Finite jet determination of local analytic CR automorphisms and their parametrization by 2-jets in the finite type case

We show that germs of local real-analytic CR automorphisms of a real-analytic hypersurface M in $\mathbb{C}$² at a point p M are uniquelydetermined by their jets of some finite order at p if and only if M is not Levi-flat near p. This seems to be the first necessary and sufficient result on finite jet determination and the first result of this kind in the infinite type case.If M is of finite type at p, we prove a stronger assertion: the local real-analytic CR automorphisms of M fixing p are analytically parametrized (and hence uniquely determined) by their 2-jets at p. This result is optimal since the automorphisms of the unit sphere are not determined by their 1-jets at a point of the sphere. The finite type condition is necessary since otherwise the needed jet order can be arbitrarily high [Kow1,2], [Z2]. Moreover, we show, by an example, that determination by 2-jets fails for finite type hypersurfaces already in $\mathbb{C)$³.We also give an application to the dynamics of germs of local biholomorphisms of $\mathbb{C)$².     

Graphene-based nano-patch antenna for terahertz radiation

The scattering of terahertz radiation on a graphene-based nano-patch antenna is numerically analyzed. The extinction cross section of the nano-antenna supported by silicon and silicon dioxide substrates of different thickness are calculated. Scattering resonances in the terahertz band are identified as Fabry–Perot resonances of surface plasmon polaritons supported by the graphene film. A strong tunability of the antenna resonances via electrostatic bias is numerically demonstrated, opening perspectives to design tunable graphene-based nano-antennas. These antennas are envisaged to enable wireless communications at the nanoscale.     

Stereo‐ and Regioselective Synthesis of Tricyclic Spirolactones by Diastereoisomeric Differentiation of a Collective Key Precursor

A general, parallel, and collective synthesis of 5/5/5‐ and 5/5/6‐ring fusion topologies of tricyclic spiranoid lactones through the controlled cyclizations of easily accessible, common key precursors is described. The rapid composition of key cycloalkyl methylene precursors yielded an assembly of bicyclic diastereoisomeric iodolactones, which were individually converted into a wide range of tricyclic, angularly fused spiranoid lactones in a regioselective and stereodirected fashion through the diastereoisomeric differentiation of a collective key precursor. The critical stereochemical assignment of the bicyclic starting materials, as well as the tricyclic targets, was confirmed by X‐ray crystal structure determination.     

Self-trapping of the N-H vibrational mode in alpha-helical polypeptides

Recent calculations on the formation of self-trapped amide group vibrational states in alpha-helical polypeptides [J. Chem. Phys. 124, 134907 (2006)] are extended to the amide N-H normal mode vibrations. First, the adiabatic N-H vibrational single- and two-exciton states are examined by treating the longitudinal chain coordinates as parameters. Then, in using the multiconfiguration time-dependent Hartree method coupled exciton-chain vibrational quantum dynamics are accounted for. Based on the respective exciton-chain vibrational wave function propagation the infrared transient absorption related to a sequential pump-probe experiment is calculated. The modulation of local amide vibrational energies by the longitudinal chain coordinates is found to have a pronounced effect on the broadening of absorption lines. Moreover, the ultrafast exciton transfer in the system is studied in order to characterize the dynamics of the self-trapped single-exciton states on a time scale below 10 ps.     

Quadrupolar solvatochromism: 4-amino-phthalimide in toluene

We present calculations of the temperature dependence of the solvent reorganization energy of 4-amino-phthalimide chromophore in quadrupolar toluene. The reorganization energy is a sum of the contributions from quadrupolar and induction solvation. We employ several calculation formalisms in order to evaluate their performance against the experiment. The point-dipole and full atomic distributions of solute charge are compared to show that the point-dipole approximation works well for this chromophore. We also show that most of the reorganization entropy comes from the quadrupolar response. Induction solvation amounts to about 10% of the entropy. Both the reorganization energy and the reorganization entropy are greatly affected by the local solute-solvent density profile (density reorganization) which contributes about half of their values. The induction reorganization energy is strongly affected by the microscopic, nonlocal nature of the density fluctuations of the solvent around the solute.     

