Uniform separation of points and measures and representation by sums of algebras

LetX andY _i, 1 ≦i ≦k, be compact metric spaces, and letρ _i:X →Y _i be continuous functions. The familyF={ρ _i} _i ^1/k is said to be ameasure separating family if there exists someλ > 0 such that for every measureμ inC(X)*, ‖μ ^o ρ _i ^?1 ‖ ≧λ ‖μ ‖ holds for some 1 ≦i ≦k.F is auniformly (point) separating family if the above holds for the purely atomic measures inC(X)*. It is known that fork ≦ 2 the two concepts are equivalent. In this note we present examples which show that fork ≧ 3 measure separation is a stronger property than uniform separation of points, and characterize those uniformly separating families which separate measures. These properties and problems are closely related to the following ones: letA ₁,A ₂, ...,A _k be closed subalgebras ofC(X); when isA ₁ +A ₂ + ... +A _k equal to or dense inC(X)?     

Magnetization dynamics in arrays of strongly interacting magnetic nanocrystals

Arrays of 6.6 nm iron oxide nanocrystals coated with fatty acid molecules were produced using the Langmuir-Blodgett technique. The arrays had a varying number of layers stacked together, going from two dimensional to three dimensional and two different in-plane interparticle separations. While temperature-dependent ac susceptibility measurements of the isolated nanocrystals obeyed the Neel-Brown relaxation law, the array relaxation deviated significantly from this simple law. This deviation together with the observed dc field influence on the susceptibility-temperature curves, the large shifts in blocking temperatures and reduction in susceptibility-temperature curve widths on going from isolated particles to the arrays indicated collective magnetization dynamics during magnetization freezing. A scaling law analysis of this freezing dynamics yielded different powers for the two different interparticle separations with no dependence on dimensionality. In spite of the spin-glass-like behavior, it is possible that small, magnetically ordered domains of nanocrystals form at low temperature.     

Coherence spectroscopy in dissipative media: a Liouville space pathway approach

We address the possibility of using coherent control tools to extract useful information about the interaction of a system with a dissipative environment. To that end we extend previous work, which developed a coherence spectroscopy based on two-pathway excitation phase control, from the isolated molecule limit to dense media. Specifically, we explore the properties of the channel phase, an observable of energy-domain two-pathway excitation experiments that was shown in the isolated molecule limit to carry information about the phase properties of the material system. Our analysis is based on the combination of steady state and time-dependent analytical perturbative approaches within the density matrix formalism, complemented by nonperturbative numerical simulations. We find that the channel phase carries significantly richer information in the presence of decoherence mechanisms than in their absence. In particular, rescattering events in the structured continuum introduce new features in the channel phase spectrum, whose structure conveys information about both the molecular continuum and the system bath interaction.     

Noncovalent synthesis in aqueous solution and spectroscopic characterization of multi-porphyrin complexes

The interactions of the tetracationic meso-tetrakis(N-methyl-4-pyridyl)porphyrin (H(2)TMPyP) and its metallo derivatives (MTMPyP) (where M=copper(II), zinc(II), and gold(III) with the octa-anionic form (at neutral pH) of 5,11,17,23-tetrasulfonato-25,26,27,28-tetrakis(hydroxycarbonylmethoxy)calix[4]arene (C(4)TsTc) lead to a series of complex species whose stoichiometry and porphyrin sequence can be easily tuned. Crystallographic, spectroscopic, and diffusion NMR studies converge towards a common picture in which a central 1:4 porphyrin/calixarene unit serves as a template for the formation of more complex species. These species arise by successive, stepwise addition of single porphyrin molecules above and below the plane of the 1:4 central core to ultimately give a 7:4 complex. Noticeably, the stoichiometry of the various complex species corresponds to the actual concentration ratio of porphyrins and calixarenes in solution allowing the stoichiometry of these species to be easily tuned. This behavior and the remarkable stability of these species allow homo-porphyrin and hetero-(metallo)porphyrin species to be formed with control of not only the stoichiometry but also the sequence of the porphyrin array. The flexibility and ease of this approach permit, in principle, the design and synthesis of porphyrin arrays for predetermined purposes. For example, we have shown that it is very easy to design and obtain mixed porphyrin species in which a foreseen photoinduced electron-transfer is indeed observed.     

