Ionization potentials and geometrical structure of pure and oxygenated barium clusters

In this article, we present results obtained on structures of small bare and oxygenated barium clusters produced by the laser vaporization technique. Contrary to the very weak Ba—Ba binding (0.202 eV), the Ba—O binding is rather strong (5.8 eV). As a consequence, extremely small amounts of oxygen in the cluster source are sufficient to induce the nucleation of oxygenated barium clusters. Surprisingly, at least for substoechiometric systems, Ba_nO_m clusters exhibit the same icosahedral structure as bare clusters do. Mass spectra seem to indicate that replacing a barium atom with a strongly polar BaO molecule does not affect the geometrical structure of the cluster. This aspect is more easily understandable if we assume that the oxygen atom takes place inside the structure of the Ba_n cluster without significant distortions. Ab-initio calculations have been undertaken in order to give a satisfactory account of this hypothesis.     

Dirichlet Series and Curious infinite Products

By number-theoretical methods we give a result generalizingthose of J. O. Shallit, one particular case of which reads asfollows: ...=2^–;, where a(n) is equal to 1 if the sum of the digits of n in basetwo is even, and – 1 if this sum is odd. Moreover we provea conjecture of Shallit concerning a way of approximating 2^–     

Theoretical study of the adsorption of silver atoms on the (111) face of silicon

The adsorption of one or many silver atoms on a (111) silicon face (reduced to 61 dangling atomic orbitals) is investigated by means of a self-consistent Hartree–Fock method parametrized from atomic and thermodynamical data. The valley sites (above three Si atoms) are favored over the top sites (above one Si atom). The extrapolation of the results obtained for several structures corresponding to the adsorption of n = 1, 2, 3, 4, 6, and 7 Ag atoms allows us to conclude that the most stable structures correspond: for \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = \frac{1}{3} $\end{document} to linear Ag chains (3 × 1 phase), for \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = \frac{2}{3} $\end{document} to an honeycomb lattice (\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt 3 \times \sqrt 3 $\end{document} phase), and for θ = 1 to a centred hexagonal lattice (\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt 3 \times \sqrt 3 $\end{document} phase), the Ag atoms located at the centers of the hexagons being beneath the plan of the hexagons. The adsorption energies corresponding to the various θ are practically equal (ca. 3 eV/Ag). The net charges of Ag atoms are equal to 0.35.     

Electron solvation by highly polar molecules: density functional theory study of atomic sodium interaction with water, ammonia, and methanol

This study further extends the scope of a previous paper [Y. Ferro and A. Allouche, J. Chem. Phys. 118, 10461 (2003)] on the reactivity of atomic Na with water to some other highly polar molecules known for their solvation properties connected to efficient hydrogen bonding. The solvation mechanisms of ammonia and methanol are compared to the hydration mechanism. It is shown that in the case of ammonia, the stability of the solvated system is only ensured by electrostatic interactions, whereas the methanol action is more similar to that of water. More specific attention is given to the solvation process of the valence 3s Na electron. The consequences on the chemical reactivity are analyzed: Whereas ammonia is nonreactive when interacting with atomic sodium, two chemical reactions are proposed for methanol. The first process is dehydrogenation and yields methoxy species and hydrogen. The other one is dehydration and the final products are methoxy species, but also methyl radical and water. The respective roles of electron solvation and hydrogen bonds network are analyzed in detail in view of the density of states of the reactive systems.     

A constructive approach to examination timetabling based on adaptive decomposition and ordering

In this study, we investigate an adaptive decomposition and ordering strategy that automatically divides examinations into difficult and easy sets for constructing an examination timetable. The examinations in the difficult set are considered to be hard to place and hence are listed before the ones in the easy set in the construction process. Moreover, the examinations within each set are ordered using different strategies based on graph colouring heuristics. Initially, the examinations are placed into the easy set. During the construction process, examinations that cannot be scheduled are identified as the ones causing infeasibility and are moved forward in the difficult set to ensure earlier assignment in subsequent attempts. On the other hand, the examinations that can be scheduled remain in the easy set. Within the easy set, a new subset called the boundary set is introduced to accommodate shuffling strategies to change the given ordering of examinations. The proposed approach, which incorporates different ordering and shuffling strategies, is explored on the Carter benchmark problems. The empirical results show that the performance of our algorithm is broadly comparable to existing constructive approaches.     

Beyond odious and evil

In a recent post on the Seqfan list the third author proposed conjectures concerning the summatory function of odious numbers (i.e., of numbers whose sum of binary digits is odd), and of evil numbers (i.e., of numbers whose sum of binary digits is even). We prove these conjectures here. We will also study the sequences of “generalized” odious and evil numbers, and their iterations, giving in particular a characterization of the sequences of usual odious and evil numbers in terms of functional equations satisfied by their compositions.     

N-Terminal Selective C−H Azidation of Proline-Containing Peptides: a Platform for Late-Stage Diversification

A methodology for the C−H azidation of N-terminal proline-containing peptides was developed employing only commercially available reagents. Peptides bearing a broad range of functionalities and containing up to 6 amino acids were selectively azidated at the carbamate-protected N-terminal residue in presence of the numerous other functional groups present on the molecules. Post-functionalizations of the obtained aminal compounds were achieved: cycloaddition reactions or C−C bond formations via a sequence of imine formation/nucleophilic addition were performed, offering an easy access to diversified peptides.     

Influence of counterion charge on the electrochemistry and impedance of polypyrrole

Polypyrroles doped with multiply charged anions are becoming increasingly important in a wide range of energy, environmental and biomedical applications. The increased counterion charge promotes anion binding and retention and can significantly increase stability and performance. The electrochemical properties of polypyrrole films prepared galvanostatically in Na₂SO₄ (PPySO₄) where found to be similar those of PPyClO₄ prepared in NaClO₄, although there was significantly more anion retention during potential cycling. In contrast, PPyPO₄ films prepared in Na₃PO₄ under the same conditions were over-oxidised and more dense, which is beneficial for corrosion protection and electroanalysis. Paradoxically, the low mobility of SO₄²⁻ counterions results in more facile charging and discharging of the film, as observed with large and polymeric counterions. This can create significant benefits in applications that require fast cycling, such as supercapacitors and high-rate batteries. These conclusions are corroborated by electrochemical impedance measurements in various aqueous electrolytes. Ionic conductivity was dominated by anion transport for both PPyClO₄ and PPySO₄, whilst PPyPO₄ was predominantly a cation conductor.

     

Fluorination of the epsilon-Keggin Al13 polycation

Fluorination of the Al13 polycation in epsilon-Keggin (Kepsilon-J) conformation, leads to partial substitution of di-mu2-OH bridges by fluorine and enhances the formation of Al30 polycation.