The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.     

Photoelectron Spectra of Nonmetal Compounds and Their Interpretation by MO Models

The results of (low energy) photoelectron spectroscopy render possible a better appreciation of the “Nature of the Chemical Bond”. The application of this new experimental method is demonstrated utilizing representative compounds of the nonmetal elements, and a close symbiosis delineated with molecular orbital models. In particular, general consequences are discussed concerning electron deficiency, σ- and π-interactions, electron pair delocalization, and substituent effects or geometric perturbations. Photoelectron spectroscopic ionization energies permit evaluation of parameters for specified molecular groups, allow correlation with numerous other experimental data, and are didactically valuable in the teaching of general chemistry.     

On the choice of active space orbitals in MCSCF calculations

We describe a procedure which may be used to aid selection of the active space in multiconfigurational self-consistent field (MCSCF) calculations for general chemical systems. Starting from a restricted Hartree-Fock calculation, we define a hierarchy of interacting virtual orbitals for every occupied orbital. The most strongly interacting orbitals are then taken to constitute the active space in a configuration interaction (CI) calculation. The natural orbital occupation numbers obtained from the CI calculation are then used to choose the active space to be used in a subsequent MCSCF calculation. We illustrate our method on a number of systems (Li₂, B₂, C₂, carbonyl oxide and the transition state for oxidation of H₂S by dioxirane). In all these cases, ‘intuitive’ active spaces are inadequate, as are active spaces derived from the natural orbitals of unrestricted Hartree-Fock calculations.     

建立在群对称轨道(SMO)及特征组态(CD)基础上的CI方法与程序发展

ISMO－CDCI方法点群理论，特别是不可约张量方法，在量子化学理论方法发展以及简化概念与计算方面，发挥了重要作用．但在国外的量子化学计算程序（如G94）中，在后自洽场（opt－SCF）计算方面，很少用到对称约化．在文献中，只见有关hbeltah群（DZh与它的子群）对称约化用于组态相关计算的报导．由于多重耦合系数的计算复杂，蜕化不可约表示多体问题的对称约化难于得到解决．我们提出了一个统一与普遍的方法，它能解决所有分子体系多体相关的点群对称约化问题［‘－6］，这个方法的核心是群对称轨道（SMO）概念的提出．SMO的基本特…     

The role of the π-bonding network for trigonal level splittings of tris-bidentate Cr(acac)3 and Cr(ox) 3 3−

The varying -bonding contributions in the title compounds caused by the different electronic and molecular structure of the chelate rings are used for explaining the large band splittings in the absorption spectra by trigonal symmetry. It is shown that usual ligand field theory and the angular overlap model are not able to account for the trigonal level splitting of Cr(acac)₃ for which the coordination sphere of oxygen atoms is nearly octahedrally arranged. The experimental finding can, however, be rationalized by an extended angular overlap model which considers the phase coupling of -orbitals in the ligands leading to non-additive contributions to the metal-ligand bond energy.On leave of absence from the Bulgarian Academy of Sciences, Sofia, Bulgaria     

On the Criteria of Instability for Electrochemical Systems

Both cyclic-voltammetry-based and impedance-based experimental criteria that have been developed recently for the oscillatory electrochemical systems are critically appraised with two typical categories of oscillators.Consistent conclusions can be drawn by the two criteria for the category of oscillators that involve the coupling of charge transfer mainly with surface steps(e.g.ad-and desorption)such as in the electrooxidation of C1 organic molecules.Whereas,impedance-based criterion is not applicable to the category of oscillators that involve the coupling of charge transfer mainly with mass transfer(e.g.diffusion and convection) such as in the Fe(CN)6^3- reduction accompanying periodic hydrogen evolution.The reason is that the negative impedance cannot include the feedback information of convection mass transfer induced by the hydrogen evolution.However,both positive and negative nonlinear feedbacks,i.e., the diffusion-limited depletion and convection-enhanced replenishment of the Fe(CN)6^3- surface concentration,that coexist between the bistability,i.e.,Fe(CN)6^3- reduction with and without hydrogen evolution at lower and higher potential sides respectively,are all reflected in the crossed cyclic voltammogram(CCV).It can be concluded that the voltammetry-based criterion(in time domain)is more intuitive,less time-consuming and has a wider range of applications than the impedancebased one (in frequency domain).     

Negative-mass instability at nonsymmetrical perturbations

The negative-mass (space-charge) instability is studied within the model of a flat thin electron beam moving along the stationary uniform magnetic field in the case of nonsymmetrical perturbations. It is shown that due to the phenomenon of "phase mixing" of electron bunches the instability increments are small for perturbations with spatial scales smaller than the Larmor diameter.     

Second-order Green's function calculations of the ionization potential of a (H2)7 chain embedded in a homogeneous electric field

Summary The vertical ionization potential and the related pole strength of a model alternant chain of 14 hydrogen atoms subject to a homogeneous electric field, parallel to the chain and of increasing intensity are calculated, in the framework of a 6–31G** basis set, at the second-order level of the many-body Green's function theory. Trends observed with orbital relaxation, pair removal and pair relaxation effects are interpreted in terms of deformations of the electron density.     

Effect of surfactants on the stability of thin liquid film flow on a rotating disk

The effect of surfactants on surface instabilities of thin liquid film flow on a rotating disk was studied at different flow rates Q (0.5相似文献   

On the origin of dynamic instability of molecular systems

The vibronic origin of dynamic instability of molecular systems considered earlier, is here given a more complete and rigorous treatment. It is shown that the nonvibronic contribution to the curvature of the adiabatic potential arising due to nuclear displacements under fixed electronic density distribution, is always positive, and hence the only reason for dynamic instability is the pseudo Jahn-Teller effect. For some examples of special interest (planar equilateral NH₃, planar square CH₄ and linear H ₃ ⁺ ) the molecular excited states, responsible for the instability of the ground state, are revealed by means of ab initio calculations.