Backscattering in the vicinity of a mode cutoff

In a recent paper to this journal (Whitman A M et al 2003 Waves Random Media 13 269-86) we derived a set of coupled equations that describe the intermodal scattering of acoustic radiation in a duct whose speed of sound varies randomly in space and time. In the paper we were mainly interested in modes that were not near cutoff. Here we study the solution of these equations in the vicinity of the cutoff. We find that near cutoff almost all the energy is reflected back independent of the other duct parameters. In addition to presenting these results, we analyse the mathematical structure of the equations in these regions in order to elucidate the reason for this behaviour.     

Isomers of C20: an energy profile III

Semiempirical calculations, at the PM3 level provided within the Winmopac v2.0 software package, are used to geometrically optimize and determine the absolute energies (heats of formation) of a variety of C(20) isomers that are predicted to exist in and around the ring and cage isomers. Using the optimized Cartesian coordinates for the ring and the cage isomers, a saddle-point calculation was performed. The resulting energy profile, consisting of a series of peaks and valleys, is used as a starting point for the identification and location of fifteen additional isomers of C(20) that are predicted to be energetically stable, both via geometry optimizations and force constant analysis. These additional isomers were subsequently determined to lie adjacent to one another on the potential surface and establish a step-wise transformation between the ring and the cage. Transition-state optimization of the Cartesian coordinates at the saddle point between adjacent isomers was performed to quantify the energy of the transition state. The step-wise process from one isomer to another, which extends out over the three-dimensional surface, is predicted to require approximately 15% less energy than that of the direct, two-dimensional transformation predicted in the bowl-cage profile. However, the net atomic rearrangement for the step-wise process is about four times greater than that of the direct process. Although less in energy, the amount of atomic rearrangement in the step-wise process would make the occurrence of such a route prohibitive. Utilizing the direct distance separating the three primary isomers (ring, bowl, cage), the method of triangulation is performed to quantitatively position other C(20) structures on the potential surface, relative to the ring, bowl, and cage isomers.     

Quantum chemical study of the influence of the zeolite electrostatic field on the physical characteristics of ethylene

A modified CNDO/2 method whose Hamiltonian includes the terms describing the interaction of electrons with the electrostatic field of the zeolite crystal is employed for studying the influence of the faujasite electrostatic field on the physical characteristics of ethylene. It is shown that this field causes significant changes in the distribution of electron density in the ethylene molecule as a function of its orientation and localization in the large cavity of faujasites.

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Automatic geometry optimization for molecules with d orbitals. I. General analytic formulas for derivatives of slater orbitals

General analytic formulas for derivatives of real Slater orbitals with respect to the Cartesian coordinates x and y have been derived. The application of this result to molecular geometry optimization or to the construction of a force constant matrix is briefly discussed.     

Unrestricted perfect pairing: the simplest wave-function-based model chemistry beyond mean field

The perfect pairing (PP) approximation from generalized valence bond theory is formulated in an unrestricted fashion for both closed- and open-shell systems using a coupled cluster ansatz. In the model chemistry proposed here, active electron pairs are correlated, but the unpaired or radical electrons remain uncorrelated, leading to a linear number of decoupled cluster amplitudes which can be solved for analytically. The alpha and beta spatial orbitals are variationally optimized independently. This minimal treatment of electron-electron correlation noticeably improves upon symmetry-breaking problems and other pathologies in Hartree-Fock (HF) theory and may be computed using the resolution of the identity approximation at only a factor of several times more effort than HF itself. PP also generally predicts improved molecular structures over HF. This compact, correlated wave function potentially provides a useful starting point for dynamical correlation corrections.     

Quantum chemical study of the physical characteristics of the hydroxy groups of zeolites, III

The CNDO/2 method was applied to calculate the electronic structure of HY zeolite using cluster models Si₃AlO₁₂H ₈ ^– and Si₃AlO₁₂H₉. It has been shown that the probability of occurrence of H on a particular type of oxygen as well as the other physical characteristics of zeolite depend on both the type of oxygen and the position of the Al atom.

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/2 , Si₃AlO₁₂H₈ Si₃AlO₁₂H₉. , , , Al.

