THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Molecular dynamics investigation of ferrous-ferric electron transfer in a hydrolyzing aqueous solution: calculation of the pH dependence of the diabatic transfer barrier and the potential of mean force

We present a molecular model for ferrous-ferric electron transfer in an aqueous solution that accounts for electronic polarizability and exhibits spontaneous cation hydrolysis. An extended Lagrangian technique is introduced for carrying out calculations of electron-transfer barriers in polarizable systems. The model predicts that the diabatic barrier to electron transfer increases with increasing pH, due to stabilization of the Fe3+ by fluctuations in the number of hydroxide ions in its first coordination sphere, in much the same way as the barrier would increase with increasing dielectric constant in the Marcus theory. We have also calculated the effect of pH on the potential of mean force between two hydrolyzing ions in aqueous solution. As expected, increasing pH reduces the potential of mean force between the ferrous and ferric ions in the model system. The magnitudes of the predicted increase in diabatic transfer barrier and the predicted decrease in the potential of mean force nearly cancel each other at the canonical transfer distance of 0.55 nm. Even though hydrolysis is allowed in our calculations, the distribution of reorganization energies has only one maximum and is Gaussian to an excellent approximation, giving a harmonic free energy surface in the reorganization energy F(DeltaE) with a single minimum. There is thus a surprising amount of overlap in electron-transfer reorganization energies for Fe(2+)-Fe(H2O)6(3+), Fe(2+)-Fe(OH)(H2O)5(2+), and Fe(2+)-Fe(OH)2(H2O)+ couples, indicating that fluctuations in hydrolysis state can be viewed on a continuum with other solvent contributions to the reorganization energy. There appears to be little justification for thinking of the transfer rate as arising from the contributions of different hydrolysis states. Electronic structure calculations indicate that Fe(H2O)6(2+)-Fe(OH)n(H2O)(6-n)(3-n)+ complexes interacting through H3O2- bridges do not have large electronic couplings.     

An electron-diffraction study of the molecular structure of gaseous perbromyl fluoride and calculation of its force field and vibrational amplitudes

The molecular structure of FBrO₃ has been studied by gas-phase electron diffraction. Least-squares refinements of the molecular geometry using fixed spectroscopic amplitudes revealed two geometrical minima. Initially, the amplitudes employed were derived from diagonal force fields obtained by spectroscopic least-squares refinements to fit observed and calculated wave numbers; for each geometry there are two spectroscopic minima. In the lowest geometrical minimum the wave number agreement is poor, however, the introduction of the ∠OBrO/∠FBrO interaction force constant removed the discrepancies; the resulting force field is F(Br-O) = 6.92 ± 0.02 mdyn Å^?1F(Br-F) = 3.22 ± 0.03 mdyn Å^?1, F(∠OBrO) = 1.06 ± 0.02 mdyn Å, F(∠FBrO) = 0.81 ± 0.03 mdyn Å, F(∠OBrO/∠FBrO) = ?0.19 ± 0.02 mdyn Å. In the corresponding geometrical minimum r_g(Br-O) = 1.582 ± 0.001 Å, r_g(Br-F) = 1.708 ± 0.003 Å, r_α(∠OBrO) = 114.9 ± 0.3°, r_α(∠FBrO) = 103.3 ± 0.3°. Perpendicular amplitude correction coefficients, calculated for each force field employed, were used throughout to relate the interatomic distances through the r_α-structure. The geometries of the r_α^o- and r_e-structures are estimated.     

A gas-phase electron diffraction study of the molecular structure of tetravinylsilane

The molecular structure of tetravinylsilane has been studied by gas-phase electron diffraction. The radial distribution curve suggests the absence of conformers having vinyl double bonds staggered with respect to the SiC₄ skeleton. Of the eclipsed or approximately-eclipsed conformers, the one with S₄ symmetry gives the best fit with experiment, although a small admixture of a C₁ conformation cannot be ruled out. Least-squares refinement gave the following values for the independent structural parameters (lengths, r_a basis; angles, r_α basis): C-H = 1.118 ± 0.003 Å, CC = 1.355 ± 0.002 Å, Si-C = 1.855 ±0.002 Å, ∠SiCC = 124.0 ± 0.3°, ∠SiCH = 118.4 ± 1.0°, torsion angles CSiCC are 17.5 ± 0.6° from the eclipsed conformation. During the refinement the vibrational amplitudes u and perpendicular amplitude corrections K were held constant at calculated values. The CC bond length provides evidence of interaction between the vinyl π-bonds and the vacant d-orbitals of silicon.     

Gårding's Theory of Hyperbolic Polynomials

This paper presents a simple, self‐contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke‐Güler‐Lewis‐Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated “branches” are independent of the choice of hyperbolic direction. © 2013 Wiley Periodicals, Inc.     

Thermal Characterizations of Inorganic and Organometallic Polymers

This review emphasizes the breadth of metallic and metallic-like polymers evaluated as to thermal properties. Techniques usefully applied to particular systems are noted with the aim of suggesting their application to other systems.