Inhomogeneous Electron Liquid in a Homogeneous Magnetic Field of Arbitrary Strength

Abstract

Our recent paper [Phys. Rev. A, 60, 2853 (1999)] on the field dependence of the energy of a molecule in an arbitrary magnetic field is extended here by results which can be expressed solely in terms of the total kinetic energy of the electron liquid of a molecule or an atom in a homogeneous magnetic field.     

Discrete-spectrum contribution to the Lamb-shift of the 2S and 2P hydrogenic states

A general formula due to Moses [Phys. Rev. A8, 1710 (1973)] for exact electric and magnetic multipole transition matrix elements in nonrelativistic hydrogenic atoms is reduced by carrying out additional integrations. By using the obtained reduced formula unrenormalized (finite) and renormalized Lamb-shift contributions stemming from individual discrete states as well as from the whole discrete spectrum are calculated in the case of the states 2S and 2P.     

A study for structure and inter-diffusion coefficient of liquid K1− x Cs x metal alloys

Inter-diffusion coefficients of liquid K_{1? x} Cs _x metal alloys are calculated using scaling law proposed by Samanta et al. [A. Samanta, Sk.M. Ali, and S.K. Ghosh, Phys. Rev. Lett. 87, 245901 (2001)] following Dzugutov [M. Dzugutov, Nature 381, 137 (1996)], which express the possible relationship between the excess entropy and diffusion coefficient. The interatomic interactions are described from the individual version of the electron–ion potential proposed by Fiolhais et al. [C. Fiolhais, J.P. Perdew, S.Q. Armster, J.M. McLaren, and M. Brajczewska, Phys. Rev. B 51, 14001 (1995)]. The partial pair distribution functions and structure factors are calculated from the solution of Ornstein–Zernike integral equation with Rogers–Young closure. The evaluations with the composition of static structure and the inter-diffusion properties are discussed.     

Towards an exact orbital-free single-particle kinetic energy density for the inhomogeneous electron liquid in the Be atom

Holas and March [Phys. Rev. A51, 2040 (1995)] wrote the gradient of the one-body potential V(r) in terms of low-order derivatives of the idempotent Dirac density matrix built from a single Slater determinant of Kohn–Sham orbitals. Here, this is first combined with the study of Dawson and March [J. Chem. Phys. 81, 5850 (1984)] to express the single-particle kinetic energy density of the Be atom ground-state in terms of both the electron density n(r) and potential V(r). While this is the more compact formulation, we then, by removing V(r), demonstrate that the ratio t(r)/n(r) depends, though non-locally, only on the single variable n′(r)/n(r), no high-order gradients entering for the spherical Be atom.     

Pair potential of liquid metallic Be from electron theory compared and contrasted with recent ab initio work on the free-space beryllium dimer

Two decades ago, Perrot and March [F. Perrot and N.H. March, Phys. Rev. A. 41, 4521 (1990)] used electron theory to derive an oscillatory pair potential between the beryllium nuclei in liquid metal beryllium. They predict a first minimum at 2.1?Å, followed by a larger repulsive hump at 2.8?Å. Here, we compare and contrast this result for liquid beryllium with the recent ab initio work by Koput and the present quantum Monte Carlo (QMC) calculation on the beryllium dimer in free space. Koput situates the minimum in the potential curve for the free-space dimer at 2.4?Å and it is quite similar in depth to that for liquid metallic beryllium. Our QMC curve is similar, with the minimum at 2.33?Å. They are tabulated in this letter.     

Entropic effects on the rheological behaviour of n-eicosane and comparison with n-heptadecane

Abstract

The motivation for this study is the review by Timusk and Statt [Rep. Prog. Phys. 62, 61 (1999)] on the pseudogap in high-temperature superconductors. Here, we confront the experimental data they present, plus that of Norman et al. [Nature 392, 157 (1998)] on the Fermi surface in underdoped high-T_c materials with the theoretical asymptotic scenario of precursor r space Boson formation. This reveals no inconsistencies with available observations concerning electron (hole) liquids flowing through such underdoped cuprates with their antiferromagnetic spin fluctuations.     

