Some remarks on the identity between a variational integral and its relaxed functional

Summary Letf: (x, z)∈R ⁿ×Rⁿ→f(x, z)∈[0, +∞] be measurable inx and convex inz. It is proved, by an example, that even iff verifies a condition as|z| ^p≤f(x, z)≤Λ(a(x)+|z|^q) with 1<p<q,a∈L _loc ^s (R ⁿ),s>1, the functional that isL ¹(Ω)-lower semicontinuous onW ^1,1(Ω), does not agree onW ^1,1(Ω) with its relaxed functional in the topologyL ¹(Ω) given by inf

---

Riassunto Siaf: (x, z)∈R ⁿ×Rⁿ→f(x, z)∈[0, +∞] misurabile inx e convessa inz. Si mostra con un esempio che anche sef verifica una condizione del tipo|z| ^p≤f(x, z)≤Λ(a(x)+|z|^q) con 1<p<q,a∈L _loc ^s (R ⁿ),s>1, il funzionale , che èL ¹(Ω)-semicontinuo inferiormente suW ^1,1(Ω), non coincide suW ^1,1(Ω) con il suo funzionale rilassato nella topologiaL ¹(Ω) definito da inf

     

New pi-extended water-soluble squaraines as singlet oxygen generators

[graph: see text] Condensation of squaric acid with a number of differently substituted 2-pyrrolyl derivatives afforded three new classes of squaraines. Their sharp and intense absorption bands in the biological window (700-900 nm), inherent singlet oxygen generation capabilities, together with proper functionalization allowing good water solubility make them suitable candidates as new non-porphyrinic singlet oxygen photosensitizers for photodynamic therapy (PDT).     

Photoelectron spectroscopy on thin films of extended zinc porphyrazines

Photoemission measurements were performed on a series of stepwise benzoannelated zinc porphyrazine molecules in thin films. The electronic structure of tert-butyl-substituted zinc tetraazaporphyrin, phthalocyanine, and naphthalocyanine is investigated using mainly EUV synchrotron radiation. A detailed analysis of the zinc satellites in the spectra of the valence region is performed in an attempt to infer the effect of ligand size extension on the metal-ligand interactions. No differences in the character of the bond between zinc and ligand were detected as a function of ligand size. The results are compared with those for the respective metal-free and copper-containing molecules.     

Are ring currents still useful to rationalize the benzene proton magnetic shielding?

[structure: see text] The conventional interpretation of proton NMR chemical shifts is supported by large basis set ab initio quantum mechanical calculations. The benzene protons are predicted to lie within the deshielding zone defined in terms of the out-of-plane magnetic shielding domain. However, ring currents by themselves are not sufficient to account quantitatively for the observed benzene proton downfield chemical shift. sigma-Electron contributions must also be taken into account. The conventional explanation for the ethyne proton chemical shift is valid.     

Stability boundaries, percolation threshold, and two-phase coexistence for polydisperse fluids of adhesive colloidal particles

We study the polydisperse Baxter model of sticky hard spheres (SHS) in the modified mean spherical approximation (mMSA). This closure is known to be the zero-order approximation C0 of the Percus-Yevick closure in a density expansion. The simplicity of the closure allows a full analytical study of the model. In particular we study stability boundaries, the percolation threshold, and the gas-liquid coexistence curves. Various possible subcases of the model are treated in details. Although the detailed behavior depends upon the particularly chosen case, we find that, in general, polydispersity inhibits instabilities, increases the extent of the nonpercolating phase, and diminishes the size of the gas-liquid coexistence region. We also consider the first-order improvement of the mMSA (C0) closure (C1) and compare the percolation and gas-liquid boundaries for the one-component system with recent Monte Carlo simulations. Our results provide a qualitative understanding of the effect of polydispersity on SHS models and are expected to shed new light on the applicability of SHS models for colloidal mixtures.     

The use of “actinometer” gases in optical diagnostics of plasma etching mixtures: SF6-O2

The spectroscopic emission intensities from excited F atoms in SF₆-O₂ discharges at 1 torr have been correlated to the densities of atoms in their ground electronic state by measuring the excitation efficiencies of the electrons in the energy range 11 to 17 eV with a method which essentially consists in the analysis of the emission of Ar or N₂, added as actinometer gases to the discharge mixtures. The general applicability of the method has been tested by a direct titration of F atoms with chlorine. The spectroscopic analysis has allowed the determination of useful information on the trends of both the electron densities and their energies as a function of the oxygen percent in the feed.     

Proton transfer in ammonia cluster cations: molecular dynamics in a self consistent field

A theoretical study of the energetics and intramolecular dynamics for ammonia cluster cations (NH₃) ₂ ⁺ and (NH₃) ₃ ⁺ is presented. The proton transfer mechanism after a vertical ionisation is followed in detail. Structural and energetic calculations are performed near the Hartree-Fock self consistent field (HF-SCF) limit; all open shell calculations are spin restricted (RHF). The calculations reconcile experimental results from thermochemical and photoionisation measurements: discrepancies in the energetics are shown to be due to the probing of different regions of the potential energy surface (PES). For the dynamics calculations, it is impractical to determine a large region of the multidimensional PES and then integrate Newton's equations. The calculations therefore incorporate a quantum mechanical determination of the electronic energy of the system after each time increment while nuclear degrees of freedom are handled classically. In this way, the classical reaction path across the Born-Oppenheimer surface is obtained.     

Coherence effects in low energy Na*(3p)+Na+ scattering: Experiment and semiclassical calculations

Pronounced polarization effects have been observed in inelastic collisions of laser state-prepared Na^*(3p,M _L) with Na⁺ leading to Na^*(3d) for the energy rangeE _CM=20–45 eV. Using linearly polarized light the dependence of the inelastic process on the alignment of the electronic charge cloud of the Na^*(3p) prior to the collision has been measured. In studies with left and right hand circularly polarized light the angular momentum transferred in the collision process has been determined. The results are compared with similar data for the 3p→3s deexitation process studied previously [6]. The density matrix of the Na^*(3p) state has been evaluated with respect to the collisional excitation to Na^*(3d). Semiclassical calculations based on the coupled channel impact parameter approximation using pseudopotentials [7] and nonadiabatic rotational coupling elements for the Na ₂ ^* system [12] have been performed. The agreement with the experimental results is good, in particular for the higher collision energies.     

On the use of symmetry in first-order perturbed HF theory. II

A method is described whereby molecular symmetry is employed to reduce the number of two-electron integrals in perturbed Hartree–Fock calculations of second-order properties. The method is a generalization of the Dacre–Elder procedure. First- and second-rank perturbing tensor operators are examined in the coupled HF approach to electric dipole polarizabilities, magnetic susceptibilities, quadrupole polarizabilities, and spin-dopolar contributions to spin–spin coupling constants. The procedure sketched here permits a large saving of computer efforts, which is shown by some illustrative examples.