Electron-phonon interaction in atomic-scale conductors: Einstein oscillators versus full phonon modes

Two extreme pictures of electron-phonon interactions in nanoscale conductors are compared: one in which the vibrations are treated as independent Einstein atomic oscillators, and one in which electrons are allowed to couple to the full, extended phonon modes of the conductor. It is shown that, under a broad range of conditions, the full-mode picture and the Einstein picture produce essentially the same net power at any given atom in the nanojunction. The two pictures begin to differ significantly in the limit of low lattice temperature and low applied voltages, where electron-phonon scattering is controlled by the detailed phonon energy spectrum. As an illustration of the behaviour in this limit, we study the competition between trapped vibrational modes and extended modes in shaping the inelastic current-voltage characteristics of one-dimensional atomic wires.

A critical evaluation of Raman spectroscopy for the analysis of lipids: fatty acid methyl esters.

The work presented here is aimed at determining the potential and limitations of Raman spectroscopy for fat analysis by carrying out a systematic investigation of C-4-C-24 FAME. These provide a simple, well-characterized set of compounds in which the effect of making incremental changes can be studied over a wide range of chain lengths and degrees of unsaturation. The effect of temperature on the spectra was investigated over much larger ranges than would normally be encountered in real analytical measurements. It was found that for liquid FAME the best internal standard band was the carbonyl stretching vibration nu(C = O), whose position is affected by changes in sample chain length and physical state; in the samples studied here, it was found to lie between 1729 and 1748 cm(-1). Further, molar unsaturation could be correlated with the ratio of the nu(C = O) to either nu(C = C) or delta(H-C = ) with R-2 > 0.995. Chain length was correlated with the delta(CH2)(tw)/nu(C = O) ratio, (where "tw" indicates twisting) but separate plots for odd- and even-numbered carbon chains were necessary to obtain R-2 > 0.99 for liquid samples. Combining the odd- ani even-numbered carbon chain data in a single plot reduced the correlation to R-2 = 0.94-0.96, depending on the band ratios used. For molal unsaturation the band ratio that correlated linearly with unsaturation (R-2 > 0.99) was nu(C = C)/delta(CH2)(SC) (where "sc" indicates scissoring). Other band ratios show much more complex behavior with changes in chemical and physical structure. This complex behavior results from the fact that the bands do not arise from simple vibrations of small, discrete regions of the molecules but are due to complex motions of large sections of the FAME so that making incremental changes in structure does not necessarily lead to simple incremental changes in spectra.

A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol–Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge–Kutta method. The presence of chaotic limit cycles is pointed out.

Positive dilations of piecewise monotonic Markov maps

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.

Resonances of the cusp family

We study a family of chaotic maps with limit cases-the tent map and the cusp map (the cusp family). We discuss the spectral properties of the corresponding Frobenius-Perron operator in different function spaces including spaces of analytical functions and study numerically the eigenvalues and eigenfunctions.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

Resonance Raman and DFT studies of tetra-tert-butyl porphine: Assignment of strongly enhanced distortion modes in a ruffled porphyrin

The free-base form of tetra-tert-butyl porphine (TtBP), which has extremely bulky meso substituents, is severely distorted from planarity, with a ruffling angle of 65.5degrees. The resonance Raman spectrum of TtBP (lambda(ex) = 457.9 nm) and its d(2), d(8), and d(10) isotopomers have been recorded, and while the spectra show high-frequency bands similar to those observed for planar meso-substituted porphyrins, there are several additional intense bands in the low-frequency region. Density functional calculations at the B3-LYP/6-31G(d) level were carried out for all four isotopomers, and calculated frequencies were scaled using a single factor of 0.98. The single factor scaling approach was validated on free base porphine where the RMS error was found to be 14.9 cm(-1). All the assigned bands in the high-frequency (> 1000 cm(-1)) region of TtBP were found to be due to vibrations similar in character to the in-plane skeletal modes of conventional planar porphyrins. In the low-frequency region, two of the bands, assigned as nu(8) (ca. 330 cm(-1)) and nu(16) (ca. 540 cm(-1)), are also found in planar porphyrins such as tetra-phenyl porphine (TPP) and tetra-iso-propyl porphine (IPP). Of the remaining three very strong bands, the lowest frequency band was assigned as gamma(12) (pyr swivel, obsd 415 cm(-1), calcd 407 cm(-1) in do). The next band, observed at 589 cm-1 in the do compound (calcd 583 cm(-1)), was assigned as a mode whose composition is a mixture of modes that were previously labeled gamma(13) (gamma(CmCaHmCa)) andy gamma(11) (pyr fold(asym)) in NiOEP. The final strong band, observed at 744 cm(-1) (calcd 746 cm(-1)), was assigned to a mode whose composition is again a mixture of gamma(11) and gamma(13), although here it is gamma(11) rather than gamma(13) which predominates. These bands have characters and positions similar to those of three of the four porphyrin ring-based, weak bands that have previously been observed for NiTPP. In addition there are several weaker bands in the TtBP spectra that are also

