Spectral statistics of random Schrödinger operator with growing potential

In this work we investigate the spectral statistics of random Schrödinger operators acting on where are i.i.d random variables distributed uniformly on [0,1].     

Strategy to design aqueous-soluble iron-oxide molecular cluster and nanostructure using polyoxometalate ligand scaffold

Profound availability of iron on earth crust and diversely accessible redox states, makes it a significant metal ion in biology as well as to design molecular catalysts and nanostructured materials. Low-oxidation potential and prone to hydrolysis in an aqueous medium, predominantly in neutral to basic pH, of the divalent iron in the active site of the catalysts, results in the formation of bulk and/or colloidal ferric-hydroxide, oxy-hydroxide, and -oxide. However, nature has developed its own strategy to preserve iron-oxide cluster core, e.g., Ferritin, without aggregation in physiological pH via designing protein scaffold as protector ligand. Although molecular iron-oxo clusters, isolated by using small organic ligands, are depicted as potent catalysts, they usually don't sustain under catalytic turnover condition. In this context, the isolation of multinuclear iron-oxo clusters soluble in water and their subsequent catalysis in the aqueous phase remains a perdurable challenge. Polyoxometalates (POM) are themselves small metal-oxo cluster anions where the metals are in the highest valent-state and a diverse POM structure can be obtained simply by varying the metal ions. Depending on the structure of the POM, the available terminal or bridging oxo groups can act as donor atoms to one or more iron centers. Consequently, a variety of iron clusters can be stabilized by using POM scaffold. Thereby, polyoxoanions, extremely aqueous-soluble and oxidatively inert under reaction conditions, behaved as versatile ligand platform to stabilize iron clusters of different nuclearity (n = 2–30) in water. Moreover, different possible structures and diversity in chemical property by varying hetero atoms or metal ions led to the isolation of a unique aqueous soluble iron-oxide and/or iron-oxy-hydroxide nanostructure where a significant number of polyoxoanions were covalently attached, making them extremely soluble nanostructures. This review summarizes the adapted synthetic strategies to isolate such molecular and nano-scopic iron clusters stabilized by POM anions and describes their stability in an aqueous medium and showcases their prospective applications in different emerging areas.     

Mechanistic aspects of ligand substitution on <Emphasis Type="Italic">cis</Emphasis>-diaqua(<Emphasis Type="Italic">cis</Emphasis>-1,2-diaminocyclohexane)platinum(II) by Glycine-<Emphasis Type="SmallCaps">l</Emphasis>-Leucine

The kinetics of the interaction of glycine-l-leucine (Glyleu) with cis-[Pt(cis-dach)(OH₂)₂]²⁺ (dach = 1,2-diaminocyclohexane) has been studied spectrophotometrically as a function of [cis-[Pt(cis-dach)(OH₂)₂]²⁺], [Glyleu] and temperature at pH 4.0, where the complex exists predominantly as the diaqua species and Glyleu as a zwitterion. The substitution reaction shows two consecutive steps: the first is the ligand-assisted anation and the second is the chelation step. The activation parameters for both the steps were evaluated using Eyring’s equation. The low ∆H₁^≠ (51.9 ± 2.8 kJmol⁻¹) and large negative value of ∆S₁^≠ (−152 ± 8 JK⁻¹mol⁻¹) as well as ∆H₂^≠ (54.4 ± 1.7 kJmol⁻¹) and ∆S₂^≠ (−162 ± 5 JK⁻¹mol⁻¹) indicate an associative mode of activation for both the aqua ligand substitution processes.     

Kinetics and mechanism of the reaction of hydroxopentaaquarhodium(III) ion with <Emphasis Type="SmallCaps">l</Emphasis>-Arginine in aqueous solution

The kinetics of the aqua ligand substitution from hydroxopentaaquarhodium(III) ion, [Rh(H₂O)₅(OH)]²⁺, by l-Arginine has been studied spectrophotometrically as a function of Arginine concentration, and temperature, at pH 4.3. The reaction proceeds via a rapid outer sphere association complex formation step followed by two consecutive steps. The first of these involves ligand-assisted anation, while the second involves chelation as the second aqua ligand is displaced. The association equilibrium constant for the outer sphere complex formation has been evaluated together with the rate constants for the two subsequent steps. The activation parameters for both steps have been evaluated using Eyring’s equation. Thermodynamic parameters calculated from the temperature dependence of the outer sphere association equilibrium constants are also consistent with an associative mode of activation. The product of the reaction has been characterized by conductivity measurement and IR spectroscopic analysis.     

Kinetic and mechanistic studies on the reaction of thiosemicarbazide with [(H<Subscript>2</Subscript>O)(tap)<Subscript>2</Subscript>RuORu(tap)<Subscript>2</Subscript>(H<Subscript>2</Subscript>O)]<Superscript>2+</Superscript> {tap = 2-(m-tolylazo)pyridine}

The interaction of thiosemicarbazide with the title complex has been studied spectrophotometrically in aqueous medium as a function of [complex], [thiosemicarbazide], pH and temperature at constant ionic strength. At pH 7.4, the reaction shows two distinct paths; both of which are [thiosemicarbazide] dependent. A parallel reaction scheme fits well with the experimental findings. An associative interchange mechanism is proposed for both the paths; the activation parameters calculated from Eyring plots are ΔH₁^≠ = 14.2 ± 0.8 kJ mol⁻¹, ΔS₁^≠ = −241 ± 2 JK⁻¹ mol⁻¹, ΔH₂^≠ = 30.8 ± 1.4 kJ mol⁻¹ and ΔS₂^≠ = −236 ± 4 JK⁻¹ mol⁻¹. From the temperature dependence of the outer sphere association complex equilibrium constants, the thermodynamic parameters calculated are ΔH₁^° = 34.25 ± 1.9 kJ mol⁻¹, ΔS₁^° = 146 ± 6 J K⁻¹ mol⁻¹ and ΔH₂^° = 9.4 ± 1.1 kJ mol⁻¹, ΔS₂^° = 71 ± 3 JK⁻¹ mol⁻¹, which gives a negative ΔG° at all temperatures studied, supporting the spontaneous formation of an outer sphere association complex.     

