Dynamical effects of a one-dimensional multibarrier potential of finite range

We discuss the properties of a large number N of one-dimensional (bounded) locally periodic potential barriers in a finite interval. We show that the transmission coefficient, the scattering cross section σ, and the resonances of σ depend sensitively upon the ratio of the total spacing to the total barrier width. We also show that a time dependent wave packet passing through the system of potential barriers rapidly spreads and deforms, a criterion suggested by Zaslavsky for chaotic behaviour. Computing the spectrum by imposing (large) periodic boundary conditions we find a Wigner type distribution. We investigate also the S-matrix poles; many resonances occur for certain values of the relative spacing between the barriers in the potential. Received 1st August 2001 and Received in final form 18 November 2001     

Stable solution of tridiagonal systems

In this paper we present three different pivoting strategies for solving general tridiagonal systems of linear equations. The first strategy resembles the classical method of Gaussian elimination with no pivoting and is stable provided a simple and easily checkable condition is met. In the second strategy, the growth of the elements is monitored so as to ensure backward stability in most cases. Finally, the third strategy also uses the right‐hand side vector to make pivoting decisions and is proved to be unconditionally backward stable. This revised version was published online in August 2006 with corrections to the Cover Date.     

Chemical turbulence and standing waves in a surface reaction model: The influence of global coupling and wave instabilities

Among heterogeneously catalyzed chemical reactions, the CO oxidation on the Pt(110) surface under vacuum conditions offers probably the greatest wealth of spontaneous formation of spatial patterns. Spirals, fronts, and solitary pulses were detected at low surface temperatures (T<500 K), in line with the standard phenomenology of bistable, excitable, and oscillatory reaction-diffusion systems. At high temperatures (T greater, similar 540 K), more surprising features like chemical turbulence and standing waves appeared in the experiments. Herein, we study a realistic reaction-diffusion model of this system, with respect to the latter phenomena. In particular, we deal both with the influence of global coupling through the gas phase on the oscillatory reaction and the possibility of wave instabilities under excitable conditions. Gas-phase coupling is shown to either synchronize the oscillations or to yield turbulence and standing structures. The latter findings are closely related to clustering in networks of coupled oscillators and indicate a dominance of the global gas-phase coupling over local coupling via surface diffusion. In the excitable regime wave instabilities in one and two dimensions have been discovered. In one dimension, pulses become unstable due to a vanishing of the refractory zone. In two dimensions, turbulence can also emerge due to spiral breakup, which results from a violation of the dispersion relation.     

Overtone spectroscopy of C-H ethyl stretches of 1-butyne

Room-temperature photoacoustic (PA) spectra and jet-cooled action spectra of the first to third overtone regions of the ethyl C-H stretches in vapor phase 1-butyne, CH3CH2C[Triple Bond]C-H, were measured. Both the PA and action spectra exhibit a complex multiple peak structure being better resolved and more pronounced in the latter, due to inhomogeneous structure reduction. The observed manifolds were analyzed in terms of a simplified joint local-/normal-mode (LM/NM) model accounting for two types of C-H stretches (methyl and methylene) and for Fermi resonances between stretches and deformations. The retrieved parameters, used for calculation of the eigenstates, come from the best-fit parameters based on the diagonalization of the vibrational Hamiltonian in the LM/NM basis. The parameters were obtained by comparing the eigenvalues and the sum of the squares of the expansion coefficients of the eigenvectors of the C-H stretches of methyl and methylene to the action spectra peak positions and intensities, respectively. This approximate model vibrational Hamiltonian is proposed to explain most observed spectral features, corresponding to C-H stretch bands and to combinations of C-H stretches and deformations, indicating the importance of the Fermi resonance. The model was also applied to calculate the dynamics of the C-H stretching modes resulting from coupling with the deformations, implying rapid initial state decay on subpicosecond time scale. Decays of several picoseconds were found for complete transfer of probability from the initially prepared state of methylene and methyl to the counterpart LM states.     

Evidence for new bands in the 3nu1 and 4nu1 regions of propyne

Vibrationally mediated photodissociation and room-temperature photoacoustic (PA) spectroscopy have been used for obtaining action (monitoring the yield of H photofragments) and absorption spectra of the second (3nu(1)) and third (4nu(1)) C-H acetylenic stretches overtone regions in propyne. The band contours appearing in these regions seem mostly regular even though they are perturbed, as expressed by the origin shifts in different K components, splitting of the K structure, and splitting due to resonances between neighboring states. Symmetric rotor simulations of the band contours of the PA and action spectra allowed extraction of the molecular parameters and rough estimates for the homogeneous broadening arising from energy flow to the bath vibrational states. We particularly benefited from the reduced congestion in the jet-cooled action spectra and their simulations, which enabled observation of yet unknown features in the vicinity of the 3nu(1) and 4nu(1) states. Particularly, the emergence of the new state in the 3nu(1) region was confirmed by the action spectra monitored at several differing jet temperatures, suggesting that it is a dark state in IR vibrational excitation that becomes brighter in UV excitation to the upper electronic state. The monitored and Gaussian-fitted Doppler profiles point to the release of H photofragments with low average translational energies, attributed to an indirect dissociation process occurring after internal conversion to the ground electronic state and isomerization to allene.     

