Syzygies among reduction operators

We introduce the notion of syzygy for a set of reduction operators and relate it to the notion of syzygy for presentations of algebras. We give a method for constructing a linear basis of the space of syzygies for a set of reduction operators. We interpret these syzygies in terms of the confluence property from rewriting theory. This enables us to optimise the completion procedure for reduction operators based on a criterion for detecting useless reductions. We illustrate this criterion with an example of construction of commutative Gröbner basis.     

pH-Dependent Hydration Change in a Gd-Based MRI Contrast Agent with a Phosphonated Ligand

The heptadentate ligand L was shown to form an extremely stable Gd complex at neutral pH with a pGd value of 18.4 at pH 7.4. The X-ray crystal structures of the complexes formed with Gd and Tb displayed two very different coordination behaviors being, respectively, octa- and nonacoordinated. The relaxometric properties of the Gd complex were studied by field-dependent relaxivity measurements at various temperatures and by ¹⁷O NMR spectroscopy. The pH-dependence of the longitudinal relaxivity profile indicated large changes around neutral pH leading to a very large value of 10.1 mm ⁻¹⋅s⁻¹ (60 MHz, 298 K) at pH 4.7. The changes were attributed to an increase of the hydration number from one water molecule in basic conditions to two at acidic pH. A similar trend was observed for the luminescence of the Eu complex, confirming the change in hydration state. DOSY experiments were performed on the Lu analogue, pointing to the absence of dimers in solution in the considered pH range. A breathing mode of the complex was postulated, which was further supported by ¹H and ³¹P NMR spectroscopy of the Yb complex at varying pH and was finally modeled by DFT calculations.     

Visible‐Light‐Mediated Metal‐Free Synthesis of Trifluoromethylselenolated Arenes

The first visible‐light‐mediated synthesis of trifluoromethylselenolated arenes under metal‐free conditions is reported. The use of an organic photocatalyst enables the trifluoromethylselenolation of arene diazonium salts using the shelf‐stable reagent trifluoromethyl tolueneselenosulfonate at room temperature. The reaction does not require the presence of any additives and shows high functional‐group tolerance, covering a very broad range of starting materials. Mechanistic investigations, including EPR spectroscopy, luminescence investigations, and cyclic voltammetry allow rationalization of the reaction mechanism.     

Complexation of lead(II) by chlorogenic acid: experimental and theoretical study

Density functional theory (DFT) structure calculations and time-dependent DFT electronic excitation calculations have been performed on chlorogenic acid (H(3)CGA), a polyphenolic compound, used as a model molecule of humic substances. The different deprotonated forms of H(3)CGA have also been investigated. H(3)CGA is a multisite ligand that presents several metal complexing sites in competition, notably the carboxylic and catechol moieties. In low acidic aqueous medium, the complexation of Pb(II) has been followed by electronic absorption spectrometry. The formation of two complexes of stoichiometry metal:ligand 1:1 (log beta(1:1) = 3.39) and 2:1 (log beta(2:1) = 7.12) has been highlighted with use of chemometric methods. The theoretical spectrum of the 1:1 complex obtained by TD-DFT methodology shows the formation of a chelate [Pb(H(2)CGA)(H(2)O)(3)](+) with the metal fixation at the level of the carboxylate function. The second complexing site, the catechol moiety, is rapidly involved in the formation of the 2:1 complex from molar ratios [metal]/[ligand] higher than 0.1. The electronic transitions calculated for both free ligand and complexes involved the same molecular orbitals, and no ligand-metal or metal-ligand charge transfer is observed.     

Crystal-packing-induced antiferromagnetic interactions of metallocenes: cyanonickelocenes, -cobaltocenes, and -ferrocenes

The cyano-substituted metallocenes [M(C5H4CN)2] (M=Fe, 1; Co, 2; Ni 3) and [M(C5Me5)(C5H4CN)] (M=Fe, 4; Co, 5; Ni, 6) were synthesized in yields up to 58 % by treating K(C5H4CN) or Tl(C5H4CN) with suitable transition-metal precursors. Cyclic voltammetry indicated that the oxidation and reduction potentials of all the cyanometallocenes were shifted to positive values by up to 0.8 V. Single-crystal X-ray structure analysis showed that 1 had eclipsed ligands, formed planes in the lattice, and--unlike usual metallocenes--lined up in stacks perpendicular to these planes. Powder X-ray studies established that 1 and 2 are isotypic. The 1H and 13C NMR spectra were recorded for all the new compounds. Signal shifts of up to delta=1500 ppm were recorded for the paramagnetic molecules 2 and 3 and were, at a given temperature, strikingly different for solution and solid-state spectra. These results pointed to antiferromagnetic interactions as a consequence of molecular ordering in the lattice, as confirmed by magnetic measurements. The temperature-dependent susceptibilities were reproduced by Heisenberg spin-chain models (H=-J sum n- 1 i=1 SiSi+1), thus yielding J=-28.3 and -10.3 cm(-1) for 2 and 3, respectively, whereas J=-11.8 cm(-1) was obtained for 3 from the Ising spin-chain model. In accordance with molecular orbital (MO) considerations, much spin density was found to be delocalized not only on the cyclopentadienyl ligand but also the cyano substituents. The magnetic interaction was interpreted as a Heitler-London spin exchange and was analyzed based on how the interaction depends on the singly occupied MOs and the shift of parallel metallocenes relative to each other.     