Ten-Electron Central Field Problem: An Inhomogeneous Electron Liquid

Abstract

Recent work has been carried out on the exchange energy density epsive;_x(r) of a ten-electron atomic ion in the (bare Coulomb) limit of large atomic number Z [Howard, I. A. et al (2000). Phys. Rev. A, 62, 062512]. This analytical study of epsive; x(r) was made possible by the existence of a closed form of the first-order (idempotent) density matrix (IDM).

Here, some generalizations are effected to a central potential energy V(r) which (a) localizes the ten electrons and (b) yields closed K and L shells for these ten electrons occupying the lowest eigenstates with spin compensation. In particular, it is shown that p-shell properties alone determine the IDM in this example of a confined inhomogeneous electron liquid.     

Electron or hole liquids in high-T c cuprates: evidence for d-wave order parameter

Phillips and Jung [J.C. Phillips and J. Jung (2002). Phil. Mag. B, 82, 1163] refute nodal properties of the gap function Δ_k and propose an isotropic s-wave picture with electron–phonon interaction as the mechanism for high-T _c superconductivity in the cuprates. Here, we compare and contrast predictions of various physical properties with the gap function Δ_k reflecting three scenarios: (i) isotropic s-wave pairing, (ii) extended s-wave with eight line nodes as championed quite recently by Zhao [G.M. Zhao (2001). Phys. Rev. B, 64, 024503], and (iii) d-wave pairing. By referring to (a) scanning tunnelling microscopy imaging of a Zn impurity, supported by our own subsequent theoretical study, (b) linear decrease of T _c with non-magnetic impurity concentration, and (c) calculations on the extended s-wave scenario applied to tunnelling conductance, strong evidence for nodal properties of Δ_k is given. The contentions of Phillips and Jung [J.C. Phillips and J. Jung (2002). Phil. Mag. B, 82, 1163] should therefore be treated with considerable caution, isotropic s-wave behaviour being truly exceptional among the high-T_c cuprates.     

Polyatomic molecular liquids under extreme compression: facts,models, and a few predictions

Early work by Siringo, Pucci and March (Phys. Rev. B, 37, 2491 (1988)) studied solid I₂ under high pressure at T = 0. Their conclusion was that insulating crystalline I₂ at low pressures eventually transformed into a molecular metal. This has subsequently been confirmed experimentally. Later studies by Weir et al. (Phys. Rev. Lett., 76, 1860 (1996)) on solid H₂ under pressure point in the same direction, though in the solid phase the metallic state has still not been achieved at low temperatures. However, in the liquid phase, an insulating metallic transition has been proposed, as in solid iodine, again on the basis of experimental high-pressure studies. Here, attention is shifted to some polyatomic molecules, such as the 10-electron series H₂O, NH₃ and CH₄. Particular attention is focused on the measured Hugoniots of the polyatomic molecular liquids.     

Differential virial theorem in relation to a sum rule for the exchange-correlation force in density-functional theory

Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions.     

Three-dimensional bond-charge models for potential curves of diatomic molecules

Several simple three-dimensional Fermi-gas models for potential energy curves of diatomic molecules are suggested. Bond-charge parameters close to those predicted by the earlier point bondcharge model of Borkman, Simons and Parr [J. Chem. Phys. 49, 1055 (1968); 50, 58 (1969)] are obtained for models assuming uniform spherical or elliptical electron distributions in the bond region.Aided by a research grant to The Johns Hopkins University from the National Science Foundation.     

Superfluidity with and without a condensate in two and three dimensions

The recent study of He and You [P.-S. He and W.-L. You, Int. J. Mod. Phys. B26, 1250107 (2012)] on the relation between superfluid and condensate densities in a two-dimensional weakly interacting Boson system assumed a δ(x???x′) interaction between two particles at sites x and x′. The main purpose of this article is to point out the sensitivity of the conclusions of He and You to the choice of interaction. Thus, it is known for logarithmic interactions that one can have superfluidity without a condensate. Finally, some related ideas are mentioned in relation to superfluidity in liquid ⁴ He at exceedingly low temperatures.     

