Are closed clusters expected from the (n + 1) skeletal electron pairs rule in alanes and gallanes? A DFT structural study of AnHn + 2 (A = Al, Ga, and n = 4-6)

It has been suggested recently that the alanes Al_nH_n + 2 can be treated by the polyhedral skeletal electron pair theory (PSEPT) of Wade and Mingos (W-M) as it was successful for their borane congeners such as B_nH_n + 2, well known as the deprotonated B_nH_n²⁻. To do so, the neutral Al_nH_n + 2 have been considered as Al_nH_n²⁻ + 2H⁺. The additional hydrogens donate their electrons to the Al_nH_n polyhedral framework and according to the n + 1 electron pairs rule; these clusters should have closo-polyhedral structures. In this work the homologous gallanes, the structures and stabilities of Ga_nH_n + 2 are studied at high levels of calculational theory and we investigated the applicability of the W-M rule to the alanes and gallanes A_nH_n + 2 (n = 4-6; A = Al, Ga). It will be shown that the presence of bridging hydrogen atoms reduces the compactness of the corresponding polyhedron and so these species do not have the closed structures. The computations were performed at B3LYP/6-311+G(d,p), BPW91/6-311G(d,p) and B3LYP/6-311+G(3df,2p) levels of theory. Our interest in these compounds includes their potential use as hydrogen storage species and future clean sources of energy.     

Optical,structural, and photoelectrochemical properties of nanostructured ln-doped ZnO via electrodepositing method

Indium-doped zinc oxide nanorods were electrochemically deposited at low temperature on ITO substrates. The synthesized ZnO-arrayed layers were investigated by using X-ray diffraction, scanning electron microscopy, UV–vis transmittance, electrochemical impedance spectroscopy, and photocurrent spectroscopy. X-ray diffraction analysis demonstrates that the electrodeposited films are crystalline and present the hexagonal Würtzite ZnO phase with preferential (002) orientation. The ZnO films obtained forms aligned hexagonal nanorods, and depending on the increasing In concentration, the surface morphologies of the films are changed. The ln-doped ZnO nanorods (NRs) are well-aligned with the c-axis being perpendicular to the substrates when the ln concentration was between 0 and 2 at.%. of In, the grown films with In contents up to 4 at.%, changes in the optical band gap from 3.31 to 3.39 eV, and the blue shift in the band gap energy was attributed to the Burstein–Moss effect. The effect of In concentration on the photocurrent generated by films shows that the obtained thin films can be used as a photovoltaic material. Changes in the photocurrent response and the electronic disorder were also discussed in the light of In doping. It was found that the carrier density of IZO thin films varied between 1.06?×?10¹⁸ and 1.88?×?10¹⁸ cm^?3 when the In concentration was between 0 and 4 at.%.

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Graphical Abstract Photocurrent response of IZO samples

     

New inexact implicit method for general mixed quasi variational inequalities

In this paper, we suggest and analyze a new self-adaptive inexact implicit method with a variable parameter for general mixed quasi variational inequalities, where the skew-symmetry of the nonlinear bifunction plays a crucial part in the convergence analysis of this method. We use a self-adaptive technique to adjust parameter ρ at each iteration. The global convergence of the proposed method is proved under some mild conditions. Preliminary numerical results indicate that the self-adaptive adjustment rule is necessary in practice. Muhammad Aslam Noor is supported by the Higher Education Commission, Pakistan, through research grant No: 1-28/HEC/HRD/2005/90.     

An inexact implicit method for general mixed variational inequalities

In the present paper, we present an inexact implicit method with a variable parameter for general mixed variational inequalities. We use a self-adaptive technique to adjust parameter ρ$\rho$ at each iteration. The main advantage of this technique is that the method can adjust the parameter automatically and the numbers of iteration are not very sensitive to different initial parameter _ρ0.${\rho }_0.$     

Self-adaptive methods for general variational inequalities

It is well known that the general variational inequalities are equivalent to the fixed point problems and the Wiener-Hopf equations. In this paper, we use these alternative equivalent formulations to suggest and analyze some new self-adaptive iterative methods for solving the general variational inequalities. Our results can be viewed as a significant extension of the previously known results for variational inequalities. An example is given to illustrate the efficiency of the proposed method.     

Modified descent-projection method for solving variational inequalities

In this paper, we propose a modified descent-projection method for solving variational inequalities. The method makes use of a descent direction to produce the new iterate and can be viewed as an improvement of the descent-projection method by using a new step size. Under certain conditions, the global convergence of the proposed method is proved. In order to demonstrate the efficiency of the proposed method, we provide numerical results for a traffic equilibrium problems.     

Fuchsian groups, automorphic functions and Schwarzians

In this paper, a close connection is established between the geometry of certain genus zero Fuchsian groups and the analytic properties of the automorphic forms obtained by applying a certain differential operator to the Hauptmoduls of the groups. Received April 8, 1999 / Revised January 10, 2000 / Published online July 20, 2000     

ChemInform Abstract: G2(MP2) Molecular Orbital Study of [H3AlXH3]‐ (X: C,Si, and Ge) and H3AlYH3 (Y: N,P, and As) Complexes.

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