Kohn-Sham perturbation theory: simple solution to variational instability of second order correlation energy functional

The orbital-dependent correlation energy functional resulting from second order Kohn-Sham perturbation theory leads to atomic correlation potentials with correct shell structure and asymptotic behavior. The absolute magnitude of the exact correlation potential, however, is greatly overestimated. In addition, this functional is variationally instable, which shows up for systems with nearly degenerate highest occupied and lowest unoccupied levels like Be. In this contribution we examine the simplest resummation of the Kohn-Sham perturbation series which has the potential to resolve both the inaccuracy and the instability problem of the second order expression. This resummation includes only the hole-hole terms of the Epstein-Nesbet series of diagrams, which has the advantage that the resulting functional is computationally as efficient as the pure second order expression. The hole-hole Epstein-Nesbet functional is tested for a number of atoms and ions. It is found to reproduce correlation and ground state energies with an accuracy comparable to that of state-of-the-art generalized gradient approximations. The correlation potential, on the other hand, is dramatically improved compared to that obtained from generalized gradient approximations. The same applies to all quantities directly related to the potential, as, for instance, Kohn-Sham eigenvalues and excitation energies. Most importantly, however, the hole-hole Epstein-Nesbet functional turned out to be variationally stable for all neutral as well as all singly and doubly ionized atoms considered so far, including the case of Be.     

On matrix mappings into some strong Cesàro sequence spaces

We determine the classes (X, Y_T) of matrix transformations from X into Y_T where X is one of the classical sequence spaces c₀, c, ?_∞ and ?₁ of all null, convergent and bounded complex sequences and all absolutely convergent complex series, T is a triangle, Y_T is the matrix domain of T in Y and Y is any of the sets of all sequences that are summable, summable to zero or bounded by the strong Cesàro method of order 1, with index 1 ? p < ∞. Furthermore, we determine the representations of the general bounded linear operators from c into Y. We also establish estimates for the norms of the operators in each case.     

Conductivity in nonpolar media: Experimental and numerical studies on sodium AOT-hexadecane, lecithin-hexadecane and aluminum(III)-3,5-diisopropyl salicylate-hexadecane systems

The conductivity behavior of doped hydrocarbon systems is studied by applying impedance spectroscopy. In the case of 3,5-diisopropyl salicylato aluminum (III) the charge carriers are formed by dissociation of the compound and their concentration is proportional to the square root of the solute concentration. In hydrocarbon systems that consist of micelle forming compounds (sodium AOT/ lecithin) a linear dependence of charge carrier concentration on solute concentration is observed in the concentration regime where micelles are present. The conduction mechanisms are studied by numerical solution of a Poisson-Nernst-Planck system that describes the charge transport. We follow two different approaches to extract the degree of micelle dissociation from the impedance data. Firstly, by computing the response of a linear approximation of the Poisson-Nernst-Planck model, and secondly by computing the fully nonlinear response from direct numerical simulations using finite elements. For high and moderate frequencies both approaches agree very well with the experimental data. For small frequencies the response becomes nonlinear and the concept of impedance fails. Furthermore, the numerically computed values for the degree of dissociation are of the same order of magnitude as the values obtained with classical formulas, but still differ by a factor of about 1/3. The direct numerical simulation allows new insight into the conduction mechanisms for different frequency regimes.     

Integrated and compact fiber-coupled single-photon system based on nitrogen-vacancy centers and gradient-index lenses

A fiber-coupled single-photon system is presented. Gradient-index lenses are utilized for single-photon collection and fiber coupling of a nitrogen-vacancy defect center in a nanodiamond. Integrated filter technology separates excitation and laser light. Therefore, the system is ultracompact with 120 mm(3) in dimension as no bulky free beam optics are used. The commercial availability of all components and their simple assembly allows the implementation of a low-cost single-photon system, possibly approaching single-photon count rates of 500 kcts/s.     

On the functional equation <Emphasis Type="Italic">Af</Emphasis><Superscript>2</Superscript> + <Emphasis Type="Italic">Bg</Emphasis><Superscript>2</Superscript> = 1 on the field of complex <Emphasis Type="Italic">p</Emphasis>-adic numbers

For a fixed prime p, let C _p denote the complex p-adic numbers. For polynomials A, B ε C p [x] we consider decompositions A (x) f ² (x) + B (x) g ² (x) = 1 of entire functions f, g on C p and try to improve an impossibility result due to A. Boutabaa concerning transcendental f, g. We also provide a new proof of a p-adic diophantic statement due to D. N. Clark, which is an important ingredient of Boutabaa’s method.     

Organoplatinum compounds : III. [Me3PtCl04]4, preparative and structural aspects of a new organoplatinum cluster compound

Several methods for the preparation of Me₃PtClO₄ have been investigated: anhydrous, pure Me₃PtCl0₄ was obtained by treating AgClO₄ with Me₃PtI in dry benzene. The compound issensitive to moisture and explodes on heat or shock treatment. Molecular weight determination indicates a tetrameric structure [Me₃PtClO₄]₄, and spectroscopic data are consistent with this. Preliminary X-ray investigation of a single crystal indicates a crystal symmetry I_4I/amd (Schoenflies: D¹⁹_4h) with four [Me₃PtClO₄]₄ units in a tetragonal cell (a = b = 11.267(5); c = 25.09(1)) and local symmetry D_2d of the [Me₃PtCl0₄]₄ structure.     

Approximation numbers of bounded operators

The theory of ideals of linear operators is well developed and has a lot of applications in theory and practise. The purpose of this paper is to give a first idea of a similar theory for bounded (nonlinear) operators. In view of applications we will not give an abstract (perhaps general nonsense) theory, but an example of a class λ_p of bounded operators with a structure similar to an $\text{L}$-module($\text{L}$ represents the class of all linear operators between Banach spaces), and applications to projection methods for solving equations with λ_p-type operators.