Voltammetry of labile metal—complex systems with induced reactant adsorption. Theoretical analysis for any ligand-to-metal ratio

The validity of the hypothesis of ligand excess is discussed for the voltammetric reduction of a metal ion (M) in the presence of a ligand (L). The following basic assumptions are made: (i) formation of the electroinactive ML complex, (ii) equal mobility of species M, ML and L, (iii) reversible charge transfer, (iv) labile complex and (v) Langmuirian adsorption of the ligand and the complex. The model proposed is solved rigorously for normal pulse polarography (NPP) in the four possible cases assuming either ligand excess or ligand deficiency or either adsorption or non-adsorption. For the case without adsorption, the assumption of ligand excess affects only the increasing part of the NPP wave independent of the total ligand-to-metal ratio. Then (I_NNP)_lim has the same value for both ligand excess and ligand deficiency while E differs, thus preventing the use of the DeFord—Hume method to obtain the stability constant. An analytical expression for E is performed, which allows the evaluation of the stability constant at any total ligand-to-metal ratio and provides a quantitative estimation of the error made by applying the classical procedure assuming ligand excess. In the presence of adsorption, the assumption of ligand excess modifies the whole wave. The discrepancy between the currents obtained from the hypothesis of ligand excess with respect to that with ligand deficiency is even higher for the case with adsorption than for the case without adsorption.     

Higher order corrections to the processe^ + e^ - \to v\bar vy

A calculation of the neutrino counting reaction \(e^ + e^ - \to v\bar vy\) is presented and implemented in a Monte Carlo generator of unweighted events. The non-photonic corrections are included following the star-scheme. The photonic corrections have been exponentiated following the “inductive” and the “structure functions” approach. For a realistic experimental set-up, the total corrections around theZ ⁰ pole amount to ～5% with respect to the one-loop result. The final precision achieved is better than 1%.     

Comparing the relative volume with a revolution manifold as a model

Given a pair (P, M), whereM is ann-dimensional connected compact Riemannian manifold andP is a connected compact hypersurface ofM, the relative volume of (P, M) is the quotient volume(P)/volume(M). In this paper we give a comparison theorem for the relative volume of such a pair, with some bounds on the Ricci curvature ofM and the mean curvature ofP, with respect to that of a model pair where ℳ is a revolution manifold and a “parallel” of ℳ. Work partially supported by a DGICYT Grant No. PB91-0324.     

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Excess charge delocalization in organic and biological molecules: some theoretical notions

Theoretical and computational investigations of the excess charge distribution (ECD) in molecular complexes have attracted considerable attention as ECD is closely related to electronic properties of organic semiconductors, such as the efficiency of photoinduced charge separation in organic solar cells and charge transport in DNA and proteins. In this paper, we analyze the ECD in several representative models on the basis of ab initio and DFT calculations. We consider how changes in the reorganization energy, electronic coupling and charge transfer energy affect the ECD in the systems. In particular, we compare ECD in π stacks of polycyclic aromatic hydrocarbons and DNA nucleobases. While the π interaction between subunits in the systems is similar in both cases, ECD is quite different: the excess charge is found to be completely delocalized over the hydrocarbon stacks but strongly confined to a single nucleobase in DNA stacks. We also discuss the effects of conformational fluctuations on ECD in the stacks. Finally, ECD in amino acids and its dependence on the conformational changes are briefly considered.     

High nonlinear optical properties in TeO2-based glasses: A modifier’s influence study from the localized hyperpolarizability approach

Ab initio localized molecular orbital theory (GAMESS program) has been used to evaluate the effects of a second cation on nonlinear optical properties of tellurium oxide based glasses. Calculations were performed on [H_nTeO₃A_3?n]⁺ (n = 0–3) molecules with alkali cations (A = Li, Na). Results of the calculations on optimized structures show that the effects of the second cation on the nonlinear optical properties are significant and related to the geometric modification of the structural unit. However, the introduction of the second cation induces an increase of both linear polarizability and second hyperpolarizabilty whereas experiments show the opposite, second hyperpolarizabilty is much more affected by the introduction of the second cation. Such calculations have to be performed on bigger size clusters in which the introduction of a second cation implies breaking a Te–O–Te bridge.     

Polystyrene-supported (R)-2-piperazino-1,1,2-triphenylethanol: a readily available supported ligand with unparalleled catalytic activity and enantioselectivity

A very active and highly enantioselective catalytic resin, designed for minimal perturbation of the catalytic center by the polymer matrix, has been assembled in two steps from (S)-triphenylethylene oxide, piperazine, and Merrifield resin and tested in the enantioselective ethylation of aldehydes. 1-Arylpropanols of 94-95% ee are obtained in high yield by the use of only 2 mol % of catalytic resin at 0 degrees C for 4 h.     

Generalizing the breakdown of the maximum hardness and minimum polarizabilities principles for nontotally symmetric vibrations to non-pi-conjugated organic molecules

In previous works we have shown that certain pi-conjugated organic molecules possess nontotally symmetric vibrations that break the maximum hardness (MHP) and minimum polarizability principles (MPP). We have also derived a set of simple rules to determine a priori without calculations whether a particular pi-conjugated organic molecule violates these two principles. In the present work, we generalize these results, and we show that not only pi-conjugated organic molecules but also other molecules without pi-conjugated structure or even pi-bonds can exhibit nontotally symmetric molecular distortions that do not follow these two principles. We have also found that the breakdowns of the MHP and the MPP are not necessarily connected, since the polarizability is not always proportional to the softness. Finally, we also introduced a methodology based on the diagonalization of the hardness Hessian matrix with respect to the vibrational normal coordinates to determine the nontotally symmetric molecular displacements that do not follow the MHP.     

Electron localization and delocalization in open-shell molecules

Localization and delocalization indices derived in the framework of the quantum Atoms in Molecules theory have recently been used to analyze the electron-pair structure of closed-shell molecules. Here we report calculations of localization and delocalization indices for open-shell molecules at the Hartree-Fock (HF) level. Several simple doublet and triplet radical molecules are studied. In general, interatomic delocalization between bonded atoms is heavily dependent on the order and polarity of the bond. Unpaired electrons also have a significant effect on the interatomic delocalization indices. Indeed, for many radicals, the analysis of the spin components reveals that the interatomic delocalization is very different for alpha and beta spin electrons in many cases. In general, at the HF level, the results can be rationalized in terms of orbital contributions. However, the definition of localization and delocalization indices is completely general, and they could be calculated at any level of theory, provided that the one- and two-electron densities are available.