Synthesis, structure, and electronic properties of a dimer of Ru(bpy)2 doubly bridged by methoxide and pyrazolate

The heterobridged dinuclear complex cis,cis-[(bpy) 2Ru(mu-OCH 3)(mu-pyz)Ru(bpy) 2] (2+) ( 1; bpy = 2,2'-bipyridine; pyz = pyrazolate) was synthesized and isolated as a hexafluorophosphate salt. Its molecular structure was fully characterized by X-ray crystallography, (1)H NMR spectroscopy, and ESI mass spectrometry. The compound 1.(PF 6) 2 (C 44H 38F 12N 10OP 2Ru 2) crystallizes in the monoclinic space group P2 1/ c with a = 13.3312(4) A, b = 22.5379(6) A, c = 17.2818(4) A, beta = 99.497(2) degrees , V = 5121.3(2) A (3), and Z = 4. The meso diastereoisomeric form was exclusively found in the crystal structure, although the NMR spectra clearly demonstrated the presence of two stereoisomers in solution (rac and meso forms at approximately 1:1 ratio). The electronic properties of the complex in acetonitrile were investigated by cyclic voltammetry and UV-vis and NIR-IR spectroelectrochemistries. The stepwise oxidation of the Ru (II)-Ru (II) complex into the mixed-valent Ru (II)-Ru (III) and fully oxidized Ru (III)-Ru (III) states is fully reversible on the time scale of the in situ (spectro)electrochemical measurements. The mixed-valent species displays strong electronic coupling, as evidenced by the large splitting between the redox potentials for the Ru(III)/Ru(II) couples (Delta E 1/2 = 0.62 V; K c = 3 x 10 (10)) and the appearance of an intervalence transfer (IT) band at 1490 nm that is intense, narrow, and independent of solvent. Whereas this salient band in the NIR region originates primarily from highest-energy of the three IT transitions predicted for Ru(II)-Ru(III) systems, a weaker absorption band corresponding to the lowest-energy IT transition was clearly evidenced in the IR region ( approximately 3200 cm (-1)). The observation of totally coalesced vibrational peaks in the 1400-1650 cm (-1) range for a set of five bpy spectator vibrations in Ru (II)-Ru (III) relative to Ru (II)-Ru (II) and Ru (III)-Ru (III) provided evidence for rapid electron transfer and valence averaging on the picosecond time scale. Other than a relatively short Ru...Ru distance (3.72 A for the crystalline Ru (II)-Ru (II) complex), the extensive communication between metal centers is attributed mostly to the pi-donor ability of the bridging ligands (pyz, OMe) combined with the pi-acceptor ability of the peripheral (bpy) ligands.     

Chemistry and the problem of pluralism in science: an analysis concerning philosophical and scientific disagreements

Chemistry, especially its historical practice, has in the philosophy of science in recent decades attracted more and more attention, influencing the turn from the vision of science as a timeless logic-centred system of statements towards the history- and practice-centred approach. The problem of pluralism in science has become a popular topic in that context. Hasok Chang’s “active normative epistemic pluralism” manifested in his book (2012) Is water H₂O? Evidence, realism and pluralism, pursuing an integrated study of history and philosophy of science, has provoked quite a widespread debate. It provides a good opportunity to discuss the topical philosophical issue of the nature of disagreements. The differences among disagreements in different domains have been pointed out in the disagreement literature. It has been noticed that in mathematics and science consensus is established more clearly than in philosophy where it remains largely unachievable (Kornblith in Disagreement, Oxford University Press, Oxford, pp. 29–52, 2010). However, this conclusion is derived in the context of traditional logic-centred view of science. The aim of this paper is to consider the different nature of disagreements in science and in philosophy in the context of the history- and practice-centred approach. The analysis is focused on the critique of the received view of the Chemical Revolution which played quite a central role in Chang’s becoming a pluralist about science. Unlike Chang, however, a modified Kuhnian paradigm-conception of science and scientific revolutions is defended.     

