Perturbation of resonances in quantum mechanics

Schrödinger operators on L²($\text{R}$³) of the form ?Δ + V_λ with potentials V_λ real-analytic in λ are discussed. The analytic structure in V_λ and k (with k² the energy variable) of the resolvent kernel, the eigenvalues and resonances is exhibited and we obtain in particular convergent perturbation expansions for the resonances and the corresponding resonance functions. The lower order expansion coefficients are computed explicitly. The resonances and the corresponding functions are also computed for a particle moving under the action of n point interactions. This gives asymptotic low energy information about Schrödinger Hamiltonians with short range potentials. The perturbation theory of resonances, eigenvalues and of the corresponding functions for Hamiltonians describing n point interactions perturbed by a potential is also given.     

On fractal properties of non-normal numbers with respect to Rényi f-expansions generated by piecewise linear functions

The paper is devoted to the study of fractal properties of subsets of the set of non-normal numbers with respect to Rényi f  -expansions generated by continuous increasing piecewise linear functions defined on [0,+∞)$[0,+\infty )$. All such expansions are expansions for real numbers generated by infinite linear IFS f={_f0,_f1,…,_fn,…}$f=\{f_0,f_1,\dots ,f_n,\dots \}$ with the following list of ratios _Q∞=(_q0,_q1,…,_qn,…)$Q_{\infty }=(q_0,q_1,\dots ,q_n,\dots )$.     

Stability properties of an inverse parabolic problem with unknown boundaries

We treat the stability issue for an inverse problem arising from non-destructive evaluation by thermal imaging. We consider the determination of an unknown portion of the boundary of a thermic conducting body by overdetermined boundary data for a parabolic initial-boundary value problem. We obtain that when the unknown part of the boundary is a priori known to be smooth, the data are as regular as possible and all possible measurements are taken into account, the problem is exponentially ill-posed. Then, we prove that a single measurement with some a priori information on the unknown part of the boundary and minimal assumptions on the data, in particular on the thermal conductivity, is enough to have stable determination of the unknown boundary. Given the exponential ill-posedness, the stability estimate obtained is optimal. AMS 2000 Mathematics Subject Classification. Primary 35R30, Secondary 35B60, 33C90     

New palladium (II) complexes containing phosphine‐nitrogen ligands and their use as catalysts in aminocarbonylation reaction

Aminocarbonylation of aryl halides, homogeneously catalysed by palladium, is an efficient method that can be employed for obtaining amides for pharmaceutical and synthetic applications. In this work, palladium (II) complexes containing P^N ligands were studied as catalysts in the aminocarbonylation of iodobenzene in the presence of diethylamine. Two types of systems were used: a palladium (II) complex formed in situ; and one prepared prior to the catalytic reaction. In general, the palladium complexes studied achieved high conversions in an average reaction time of less than 2 hr, which is less than that for the standard system (Pd (II)/PPh₃) used. The pre‐synthesized complexes were faster than their in situ counterparts, as the latter require an induction time to form the Pd/P^N species. The structure and electronic properties of the ligand P^N can influence both the activity and the selectivity of the reaction, stabilizing the acyl‐palladium intermediates formed in a better manner.     

Highly Enantioselective Construction of Tricyclic Derivatives by the Desymmetrization of Cyclohexadienones

The asymmetric synthesis of tricyclic compounds by the desymmetrization of cyclohexadienones is presented. The reaction tolerated a large variety of substituents at different positions of the cyclohexadienone, and heterocyclic rings of different sizes were accessible. Density functional theory calculations showed that the reaction proceeds through an asynchronous [4+2] cycloaddition.     

Synthesis,Characterization and Photocleavage of Bis-decyl Pteroic Acid: A Folate Derivative with Affinity to Biomembranes†

Here, we provide mechanistic insight to the photocleavage of a compound in the folate family, namely pteroic acid. A bis-decyl chain derivative of pteroic acid was synthesized, structurally characterized and photochemically investigated. We showed that, like folic acid, pteroic acid and the decylated derivative undergo a photocleavage reaction in the presence of H₂O, while no reaction was observed in methanol solution. Furthermore, density functional theory calculations were carried out to predict relative stabilities of hypothetical mono-, bis- and tris-decylated pteroic acid derivatives to help rationalize the regioselectivity of the bis-decyl pteroic acid product. Additionally, the lipophilicity of the bis-decyl pteroic acid appears to confer a hydrophobic property enabling an interaction with biomembranes.     

