The chemical potential for the inhomogeneous electron liquid in terms of its kinetic and potential parts with special consideration of the surface potential step and BCS-BEC crossover

The chemical potential μ of a many-body system is valuable since it carries fingerprints of phase changes. Here, we summarize results for μ for a three-dimensional electron liquid in terms of average kinetic and potential energies per particle. The difference between μ and the energy per particle is found to be exactly the electrostatic potential step at the surface. We also present calculations for an integrable one-dimensional many-body system with delta function interactions, exhibiting a BCS-BEC crossover. It is shown that in the BCS regime the chemical potential can be expressed solely in terms of the ground-state energy per particle. A brief discussion is also included of the strong coupling BEC limit.     

Exact asymptotic solution of the Della Sala-Görling integral equation for the exchange-only potential for Be-like atomic ions at large Z

Della Sala and Görling (DSG) have written an integral equation for the exchange-only potential Vx(r) in terms of the Dirac density matrix. Here, an exact asymptotic solution of this integral equation is presented, for the ground state of Be-like atomic ions, in terms of γ(r,r^′) plus the 2s HOMO orbital. In the large Z limit of such ions, the DSG integral equation corrects the asymptotic form −e²/r of Vx(r) by exponentially decaying terms. This amounts to setting the polarizability equal to zero.     

Analysis of flavonoids: tandem mass spectrometry, computational methods, and NMR

Due to the increasing understanding of the health benefits and chemopreventive properties of flavonoids, there continues to be significant effort dedicated to improved analytical methods for characterizing the structures of flavonoids and monitoring their levels in fruits and vegetables, as well as developing new approaches for mapping the interactions of flavonoids with biological molecules. Tandem mass spectrometry (MS/MS), particularly in conjunction with liquid chromatography (LC), is the dominant technique that has been pursued for elucidation of flavonoids. Metal complexation strategies have proven to be especially promising for enhancing the ionization of flavonoids and yielding key diagnostic product ions for differentiation of isomers. Of particular value is the addition of a chromophoric ligand to allow the application of infrared (IR) multiphoton dissociation as an alternative to collision-induced dissociation (CID) for the differentiation of isomers. CID, including energy-resolved methods, and nuclear magnetic resonance (NMR) have also been utilized widely for structural characterization of numerous classes of flavonoids and development of structure/activity relationships.The gas-phase ion chemistry of flavonoids is an active area of research particularly when combined with accurate mass measurement for distinguishing between isobaric ions. Applications of a variety of ab initio and chemical computation methods to the study of flavonoids have been reported, and the results of computations of ion and molecular structures have been shown together with computations of atomic charges and ion fragmentation. Unambiguous ion structures are obtained rarely using MS alone. Thus, it is necessary to combine MS with spectroscopic techniques such as ultraviolet (UV) and NMR to achieve this objective. The application of NMR data to the mass spectrometric examination of flavonoids is discussed.     

An environmental friendly method for the automatic determination of hypochlorite in commercial products using multisyringe flow injection analysis

A multisyringe flow injection analysis system was used for the determination of hypochlorite in cleaning agents, by measurement of the native absorbance of hypochlorite at 292 nm. The methodology was based on the selective decomposition of hypochlorite by a cobalt oxide catalyst giving chloride and oxygen. The difference of the absorbance of the sample before and after its pass through a cobalt oxide column was selected as analytical signal. As no further reagent was required this work can be considered as a contribution to environmental friendly analytical chemistry. The entire analytical procedure, including in-line sample dilution in three steps was automated by first, dilution in a stirred miniature vessel, second by dispersion and third by in-line addition of water using multisyringe flow injection technique. The dynamic concentration range was 0.04-0.78 g L⁻¹ (relative standard deviation lower than 3%), where the extension of the hypochlorite decomposition was of 90 ± 4%. The proposed method was successfully applied to the analysis of commercial cleaning products. The accuracy of the method was established by iodometric titration.     

Proposed sets of critical exponents for randomly branched polymers,using a known string theory model

The critical exponent ν for randomly branched polymers with dimensionality d equal to 3, is known exactly as 1/2. Here, we invoke an already available string theory model to predict the remaining static critical exponents. Utilizing results of Hsu et al. (Comput Phys Commun. 2005;169:114–116), results are added for d = 8. Experiment plus simulation would now be important to confirm, or if necessary to refine, the proposed values.     

Optimized geometry of the cluster Gd2O3 and proposed antiferromagnetic alignment of f-electron magnetic moment

There is currently experimental interest in assemblies of Gd2O3 clusters. This has motivated the present study in which a single such cluster in free space is examined quantitatively by spin-density functional theory, with appropriate relativistic corrections incorporated for Gd. First, the nuclear geometry of the cluster is optimized, and it is found to be such that the two Gd atoms lie in a symmetry axis perpendicular to the isosceles triangle formed by the O atoms. Then, a careful study is made of the magnetic arrangement of the localized f-electron moments on the two Gd atoms. The prediction of the present treatment is that the localized spins are aligned antiferromagnetically. An alternative picture using superexchange ideas leads to the same conclusion.     

Fragmentation of 3-hydroxyflavone; a computational and mass spectrometric study

In a recent study of the collision-induced dissociation of protonated and deprotonated molecules of 3-, 5-, 6-, 7-, 2'-, 3'- and 4'-hydroxyflavone, it was observed that the ratio, gamma, of the propensities for cross-ring cleavage (CRC) to ring opening (RO) varied by a factor of 660, i.e., from 0.014:1 (for deprotonated 3-hydroxyflavone) to 9.27:1 (for deprotonated 5-hydroxyflavone). An explanation for the variation of gamma was presented in terms of experimental NMR (13)C and (1)H spectra modified by computation. Deprotonated 3-hydroxyflavone exhibited the highest ion signal intensity for fragmentation following RO relative to that for CRC in that gamma = 0.014:1. Because no chemical computations of the fragmentation of protonated and deprotonated monohydroxyflavone molecules have been carried out thus far, the basis on which fragmentation mechanisms for deprotonated 3-hydroxyflavone have been proposed is principally chemical intuition. The energy states of product ions formed in the fragmentation of deprotonated 3-hydroxyflavone molecules were computed by the CBS-4M method implemented in Gaussian 03. The overly demanding calculations needed to handle diradicals reliably and directly were circumvented by a process in which each of the bond-breaking reactions was approximated by a process that gave two monoradicals. Bond energies were calculated, with one exception, from the approximation reactions as the energy of products minus the energy of reactants.     

Legendre transform of the noninteracting kinetic energy: Especially from March–Murray perturbation theory based on plane waves

The Legendre transform of the noninteracting kinetic energy is derived from the March–Murray perturbation theory based on plane waves. Further useful relations are summarized, and it is shown that insight can be gained from simple model systems where nonperturbative equations can be derived. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 138–142, 2001