Semiclassical limit of quantum dynamics with rough potentials and well‐posedness of transport equations with measure initial data

In this paper we study the semiclassical limit of the Schrodinger equation. Under mild regularity assumptions on the potential U, which include Born‐Oppenheimer potential energy surfaces in molecular dynamics, we establish asymptotic validity of classical dynamics globally in space and time for “almost all” initial data, with respect to an appropriate reference measure on the space of initial data. In order to achieve this goal we prove existence, uniqueness, and stability results for the flow in the space of measures induced by the continuity equation. © 2011 Wiley Periodicals, Inc.     

Preface

This paper deals with two fundamental models for convection in a reacting porous medium with magnetic field effect. We demonstrate that the solution depends continuously on changes in the chemical reaction and the electrical conductivity coefficients.     

Vibrational spectroscopy for probing molecular-level interactions in organic films mimicking biointerfaces

Investigation into nanostructured organic films has served many purposes, including the design of functionalized surfaces that may be applied in biomedical devices and tissue engineering and for studying physiological processes depending on the interaction with cell membranes. Of particular relevance are Langmuir monolayers, Langmuir–Blodgett (LB) and layer-by-layer (LbL) films used to simulate biological interfaces. In this review, we shall focus on the use of vibrational spectroscopy methods to probe molecular-level interactions at biomimetic interfaces, with special emphasis on three surface-specific techniques, namely sum frequency generation (SFG), polarization-modulated infrared reflection absorption spectroscopy (PM-IRRAS) and surface-enhanced Raman scattering (SERS). The two types of systems selected for exemplifying the potential of the methods are the cell membrane models and the functionalized surfaces with biomolecules. Examples will be given on how SFG and PM-IRRAS can be combined to determine the effects from biomolecules on cell membrane models, which include determination of the orientation and preservation of secondary structure. Crucial information for the action of biomolecules on model membranes has also been obtained with PM-IRRAS, as is the case of chitosan removing proteins from the membrane. SERS will be shown as promising for enabling detection limits down to the single-molecule level. The strengths and limitations of these methods will also be discussed, in addition to the prospects for the near future.     

Controlled Formation of Fluorescent Metalloporphyrin‐Containing Coordination Polymer Particles from Seed Structures by Designed Shape‐Transformation Reactions

Herein, nanorod structures and four‐leaf clover structures of fluorescent zinc 5,10,15,20‐tetra(4‐pyridyl)‐21H,23H‐porphine (ZnTPyP)‐containing coordination polymer particles (CPPs) were first synthesized by a bottom‐up strategy assisted by surfactants and then employed as seed structures for further shape‐transformation reactions. We have successfully designed the morphological transformation for different dimensions, achieving the controlled formation of octahedron structures at both the nanometer scale and micrometer scale from the seed structures. Our approach illustrates a new method to design and synthesize metalloporphyrin‐containing CPPs in a systematic and controllable manner.     

Pushing the Boundaries of Vinylogous Reactivity: Catalytic Enantioselective Mukaiyama Aldol Reactions of Highly Unsaturated 2‐Silyloxyindoles

The first example of catalytic, enantioselective hypervinylogous Mukaiyama aldol reaction (HVMAR) involving multiply unsaturated 2‐silyloxyindoles is reported. The reaction utilizes a chiral Lewis base‐catalyzed Lewis acid‐mediated technology to deliver homoallylic 3‐polyenylidene 2‐oxindoles with extraordinary levels of regio‐, enantio‐, and geometrical selectivity. This work highlights a subtle yet decisive influence of the indole N‐substituents on the propagation of the vinylogous reactivity space of the donor substrates up to ten bonds away from the origin of the vinylogy effect. Analysis of the ¹³C NMR chemical shifts of the C‐ω remote site within homologous silyloxyindole donors enabled rationalization of the results and easy qualitative prediction of the HVMAR reactivity/inertia toward a given aldehyde acceptor.