Theory of current-induced dynamics in molecular-scale devices

We develop a theoretical framework for the study of inelastic resonant transport and current-driven dynamics in molecular nanodevices. Our approach combines a Born-Oppenheimer solution of the coordinate-, energy-, and voltage-dependent self-energy with a time-dependent scattering solution of the vibrational dynamics. The formalism is applied to two classic problems in current-triggered dynamics. As a simple example of bound-bound events in the nuclear subspace we study the problem of current-induced oscillations in Au-C60-Au heterojunctions. As a well-studied example of bound-free events in the nuclear subspace we revisit the problem of scanning-tunneling-microscopy-triggered H-atom desorption from a Si(100) surface. Our numerical results are supported by a simple analytically soluble model.     

Anions and Polyanions of Oligoindenopyrenes: Modes of Electron Delocalization and Dimerization

A series of pyrene‐based polycyclic aromatic compounds, indeno[cd]pyrene, diindeno[cd,fg]pyrene, diindeno[cd,jk]pyrene, tris‐(tert‐butylindeno[cd,fg,jk])pyrene, and tetrakis‐(tert‐butylindeno[cd,fg,jk,mn])pyrene, were reduced with alkali metals in [D₈]tetrahydrofuran, and the resulting anions were studied by NMR spectroscopy. It was found that the diatropic character of the dianions obtained depends on the number of annulated indeno groups. When one such group is present, a paratropic dianion is obtained, which is similar to the dianion of the parent pyrene; the effect, however, is weak. When more indeno groups are annulated, the dianions become diatropic owing to the greater number of five‐membered rings that can acquire aromatic character as a result of reduction. The ¹H NMR chemical shifts of tetrakis‐(tert‐butylindeno[cd,fg,jk,mn])pyrene in the neutral state show an interesting dependence on concentration that reflects an association of the molecules in solution by π stacking. This phenomenon was not observed for the reduced species. The trianion radicals of tris‐(tert‐butylindeno[cd,fg,jk])pyrene and tetrakis‐(tert‐butylindeno[cd,fg,jk,mn])pyrene undergo reductive dimerization and form bilayered hexaanions.     

Theory of time-resolved photoelectron imaging. Comparison of a density functional with a time-dependent density functional approach

Time-resolved photoelectron differential cross sections are computed within a quantum dynamical theory that combines a formally exact solution of the nuclear dynamics with density functional theory (DFT)-based approximations of the electronic dynamics. Various observables of time-resolved photoelectron imaging techniques are computed at the Kohn-Sham and at the time-dependent DFT levels. Comparison of the results serves to assess the reliability of the former method and hence its usefulness as an economic approach for time-domain photoelectron cross section calculations, that is applicable to complex polyatomic systems. Analysis of the matrix elements that contain the electronic dynamics provides insight into a previously unexplored aspect of femtosecond-resolved photoelectron imaging.     

Ab initio study of the alternating current impedance of a molecular junction

The small-bias conductance of the C6 molecule, stretched between two metallic leads, is studied using time-dependent density functional theory within the adiabatic local density approximation. The leads are modeled by jellium slabs, the electronic density and the current density are described on a grid, whereas the core electrons and the highly oscillating valence orbitals are approximated using standard norm-conserving pseudopotentials. The jellium leads are supplemented by a complex absorbing potential that serves to absorb charge reaching the edge of the electrodes and hence mimic irreversible flow into the macroscopic metal. The system is rapidly exposed to a ramp potential directed along the C6 axis, which gives rise to the onset of charge and current oscillations. As time progresses, a fast redistribution of the molecular charge is observed, which translates into a direct current response. Accompanying the dc signal, alternating current fluctuations of charge and currents within the molecule and the metallic leads are observed. These form the complex impedance of the molecule and are especially strong at the plasmon frequency of the leads and the lowest excitation peak of C6. We study the molecular conductance in two limits: the strong coupling limit, where the edge atoms of the chain are submerged in the jellium and the weak coupling case, where the carbon atoms and the leads do not overlap spatially.