Semi‐classical formulation of time‐dependent discrete variable representation method

In this article, we apply a novel time‐dependent discrete variable representation (TDDVR) method proposed by Barkakaty and Adhikari to investigate tunneling through an Eckart barrier. This semi‐classical method is theoretically rigorous and straightforward to implement. Among the TDDVR formulations, this report presents the first derivation of a rigorous form of quantum force (QF) for the present perspective. The validity of this semi‐classical approach is demanded based on the excellent agreement of the tunneling probability with the corresponding quantum results. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Exponential stability of discrete-time systems with slowly time-varying delays

Slowly time-varying delays are seldom, but do need to be, considered in the context of discrete-time systems. This paper addresses the exponential stability issue of discrete-time systems with slowly time-varying delays. The basic idea is to transform, by utilizing the switching transformation approach, the original system with slowly time-varying delays into an equivalent switched system with special switching signal. Different types of delays correspond to different types of switching signals, and the stability issue of the original system is converted into that of a switched system. It is the first time that the method of switched homogeneous polynomial Lyapunov function is applied to general delayed systems. Some sufficient exponential stability conditions for the original system are proposed in several situations. It is numerically shown that the conservativeness of the proposed conditions reduces as the degree of the switched homogeneous polynomial Lyapunov function increases.     

Retrieval and chaos in extremely dilutedQ-Ising neural networks

Using a probabilistic approach, the deterministic and the stochastic parallel dynamics of aQ-Ising neural network are studied at finiteQ and in the limitQ. Exact evolution equations are presented for the first time-step. These formulas constitute recursion relations for the parallel dynamics of the extremely diluted asymmetric versions of these networks. An explicit analysis of the retrieval properties is carried out in terms of the gain parameter, the loading capacity, and the temperature. The results for theQ network are compared with those for theQ=3 andQ=4 models. Possible chaotic microscopic behavior is studied using the time evolution of the distance between two network configurations. For arbitrary finiteQ the retrieval regime is always chaotic. In the limitQ the network exhibits a dynamical transition toward chaos.     

Fermionic perturbation theory for the statistical mechanics of the nonlinear Schrödinger model

A fermionic perturbation theory is developed for the statistical mechanics of the nonlinear Schrödinger model. The theory is based on an interacting-fermion picture of the Bethe wave function. The inner product of the Bethe wave function is explicitly evaluated, and a simple graphical representation of it is given. The basic equations obtained for the free energy agree with those of Yang and Yang. In particular, the present theory gives a clear-cut meaning to the function of Yang and Yang: It represents a fermion energy at finite temperatures.     

Ion interaction approach to calculations of volumetric properties of aqueous multiple-solute electrolyte solutions

The ion interaction approach developed by Pitzer was used for the prediction of volumetric properties of mixed electrolyte solutions at 25°C based on parameters calculated from experimental data for single-solute electrolyte solutions. Such an approach was shown to be especially effective for application to the calculation of volumetric properties of natural hypersaline brines and of industrial electrolyte solutions of large complexity. The use of the latest recommended sets of volumetric ion interaction parameters for single electrolyte solutions and symmetrical mixing parameters for Na–K–Cl ion combinations considerably improved the precision of the density calculations of highly concentrated mixed electrolyte solutions and of various natural waters.     

A comparative study of various computational approaches in calculating the structure of pyridoxal 5'-phosphate (PLP)-dependent beta-lyase protein. The importance of protein environment

Various computational approaches, using molecular mechanics (Amber), semiempirical (AM1), density functional (B3LYP), and various ONIOM methods, have been comparatively investigated for the structure of Escherichia coli NifS CsdB protein. The structure of the entire monomer containing 407 amino acid residues and 579 surrounding water molecules has been optimized. The full geometry optimization in the "active site-only" approach (including only active site atoms) has been found to give the largest root-mean-square (RMS) deviation from the X-ray structure; a much better agreement has been achieved by keeping the atoms leading to the backbones of some amino acids frozen in their positions in the X-ray structure. The best agreement has been attained by including the surrounding protein in the calculations using the two-layer ONIOM (B3LYP:Amber) approach. The results presented in this study conclusively demonstrate the importance of the protein/active-site interaction on the active-site structure of the enzyme. The present theoretical study represents the largest system studied at the ONIOM level to date, containing 7992 atoms, including 84 atoms in the QM region and rest in the MM region.     