Fluorometric and isothermal titration calorimetric studies on binding interaction of a telechelic polymer with sodium alkyl sulfates of varying chain length

Steady-state fluorescence measurements and isothermal titration calorimetric experiments have been performed to study the interaction between a telechelic polymer, pyrene-end-capped poly(ethylene oxide) (PYPY), and sodium alkyl sulfate surfactants having decyl, dodecyl, and tetradecyl hydrocarbon tails. Fluorometric results suggest polymer-surfactant interaction in the very low range of polymer concentrations. The relative variation in the excimer to monomer pyrene emission intensities with varying surfactant concentration reveals that initial addition of surfactant favors intramolecular preassociation until the surfactant molecules start binding with the ethylene oxide (EO) chain. With the growing number of surfactant aggregates along the EO chain, the association becomes hindered due to the polyelectrolyte effect. The results from microcalorimetric titrations in the low concentration range of PYPY solution (approximately 10(-6) M) with alkyl sulfates suggest two kinds of surfactant-polymer interactions, one with the polymer hydrophobic end groups and the other with the ethylene oxide backbone. The overall polymer-surfactant interaction starts at a much lower surfactant concentration for the hydrophobically modified polymers compared to that in the case of unsubstituted poly(ethylene oxide) homopolymer. From the experiments critical aggregation concentration values and the second critical concentration where free micelles start forming have been determined. An endeavor has been made to unveil the mechanism underlying the corresponding associations of the surfactants with the polymer.     

Effect of nanocavity confinement on the rotational relaxation dynamics: 3-acetyl-4-oxo-6,7-dihydro-12H indolo-[2,3-a] quinolizine in micelles

In continuation of our recent study on the steady state photophysics of a biologically active beta-carboline derivative, 3-acetyl-4-oxo-6,7-dihydro-12H indolo-[2,3-a] quinolizine (AODIQ), in the present article we have investigated the effect of nanocavity confinement on the excited state dynamics and rotational relaxation of the probe using picosecond time resolved fluorescence and fluorescence anisotropy techniques. The polarity dependent intramolecular charge transfer process is responsible for the remarkable sensitivity of this biological fluorophore in micellar environments. The fluorescence anisotropy decay of AODIQ incorporated inside the micelle is biexponential. The rotational motion of the probe was interpreted on the basis of a two step model consisting of a fast restricted rotation of the probe and a slow lateral diffusion of the probe in the micelle; both coupled to the overall rotation of the micelle. Experimental results reveal that micellar environment causes significant retardation of both the wobbling as well as the translational motion of the probe.     

Photophysical study of 3-acetyl-4-oxo-6,7-dihydro-12H-indolo[2,3-a]quinolizine in biomimetic reverse micellar nanocavities: a spectroscopic approach

Photophysical properties of 3-acetyl-4-oxo-6,7-dihydro-12H-indolo[2,3-a]quinolizine (AODIQ), a bioactive molecule, has been investigated in well-characterized, monodispersed biomimicking nanocavities formed by sodium bis(2-ethylhexyl)sulfosuccinate (AOT) in heptane using steady-state and picosecond time resolved fluorescence and fluorescence anisotropy. The emission behavior of AODIQ is very much dependent upon the water/surfactant mole ratio (W), i.e., on the water pool size of the reverse micellar core. AODIQ exhibits a sharp decrease in fluorescence anisotropy with increasing W, implying that the overall motional restriction experienced by the molecule is decreased with increased hydration. Some of the depth-dependent relevant fluorescence parameters, namely, fluorescence maxima and fluorescence anisotropy (r), have been monitored for exploiting the distribution and microenvironment around the probe in the reverse micelles. Fluorescence spectral position and fluorescence quenching studies suggest that the probe does not penetrate into the reverse micellar core; rather it binds at the interfacial region. Quantitaive estimates of the micropolarity and microviscosity at the binding sites of the probe molecule have been determined as a function of W.     

Interaction of pyrene-end-capped poly(ethylene oxide) with bovine serum albumin and human serum albumin in aqueous buffer medium: a fluorometric study

The photophysical behavior of a hydrophobically tailored water-soluble polymer, pyrene-end-capped poly(ethylene oxide) (PYPY), has been studied in aqueous buffered bovine serum albumin (BSA) and human serum albumin (HSA) media. In buffered aqueous solution the polymer shows dual emission corresponding to the monomer and the excimer of pyrene moiety. The relative intensity of the monomer to the excimer emission shows interesting variation with the addition of BSA and HSA and is indicative of significant interaction of these albumin proteins with the polymer. The binding interaction has been shown to have a prominent role on the steady state fluorescence anisotropy of the two emission bands. Attempt has been made to determine the micropolarities of the protein microenvironments from a comparison of the variation of the monomer to excimer relative fluorescence intensities of the probe in water–dioxane mixtures with varying composition.