the tripodal ligands included in this study contain a bridgehead amine nitrogen with the three legs consisting of 2-methylthioethyl or 2-ethylthioethyl and/or 2-pyridylethyl or 2-pyridylmethyl. Since the bridgehead nitrogen is too sterically hindered to participate in initial coordinate bond formation, the first bond must involve a thiaether sulfur or a pyridine nitrogen on one of the pendant legs followed by coordination to the bridgehead nitrogen to complete the first chelate ring. All kinetic data are interpreted in terms of this presumed sequence in the bond formation steps. For the two ligands in which all three pendant legs contain thiaether sulfur donor atoms, the rate-determining step appears to be at the point of second bond formation (chelate ring closure), although the distinction is not well defined. For all other unprotonated ligands, the kinetic behavior is consistent with the first-bond formation being rate-determining. Upon protonation, the rate-determining step appears to shift to the point of proton loss associated with second-bond formation in several cases. A particularly interesting observation is that the tripodal ligand tris(ethylthioethyl)amine (TEMEA) exhibits specific Cu(II) complex formation rate constants that are virtually identical to those for a closely related macrocyclic ligand, 1,4,8-trithia-11-azacyclotetradecane ([14]aneNS3), but the calculated CuIIL dissociation rate constants differ by a factor of 1000. A further comparison of the calculated dissociation rate constants for Cu(II)-tripodal ligand complexes indicates that a Cu(II)-N(pyridine) bond is approximately 10(4) times stronger than a Cu(II)-SR2 bond. This leads to the conclusion that a 1:1 Cu(II)-SR2 complex would have a predicted stability constant of about 0.04 M-1 in aqueous solution--the first estimate obtained for the strength of a single Cu(II)-S(thiaether) bond.