Heavy alkaline earth metal pyrazolates: synthetic pathways, structural trends, and comparison with divalent lanthanoids

Two series of heavy alkaline earth metal pyrazolates, [M(Ph(2)pz)(2)(thf)(4)] 1 a-c (Ph(2)pz=3,5-diphenylpyrazolate, M=Ca, Sr, Ba; THF=tetrahydrofuran) and [M(Ph(2)pz)(2)(dme)(n)] (M=Ca, 2 a, Sr, 2 b, n=2; M=Ba, 2 c, n=3; DME=1,2-dimethoxyethane) have been prepared by redox transmetallation/ligand exchange utilizing Hg(C(6)F(5))(2). Compounds 1 a and 2 b were also obtained by redox transmetallation with Tl(Ph(2)pz). Alternatively, direct reaction of the alkaline earth metals with 3,5-diphenylpyrazole at elevated temperatures under solventless conditions yielded compounds 1 a-c and 2 a-c upon extraction with THF or DME. By contrast, [M(Me(2)pz)(2)(Me(2)pzH)(4)] 3 a-c (M=Ca, Sr, Ba; Me(2)pzH=3,5-dimethylpyrazole) were prepared by protolysis of [M[N(SiMe(3))(2)](2)(thf)(2)] (M=Ca, Sr, Ba) with Me(2)pzH in THF and by direct metallation with Me(2)pzH in liquid NH(3)/THF. Compounds 1 a-c and 2 a-c display eta(2)-bonded pyrazolate ligands, while 3 a,b exhibit eta(1)-coordination. Complexes 1 a-c have transoid Ph(2)pz ligands and an overall coordination number of eight with a switch from mutually coplanar Ph(2)pz ligands in 1 a,b to perpendicular in 1 c. In eight coordinate 2 a,b the pyrazolate ligands are cisoid, whilst 2 c has an additional DME ligand and a metal coordination number of ten. By contrast, 3 a,b have octahedral geometry with four eta(1)-Me(2)pzH donors, which are hydrogen-bonded to the uncoordinated nitrogen atoms of the two trans Me(2)pz ligands. The application of synthetic routes initially developed for the preparation of lanthanoid pyrazolates provides detailed insight into the similarities and differences between the two groups of metals and structures of their complexes.     

Analysis of the Electronic Vibrational Spectra of Bisanthene by Calculating Normal Modes

At 4.2 K, the quasiline fluorescence and fluorescence-excitation spectra (in the region of the S ₁ S ₀- and S ₂ S ₀ transitions) of bisanthene in n-hexane have been obtained. Using the MO/M8ST method, the calculation of the A _g normal modes in the S ₀, S ₁, and S ₂ electronic states was carried out for the bisanthene molecule; the relative intensities of the transitions in the corresponding vibronic spectra were also calculated. The analysis of the results of calculations and experiment made it possible to draw conclusions on the form of the modes for a number of normal vibrations which are active in the bisanthene vibronic spectra.     

Entropy of Einstein—Maxwell-Dilaton—Axion Black Holes

The entropy of Einstein—Maxwell-dilaton—axion black holes is calculated by using the improved brick-wall model. Taking into account of the statistical physics, we propose not to consider the superradiant modes. The result shows that the nonsuperradiant modes do contribute exactly the area-law entropy for extreme black hole. Moreover, our cut-off which does not require an angular cut-off is independent of angle . As for the extreme black hole, we found that its entropy is zero.     

Theoretical study of rhodium(I) carbene complexes: the structural versatility of phosphino- compared with aminocarbenes

Density functional calculations are reported for complexes of general formula [(carbene)RhClL(2)] featuring model phosphino- and aminocarbenes. Both the cis and trans isomers of the rhodium(I) eta(1)-complexes (1-9) were investigated, and the influence of the rhodium co-ligands (L=ethylene, phosphine, or carbon monoxide) was evaluated. In the case of phosphinocarbenes and carbon monoxide as a ligand, a somewhat unusual coordination mode was observed, in which a significant intramolecular Cl-->C(carbene) interaction is present. The propensity of phosphino- and aminocarbenes to behave as four electron donors was also investigated both structurally and energetically on the related eta(2)-complexes 10-18. These results as a whole emphasize the structural versatility of phosphino- compared with aminocarbene complexes.     

A Mechanical Model for Analyzing the Runaway Solutions in the Radiation Reaction Problem

In order to understand the rise of runaway solutions in the radiation reaction problem a mechanical model is used. An alternative demonstration of Daboul’s theorem, through Hurwitz’s criterion, is given. The origin of runaway solutions in electrodynamics is discussed. They arise when the particle has a negative mechanical mass or when approximations are used in the equation of motion. In the 1-dimensional mechanical model an exact and linear equation of motion for the particle is obtained, the corresponding exact solution is again runaway when the mechanical mass is negative. The exact solution is not runaway when the mechanical mass is positive. However, the use of approximations leads to an equation of motion which has runaway solutions. It is exhibited that the use of approximations in the 3-dimensional mechanical model is completely necessary because the general equation of motion for the particle is non-linear. The analysis of this case proceeds in a very similar way to the one carried out in electrodynamics. This means that the number of dimensions also plays an important role in the analysis.     

Quasinormal modes of a Schwarzschild black hole surrounded by free static spherically symmetric quintessence: electromagnetic perturbations

In this paper, we evaluated the quasinormal modes of electromagnetic perturbation in a Schwarzschild black hole surrounded by the static spherically symmetric quintessence by using the third-order WKB approximation when the quintessential state parameter w _q in the range of −1/3 < w _q < 0. Due to the presence of quintessence, Maxwell field damps more slowly. And when at −1 < w _q < −1/3, it is similar to the black hole solution in the ds/Ads spacetime. The appropriate boundary conditions need to be modified.     

Dephasing of Andreev pairs entering a charge density wave

A Cooper pair from a s-wave superconductor (S) entering a conventional charge density wave (CDW) below the Peierls gap dephases on the Fermi wavelength while one particle states are localized on the CDW coherence length ξ_CDW. It is thus practically impossible to observe a Josephson current through a CDW. The paths following different sequences of impurities interfere destructively, due to the different electron and hole densities in the CDW. The same conclusion holds for averaging over the conduction channels in the ballistic system. We apply two microscopic approaches to this phenomenon: (i) a Blonder, Tinkham, Klapwijk (BTK) approach for a single highly transparent S-CDW interface; and (ii) the Hamiltonian approach for the Josephson effect in a clean CDW and a CDW with non magnetic disorder. The Josephson effect through a spin density wave (SDW) is limited by the coherence length ξ_SDW, not by the Fermi wave-length. A Josephson current through a SDW might be observed in a structure with contacts on a SDW separated by a distance ξ_SDW.