On the theory of radiative transitions in centrosymmetric complexes

The theory of radiative transitions, in centrosymmetric complexes, is examined in great detail, within the framework of the crystal field method.In connection with radiative transitions, the current method of calculations, with and without invoking closure approximation, are considered from a purely theoretical point of view, by taking advantage of the irreducible tensor method put forward by Griffith.Explicit equations are derived throughout the course of this work to account for the vibronic electric dipole moments, associated with d-d and f-f type of excitations.At high Academy of Pedagogic Sciences, Santiago, Chile.     

Solution of periodic Poisson's equation and the Hartree–Fock approach for solids with extended electron states: Application to linear augmented plane wave method

We formulate a Hartree–Fock‐LAPW method for electronic band structure calculations. The method is based on the Hartree–Fock–Roothaan approach for solids with extended electron states and closed core shells where the basis functions of itinerant electrons are linear augmented plane waves. All interactions within the restricted Hartree–Fock approach are analyzed and in principle can be taken into account. In particular, we obtained the matrix elements for the exchange interactions of extended states and the crystal electric field effects. To calculate the matrix elements of exchange for extended states, we first introduce an auxiliary potential and then integrate it with an effective charge density corresponding to the electron exchange transition under consideration. The problem of finding the auxiliary potential is solved by using the strategy of the full potential LAPW approach, which is based on the general solution of periodic Poisson's equation. Here, we use an original technique for the general solution of periodic Poisson's equation and multipole expansions of electron densities. We apply the technique to obtain periodic potentials of the face‐centered cubic lattice and discuss its accuracy and convergence in comparison with other methods. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Vibronisches Spektralverhalten von Molekülen: XIV. Zum Einfluß der vibronischen Kopplung auf die S0-S1-Absorption und Fluoreszenz von ausgewählten 1,3-Diketonato-bor-komplexen im Rahmen der Herzberg-Teller-Näherung

Summary Based upon completely-optimized S₀ and S₁ molecular geometries the vibrational structures of S₀-S₁ absorption and fluorescence transitions of selected 1,3-diketonato boron complexes being differently substituted, are calculated within the Herzberg-Teller approach taking into account vibronic coupling contributions. In dependence on substituted diketone as well as on the co-ligand, the influence of vibronic coupling and the consequences of intensity borrowing on the spectral behaviour in absorption and fluorescence are found to be quite different for the studied boron complexes. Consequently, for some complexes their spectroscopic properties may be interpreted exclusively by means of the Herzberg-Teller approach. An analysis of the relevant vibrational modes is given.

     

Gold nanoparticle arrays directly grown on nanostructured indium tin oxide electrodes: Characterization and electroanalytical application

This work describes an improved seed-mediated growth approach for the direct attachment and growth of mono-dispersed gold nanoparticles on nanostructured indium tin oxide (ITO) surfaces. It was demonstrated that, when the seeding procedure of our previously reported seed-mediated growth process on an ITO surface was modified, the density of gold nanospheres directly grown on the surface could be highly improved, while the emergence of nanorods was restrained. By field emission scanning electron microscopy (FE-SEM) and cyclic voltammetry, the growth of gold nanoparticles with increasing growth time on the defect sites of nanostructured ITO surface was monitored. Using a [Fe(CN)₆]³⁻/[Fe(CN)₆]⁴⁻ redox probe, the increasingly facile heterogeneous electron transfer kinetics resulting from the deposition and growth of gold nanoparticle arrays was observed. The as-prepared gold nanoparticle arrays exhibited high catalytic activity toward the electrooxidation of nitric oxide, which could provide electroanalytical application for nitric oxide sensing.