Quantum chessboards in the deuterium molecular ion

We present a new algorithm for vibrational control in deuterium molecules that is feasible with current experimental technology. A pump mechanism is used for creating a coherent superposition of the D-2(+) vibrations. A short, intense infrared control pulse is applied after a chosen delay time to create selective interferences. A 'chessboard' pattern of states can be realized in which a set of even- or odd-numbered vibrational states can be selectively annihilated or enhanced. A technique is proposed for experimental realization and observation of this effect using 5 fs pulses of lambda = 790 nm radiation, with intermediate intensity (5 x 10(13) W cm(-2)).

Self-consistent geometry in the computation of the vibrational spectra of molecules

An exact and general approach to study molecular vibrations is provided by the Watson Hamiltonian. Within this framework, it is customary to omit the contribution of the terms with the vibrational angular momentum and the Watson term, especially for the study of large systems. We discover that this omission leads to results which depend on the choice of the reference structure. The self-consistent solution proposed here yields a geometry that coincides with the quantum averaged geometry of the Watson Hamiltonian and appears to be a promising way for the computation of the vibrational spectra of strongly anharmonic systems.

Fully fluorinated imidodiphosphinate shells for visible- and NIR-Emitting lanthanides: Hitherto unexpected effects of sensitizer fluorination on lanthanide emission properties

In this paper we demonstrate that the effect of aromatic C-F substitution in ligands does not always abide by conventional wisdom for ligand design to enhance sensitisation for visible lanthanide emission, in contrast with NIR emission for which the same effect coupled with shell formation leads to unprecedented long luminescence lifetimes. We have chosen an imidodiphosphinate ligand, N-{P,P-di-(pentafluorophinoyl)}-P,P-dipentafluoro-phenylphosphinimidic acid (HF(20)tpip), to form ideal fluorinated shells about all visible- and NIR-emitting lanthanides. The shell, formed by three ligands, comprises twelve fully fluorinated aryl sensitiser groups, yet no-high energy X-H vibrations that quench lanthanide emission. The synthesis, full characterisation including X-ray and NMR analysis as well as the photophysical properties of the emissive complexes [Ln(F(20)tpip)(3)], in which Ln=Nd, Sm, Eu, Gd, Tb, Dy, Er, Yb, Y, Gd, are reported. The photophysical results contrast previous studies, in which fluorination of alkyl chains tends to lead to more emissive lanthanide complexes for both visible and NIR emission. Analysis of the fluorescence properties of the HF(20)tpip and [Gd(F(20)tpip)(3)] reveals that there is a low-lying state at around 715 nm that is responsible for partially quenching of the signal of the visible emitting lanthanides and we attribute it to a pi-sigma* state. However, all visible emitting lanthanides have long lifetimes and unexpectedly the [Dy(F(20)tpip)(3)] complex shows a lifetime of 0.3 ms, indicating that the elimination of high-energy vibrations from the ligand framework is particularly favourable for Dy. The NIR emitting lanthanides show strong emission signals in powder and solution with unprecedented lifetimes. The luminescence lifetimes of [Nd(F(20)tpip)(3)], [Er(F(20)tpip)(3)] and [Yb(F(20)tpip)(3)] in deuteurated acetonitrile are 44, 741 and 1111 mu s. The highest value observed for the [Yb(F(20)tpip)(3)] complex is more than half the value of the Yb ion radiative lifetime.

