Bounds and monotonicity for the generalized Robin problem

We consider the principal eigenvalue λ ₁^Ω(α) corresponding to Δu = λ (α) u in W, \frac?u?v = au \Omega, \frac{\partial u}{\partial v} = \alpha u on ∂Ω, with α a fixed real, and W ì Rⁿ\Omega \subset {\mathcal{R}}^n a C ^0,1 bounded domain. If α > 0 and small, we derive bounds for λ ₁^Ω(α) in terms of a Stekloff-type eigenvalue; while for α > 0 large we study the behavior of its growth in terms of maximum curvature. We analyze how domain monotonicity of the principal eigenvalue depends on the geometry of the domain, and prove that domains which exhibit domain monotonicity for every α are calibrable. We conjecture that a domain has the domain monotonicity property for some α if and only if it is calibrable.     

Photo-induced pyridine substitution in cis-[Ru(bpy)(2)(py)(2)]Cl(2): a snapshot by time-resolved X-ray solution scattering

Determination of transient structures in light-induced processes is a challenging goal for time-resolved techniques. Such techniques are becoming successful in detecting ultrafast structural changes in molecules and do not require the presence of probe-like groups. Here, we demonstrate that TR-WAXS (Time-Resolved Wide Angle X-ray Scattering) can be successfully employed to study the photochemistry of cis-[Ru(bpy)(2)(py)(2)]Cl(2), a mononuclear ruthenium complex of interest in the field of photoactivatable anticancer agents. TR-WAXS is able to detect the release of a pyridine ligand and the coordination of a solvent molecule on a faster timescale than 800 ns of laser excitation. The direct measurement of the photodissociation of pyridine is a major advance in the field of time-resolved techniques allowing detection, for the first time, of the release of a multiatomic ligand formed by low Z atoms. These data demonstrate that TR-WAXS is a powerful technique for studying rapid ligand substitution processes involving photoactive metal complexes of biological interest.     

Laurdan and Prodan as Polarity-Sensitive Fluorescent Membrane Probes

The steady-state and dynamic fluorescence spectral properties of 2-dimethylamino-6-lauroylnaphthalene (LAURDAN) and several other naphthalene derivatives are summarized to illustrate their sensitivity to the polarity of the environment. Results obtained both in solvents of different polarity and in phospholipid vesicles in two phase states are presented. The emission red shift observed in polar solvents and in the phospholipid liquid–crystalline phase is explained on the basis of dipolar relaxation of solvent molecules surrounding the fluorescent naphthalene moiety of these probes. In phospholipid environments, experimental evidence is shown that excludes the intramolecular relative reorientation of the dimethylamino and carbonyl groups in the naphthalene and the reorientation of the entire fluorescent moiety. The solvent dipolar relaxation observed for LAURDAN and PRODAN in phospholipid bilayers has been attributed to a small number of water molecules present at the membrane interface. A comparison between LAURDAN emission in phospholipid vesicles prepared in D₂O and in H₂O is also presented. The definition and the derivation of the generalized polarization function are also discussed.     

Derivation of the Forchheimer Law Via Matched Asymptotic Expansions

Matched asymptotics are used formally in the linearized Navier–Stokes equations, the so-called Oseen approximation, to derive a nonlinear law for the flow of a single-phase, incompressible Newtonian fluid through a rigid porous medium. A suitable choice of the linear term gives, to order a Forchheimer-type law.     

Mechanism of Thyroxine Deiodination by Naphthyl‐Based Iodothyronine Deiodinase Mimics and the Halogen Bonding Role: A DFT Investigation

This paper deals with a systematic density functional theory (DFT) study aiming to unravel the mechanism of the thyroxine (T4) conversion into 3,3′,5‐triiodothyronine (rT3) by using different bio‐inspired naphthyl‐based models, which are able to reproduce the catalytic functions of the type‐3 deiodinase ID‐3. Such naphthalenes, having two selenols, two thiols, and a selenol–thiol pair in peri positions, which were previously synthesized and tested in their deiodinase activity, are able to remove iodine selectively from the inner ring of T4 to produce rT3. Calculations were performed including also an imidazole ring that, mimicking the role of the His residue, plays an essential role deprotonating the selenol/thiol moiety. For all the used complexes, the calculated potential energy surfaces show that the reaction proceeds via an intermediate, characterized by the presence of a X?I?C (X=Se, S) halogen bond, whose transformation into a subsequent intermediate in which the C?I bond is definitively cleaved and the incipient X?I bond is formed represents the rate‐determining step of the whole process. The calculated trend in the barrier heights of the corresponding transition states allows us to rationalize the experimentally observed superior deiodinase activity of the naphthyl‐based compound with two selenol groups. The role of the peri interactions between chalcogen atoms appears to be less prominent in determining the deiodination activity.     

