Selfdecomposable Fields

In the present paper, we study selfdecomposability of random fields, as defined directly rather than in terms of finite-dimensional distributions. The main tools in our analysis are the master Lévy measure and the associated Lévy-Itô representation. We give the dilation criterion for selfdecomposability analogous to the classical one. Next, we give necessary and sufficient conditions (in terms of the kernel function) for a Volterra field driven by a Lévy basis to be selfdecomposable. In this context, we also study the so-called Urbanik classes of random fields. We follow this with the study of existence and selfdecomposability of integrated Volterra fields. Finally, we introduce infinitely divisible field-valued Lévy processes, give the Lévy-Itô representation associated with them and study stochastic integration with respect to such processes. We provide examples in the form of Lévy semistationary processes with a Gamma kernel and Ornstein–Uhlenbeck processes.     

A distance-dependent parameterization of the extended Hubbard model for conjugated and aromatic hydrocarbons derived from stretched ethene

The Hubbard model, which is widely used in physics but is mostly unfamiliar to chemists, provides an attractive yet simple model for chemistry beyond the self consistent field molecular orbital approximation. The Hubbard model adds an effective electron-electron repulsion when two electrons occupy the same atomic orbital to the familiar Hückel Hamiltonian. Thus it breaks the degeneracy between excited singlet and triplet states and allows an explicit treatment of electron correlation. We show how to evaluate the parameters of the model from high-level ab initio calculations on two-atom fragments and then to transfer the parameters to large molecules and polymers where accurate ab initio calculations are difficult or impossible. The recently developed MS-RASPT2 method is used to generate accurate potential energy curves for ethene as a function of carbon-carbon bond length, which are used to parameterize the model for conjugated hydrocarbons. Test applications to several conjugated/aromatic molecules show that even though the model is very simple, it is capable of reasonably accurate predictions for bond lengths, and predicts molecular excitation energies in reasonable agreement with those from the MS-RASPT2 method.     

Influence of the β-substitution on the photochemistry of α,2-diacetoxystyrenes. Irradiation of phenyl,vinyl, and benzyl derivatives

Summary -Substitution shows a pronounced influence on the photochemistry of ,2-diacetoxystyrenes. As in the case of the parent compound, intramolecular cyclization with participation of the neighbouring 2-acetoxy group takes place upon irradiation of the enol esters4a–c; however other processes are also observed, depending on the substrate. The phenyl derivative4a gives theE isomer7a and the phenanthrene9. The vinyl derivative4b also undergoescis-trans isomerization and/or photooxidation, to afford7b and10. Finally, a 1,4-acyl migration occurs in the benzyl derivative4c, whereby the 1,4-diketone12 is formed.

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Einfluß der -Substitution auf die Photochemie von ,2-Diacetoxystyrolen. Bestrahlung von Phenyl-, Vinyl- und Benzylderivaten

Zusammenfassung Bei ,2-Diacetoxystyrolen haben die -Substituenten einen deutlichen Einfluß auf das photochemische Verhalten. Wie im Fall der Stammverbindung erfolgt bei der Bestrahlung der Enolester4a–c intramoleukulare Cyclisierung unter Einbeziehung der benachbarten 2-Acetoxygruppe; jedoch werden je nach Substrat auch andere Reaktionen beobachtet. Das Phenylderivat4a liefert dasE-Isomer7a und das Phenanthren9. Das Vinylderivat4b erfährt ebenfallscis/trans-Isomerisierung zu7b und/oder Photooxidation zu10. Beim Benzylderivat4c tritt eine 1,4-Acylverschiebung zum 1,4-Diketon12 auf.

     

Phenol adsorption from water solutions over microporous and mesoporous carbon surfaces: a real time kinetic study

This study illustrates the effect of the adsorbent porosity (activated carbon and high surface area graphite) on the phenol adsorption kinetics. We have developed an experimental system where on line analysis of the solution is carried out by an optic fiber probe introduced in the water solution and directly connected with the UV spectrometer. This experimental setup permits to be more precise in determining kinetic parameters, considering that measurements are taken each 20 seconds. Our results show that the choice of the particle diameter of the adsorbent is critical in the control of the adsorption process kinetic, while the porosity of the carbon materials appears to be less relevant.     

Improving the ballistic AC conductivity through quantum resonance in branched nanowires

Frequency-dependent electrical conductivity is studied by means of the Kubo-Greenwood formula and a real-space renormalization plus convolution method. An analytical solution of the alternating current (AC) conductivity is found for periodic chains. In this article, we report enhancements to this ballistic AC conductivity when periodically or quasiperiodically placed Fano-Anderson impurities are introduced to an otherwise periodic chain, which is connected to two semi-infinite periodic leads at its ends. Moreover, the temperature effects on these resonant AC conducting states are remarkably different in periodic and in quasiperiodic systems. Finally, such enhancement is further analysed in branched nanowires with a small cross section.     