Long-lived near-infrared luminescent lanthanide complexes of imidodiphosphinate

Near-infrared emitting complexes of Nd(III), Er(III), and Yb(III) based on hexacoordinate lanthanide ions with an aryl functionalized imidodiphosphinate ligand, tpip, have been synthesized and fully characterized. Three tpip ligands form a shell around the lanthanide with the ligand coordinating via the two oxygens leading to neutral complexes, Ln(tpip)(3). In the X-ray crystal structures of Er(III) and Nd(III) complexes there is evidence of CH-pi interactions between the phenyl groups. Photophysical investigations of solution samples of the complexes demonstrate that all complexes exhibit relatively long luminescence lifetimes in nondeuteurated solvents. Luminescence studies of powder samples have also been recorded for examination of the properties of NIR complexes in the solid state for potential material applications. The results underline the effective shielding of the lanthanide by the twelve phenyl groups of the tpip ligands and the reduction of high-energy vibrations in close proximity to the lanthanide, both features important in the design of NIR emitting lanthanide complexes.

On the treatment of singularities of the Watson Hamiltonian for nonlinear molecules

The applicability of the Watson Hamiltonian for the description of nonlinear molecules—especially triatomic ones—has always been questioned, as the Jacobian of the transformation that leads to the Watson Hamiltonian, vanishes at the linear configuration. This results in singular behavior of the Watson Hamiltonian, giving rise to serious numerical problems in the computation of vibrational spectra, with unphysical, spurious vibrational states appearing among the physical vibrations, especially in the region of highly excited states. In this work, we analyze the problem and propose a simple way to confine the nuclear wavefunction in such a way that the spurious solutions are eliminated. We study the water molecule and observe an improvement compared with previous results. We also apply the method to the van der Walls molecule XeHe2.

Resonant positron annihilation in ammonia

Positron annihilation in ammonia is analyzed using the framework of resonant annihilation [G. F. Gribakin and C. M. R. Lee, Phys. Rev. Lett. 97, 193201 (2006)]. In particular, we show that molecular rotations can have a measurable e?ect on the annihilation rates at room temperatures. Rotation leads to broadening of vibrational Feshbach resonances. Rotations also allow a distinct contribution at low positron energies in the form of a rotational Feshbach resonance. This resonance can enhance the annihilation rate for thermalized room-temperature positrons. Comparison of theory and experiment shows that overtone and combination vibrations, including those due to inversion doubling, likely play an important role.

Application of the zero-range potential model to positron annihilation on molecules

In this paper we use a zero-range potential (ZRP) method to model positron interaction with molecules. This allows us to investigate the e?ect of molecular vibrations on positron–molecule annihilation using the van der Waals dimer Kr2 as an example. We also use the ZRP to explore positron binding to polyatomics and examine the dependence of the binding energy on the size of the molecule for alkanes. We ?nd that a second bound state appears for a molecule with ten carbons, similar to recent experimental evidence for such a state emerging in alkanes with twelve carbons.

Mixing of dielectronic and multiply-excited states in electron-ion recombination: a study of Au24+

It has been suggested (Gribakin et al 1999 Aust. J. Phys. 52 443–57, Flambaum et al 2002 Phys. Rev. A 66 012713) that strongly enhanced low-energy electron recombination observed in Au25+ (Hoffknecht et al 1998 J. Phys. B: At. Mol. Opt. Phys. 31 2415–28) is mediated by complex multiply excited states, while simple dielectronic excitations play the role of doorway states for the electron capture process. We present the results of an extensive study of con?guration mixing between doubly excited (doorway) states and multiply excited states which account for the large electron recombination rate on Au25+ . A detailed analysis of spectral statistics and statistics of eigenstate components shows that the dielectronic doorway states are virtually ‘dissolved’ in complicated chaotic multiply excited eigenstates. This work provides a justi?cation for the use of statistical theory to calculate the recombination rates of Au25+ and similar complex multiply charged ions. We also investigate approaches which allow one to study complex chaotic many-body eigenstates and criteria of strong con?guration mixing, without diagonalizing large Hamiltonian matrices.