Semiempirical determination of Dyson's states in conjugated systems within a full-CI π-electron scheme

The Dyson states as orbitals and geminals describing one- and two-electron detachment processes in molecules are treated within a spin-free formulation of the full configuration interaction (CI) theory. The ensuing computational scheme is presented and some semiempirical calculations on π-shells are given for unsaturated hydrocarbons such as medium-sized polyenes and aromatics. It is shown that in these systems the correlation effects turn out to be more important than the relaxation effects, leading to a marked reduction in the calculated full-CI photoionization crosss ections relative to the Hartree-Fock ones.     

UV/Vis Spectroscopic Properties of <Emphasis Type="Italic">N</Emphasis>-(2′-Hydroxy-4′-<Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>-dimethyl-aminobenzylidene)-4-nitroaniline in Various Solvents and Solid Environments

Summary.  N-(2′-Hydroxy-4′-N,N-dimethylaminobenzylidene)-4-nitroaniline [HDBN] has been used as a model for investigating intra- and intermolecular D–A (donor–acceptor) interactions in various environments by means of UV/Vis spectroscopy. UV/Vis spectra of HDBN have been measured in various solvents, ethanolic solutions of different pH, adsorbed on silica, and in the solid state. A bathochromic shift of ν_max is observed with increasing the dipolarity/polarizability and HBD (hydrogen bond donor) capacity of the solvent, which is described by means of a multiple LSE (linear solvation energy) relationship in terms of the empirical Kamlet-Taft solvent polarity parameters. The adsorption of HDBN on Aerosil^? 300-silica particles in non-HBA (hydrogen bond acceptor) solvents is explained in the same sense. Mobile protons and sol–gel entrapping cause a hypsochromic shift due to protonation of the lone electron pair of the 4′-N,N-dimethylamino group. Hydroxide ions attack the 2′-hydroxy group which causes a bathochromic shift. A strong intramolecular hydrogen bond between the 2′-hydroxyl hydrogen and the imine nitrogen atom is present in the solid-state structure causing an unprecedented bathochromic shift. Corresponding author. E-mail: stefan.spange@chemie.tu-chemnitz.de Received July 8, 2002; accepted (revised) September 30, 2002     

Statistical properties of dynamical systems with singularities

We prove statistical properties of two-dimensional hyperbolic dynamical systems with singularities. Bunimovich, Sinai, and Chernov proved a theorem on the subexponential decay of correlations and a central limit theorem for billiard systems. In this paper we use their techniques to prove the same results for abstract systems.     

Fluctuations in a lévy flight gas

We consider the density fluctuations of an ideal Brownian gas of particles performing Lévy flìghts characterized by the indexf. We find that the fluctuations scale as N(t) t^H, where the Hurst exponentH locks onto the universal value 1/4 for Lévy flights with a finite root-mean-square range (f>2). For Lévy flights with a finite mean range but infinite root-mean-square range (1相似文献   

Order and disorder in the approach to equilibrium of a classical gas

We study the approach to equilibrium of a classical gas. The initial condition corresponds to a Maxwell velocity distribution, but to a nonequilibrium binary correlation. We consider two cases. In the first, there are initially no spatial correlations, while in the second, initial correlations correspond to long-range spatial order. We show that the gas leaves the Maxwell velocity distribution function in the process of building up equilibrium correlations. The spatial correlations in the equilibrium state are seen to emerge from a self-organization process in the gas. Non-Markovian effects play an essential role in this process by coupling the velocity distribution and the binary correlations. For the case of initial long-range correlations we obtain anti-Boltzmann behavior in the evolution of the velocity distribution as the Boltzmann entropy decreases from the nonequilibrium to the equilibrium state. For this case we also have nontrivial behavior on a short time scale due to the non-Markovian effects. The approach used here is based on the theory of subdynamics as developed in previous publications. The results obtained show the interplay between irreversible processes leading to disorder and to order in a classical gas.     

Random-bond Ising chain in a transverse magnetic field: A finite-size scaling analysis

We investigate the zero-temperature quantum phase transition of the randombond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two dimensions with layered disorder. The latter is studied via Monte Carlo simulations and transfer matrix calculations and the critical exponents are determined with a finite-size scaling analysis. The magnetization and susceptibility obey conventional rather than activated scaling. We observe that the order parameter and correlation function probability distribution show a nontrivial scaling near the critical point, which implies a hierarchy of critical exponents associated with the critical behavior of the generalized correlation lengths.     

On the slow decay ofO(2) correlations in the absence of topological excitations: Remark on the Patrascioiu-Seiler model

For spin models withO(2)-invariant ferromagnetic interactions, the Patrascioiu-Seiler constraint is |arg(S(x))–arg(S(y))|₀ for all |x–y|=1. It is shown that in two-dimensional systems of two-component spins the imposition of such contraints with ₀ small enough indeed results in the suppression of exponential clustering. More explicitly, it is shown that in such systems on every scale the spin-spin correlation function obeys S(x)·S(y)1/(2|x–y|²) at any temperature, includingT=. The derivation is along the lines proposed by A. Patrascioiu and E. Seiler, with the yet unproven conjectures invoked there replaced by another geometric argument.Dedicated to Oliver Penrose on the occasion of his 65th birthday.     

Nuclear probes in life sciences

The nuclear quadrupole interaction at metal sites in macromolecules monitored by time differential perturbed angular correlation provides information on the local environment of metal ions residing at these sites. This information is obtained in the ultra-trace regime and is, therefore, extremely valuable for research on reaction pathways of enzymatic heavy metal detoxification, for the development of radiopharmaceuticals, for investigations into protein architectures on surfaces, and for environmental research. This revised version was published online in August 2006 with corrections to the Cover Date.