and Au6 clusters: Superatomic molecules bearing an SP3‐hybrid Au6 core

The octahedral Au₆ core is explored for the formation of novel SP³‐hybrid superatomic molecules by considering and Au₆ clusters (X= F, Cl, Br, I). The bonding between the four capping atoms and the Au₆ core requires a combination of 1S and 1P shells of the core leading to a set of four equivalent hybrid orbitals. Thus, combining the superatom concept with both the Lewis structure model and VSEPR theory contributes to the rationalization of structure and bonding in metal clusters. For example, our results consider the Au₆ clusters as analogues of the simplest perhalogenated hydrocarbon, CX₄.     

Enhanced photocatalytic activity of zeolite-encapsulated TiO2 clusters by complexation with organic additives and N-doping.

In the literature it was found that titanium oxide clusters of a few metal atoms encapsulated inside the micropores of zeolite Y exhibit large blue shifts in the Ti-O ligand-to-metal charge-transfer band as compared to non-encapsulated bulk titanium dioxide particles. This blue shift of the Ti-O absorption band is believed to have a negative effect on the photocatalytic activity of zeolite-encapsulated TiO2. We report here on circumventing this problem and increasing visible-light absorption by means of a red shift of the absorption band caused by addition of some organic molecular modifiers containing acidic OH groups that can strongly bind with titanol groups TiOH. In the studied series of zeolite-encapsulated TiO2 samples, the red shift of the optical spectrum follows the order: catechol > 4-aminobenzoic acid > benzoic acid. Also N-doping of zeolite-encapsulated TiO2 clusters by thermal treatment with urea leads to a red shift of the TiO2 absorption band that depends on the annealing and hydration conditions. By comparison to the degradation of phenol in aqueous solution, we have demonstrated that these changes in the absorption spectrum on addition of the organic modifier are also reflected in the photocatalytic activity of the samples; a greater increase in photocatalytic activity (about 30%) was observed for the additive catechol.     

Development of Disposable Carbon Nanofibers Electrodes Supported on Filters

The purpose of this work is to develop simple and reproducible ways to fabricate carbon nanofibers (CNFs) electrodes. Disposable CNFs electrodes were fabricated after filtering CNFs through polytetrafluoroethylene filters (PTFE), using directly as electrodes these filters with the CNFs film. The electrochemical behaviour of CNFs/PTFE electrodes were tested with ferrocenemethanol and tris(2,2′‐bypyridyl)dichlororuthenium(II) (Ru(bipy)₃²⁺). As a proof of concept of the analytical usefulness of the CNFs/PFTE electrodes, the study of vitamin B₁₂ was carried out. Multivariate calibrate has been successfully used to determine vitamin B₁₂ in a complex medium with vitamins B₁ and B₆ as interferents.     

Multiscale Approach to the Study of the Electronic Properties of Two Thiophene Curcuminoid Molecules

We studied the electronic and conductance properties of two thiophene–curcuminoid molecules, 2‐thphCCM ( 1 ) and 3‐thphCCM ( 2 ), in which the only structural difference is the position of the sulfur atoms in the thiophene terminal groups. We used electrochemical techniques as well as UV/Vis absorption studies to obtain the values of the HOMO–LUMO band gap energies, showing that molecule 1 has lower values than 2 . Theoretical calculations show the same trend. Self‐assembled monolayers (SAMs) of these molecules were studied by using electrochemistry, showing that the interaction with gold reduces drastically the HOMO–LUMO gap in both molecules to almost the same value. Single‐molecule conductance measurements show that molecule 2 has two different conductance values, whereas molecule 1 exhibits only one. Based on theoretical calculations, we conclude that the lowest conductance value, similar in both molecules, corresponds to a van der Waals interaction between the thiophene ring and the electrodes. The one order of magnitude higher conductance value for molecule 2 corresponds to a coordinate (dative covalent) interaction between the sulfur atoms and the gold electrodes.     

Operator Hilbert spaces without the operator approximation property

We use a technique of Szankowski to construct operator Hilbert spaces that do not have the operator approximation property, including an example in a noncommutative space for .

     

Novel stereocontrolled addition of allylmetal reagents to alpha-imino esters: efficient synthesis of chiral tetrahydroquinoline derivatives

To prepare in multigram scale new antagonists of the glycine binding site associated to the NMDA receptor, an efficient distereoselective route was set up. The addition of suitable allyltin reagents to chiral N-aryl alpha-imino esters (R-(+)-tert-butyl lactate used as chiral auxiliary), gave the corresponding alpha amino acid-type derivative in high chemical yield and optical purity. This allylation reaction represents a novel example of efficient long-range stereodifferentiation process. In the last part of the synthesis, a regioselective Heck-type cyclization reaction enabled preparation of the target tetrasubstituted exocycle and trisubtituted endocycle double bond derivatives.     

Complexation behavior of a highly preorganized 7,7-diphenylnorbornane-derived macrocycle: towards the design of molecular clocks

The syntheses of two new cyclophane hosts, 4 and 6, are described. The main difference between them is the higher degree of preorganization of 4 as a consequence of the inclusion of the 7,7-diphenylnorbornane (DPN) subunit. The inner cavity of 4 adopts a belt-shaped structure, while 6 has a twisted geometry. In the solid state, the molecules of macrocycle 6 are stacked along an axis to form nanotubular structures. Compounds 4 and 6 form two of the strongest complexes between arene cyclophanes and Ag(+) reported up to date. The silver cation is located inside the cavity of the macrocycles. The stability of 4.Ag(+) is considerably higher than that of 6.Ag(+). The additional stabilization of 4.Ag(+) is attributed to higher preorganization of macrocycle 4. DNMR experiments as well as theoretical calculations carried out with 4.Ag(+) show evidence of Ag(+)-hopping between two different binding sites inside the macrocycle. This phenomenon could be the basis for the design of molecular clocks.     

The reproducible properties of correct forecasts

Each period, one outcome out of finitely many possibilities is observed. Each period, a forecaster announces some probability for the future outcomes based on the available data. An outsider wants to know if the forecaster has some knowledge of the data generating process. Let a test be an arbitrary function from sequences of forecasts and outcomes to {0,1}. When the test returns a 0 the test is said to reject the forecasts based on the outcome sequence. When the test resturns a 1 the test is said to not reject the forecasts based on the outcome sequence. Consider any test that does not reject the truth, i.e. it does not reject when the announced forecasts are the conditional probabilities of the data generating process. Based on Fans (1953) Minimax theorem, I show that it is possible to produce forecasts that will not be rejected on any sequence of outcomes. Journal of Economic Literature Classification Number:D83 LearningI thankfully acknowledge financial support from the National Science Foundation grant SES 0109650. I also thank a referee for useful comments. All errors are mine.     

Zeroes of complete polynomial vector fields

We prove that a complete polynomial vector field on has at most one zero, and analyze the possible cases of those with exactly one which is not of Poincaré-Dulac type. We also obtain the possible nonzero first jet singularities of the foliation at infinity and the nongenericity of completeness. Connections with the Jacobian Conjecture are established.