Re-entrant nematic behavior in the 7OCB+9OCB mixtures: evidence for multiple nematic-smectic tricritical points

The metastable phase diagram of the two-component system heptyloxycyanobiphenyl (7OCB)+nonyloxycyanobiphenyl (9OCB) was determined by means of modulated differential scanning calorimetry (MDSC) and optical microscopy measurements. It was experimentally established that the 7OCB+9OCB two-component system exhibits a monotropic re-entrant nematic behavior. A complete quantitative thermodynamic analysis, through Oonk's equal G analysis, was performed, allowing for the calculation of the monotropic re-entrant behavior and the prediction of two tricritical points, one of them experimentally accessible for the SmAd-to-N transition and the other non-experimentally accessible for the RN-to-SmAd transition. From specific-heat measurements, latent heats were obtained for those mixtures displaying a first-order SmAd-to-N transition. Additionally, for some mixtures, the specific-heat critical exponents (alpha), through the second-order SmAd-to-N transition, were obtained. Both batches of data enable us to access to the experimental tricritical temperature for the SmAd-to-N transition.     

QM/MM modeling of the hydroxylation of the androstenedione substrate catalyzed by cytochrome P450 aromatase (CYP19A1)

CYP19A1 aromatase is a member of the Cytochrome P450 family of hemeproteins, and is the enzyme responsible for the final step of the androgens conversion into the corresponding estrogens, via a three‐step oxidative process. For this reason, the inhibition of this enzyme plays an important role in the treatment of hormone‐dependent breast cancer. The first catalytic subcycle, corresponding to the hydroxilation of androstenedione, has been proposed to occur through a first hydrogen abstraction and a subsequent oxygen rebound step. In present work, we have studied the mechanism of the first catalytic subcycle by means of hybrid quantum mechanics/molecular mechanics methods. The inclusion of the protein flexibility has been achieved by means of Free Energy Perturbation techniques, giving rise to a free energy of activation for the hydrogen abstraction step of 13.5 kcal/mol. The subsequent oxygen rebound step, characterized by a small free energy barrier (1.5 kcal/mol), leads to the hydroxylated products through a highly exergonic reaction. In addition, an analysis of the primary deuterium kinetic isotopic effects, calculated for the hydrogen abstraction step, reveals values (～10) overpassing the semiclassical limit for the C? H, indicating the presence of a substantial tunnel effect. Finally, a decomposition analysis of the interaction energy for the substrate and cofactor in the active site is also discussed. According to our results, the role of the enzymatic environment consists of a transition state stabilization by means of dispersive and polarization effects. © 2015 Wiley Periodicals, Inc.     

Anodic chlorination of aromatic compounds in acetic acid part II

The anodic chlorination of aromatic compounds in anhydrous acetic acid has been further investigated. Evidence has been found for two different methods of electrochemical chlorination, in the systems Cl₂/aromatic compounds and Cl^?/aromatic compounds. These methods were also compared with the uncatalyzed chemical chlorination reaction. The yields of monochlorinated products and the related isometric distributions were taken into account. Since the isomeric distributions are equal with chemical and electrochemical chlorination methods, the formation of the same intermediate was proposed for both.     

Functional molecules in electronic circuits

Molecular electronics is a fascinating field of research contributing to both fundamental science and future technological achievements. A promising starting point for molecular devices is to mimic existing electronic functions to investigate the potential of molecules to enrich and complement existing electronic strategies. Molecules designed and synthesized to be integrated into electronic circuits and to perform an electronic function are presented in this article. The focus is set in particular on rectification and switching based on molecular devices, since the control over these two parameters enables the assembly of memory units, likely the most interesting and economic application of molecular based electronics. Both historical and contemporary solutions to molecular rectification are discussed, although not exhaustively. Several examples of integrated molecular switches that respond to light are presented. Molecular switches responding to an electrochemical signal are also discussed. Finally, supramolecular and molecular systems with intuitive application potential as memory units due to their hysteretic switching are highlighted. Although a particularly attractive feature of molecular electronics is its close cooperation with neighbouring disciplines, this article is written from the point of view of a chemist. Although the focus here is largely on molecular considerations, innovative contributions from physics, electro engineering, nanotechnology and other scientific disciplines are equally important. However, the ability of the chemist to correlate function with structure, to design and to provide tailor-made functional molecules is central to molecular electronics.