Evidence for concerted proton-electron transfer in the electrochemical oxidation of phenols with water as proton acceptor. Tri-tert-butylphenol

Proton-coupled electron transfer oxidation of phenols play a prominent role in several natural processes, and one may wonder if their high efficiency is related to the possibility that the electron and proton transfer steps are concerted. The cyclic voltammetric observation of the electrochemical oxidation and reverse reaction has allowed, with the example of 2,4,6-tri-tert-butylphenol in nonbuffered aqueous media, the clear identification of a pathway in which a phenol is directly and reversibly converted into the phenoxyl radical while the generated proton is accepted by a water molecule in a concerted manner. In very basic media, a stepwise mechanism takes place in which the phenol is deprotonated by OH- and the resulting phenoxide ion rapidly oxidized into the phenoxyl radical. As the pH decreases, this pathway progressively shuts down to the advantage of the concerted pathway. The latter assignment is confirmed by the observation of a substantial H/D kinetic isotope effect. At moderately basic pH 10.5, the contributions of the two pathways are about equal and the occurrence of the two competing routes is directly visualized in the cyclic voltammetry response.     

Six-fold oxygen-coordinated triplet (S = 1) palladium(II) moieties templated by tris(bipyridine)ruthenium(II) ions

Tris(bipyridine)ruthenium(II) is used as a templating agent to insert palladium(II) into three-dimensional oxalate-based networks. The templated-assembly of [Ru(bpy)(3)][Pd(2)(ox)(3)] (Pd(2)) and [Ru(bpy)(3)][PdMn(ox)(3)] (PdMn) is described. The latter compound is structurally characterized by powder X-ray diffraction and X-ray absorption spectroscopy. These techniques reveal an unusual 6-fold oxygen environment around the Pd(II) atoms with two short (2.02 Angstrom) and four long (2.17 Angstrom) Pd-O distances. As stated by magnetometry, this environment is associated with a triplet ground state (S = 1) of the palladium(II) ion: when the temperature is decreased, the chiMT product shows a monotonous decrease from 5.54 cm(3) K mol(-1) at 300 K, a value which is slightly lower than the one expected for independent paramagnetic Pd(II) (S = 1, g = 2) and Mn(II) (S = 5/2, g = 2) ions. This thermal variation is due to antiferromagnetic exchange interactions between the two spin bearers. Nevertheless, no long-range magnetic order is detected down to 2 K. These results are confirmed by an analysis of the [MII(C(2)O(4))(3)](4-) (M = Ni, Pd, Pt) complex and of a [Pd(II){mu-(C(2)O(4))Mn(II)(OH(2))(4)}(3)](2+) tetranuclear model using density functional theory.     

Adiabatic and non-adiabatic concerted proton-electron transfers. Temperature effects in the oxidation of intramolecularly hydrogen-bonded phenols

The one-electron electrochemical and homogeneous oxidations of two closely similar aminophenols that undergo a concerted proton-electron transfer reaction, in which the phenolic proton is transferred to the nitrogen atom in concert with electron transfer, are taken as examples to test procedures that allow the separate determination of the degree of adiabaticity and the reorganization energy of the reaction. The Marcus (or Marcus-Hush-Levich) formalism is applicable in both cases, but not necessarily in its adiabatic version. Linearization of the activation-driving force laws simplifies the treatment of the kinetic data, notably allowing the use of Arrhenius plots to treat the temperature dependence of the rate constant. A correct estimation of the adiabaticity and reorganization energy requires the determination of the variation of the driving force with temperature. Application of these procedures led to the conclusion that, unlike previous reports, the homogeneous reaction is non-adiabatic, with a transmission coefficient of the order of 0.005, and that the self-exchange reorganization energy is about 1 eV lower than previously estimated. With such systems, the intramolecular reorganization energy, although sizable, is in fact rather modest, being only slightly larger than that for the outer-sphere electron transfer that produced the cation radical. The electrochemical reaction is, in contrast, adiabatic, as revealed by the temperature dependence of its standard rate constant obtained from cyclic voltammetric experiments. This difference in behavior is deemed to derive from the effect of the strong electric field within which the electrochemical reaction takes place, stabilizing a zwitterionic form of the reactant (in which the proton has been transferred from oxygen to nitrogen). Taking this difference in adiabaticity into account, the magnitudes of the reorganization energies of the two reactions appear to be quite compatible with one another, as revealed by an analysis of the solvent and intramolecular contributions in both cases.     

Triazabicyclodecene: an effective isotope exchange catalyst in CDCl(3)

We describe the first effective H/D exchange reaction with acidic substrates in CDCl(3) at room temperature. The particularly mild reaction conditions involved (solvent, base, and temperature) allow the chemoselective deuteration of ketones over esters. An NMR study was conducted with the aim of rationalizing the results obtained in the presence of TBD as catalyst.