Density functional theories which are upper bounds to the Hartree-fock limit in one dimension

We begin by constructing the Hartree-Fock density matrix for two model systems, polynomial wavefunctions and the equal-density orbitals. The former yields the generalization of a well-known results for the harmonic oscillator whilst the latter permits the derivation of a density functional theory.     

Semiempirical fine-tuning for Hartree–Fock ionization potentials of atomic ions with non-integral atomic number

Amovilli and March (2006) [8] used diffusion quantum Monte Carlo techniques to calculate the non-relativistic ionization potential I(Z)$I(Z)$ in He-like atomic ions for the range of (fractional) nuclear charges Z   lying between the known critical value _Zc=0.911$Z_{\mathrm{c}}=0.911$ at which I(Z)$I(Z)$ tends to zero and Z=2$Z=2$. They showed that it is possible to fit I(Z)$I(Z)$ to a simple quadratic expression. Following that idea, we present here a semiempirical fine-tuning of Hartree–Fock ionization potentials for the isoelectronic series of He, Be, Ne, Mg and Ar-like atomic ions that leads to excellent estimations of _Zc$Z_{\mathrm{c}}$ for these series. The empirical information involved is experimental ionization and electron affinity data. It is clearly demonstrated that Hartree–Fock theory provides an excellent starting point for determining I(Z)$I(Z)$ for these series.     

Phase transitions driven by quasiparticle interactions

After a survey of the solid–liquid transition, driven by phonon–phonon interactions, attention is next focussed on two phase transitions caused by electron–phonon interactions. These are (i) the Barden–Cooper–Schrieffer pure metal superconducting transition and (ii) the original Peierls instability. These have closely similar forms for the respective transition temperatures, both being related to energy gaps. Spin–phonon interactions are then discussed in relation to spin-Peierls materials. Finally, magnon–magnon interactions are treated in the context of the ferromagnetic–paramagnetic transition in the itinerant electron systems Fe, Co and Ni. Heuristic and phenomenological arguments, plus of course experiment, provide the basis for the conclusions drawn here.     

Proposed interpretation of the transverse magnetic field dependence of the melting temperature T m(B) of a two-dimensional one-component plasma driven by logarithmic interactions

We propose an approximate scaling property of the classical partition function of a two-dimenisional one-component plasma in a high magnetic field based on the molecular dynamics simulations of dubey and Gumbs     

Exact Hamiltonian for an analytic correlated ground-state wave function for He-like ions

A correlated three-parameter variational ground-state Ψ(r₁,r₂,r₁₂) proposed by Chandrasekhar for helium-like ions gives a high percentage of the electron correlation energy resulting from the interaction energy e²/r₁₂ and also yields an analytic ground-state electron density ρ(r). Here, we extract via Schrödinger equation an exact Hamiltonian for which the Chandrasekhar wave function is the ground-state. Properties of the potential energy function in this Hamiltonian are quantified. Finally, kinetic energy densities are plotted and related to the Laplacian of ρ(r).     

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.