Riesz-Nágy singular functions revisited

In 1952 F. Riesz and Sz.-Nágy published an example of a monotonic continuous function whose derivative is zero almost everywhere, that is to say, a singular function. Besides, the function was strictly increasing. Their example was built as the limit of a sequence of deformations of the identity function. As an easy consequence of the definition, the derivative, when it existed and was finite, was found to be zero. In this paper we revisit the Riesz-Nágy family of functions and we relate it to a system for real number representation which we call (τ,τ−1)-expansions. With the help of these real number expansions we generalize the family. The singularity of the functions is proved through some metrical properties of the expansions used in their definition which also allows us to give a more precise way of determining when the derivative is 0 or infinity.     

On the relation between protonium level shifts and nucleon-antinucleon scattering amplitudes

We study the Coulomb and threshold corrections to the low-energy scattering parameters for the proton-antiproton system, with numerical examples based on current optical models. Some commonly used expressions are shown to be inconsistent with our results. We check that the Trueman formula is valid for the level shifts of protonium, provided one takes properly into account the Coulomb corrections to the scattering lengths and volumes.     

Radical para-benzoic acid derivatives: transmission of ferromagnetic interactions through hydrogen bonds at long distances

Investigation of the transmission of magnetic interactions through hydrogen bonds has been carried out for two different benzoic acid derivatives which bear either a tert-butyl nitroxide (NOA) or a poly(chloro)triphenylmethyl (PTMA) radical moiety. In the solid state, both radical acids formed dimer aggregates by the complementary association of two carboxylic groups though hydrogen bonding. This association ensured that atoms with most spin density are separated from one another by more than 15 A. Thus, no competing through-space magnetic exchange interactions are expected in these dimers and, hence, they provide good models to investigate whether noncovalent hydrogen bonds play a role in the long-range transmission of magnetic interactions. The nature of the magnetic exchange interaction and their strengths within similar dimer aggregates in solution was assessed by electron spin resonance (ESR) spectroscopy. In the case of radical NOA, low-temperature ESR experiments showed a weak ferromagnetic interaction between the two radicals in the dimer aggregates (which have the same geometry as in the solid state). In contrast, the corresponding solution ESR study performed with radical PTMA did not lead to any conclusive results, as aggregates were formed by noncovalent interactions other than hydrogen bonds. However, the bulkiness of the poly(chloro)triphenylmethyl radical prevented interdimer contacts in the solid state between regions of high spin density. Hence, solid-state measurements of the alpha phase of PTMA radical provided evidence of the intradimer interaction to confirm the transmission of a weak ferromagnetic interaction through the carboxylic acid bridges, as found for the NOA radical. Moreover, crystallization of the PTMA radical in presence of ethanol to form the beta phase of PTMA radical prevented the dimer formation; this resulted in the suppression of this interaction and provides further evidence of the magnetic exchange mechanism through noncovalent hydrogen bonds at long distances.     

Linked crystallites in the conducting topmost layer of polymer bilayer films controlled by temperature: from micro- to nanocrystallites.

Temperature has great impact on the structure and size of the linked crystallites of the conducting topmost layer formed at the surface of a polycarbonate film via the reaction BEDT-TTF+IBr [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene]. We show that fine temperature control permits formation of a semiconducting topmost layer of alpha'-(BEDT-TTF)(2)(I(x)Br(1-x))(3) crystallites with either micro- or nanometre size, a result that opens a route to miniaturized conducting plastic materials.     

Advantages of the Ns group in the reactions of N-SO2R inosines with benzylamine and with NH3

The reactivity of N¹-alkylsulfonyl- and N¹-arylsulfonyl-2′,3′,5′-tri-O-acetylinosine with benzylamine and with ¹⁵NH₃, regarding the attack on C2, has been shown to be in the order CF₃SO₂ (Tf) > 2,4-(NO₂)₂C₆H₃SO₂ (DNs) ? 4-NO₂C₆H₄SO₂ (pNs) ≈ C₆F₅SO₂ (PFBs) > 2-NO₂C₆H₄SO₂ (Ns) ? CH₃SO₂ (Ms) > 4-CH₃C₆H₄SO₂ (Ts) > 2,4,6-(CH₃)₃C₆H₂SO₂ (Mts). In spite of its intermediate reactivity, the Ns group is the most appropriate, since in this case the formation of by-products is minimised during the ring-opening and ring-closing steps of the process. Another advantage of the Ns group is thus disclosed.     

Synthesis and Characterization of a [Mn12O12(O2CR)16(H2O)4] Complex Bearing Paramagnetic Carboxylate Ligands. Use of a Modified Acid Replacement Synthetic Approach

Summary.  A new modified approach for the synthesis of Mn₁₂ clusters, based on the use of complex [Mn₁₂O₁₂(O₂C ^t Bu)₁₆(H₂O)₄] (2) as starting material to promote the acidic ligand replacement, is presented here. This new synthetic approach allowed us to obtain complex [Mn₁₂O₁₂(O₂CC₆H₄N(O^•) ^t Bu)₁₆(H₂O)₄] (3), whose preparation remained elusive by direct replacement of the acetate groups of Mn₁₂Ac (1). Complex 3 bearing open-shell radical units, was prepared to increase the total spin number of its ground state, and consequently, to increase T _B , with the expectation that the radical ligands may couple ferromagnetically with the Mn₁₂ core. Unfortunately, magnetic measurements of complex 3 revealed that the sixteen radical carboxylate ligands interact antiferromagnetically with the Mn₁₂ core to yield a S = 2 magnetic ground state. Corresponding author. E-mail: vecianaj@icmab.es Received March 27, 2002; accepted May 2, 2002     