Nonlinear optical properties of confined excitons in clusters

Size effects in femtosecond photon echo spectroscopy of neat clusters are calculated using a quasiparticle representation of the nonlinear response. We extend our previous study of cooperative effects on the nonlinear response of assemblies of two level molecules [J. A. Leegwater and S. Mukamel, Phys. Rev. A46, 452 (1992)] to allow for nuclear motion and to have an s-p model of polarizable atoms. Photon echos in Benzene/Argon clusters are calculated using a semiclassical phase averaging procedure [L. E. Fried and S. Mukamel, Adv. Chem. Phys. (in Press)].     

Ionization energies and stabilities of Na n,n<25: shell structure from measurements on cold clusters

The stability patterns found in alkali-atomic clusters and their explanation in terms of electronic and structural factors have been controversial for some time. Generation of very cold Na _n clusters in a novel source and use of a special photoion normalization method resolve the remaining questions by allowing precise determination of photoionization thresholds. This is demonstrated here for several sizes in the 7<n<26 range, where in two crucial cases the interpretations of earlier ionization threshold measurements on oven-beam clusters [M. Kappes, M. Schär, P. Radi, and E. Schumacher, J. Chem. Phys.84, 1863 (1986)] disagreed with the explanation of the observed stability pattern. Combining the new values with the charged-cluster fragmentation energies of Bréchignac et al. [C. Bréchignac, P. Cahuzac, J. Leygnier, and J. Weiner, J. Chem. Phys.90, 1492 (1989)] yields neutral cluster fragmentation energies that successfully account for the famous “magic-number” ledges [W.D. Knight, K. Clemenger, W.A. de Heer, W.A. Saunders, M.Y. Chou, and M.L. Cohen, Phys. Rev. Lett.52, 2141 (1984)]. Our measurements offer decisive support for the applicability of the spherical/spheroidal electronic shell-model to smaller Na _n clusters, even in their low-temperature form.     

High‐precision Hy–CI variational calculations for the ground state of neutral helium and helium‐like ions

Hylleraas–configuration interaction (Hy–CI) method variational calculations with up to 4648 expansion terms are reported for the ground ¹S state of neutral helium. Convergence arguments are presented to obtain estimates for the exact nonrelativistic energy of this state. The nonrelativistic energy is calculated to be ?2.9037 2437 7034 1195 9829 99 a.u. Comparisons with other calculations and an energy extrapolation give an estimated nonrelativistic energy of ?2.9037 2437 7034 1195 9830(2) a.u., which agrees well with the best previous variational energy, ?2.9037 2437 7034 1195 9829 55 a.u., of Korobov (Phys Rev A 2000, 61, 64503), obtained using the universal (exponential) variational expansion method with complex exponents (Frolov, A. M.; Smith, V. H. Jr. J Phys B Atom Mol Opt Phys 1995, 28, L449). In addition to He, results are also included for the ground ¹S states of H^?, Li⁺, Be⁺⁺, and B⁺³. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Minimum uncertainty wavelets in non-relativistic super-symmetric quantum mechanics

We consider the connection to the harmonic oscillator, super-symmetric quantum mechanics (SUSY-QM) and coherent states of the recently derived constrained Heisenberg “minimum uncertainty” (μ-) wavelets [Phys Rev Lett 85:5263 (2000); Phys Rev A65: 052106-1 (2002); J Phys Chem A107:7318 (2003)]. We analyze several new types of raising and lowering operators,which also can be viewed as arising from a (non-unitary) similarity transformation of the Harmonic Oscillator Hamiltonian and ladder operators. We show that these new ladder operators lead to a new SUSY formalism for harmonic oscillation, so that the μ-wavelets naturally manifest SUSY properties. Using these new ladder operators, we construct coherent and supercoherent states for the oscillator. In the discussion, we consider possible implications of similarity transformations for quantum mechanics. In an appendix we consider the classical limit of the μ-wavelet oscillator.     