Nucleation of bulk phases in the HCl/H2O system

We report experimental results on the low-temperature uptake of HCl on H(2)O ice (ice). HCl was deposited on the surface at greater than monolayer amounts at 85 K, and the ice substrate was heated. The temperature dependence of the HCl vapor pressure from this phase was measured from 110 to 150 K, with the nucleation of a bulk hydrate phase observed at 150 K. Measurements were conducted in a closed system by simultaneous application of gas phase mass spectrometry and surface spectroscopy to characterize vapor/solid equilibrium and the nucleation of bulk hydrate phases. Combining the nucleation data reported here with data we reported previously (180 to 200 K) and data from two other laboratories (165 and 170 K), the thermodynamic boundaries for the nucleation of both the metastable bulk solution and bulk hydrate phases subsequent to monolayer adsorption of HCl have been determined. The nucleation of the metastable bulk solution phase occurs promptly at monolayer coverage at the ice/liquid coexistence boundary on the binary bulk phase diagram. The nucleation of the bulk hexahydrate occurs from this metastable solution along a locus of points defining a state of constant solution free energy. This measured free energy is -51.2 +/- 0.9 kJ/mol. Finally, the temperature dependence of the HCl vapor pressure from the low-temperature phase is reported here for the first time and is consistent with that of the metastable solution predicted by this thermodynamic model of uptake, extending the range of validity of this model of adsorption followed by bulk solution and hydrate nucleation to a lower bound in temperature of 110 K.     

The tail behaviour of a random sum of subexponential random variables and vectors

Let $\left\{ X,X_{i},i=1,2,...\right\} $ denote independent positive random variables having common distribution function (d.f.) F(x) and, independent of X, let ν denote an integer valued random variable. Using X ₀=0, the random sum Z=∑ _i=0 ^ν X _i has d.f. $G(x)=\sum_{n=0}^{\infty }\Pr\{\nu =n\}F^{n\ast }(x)$ where F ^n?(x) denotes the n-fold convolution of F with itself. If F is subexponential, Kesten’s bound states that for each ε>0 we can find a constant K such that the inequality $$ 1-F^{n\ast }(x)\leq K(1+\varepsilon )^{n}(1-F(x))\, , \qquad n\geq 1,x\geq 0 \, , $$ holds. When F is subexponential and E(1 +ε) ^ν <∞, it is a standard result in risk theory that G(x) satisfies $$ 1 - G{\left( x \right)} \sim E{\left( \nu \right)}{\left( {1 - F{\left( x \right)}} \right)},\,\,x \to \infty \,\,{\left( * \right)} $$ In this paper, we show that (*) holds under weaker assumptions on ν and under stronger conditions on F. Stam (Adv. Appl. Prob. 5:308–327, 1973) considered the case where $ \overline{F}(x)=1-F(x)$ is regularly varying with index –α. He proved that if α>1 and $E{\left( {\nu ^{{\alpha + \varepsilon }} } \right)} < \infty $ , then relation (*) holds. For 0<α<1, it is sufficient that Eν<∞. In this paper we consider the case where $\overline{F}(x)$ is an O-regularly varying subexponential function. If the lower Matuszewska index $\beta (\overline{F})<-1$ , then the condition ${\text{E}}{\left( {\nu ^{{{\left| {\beta {\left( {\overline{F} } \right)}} \right|} + 1 + \varepsilon }} } \right)} < \infty$ is sufficient for (*). If $\beta (\overline{F} )>-1$ , then again Eν<∞ is sufficient. The proofs of the results rely on deriving bounds for the ratio $\overline{F^{n\ast }}(x)/\overline{F} (x)$ . In the paper, we also consider (*) in the special case where X is a positive stable random variable or has a compound Poisson distribution derived from such a random variable and, in this case, we show that for n≥2, the ratio $\overline{F^{n\ast }}(x)/\overline{F}(x)\uparrow n$ as x↑∞. In Section 3 of the paper, we briefly discuss an extension of Kesten’s inequality. In the final section of the paper, we discuss a multivariate analogue of (*).     