Stereoselective reduction of new fused azoninones with a bridgehead nitrogen

The synthesis of methanothienoazoninones 5a,b is described starting from 2(3)-halogenomethylthio-phenes. Their reduction with sodium borohydride led to the corresponding aminoalcohols 6a,b with a complete stereoselectivity.     

Stereoselective radical reactions

For many years, the reputed lack of selectivity in some free-radical reactions has resulted in this class of reaction being overlooked in the stereoselective synthesis of important target molecules. More recently, however, the situation has changed as new and milder methods of radical generation have been developed, which have helped researchers to gain a better understanding of the key factors that influence selectivity in radical transformations. As a consequence, the use of radicals in stereoselective synthesis is increasing and there are a number of important intra- and intermolecular additions, where high levels of stereoselectivity have been achieved in the formation of carbon-carbon bonds.     

Photodissociation from an in-plane rotation in water as a direct probe of dynamics

The state-to-state photodissociation at 193 nm of the initially prepared in-plane rotational state, 3₀₃, of the fundamental symmetric stretch of water, H₂O, (1,0,0), is studied. Stimulated Raman excitation and coherent anti-Stokes Raman scattering prepare and detect respectively the single rotational state of H₂O (1,0,0). Laser-induced fluorescence and Doppler polarization spectroscopy determine the rotational distribution and the vector correlations respectively of the OH photofragment resulting from the photodissociation of the specific rovibrational state. The distribution is structured and the Λ-doublet ratio in the two spin-orbit states shows preference of the A″ component. The correlations are close to the maximum attainable values expected for an idealized orientation in which the transition dipole moment of the parent is parallel to the fragment angular momentum and perpendicular to its velocity. This shows that experiments which prepare the parent molecule in a particular state before a second laser dissociates it provide a powerful means for molecular dynamics.     

Determining the vibrational pattern via overtone cold spectra: C-H methyl stretches of propyne

Vibrationally mediated photodissociation and photoacoustic (PA) spectroscopy were employed for studying the intramolecular dynamics of propyne initially excited to the first through fourth overtone of methyl C-H stretching modes. Room-temperature PA and jet-cooled action spectra, monitoring the absorption of the parent and the yield of the ensuing H photofragments, respectively, were obtained. The PA spectra exhibit mainly broad features, while the action spectra, due to inhomogeneous structure reduction, expose multiple peaks of recognizable shapes in the differing overtone manifolds. Symmetric rotor simulations of the band contours of the action spectra allowed retrieving of band origins and linewidths. The linewidths of the bands in each manifold enabled estimates for energy redistribution times out of the corresponding states to the bath states, the times ranging from 18+/-6 ps for two quanta of C-H excitation to subpicosecond for five quanta. The data were also analyzed in terms of a normal-mode model and a joint local-/normal-mode model. These models enabled determination of harmonic frequencies, anharmonicities, and interaction parameters reproducing the observed data in all monitored regions and provided spectral assignments. The measured Doppler profiles were well fitted by Gaussians with widths suggesting low average translational energies for the released H photofragments. These low energies and their similarities to those for dissociation of propyne isotopomers preexcited to acetylenic C-H stretches were ascribed to an indirect dissociation process occurring after internal conversion to the ground electronic state and isomerization to allene.     

Isocratic high-performance liquid chromatographic determination of plasma adenosine

Summary Due to manifold physiological and cardioprotective actions of adenosine, the demand for a simple but accurate method to determine its concentration in plasma is increasing. The aim of this study was firstly to develop a simple isocratic method instead of the gradient elution or peak-shifting techniques used earlier and secondly to check conflicting data on the composition of stop-solution, added to the sample in order to prevent changes in adenosine concentration. Isocratic elution improved signal to noise ratio and concentrations of 100 mol L^–1 dipyridamole and 2.5 mol L^–1 erythro-9(2-hydroxy-3-nonyl)adenine in the blood sample effectively prevented both adenosine formation and degradation, even without the use of a 5-ecto-nucleotidase inhibitor. Lowering the concentration of dipyridamole to 25 mol L^–1 caused more than a tenfold increase of adenosine concentration in two out of five cases and even 100 mol L^–1 dipyridamole alone is not sufficient to inhibit adenosine deaminase in blood samples.