Stacking effect of polyfluorene on the chemical shift and electron transport

We investigate the structures, NMR chemical shifts, absorption spectra, frontier molecular orbitals, and transition density matrices of pi-stacked polyfluorenes by ab initio calculations. For F1-F4, we consider two different conformations, syn and anti. The simulated 1H NMR chemical shifts are in good agreement with the previous experiment, and the significantly upfielded chemical shifts explain that the fluorene moieties are stacked on each other. It is found that the relative stability for syn and anti conformers is almost equivalent in B3LYP calculations; however, the syn conformer becomes much more stable than the anti conformer in MP2 calculations, which is consistent with the experimental finding that only the syn conformers are relevant. The vertical detachment energy, which is linearly proportional to the ionization potential, shows the same size dependence as the previous experiment. The electron attachment energy decreases exponentially as the size increases, which implies that the electron transport would be possible even for long chains such as F3 and F4. This was evident from the frontier molecular orbitals (HOMO and LUMO). Also, it is found that the syn conformers are very favorable for electron transport through the pi-stacked fluorene moieties.     

Coherent low-frequency motions of hydrogen bonded acetic acid dimers in the liquid phase

Ultrafast vibrational dynamics of cyclic hydrogen bonded dimers and the underlying microscopic interactions are studied in temporally and spectrally resolved pump-probe experiments with 100 fs time resolution. Femtosecond excitation of the O-H and/or O-D stretching mode gives rise to pronounced changes of the O-H/O-D stretching absorption displaying both rate-like kinetic and oscillatory components. A lifetime of 200 fs is measured for the v=1 state of the O-H stretching oscillator. The strong oscillatory absorption changes are due to impulsively driven coherent wave packet motions along several low-frequency modes of the dimer between 50 and 170 cm(-1). Such wave packets generated via coherent excitation of the high-frequency O-H/O-D stretching oscillators represent a clear manifestation of the anharmonic coupling of low- and high-frequency modes. The underdamped low-frequency motions dephase on a time scale of 1-2 ps. Calculations of the vibrational potential energy surface based on density functional theory give the frequencies, anharmonic couplings, and microscopic elongations of the low-frequency modes, among them intermolecular hydrogen bond vibrations. Oscillations due to the excitonic coupling between the two O-H or O-D stretching oscillators are absent as is independently confirmed by experiments on mixed dimers with uncoupled O-H and O-D stretching oscillators.     

Quantum extension of the Jarzynski relation: analogy with stochastic dephasing

The relation between the distribution of work performed on a classical system by an external force switched on an arbitrary time scale and the corresponding equilibrium free energy difference is generalized to quantum systems. Using the adiabatic representation, we show that this relation holds for isolated systems as well as for systems coupled to a bath described by a master equation. A close formal analogy is established between the present "classical trajectory" picture over populations of adiabatic states and phase fluctuations (dephasing) of a quantum coherence in spectral line shapes, described by the stochastic Liouville equation.     

Characterizations of natural exponential families with power variance functions by zero regression properties

Summary Series of new characterizations by zero regression properties are derived for the distributions in the class of natural exponential families with power variance functions. Such a class of distributions has been introduced in Bar-Lev and Enis (1986) in the context of an investigation of reproductible exponential families. This class is broad and includes the following families: normal, Poisson-type, gamma, all families generated by stable distributions with characteristic exponent an element of the unit interval (among these are the inverse Gaussian, Modified Bessel-type, and Whittaker-type distributions), and families of compound Poisson distributions generated by gamma variates. The characterizations by zero regression properties are obtained in a unified approach and are based on certain relations which hold among the cumulants of the distributions in this class. Some remarks are made indicating how the techniques used here can be extended to obtain characterizations of general exponential families.The work of this author was performed while he was a visitor in the Department of Statistics, State University of New York at Buffalo     

A model for isotope separation via molecular multiphoton photodissociation

Multiphoton photofragmentation of an “isolated” molecule on the lowest potential surface is considered in terms of a truncated anharmonic oscillator driven by a pulsed, intense laser field. Intramolecular vibrational relaxation and indirect photodissociation are accounted for by assignment of decay widths to the appropriate levels. The effective-hamiltonian formalism is applied to derive explicit expressions for the photofragmentation yield and for the isotopic separation factor.     

Continuity Corrections for Discrete Distributions Under the Edgeworth Expansion

The approximation of discrete distributions by Edgeworth expansion series for continuity points of a discrete distribution F _n implies that if t is a support point of F _n, then the expansion should be performed at a continuity point . When a value is selected to improve the approximation of , and especially when a single term of the expansion is used, the selected is defined to be a continuity correction. This paper investigates the properties of the approximations based on several terms of the expansion, when is the value at which the infimum of a residual term is attained. Methods of selecting the estimation and the residual terms are investigated and the results are compared empirically for several discrete distributions. The results are also compared with the commonly used approximation based on the normal distribution with . Some numerical comparisons show that the developed procedure gives better approximations than those obtained under the standard continuity correction technique, whenever is close to 0 and 1. Thus, it is especially useful for p-value computations and for the evaluation of probabilities of rare events.     

Effect of quantum collapse on the distribution of work in driven single molecules

Two sources of quantum deviations from Jarzynski's celebrated classical relation between the free energy change and the distribution of work are analyzed using an exactly solvable harmonic model: Quantum dynamics retains the Gaussian profile of the distribution and merely gives rise to analytic corrections in variant Planck's over 2pi, whereas quantum measurements (wave function collapse) induce extended power-law tails which fundamentally alter the distribution. These results may be observed in quantum information processing and in experiments involving mechanically or optically driven single quantum objects.     

Criterion for phase separation in one-dimensional driven systems

A general criterion for the existence of phase separation in driven density-conserving one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steady-state currents of domains in the system. A quantitative criterion for the existence of phase separation is conjectured using a correspondence made between driven diffusive models and zero-range processes. The criterion is verified in all cases where analytical results are available, and predictions for other models are provided.