Electronic Absorption Spectra of Two 3-Aryl-pyridazinium-2,4,6-picryl-benzoyl-methylids

The visible electronic absorption spectra of two carbanion disubstituted cycloimmonium ylids having a 3-aryl-pyridazinium derivative as cation and a common disubstituted carbanion (-2,4,6-picryl-benzoyl) were studied in solvents with different physical and chemical properties. The visible electronic absorption band of 3-aryl-pyridazinium ylids is attributed to an electron charge transfer from the carbanion toward the heterocycle. The solvent effects on the visible electronic band of the studied ylids were described both by empirical parameters defined by Kosower and by using the theory of a dielectric homogeneous solution. Some remarks about the nature of the molecular interactions in the 3-aryl-phthalazinium-2,4,6-picryl-benzoyl methylid solutions are made in this paper on the basis of solvatochromic study.     

Automatic continuity of biseparating homomorphisms defined between groups of continuous functions

Let C(X,T) be the group of continuous functions of a compact Hausdorff space X to the unit circle of the complex plane T with the pointwise multiplication as the composition law. We investigate how the structure of C(X,T) determines the topology of X. In particular, which group isomorphisms H between the groups C(X,T) and C(Y,T) imply the existence of a continuous map h of Y into X such that H is canonically represented by h. Among other results, it is proved that C(X,T) determines X module a biseparating group isomorphism and, when X is first countable, the automatic continuity and representation as Banach-Stone maps for biseparating group isomorphisms is also obtained.     

Renormalization-convolution approach to the electronic transport in two-dimensional aperiodic lattices

A novel method combining the renormalization and convolution techniques is developed for the Kubo-Greenwood formula. Using this method, the dc and ac conductance at zero temperature in two-dimensional (2D) quasiperiodic systems are studied. The results show that the ac conductance of quasiperiodic systems could be significantly modified by the presence of periodic leads, which are usually employed as the measurement connections. Furthermore, when the system is periodic along the applied electrical field, a quantized dc conductance spectrum is observed at zero temperature and this quantized spectrum is destroyed when an oscillating electrical field is introduced. However, when the electric field is applied along a quasiperiodic direction of the system, the ac conductance spectrum shows a non-Drude behaviour, in good agreement with experiment results.     

Distinct photophysics of the isomers of B18H22 explained

The photophysics of the two isomers of octadecaborane(22), anti- and syn-B(18)H(22), have been studied by UV-vis spectroscopic techniques and theoretical computational methods. In air-saturated hexane, anti-B(18)H(22) shows fluorescence with a high quantum yield, Φ(F) = 0.97, and singlet oxygen O(2)((1)Δ(g)) production (Φ(Δ) ～ 0.008). Conversely, isomer syn-B(18)H(22) shows no measurable fluorescence, instead displaying much faster, picosecond nonradiative decay of excited singlet states. Computed potential energy hypersurfaces (PEHs) for both isomers rationalize these data, pointing to a deep S(1) minimum for anti-B(18)H(22) and a conical intersection (CI) between its S(0) and S(1) states that lies 0.51 eV higher in energy. Such an energy barrier to nonradiative relaxation is not present in the PEH of syn-B(18)H(22), and the system therefore has sufficient initial energy on excitation to reach the (S(0)/S(1)) CI and to then decay to the ground state without fluorescence. The computational analysis of the geometries at stationary points along the PEH of both isomers shows that the determining factor for the dissimilar photophysics of anti- and syn-B(18)H(22) may be due to the significant differences in the geometrical rearrangements at their respective conical intersections. Thus, the syn isomer shows one very large, B-B elongation of 1.2 ? from 1.8 ? in the ground state to 3.0 ? at the CI, whereas the anti isomer shows smaller elongations (below 1 ?) in several B-B connectivities at its (S(0)/S(1))(CI). The absorbed energy in S(1) for the anti-B(18)H(22) is therefore redistributed vibrationally into several regions of the molecule rather than almost completely into a single vibrational mode as in the case for the syn isomer. The consequent prolonged S(1) lifetime for the anti isomer allows for relaxation via fluorescence.     

Ballistic transport in aperiodic Labyrinth tiling proven through a new convolution theorem

In this article, we report a distinct convolution theorem developed for the Kubo-Greenwood formula in Labyrinth tiling by transforming the two-dimensional lattice into a set of independent chains with rescaled Hamiltonians. Such transformation leads to an analytical solution of the direct-current conductance spectra, where quantized steps with height of 2g₀ are found in Labyrinth tiling with periodic order along the applied electric field direction, in contrast to the step height of g₀ observed in the corresponding square lattices, being g₀ the conductance quantum. When this convolution theorem is combined with the real-space renormalization method, we are able to address in non-perturbative way the electronic transport in macroscopic aperiodic Labyrinth tiling based on generalized Fibonacci chains. Furthermore, we analytically demonstrate the existence of ballistic transport states in aperiodic Labyrinth tiling. This finding suggests that the periodicity should not be a necessary condition for the single-electron ballistic transport even in multidimensional fully non-periodic lattices.