Wigner's function and other distribution functions in mock phase spaces

This review deals with the methods of associating functions with quantum mechanical operators in such a manner that these functions should furnish conveniently semiclassical approximations. We present a unified treatment of methods and results which usually appear under expressions such as Wigner's function, Weyl's association, Kirkwood's expansion, Glauber's coherent state representation, etc.; we also construct some new associations.Section 1 gives the motivation by discussing the Thomas-Fermi theory of an atom with this end in view.Section 2 introduces new operators which resemble Dirac delta functions with operator arguments, the operators being the momenta and coordinates. Reasons are given as to why this should be useful. Next we introduce the notion of an operator basis, and discuss the possibility and usefulness of writing an operator as a linear combination of the basis operators. The coefficients in the linear combination are c-numbers and the c-numbers are associated with the operator (in that particular basis). The delta function type operators introduced before can be used as a basis for the dynamical operators, and the c-numbers obtained in this manner turn out to be the c-number functions used by Wigner, Weyl, Kirkwood, Glauber, etc. New bases and associations can now be invented at will. One such new basis is presented and discussed. The reasons and motivations for choosing different bases is then explained.The copious and seemingly random mathematical relations between these functions are then nothing else but the relations between the expansion coefficients engendered by the relations between the different bases. These are shown and discussed in this light. A brief discussion is then given to possible transformation of the p, q labels.Section 3 gives examples of how the semiclassical expansions are generated for these functions and exhibits their equivalence.The mathematical paraphernalia are collected in the appendices.     

Metalated Hexaphyrins: From Understanding to Rational Design

The heretofore unpredictable behavior of [26] and [28]hexaphyrins upon metalation has been elucidated through quantum chemical calculations. It is demonstrated that the molecular topology of Group 10 and Group 11 metal complexes of hexaphyrins depends on sensitive interplay between the intrinsic ligand strain and the metal–ligand interaction strength. As such, the aromaticity of the ligand and effective charge of the metal are revealed as key factors determining the binding mode and the preference for Möbius or Hückel structures. These findings offer a new perspective to rationalize experimental observations for metalated hexaphyrins. More importantly, the proposed guidelines could be useful for designing novel complexes of hexaphyrins, such as a hitherto unknown Möbius [26]hexaphyrin complex.     

Bis(permethylpentalene)cerium--another ambiguity in lanthanide oxidation state

Ce(eta(8)-C(8)Me(6))(2) exists in a valency close to Ce(iii) with some Ce(iv) and provides an example of the Kondo effect in a discrete molecule.     

Isomers of a dibismuthane, R2Bi-BiR2 [R = 2,6-(Me2NCH2)2C6H3], and unusual reactions with oxygen: formation of [R2Bi]2(O2) and R'R' 'Bi [R' = 2-(Me2NCH2)-6-{Me2N(O)CH2}C6H3; R' ' = 2-(Me2NCH2)-6-{O(O)C}C6H3

R2Bi-BiR2 [1; R = 2,6-(Me2NCH2)2C6H3], a dibismuthane that exists in different forms in the crystalline state, reacts in air with the formation of the peroxide [R(2)Bi]2(O2) (2) and partial oxidation of the pendant (dimethylamino)methyl groups, yielding the mononuclear bismuth complex R'R' 'Bi (3) [R' = 2-(Me2NCH2)-6-{Me2N(O)CH2}C6H3; R' ' = 2-(Me2NCH2)-6-{O(O)C}C6H3].     

Structure of algal-born phenolic polymeric adhesives

Adhesive materials extracted from the brown alga Fucus serratus are composed of phenolic polymer, alginate, and CaCl2. The phenolic polymer undergoes an oxidation reaction in the presence of bromoperoxidase, KI, and H2O2. The nanostructure of the adhesive was investigated using small angle X-ray scattering, light scattering, and cryo- transmission electron microscopy experiments. These have shown that the phenolic polymer undergoes self-assembly and forms flexible chain-like objects. Oxidation or adding alginate does not alter this structure. However, once calcium ions are added, a rigid network is formed. Presumably, this network is responsible for the cohesive strength of the glue.     

Short-range forces and surface tension in nuclei

Consider an atomic nucleus, or any closed system of Fermions under the influence of a saturating short-range interaction. If the range is sufficiently short, one finds that the thickness of the surface layer is not determined by the range of this force, but by a new,quantum mechanical characteristic length, L=(?²/8mF)^1/3, whereF is the restoring force generated at the boundary by the self-consistent potential acting on the most energetic particles. Moreover, in equilibrium, thisforce adjusts itself in such a manner that k _F L ～ 1 wherek _F is the Fermi wave number. As a consequence, one is now able to compute the binding energy, and thus the volume and surface energy coefficients in an explicit analytical fashion as a function of the coupling constants of the interaction, which in the present case is a modified Skyrme interaction. In addition, speculations are made on the existence ofsurface isomers. These are nuclei at several hundred MeV excitation with essentially the same central density, but with an increased surface region.     

Propulsion and trapping of microparticles by active cilia arrays

We model the transport of a microscopic particle via a regular array of beating elastic cilia, whose tips experience an adhesive interaction with the particle's surface. At optimal adhesion strength, the average particle velocity is maximized. Using simulations spanning a range of cilia stiffness and cilia-particle adhesion strength, we explore the parameter space over which the particle can be "released", "propelled", or "trapped" by the cilia. We use a lower-order model to predict parameters for which the cilia are able to "propel" the particle. This is the first study that shows how both stiffness and adhesion strength are crucial for manipulation of particles by active cilia arrays. These results can facilitate the design of synthetic cilia that integrate adhesive and hydrodynamic interactions to selectively repel or trap particulates. Surfaces that are effective at repelling particulates are valuable for antifouling applications, while surfaces that can trap and, thus, remove particulates from the solution are useful for efficient filtration systems.     

Baruch S. Blumberg (1925–2011): Researcher of Hepatitis B,polysaccharides, other areas of science

Baruch S. Blumberg’s career started with investigating the physical chemistry of polysaccharides. It culminated with the discovery of the Hepatitis B virus and the vaccine to prevent infection with it. It was concluded with studying life forms under extreme terrestrial conditions as part of the new science astrobiology.     

Simultaneous end-on/side-on coordination modes of a diphosphorus tetrahedral complex imposed by pre-organization of oligometallic Cu(I) acceptors

The reaction of the [{CpMo(CO)(2)}(2)(μ,η(2):η(2)-P(2))] (Cp=cyclopentadienyl) metallo-ligand 2 with pre-organized Cu(I) bi- and trimetallic precursors afforded new coordination complexes with unprecedented coordination modes for a Mo(2)P(2) complex. Variable-temperature solution and solid-state (31)P NMR spectroscopy measurements were performed and X-ray diffraction studies revealed an η(2):η(1) coordination mode for the Mo(2)P(2) unit of 2 in the Cu(I) bimetallic complexes 3 and 4. DFT calculations were carried out to highlight the bonding situation of this unprecedented coordination mode in the Cu(I) bimetallic compound 3. It is built up from a side-on coordination of the P-P σ bond to one copper ion and from the interaction of the lone pair of one phosphorus atom with the second copper ion. The remaining available lone pair of the second phosphorus atom can be involved as well to interact with an additional metal centre, as evidenced in the Cu(I) trimetallic compound 5 in which an η(2):η(1):η(1) coordination mode of the ligand 2 is observed. Derivative 3 can be used as a molecular clip to obtain discrete π-stacked dimers through a ligand exchange reaction between acetonitrile ligands and cyano-capped π-conjugated systems, indicating the stability of the new η(2):η(1) coordination mode.