Electrochemical, EPR and computational results on [Fe2Cp2(CO)2]-based complexes with a bridging hydrocarbyl ligand

The dimetallacyclopentenone complexes [Fe₂Cp₂(CO)(μ−CO){μ−η¹:η³−C_αHC_β(R)C(O)}] (R = CH₂OH, 1a; R = CMe₂OH, 1b; R = Ph, 1c) were prepared by photolytic reaction of [Fe₂Cp₂(CO)₄] with alkyne according to the literature procedure. The X-ray and the electrochemical characterization of 1c are presented. The μ-allenyl compound [Fe₂Cp₂(CO)₂(μ−CO){μ−η¹:η²_α,β−C_αHC_βCMe₂][BF₄] ([2][BF₄]), obtained by reaction of 1b with HBF₄, underwent monoelectron reduction to give a radical species which was detected by EPR at room temperature. The EPR signal has been assigned to [Fe₂Cp₂(CO)₂(μ−CO){μ−η¹:η²_α,β-C_αHC_βCMe₂}], [2]^•. The molecular structures of [2]⁺ and [2]^• were optimized by DFT calculations. The unpaired electron in [2]^• is localized mainly at the metal centers and, coherently, [2]^• does not undergo carbon-carbon dimerization, by contrast with what previously observed for the μ-vinyl radical complex [Fe₂Cp₂(CO)₂(μ−CO){μ−η¹:η²-CHCH(Ph)}]^•, [3]^•. Electron spin density distributions similar to the one of [2]^• were found for the μ-allenyl radical complexes [Fe₂Cp₂(CO)₂(μ-CO){μ-η¹:η²_α,β-C_αHC_βC(R¹)(R²)}]^• (R¹ = R² = H, [4]^•; R¹ = H, R² = Ph, [5]^•; R¹ = R² = Ph, [6]^•).     

Structure and C-S bond cleavage in aryl 1-methyl-1-arylethyl sulfide radical cations

Steady state and laser flash photolysis (LFP) of a series of p-X-cumyl phenyl sulfides (4-X-C(6)H(4)C(CH(3))(2)SC(6)H(5): 1, X = Br; 2, X = H; 3, X = CH(3); 4, X = OCH(3)) and p-X-cumyl p-methoxyphenyl sulfides (4-X-C(6)H(4)C(CH(3))(2)SC(6)H(4)OCH(3): 5, X = H; 6, X = CH(3); 7, X = OCH(3)) has been carried out in the presence of N-methoxy phenanthridinium hexafluorophosphate (MeOP(+)PF(6)(-)) under nitrogen in MeCN. Steady state photolysis showed the formation of products deriving from the C-S bond cleavage in the radical cations 1(+?)-7(+?) (2-aryl-2-propanols and diaryl disulfides). Formation of 1(+?)-7(+?) was also demonstrated by LFP experiments evidencing the absorption bands of the radical cations 1(+?)-3(+?) (λ(max) = 530 nm) and 5(+?)-7(+?) (λ(max) = 570 nm) mainly localized in the arylsulfenyl group and radical cation 4(+?) (λ(max) = 410, 700 nm) probably mainly localized in the cumyl ring. The radical cations decayed by first-order kinetics with a process attributable to the C-S bond cleavage. On the basis of DFT calculations it has been suggested that the conformations most suitable for C-S bond cleavage in 1(+?)-4(+?) and 7(+?) are characterized by having the C-S bond almost collinear with the π system of the cumyl ring and by a significant charge and spin delocalization from the ArS ring to the cumyl ring. Such a delocalization is probably at the origin of the observation that the rates of C-S bond cleavage result in very little sensitivity to changes in the C-S bond dissociation free energy (BDFE). A quite large reorganization energy value (λ = 43.7 kcal mol(-1)) has been calculated for the C-S bond scission reaction in the radical cation. This value is much larger than that (λ = 12 kcal mol(-1)) found for the C-C bond cleavage in bicumyl radical cations, a reaction that also leads to cumyl carbocations.     

Steady-state and time-resolved investigations of a crown thioether conjugated with methylacridinium and its complexes with metal ions

The crown thioether 9-[4-(4,7,10,13-tetrathia-1-azacyclopentadecyl]phenyl-N-methylacridinium perchlorate (TCMA) was synthesized and characterized with the aim to verify its ability to interact selectively with metal ions and substantiate the possibility to detect easily the presence of heavy metals in fluid samples. The spectroscopic properties of TCMA, alone and in the presence of metal ions, were therefore studied in polar solvents (MeCN and H(2)O); in particular, steady-state UV-Vis spectrophotometric and fluorimetric techniques were used together with transient absorption spectroscopy with fs time resolution to investigate the spectral and dynamic properties of the lowest excited singlet state of TCMA and of TCMA/metal ion complexes. The absorption in the Vis region is characterized by a charge-transfer nature with the methylacridinium moiety acting as the electron-acceptor and the anilic group as the electron-donor. No emission from the S(1) was detected both in MeCN and H(2)O, while a small S(2)→ S(0) fluorescence emission (λ(max) = 485 nm and ?(F) = 0.0011) was detected in water. Time-resolved measurements with fs resolution of TCMA in MeCN have shown that the relaxed S(1) state is reached ～0.6 ps after the laser pulse, while the S(1)→ S(0) time constant is 3.7 ps. Among the investigated metal ions, only Fe(3+) (in MeCN) and Hg(2+) (in MeCN and H(2)O) were able to form stable complexes (association constant, K(ass) = 1-11 × 10(4) M(-1)) with TCMA. The S(1) state of the TCMA/M(n+) complexes emits with low quantum yield (?(F) = 0.0023-0.014) and decays with time constants much longer than TCMA itself, at least in the case of TCMA/Hg(2+) in MeCN. This study showed that TCMA is a good candidate for colorimetric/fluorimetric sensing of Hg(2+) in aqueous media owing to its high selectivity towards metal ions.