Embedded silver ions-containing liposomes in polyelectrolyte multilayers: cargos films for antibacterial agents

A new antibacterial coating made of poly(L-lysine)/hyaluronic acid (PLL/HA) multilayer films and liposome aggregates loaded with silver ions was designed. Liposomes filled with an AgNO 3 solution were first aggregated by the addition of PLL in solution. The obtained micrometer-sized aggregates were then deposited on a PLL/HA multilayer film, playing the role of a spacer with the support. Finally, HA/PLL/HA capping layers were deposited on top of the architecture to form a composite AgNO 3 coating. Release of encapsulated AgNO 3 from this composite coating was followed and triggered upon temperature increase over the transition temperature of vesicles, found to be equal to 34 degrees C. After determination of the minimal inhibitory concentration (MIC) of AgNO 3 in solution, the antibacterial activity of the AgNO 3 coating was investigated against Escherichia coli. A 4-log reduction in the number of viable E. coli cells was observed after contact for 120 min with a 120 ng/cm (2) AgNO 3 coating. In comparison, no bactericidal activity was found for PLL/HA films previously dipped in an AgNO 3 solution and for PLL/HA films with liposome aggregates containing no AgNO 3 solution. The strong bactericidal effect could be linked to the diffusion of silver ions out of the AgNO 3 coating, leading to an important bactericidal concentration close to the membrane of the bacteria. A simple method to prepare antibacterial coatings loaded with a high and controlled amount of AgNO 3 is therefore proposed. This procedure is far superior to that soaking AgNO 3 or Ag nanoparticles into a coating. In principle, other small bactericidal chemicals like antibiotics could be encapsulated by this method. This study opens a new route to modify surfaces with small solutes that are not permeating phospholipid membranes below the phase transition temperature.     

Dynamical arrest of electron transfer in liquid crystalline solvents

We argue that electron transfer reactions in slowly relaxing solvents proceed in the nonergodic regime, making the reaction activation barrier strongly dependent on the solvent dynamics. For typical dielectric relaxation times of polar nematics, electron transfer reactions in the subnanosecond time scale fall into nonergodic regime in which nuclear solvation energies entering the activation barrier are significantly lower than their thermodynamic values. The transition from isotropic to nematic phase results in weak discontinuities of the solvation energies at the transition point and the appearance of solvation anisotropy weakening with increasing solute size. The theory is applied to analyze experimental kinetic data for the electron transfer kinetics in the isotropic phase of 5CB liquid crystalline solvent. We predict that the energy gap law of electron transfer reactions in slowly relaxing solvents is characterized by regions of fast change of the rate at points where the reaction switches between the ergodic and nonergodic regimes. The dependence of the rate on the donor-acceptor separation may also be affected in a way of producing low values for the exponential falloff parameter.     

Iron(III) dihydrogenphosphate(I)

The structure of rhombohedral (R) iron(III) tris­[di­hydrogen­phosphate(I)] or iron(III) hypophosphite, Fe(H₂PO₂)₃, has been determined by single‐crystal X‐ray diffraction. The structure consists of [001] chains of Fe³⁺ cations in octa­hedral sites with symmetry bridged by bidentate hypophosphite anions.     

Synthesis, molecular structure, and reactivity of the isolable silylenoid with a tricoordinate silicon

The first tricoordinate fluorosilylenoid, (t-Bu2MeSi)2SiFLi.3THF (1), was synthesized, and its X-ray molecular structure was determined. 1 was synthesized in 40% yield by a bromine-lithium exchange reaction in THF of the corresponding fluorobromosilane with t-Bu2MeSiLi. 1 is best described as an R2SiF- anion attracted to a (Li.3THF)+ cation with a small contribution of resonance structure that consists of a silylene fragment and FLi.3THF. 1 reacts as a nucleophile with MeCl, PhH2SiCl, H2O, and MeOH, as an electrophile with MeLi, and as a silylene with Li (or t-BuLi) and Na, yielding alpha-lithium and alpha-sodium silyl radicals, respectively. Either photolysis or thermolysis of 1 yields the corresponding disilene R2Si=SiR2 (R = t-Bu2MeSi), probably via dimerization of R2Si:.     

UHV STM I(V) and XPS studies of aryl diazonium molecules assembled on Si(111)

Molecular layers formed from 4-trifluoromethylbenzenediazonium tetrafluoroborate and 4-Methylbenzenediazonium tetrafluoroborate have been assembled on H-passivated Si(111) and studied by UHV STM and XPS. STM imaging shows well-developed Si(111) step edges and terraces both on Si(111):H and Si(111) substrates covered with a molecular layer. STM I(V) data acquired at different tip-substrate separations reveals a factor of approximately 10 enhancement in current for positive bias voltage when current flows through the 4-trifluoromethyl molecule when compared to the 4-methyl variant. The observed current enhancement in I(V) can be understood by comparing the projected density of states of the two molecule-Si systems calculated using a density functional theory local density approximation after geometry optimization was performed via the conjugate gradient method. XPS data independently confirm that H-passivated Si(111) remains oxygen free for short exposures to ambient conditions and provide evidence that the molecules chemically react with the silicon surface.