The crystal and molecular structure of bis(η5-trimethylsilylcyclopentadienyl)titanium(IV) dichloride,Ti(η5-C5H4SiMe 3)2Cl2

Summary The crystal and molecular structure of the titanocene complex Ti(⁵-C₅H₄SiMe ₃)₂Cl₂ has been determined by X-ray diffraction studies. The compound crystallizes in the triclinic crystal system [a=6.747(8),b=12.815(2),c=12.928(4) Å and =67.16(2), =82.29(5), =74.83(4)°] in the space group with 2 formula units in the unit cell. The coordination about the titanium atom formed by the two chlorine atoms and the centroids of the cyclopentadienyl rings is that of a distorted tetrahedron. The Cl-Ti-Cl angle is 91.63° while the (centroid)-Ti-(centroid) angle is 131.02°.

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Die Kristall- und Molekülstruktur von Bis(⁵-trimethylsilylcyclopentadienyl)titan(IV)dichlorid, Ti(⁵-C₅H₄SiMe ₃)₂Cl₂

Zusammenfassung Die Kristall- und Molekülstruktur des Titanocen-Komplexes Ti(⁵-C₅H₄SiMe ₃)₂Cl₂ wurde durch eine Röntgenstrukturanalyse bestimmt. Die Verbindung kristallisiert im triklinen Kristallsystem [a=6.747(8),b=12.815(2),c=12.928(4) Å und =67.16(2), =82.29(5), =74.83(4)°] in der Raumgruppe mit 2 Formeleinheiten pro Elementarzelle. Das Titanatom ist von zwei Chloratomen und den Centroiden der Cyclopentadienylringe umgeben, wobei die Koordination des Titanatoms verzerrt tetraedrisch ist. Die Winkel Cl-Ti-Cl und (Centroid)-Ti-(Centroid) betragen 91.63° bzw. 131.02°.

     

On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation

Summary We approximate the solutions of an initial- and boundary-value problem for nonlinear Schrödinger equations (with emphasis on the cubic nonlinearity) by two fully discrete finite element schemes based on the standard Galerkin method in space and two implicit. Crank-Nicolson-type second-order accurate temporal discretizations. For both schemes we study the existence and uniqueness of their solutions and proveL ² error bounds of optimal order of accuracy. For one of the schemes we also analyze one step of Newton's method for solving the nonlinear systems that arise at every time step. We then implement this scheme using an iterative modification of Newton's method that, at each time stept ⁿ , requires solving a number of sparse complex linear systems with a matrix that does not change withn. The effect of this inner iteration is studied theoretically and numerically.The work of these authors was supported by the Institute of Applied and Computational Mathematics of the Research Center of Crete-FORTH and the Science Alliance program of the University of TennesseeThe work of this author was supported by the AFOSR Grant 88-0019     

Study of the influence of surfactants on the transfer of gases into liquids by inverse gas chromatography

Analyses of amino acids and peptides were performed using a quartz microchip and an interface for microchip electrophoresis-electrospray ionization mass spectrometry (MCE-ESI-MS). In MCE-ESI-MS, negative pressure caused by ESI increased band broadening and deteriorated separation. We tried to suppress the negative pressure and improve separation using a microchip with a long separation channel. Separations of peptide standards were compared using two microchips with long separation channel (58.9 mm) and short one (22.9 mm). Theoretical plate numbers and resolution were improved significantly using the former. The theoretical plate numbers of [Val4]angiotensin was 8600 using the former and 1700 using the latter. When background electrolytes of low pH were used in an uncoated quartz microchip, electrokinetic injection was difficult because of weak electroosmotic flow. The use of successive multiple ionic polymer layers coating of the microchip channel stabilized electrokinetic injection and permitted analysis of amino acids and peptides even under low pH conditions. Separation of amino acids was successfully performed using formic acid solution (pH 2.5) as background electrolyte.     

Synthesis and tautomerism study of 7-substituted pyrazolo[3,4-c]pyridines

A number of 7-substituted pyrazolo[3,4-c]pyridine derivatives have been synthesized in order to investigate the N1-N2 tautomerism within this class of biologically interesting compounds. Tautomeric equilibrium has been studied using NMR ¹³C, ¹⁵N chemical shifts and heteronuclear ¹H-¹⁵N and ¹H-¹³C spin-spin couplings, in conjunction with X-ray crystallography. The N1 tautomer predominates in DMF solution in all the compounds tested.     

Some remarks on a class of rational approximations to the cosine

Some previously introduced methods for the numerical solution of second-order evolution equations based on a class of rational approximations to the cosy, y real, with denominators (1+x ² y ²) ^s are revisited. It is shown that maximal accuracy occurs for each integers1 for a suitable choice of the parameterx. An improved sufficient condition for unconditional stability is obtained. Conditional stability and periodicity of these methods are also studied.Work supported by USARO Grant DAAG 29-78-C-0024.     

An approximation theorem for second-order evolution equations

Summary A class of approximation schemes of arbitrary accuracy, generated by a two-step recurrence relation, is devised for evolution equations of the second order. The schemes are effected via a specially constructed family of rational approximations to cos for 0 and yield computationally efficient methods for systems of second-order ordinary differential equations and semidiscrete approximations for initial-boundary value problems for second-order hyperbolic equations.Research supported by ONR grant N00014-57-A-0298-0015Research supported by USARO grant DAAG 29-278-C-0024     

Kinetics of the X-ray induced gold nanoparticle synthesis

Time resolved small angle scattering has been employed to follow the formation kinetics of gold nanoparticles from a solution of gold hydrochlorate and tris-sodium citrate at room temperature. While UV irradiation leads to a slow kinetics as observed by optical spectroscopy, the irradiation by the X-rays led to a reduction of the gold within a few minutes. The size and morphology evolution during the radiolytic formation of particles displays the initial nucleation phase and the growth kinetics, which exhibit very nonuniform behavior. They show that the electrostatics of the particle stabilization plays a pronounced role in the repulsive forces and transient clustering of particles.     

A family of enneanuclear iron(II) single-molecule magnets

Complexes [Fe₉(X)₂(O₂CMe)₈{(2‐py)₂CO₂}₄] (X^?=OH^? ( 1 ), N₃^? ( 2 ), and NCO^? ( 3 )) have been prepared by a route previously employed for the synthesis of analogous Co₉ and Ni₉ complexes, involving hydroxide substitution by pseudohalides (N₃^?, NCO^?). As indicated by DC magnetic susceptibility measurements, this substitution induced higher ferromagnetic couplings in complexes 2 and 3 , leading to higher ground spin states compared to that of 1 . Variable‐field experiments have shown that the ground state is not well isolated from excited states, as a result of which it cannot be unambiguously determined. AC susceptometry has revealed out‐of‐phase signals, which suggests that these complexes exhibit a slow relaxation of magnetization that follows Arrhenius behavior, as observed in single‐molecule magnets, with energy barriers of 41 K for 2 (τ₀=3.4×10^?12 s) and 44 K for 3 (τ₀=2.0×10^?11 s). Slow magnetic relaxation has also been observed by zero‐field ⁵⁷Fe Mössbauer spectroscopy. Characteristic integer‐spin electron paramagnetic resonance (EPR) signals have been observed at X‐band for 1 , whereas 2 and 3 were found to be EPR‐silent at this frequency. ¹H NMR spectrometry in CD₃CN has shown that complexes 1 – 3 are stable in solution.     

Zero point energy of the Pullen–Edmonds Hamiltonian

Here we wish to apply the newly developed Generalized Moments Expansion (GMX) to the well-known potential