Thermal behavior of copper(II) pseudohalide complexes containing bidentate amines

Pseudohalide complexes of copper(II) with aliphatic bidentate amines, [Cu(N₃)₂(N,N-diEten)]₂ 1, [Cu(NCO)₂(N,N-diEten)]₂ 2, [Cu(NCO)₂(N,N-diMeen)]₂ 3, [Cu(N₃)(NCS)(N,N'-diMeen)]₂ 4 and [Cu(N₃)(NCO)(N,N-diMeen)]₂ 5 (N,N-diEten=N,N-diethylethylenediamine; N,N-diMeen=N,N- dimethyl-ethylenediamine and N,N'-diMeen = N,N'-dimethylethylenediamine), were prepared, characterized and their thermal behavior was investigated by TG curves. According to thermal analysis and X-ray diffraction patterns all compounds decomposed giving copper(II) oxide as final product. The mechanisms of decomposition were proposed and an order of thermal stability was established.This revised version was published online in November 2005 with corrections to the Cover Date.     

Organotin(IV) complexes with pyruvic acid phenylhydrazone (HPAPD): synthesis,spectral characterization,and in vitro antibacterial activity

The reaction of pyruvic acid phenylhydrazone [HPAPD, (1)] with organotin(IV) chloride(s) leads to the formation of five new organotin(IV) complexes: [MeSnCl₂(PAPD)] (2), [BuSnCl₂(PAPD)] (3), [PhSnCl₂(PAPD)] (4), [Me₂SnCl(PAPD)] (5), and [Ph₂SnCl(PAPD)] (6). The ligand [HPAPD, (1)] and its organotin(IV) complexes (2–6) have been characterized by CHN analyses, molar conductivity, UV-Vis, FT-IR, ¹H, ¹³C, and ¹¹⁹Sn NMR spectral studies. Spectroscopic data suggested that HPAPD is coordinated to tin(IV) through the carboxylato-O and azomethine-N as a mononegative bidentate chelating agent; the coordination number of tin is five. Compound 1 and its organotin(IV) complexes (2–6) were assayed for in vitro antibacterial activity against Staphylococcus aureus, Bacillus subtilis, Enterobacter aerogenes, Escherichia coli, and Salmonella typhi. The screening results show that 2–6 have better antibacterial activity than 1 and that 6 exhibits significantly better activity than 2–5.     

Electrospray mass spectrometric studies of a potential antitumor drug and its analogous platinum(II) and platinum(IV) complexes with the ethylenediamine-N,N′-di-3-propanoato ligand and its dibutyl ester

Abstract  The electrospray mass spectrometric (ESI–MS) behavior of the complexes trans-dichloro(ethylenediamine-N,N′-di-3-propionato)platinum(IV), trans-dibromo(ethylenediamine-N,N′-di-3-propionato)platinum(IV), dichloro(ethylenediamine-N,N′-di-3-propionic acid)platinum(II), tetrachloro(O,O′-di-n-butyl-ethylenediamine-N,N′-di-3-propanoate)platinum(IV), chlorotribromo(O,O′-di-n-butyl-ethylenediamine-N,N′-di-3-propanoate)platinum(IV), and dichloro(O,O′-di-n-butyl-ethylenediamine-N,N′-di-3-propanoate)platinum(II), with the formulae trans-[PtCl₂(eddp)] (1), trans-[PtBr₂(eddp)] (2), [PtCl₂(H₂eddp)] (3), [PtCl₄(Bu₂eddp)] (4), [PtBr₃Cl(Bu₂eddp)] (5), and [PtCl₂(Bu₂eddp)]·H₂O (6), is reported. The deprotonated molecular ions or halide adducts are usually observed. ESI–MS data demonstrate the usefulness of the method for efficient characterization of metal complexes in solution. Graphical Abstract