Flat Steady States in Stellar Dynamics – Existence and Stability

We consider a special case of the three dimensional Vlasov–Poisson system where the particles are restricted to a plane, a situation that is used in astrophysics to model extremely flattened galaxies. We prove the existence of steady states of this system. They are obtained as minimizers of an energy-Casimir functional from which fact a certain dynamical stability property is deduced. From a mathematics point of view these steady states provide examples of singular solutions of the three dimensional Vlasov–Poisson system. Received: 26 October 1998 / Accepted: 23 February 1999     

Generalised expressions for the association and dissociation rate constants of molecules with multiple binding sites

ABSTRACT

Many proteins exhibit multiple binding patches. A patch may harbour a key chemical modification site, but may also simply act as a trap for the binding to another site. Here we consider the scenario in which one molecule (enzyme) binds another molecule (substrate) which contains two sites. We present microscopic expressions for the rate at which the enzyme binds to a particular site on the substrate, both for the scenario in which the enzyme directly binds the site without first visiting the other site, and for the case in which it may visit the other site an arbitrary number of times before binding to the site of interest. We also present the expressions for the corresponding dissociation reactions. These expressions can be used to compute in a single rare-event simulation of the dissociation pathway not only both the intrinsic and effective dissociation rate constants but also both association rate constants.     

Linewidth of a quantum-cascade laser assessed from its frequency noise spectrum and impact of the current driver

We report on the measurement of the frequency noise properties of a 4.6-??m distributed-feedback quantum-cascade laser (QCL) operating in continuous wave near room temperature using a spectroscopic set-up. The flank of the R(14) ro-vibrational absorption line of carbon monoxide at 2196.6?cm^?1 is used to convert the frequency fluctuations of the laser into intensity fluctuations that are spectrally analyzed. We evaluate the influence of the laser driver on the observed QCL frequency noise and show how only a low-noise driver with a current noise density below ${\approx} 1~\mbox{nA/}\sqrt{}\mbox{Hz}$ allows observing the frequency noise of the laser itself, without any degradation induced by the current source. We also show how the laser FWHM linewidth, extracted from the frequency noise spectrum using a simple formula, can be drastically broadened at a rate of ${\approx} 1.6~\mbox{MHz/}(\mbox{nA/}\sqrt{}\mbox{Hz})$ for higher current noise densities of the driver. The current noise of commercial QCL drivers can reach several $\mbox{nA/}\sqrt{}\mbox{Hz}$ , leading to a broadening of the linewidth of our QCL of up to several megahertz. To remedy this limitation, we present a low-noise QCL driver with only $350~\mbox{pA/}\sqrt{}\mbox{Hz}$ current noise, which is suitable to observe the ??550?kHz linewidth of our QCL.     

Organically modified xerogels as supports for solid-phase chemistry

Organically modified xerogels (OMX_NH2) can be used as an easy to handle and chemically stable support in solid-phase chemistry and are compatible with enzymatic transformations.     

A Non-Variational Approach to Nonlinear Stability in Stellar Dynamics Applied to the King Model

In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was accessed by variational techniques. Here we propose a different, non-variational technique and use it to prove nonlinear stability of the King model against a class of spherically symmetric, dynamically accessible perturbations. This model is very important in astrophysics and was out of reach of the previous techniques.     

Organometallic chemical vapor deposition using allyl precursors

Homoleptic allyl derivatives of many Main-Group and transition metals, M(C₃H₅)_n, are readily available through one-pot syntheses using metal halides and allyl Grignard reagents or by alkylation of alkali-metal salts. The relatively low molecular weight of a C₃H₅ ligand contributes to high vapor pressures whilst the stability of the allyl radical is predicted to reduce decomposition temperatures. These compounds represent a class of volatile precursors for organometallic chemical vapor deposition (OMCVD) of thin films. Film growth studies using iridium, molybdenum, palladium, platinum, rhodium, selenium, tellurium and tungsten compounds are reviewed and the relationships between pyrolysis pathways and film purity are discussed.