     

Electrochemical stripping determination of traces of copper, lead, cadmium and zinc in zirconium metal and zirconium dioxide

Procedures have been developed for the determination of copper, lead, cadmium and zinc in zirconium metal and zirconium dioxide, at concentrations of 1 ppm or less. Zirconium metal was dissolved in suphuric acid, and zirconium dioxide decomposed under pressure with hydrofluoric acid. Sample solutions were prepared in dilute sulphuric acid. For the stripping determination, the sample solution was either mixed with a complexing tartrate base electrolyte or the pre-electrolysis was carried out in acid solution, with the acid solution being exchanged for a pure base electrolyte (e.g. an acetate buffer) for the stripping step. The stripping step was monitored by d.c., differential pulse and Kalousek commutator voltammetry and the three methods were compared. A stationary mercury-drop electrode can generally be used for all the methods, whereas a mercury-film electrode is suitable only for the d.c. voltammetric determination of copper, lead and cadmium, as pulse measurements with films are poorly reproducible and the electrodes are easily damaged. The relative standard deviation does not exceed 20%. Some samples contained relatively large amounts of copper, which is best separated by electrodeposition on a platinum electrode.     

High thermodynamic stability and extraordinary kinetic inertness of copper(II) complexes with 1,4,8,11-tetraazacyclotetradecane-1,8-bis(methylphosphonic acid): example of a rare isomerism between kinetically inert penta- and hexacoordinated copper(II) complexes

In an aqueous solution at room temperature, 1,4,8,11-tetraazacyclotetradecane-1,8-bis(methylphosphonic acid) (H(4)L(1)) and Cu(I) (I) form a pentacoordinated (pc) complex, pc-[Cu(L(1))](2-), exhibiting conformation I of the cyclam ring. At high temperature, the complex isomerises to a hexacoordinated isomer, trans-O,O-[Cu(L(1))](2-), with a trans-III conformation of the cyclam ring. In pc-[Cu(L(1))](2-), four ring nitrogen atoms and one phosphonate oxygen atom are arranged around Cu(I) (I) in a structure that is half-way between a trigonal bipyramid and a tetragonal pyramid, with one phosphonic acid group uncoordinated. In the trans-O,O-[Cu(L(1))](2-) isomer, the nitrogen atoms form a plane and the phosphonic acid groups are in a mutually trans configuration. A structurally very similar ligand, 4-methyl-1,4,8,11-tetraazacyclotetradecane-1,8-bis(methylphosphonic acid) (H(4)L(2)), forms an analogous pentacoordinated complex, pc-[Cu(L(2))](2-), at room temperature. However, the complex does not isomerise to the octahedral complex analogous to trans-O,O-[Cu(L(1))](2-). Because of the high thermodynamic stability of pc-[Cu(L(1))](2-), (logbeta=25.40(4), 25 degrees C, I=0.1 mol dm(-3) KNO(3)) and the formation of protonated species, Cu(I) (I) is fully complexed in acidic solution (-log [H(+)] approximately 3). Acid-assisted decomplexation of both of the isomers of [Cu(H(2)L(1))] takes place only after protonation of both uncoordinated oxygen atoms of each phosphonate moiety and at least one nitrogen atom of the cycle. The exceptional kinetic inertness of both isomers is illustrated by their half-lives tau(1/2)=19.7 min for pc-[Cu(H(2)L(1))] and tau(1/2) about seven months for trans-O,O-[Cu(H(2)L(1))] for decomplexation in 5 M HClO(4) at 25 degrees C. The mechanism of formation of pc-[Cu(L(1))](2-) is similar to those observed for other macrocyclic complexes.     

Exploiting space‐group symmetry in fragment‐based molecular crystal calculations

Recent developments in fragment‐based methods make it increasingly feasible to use high‐level ab initio electronic structure techniques to molecular crystals. Such studies remain computationally demanding, however. Here, we describe a straightforward algorithm for exploiting space‐group symmetry in fragment‐based methods which often provides computational speed‐ups of several fold or more. This algorithm does not require a priori specification of the space group or symmetry operators. Rather, the symmetrically equivalent fragments are identified automatically by aligning the individual fragments along their principle axes of inertia and testing for equivalence with other fragments. The symmetry operators relating equivalent fragments can then be worked out easily. Implementation of this algorithm for computing energies, nuclear gradients with respect to both atomic coordinates and lattice parameters, and the nuclear hessian is described. © 2014 Wiley Periodicals, Inc.