Fast reduction of a copper center in laccase by nitric oxide and formation of a peroxide intermediate

The rapid reduction of one of the copper atoms (type 2) of tree laccase by nitric oxide (NO) has been detected. Addition of NO to native laccase in the presence of oxygen leads to EPR changes consistent with fast reduction and slow reoxidation of this metal center. These events are paralleled by optical changes that are reminiscent of formation and decay of the peroxide intermediate in a fraction of the enzyme population. Formation of this species is only possible if the trinuclear copper cluster (type 2 plus type 3) is fully reduced. This condition can only be met if, as suggested previously, a fraction of the enzyme contains both type 3 coppers already reduced before addition of NO. Our data are consistent with this assumption. We have suggested recently that fast reduction of copper is the mechanism by which NO interacts with the oxidized dinuclear center in cytochrome c oxidase. The present experiments using laccase strongly support this view and suggest this reaction as a general mechanism by which copper proteins interact with NO. In addition, this provides an unexploited way to produce a stable peroxide intermediate in copper oxidases in which the full complement of copper atoms is present. This enables the O-O scission step in the catalytic cycle to be studied by electron addition to the peroxide derivative through the native electron entry site, type 1 copper.     

Three-dimensional open-frameworks based on Ln(III) ions and open-/closed-shell PTM ligands: synthesis, structure, luminescence, and magnetic properties

A series of isostructural open-framework coordination polymers formulated as [Ln(dmf)(3)(ptmtc)] (Ln = Sm (1), Eu (2), Gd (3), Tb (4), Dy (5); PTMTC = polychlorotriphenylmethyl tricarboxylate) and [Ln(dmf)(2)H(2)O(αH-ptmtc)] (Ln = Sm (1'), Eu (2'), Gd (3'), Tb (4'), Dy (5')) have been obtained by treating Ln(III) ions with PTMTC ligands with a radical (PTMTC(3-)) or a closed-shell character (αH-PTMTC(3-)). X-ray diffraction analyses reveal that these coordination polymers possess 3D architectures that combine large channels and fairly rare lattice complex T connectivity. In addition, these compounds show selective framework dynamic sorption properties. For both classes of ligands, the ability to act as an antenna in Ln sensitization processes has been investigated. No luminescence was observed for compounds 1-5, and 3' because of the PTMTC(3-) ligand and/or Gd(III) ion characteristics. Conversely, photoluminescence measurements show that 1', 2', 4', and 5' emit dark orange, red, green, and dark cyan metal-centered luminescence. The magnetic properties of all of these compounds have been investigated. The nature of the {Ln-radical} exchange interaction in these compounds has been assessed by comparing the behavior of the radical-based coordination polymers 1-5 with those of the compounds with the diamagnetic ligand set. While antiferromagnetic {Sm-radical} interactions are found in 1, ferromagnetic {Ln-radical} interactions propagate in the 3D architectures of 3, 4, and 5 (Ln = Gd, Tb, and Dy, respectively). This procedure also provided access to information on the {Ln-Ln} exchange existing in these magnetic systems.     

Correlation of the EPR properties of perchlorotriphenylmethyl radicals and their efficiency as DNP polarizers

Water soluble perchlorinated trityl (PTM) radicals were found to be effective 95 GHz DNP (dynamic nuclear polarization) polarizers in ex situ (dissolution) (13)C DNP (Gabellieri et al., Angew Chem., Int. Ed. 2010, 49, 3360). The degree of the nuclear polarization obtained was reported to be dependent on the position of the chlorine substituents on the trityl skeleton. In addition, on the basis of the DNP frequency sweeps it was suggested that the (13)C NMR signal enhancement is mediated by the Cl nuclei. To understand the DNP mechanism of the PTM radicals we have explored the 95 GHz EPR characteristics of these radicals that are relevant to their performance as DNP polarizers. The EPR spectra of the radicals revealed axially symmetric g-tensors. A comparison of the spectra with the (13)C DNP frequency sweeps showed that although the solid effect mechanism is operational the DNP frequency sweeps reveal some extra width suggesting that contributions from EPR forbidden transitions involving (35,37)Cl nuclear flips are likely. This was substantiated experimentally by ELDOR (electron-electron double resonance) detected NMR measurements, which map the EPR forbidden transitions, and ELDOR experiments that follow the depolarization of the electron spin upon irradiation of the forbidden EPR transitions. DFT (density functional theory) calculations helped to assign the observed transitions and provided the relevant spin Hamiltonian parameters. These results show that the (35,37)Cl hyperfine and nuclear quadrupolar interactions cause a considerable nuclear state mixing at 95 GHz thus facilitating the polarization of the Cl nuclei upon microwave irradiation. Overlap of Cl nuclear frequencies and the (13)C Larmor frequency further facilitates the polarization of the (13)C nuclei by spin diffusion. Calculation of the (13)C DNP frequency sweep based on the Cl nuclear polarization showed that it does lead to an increase in the width of the spectra, improving the agreement with the experimental sweeps, thus supporting the existence of a new heteronuclear assisted DNP mechanism.