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Fingerprints of antiaromaticity in the negative ion (Li3Al4)−, this species being realisable via a laser vaporisation technique, are revealed by means of anab initioquantum-chemical investigation. First, the ground-state equilibrium geometry of this ion is predicted. Also, for the corresponding inhomogeneous electron liquid, the characteristics of the HOMO are studied, both for the square and the rectangular Al4geometry in two low-lying isomers of the negative ion. There is no particular sensitivity to the change in geometry of the Al4configuration. Therefore, we have calculated theoretically nucleus-independent chemical shifts (NICS), which contain remarkable fingerprints of antiaromaticity. As to future directions, some comments are added in relation to the Shannon entropy. [ABSTRACT FROM AUTHOR]

Three aspects of low-order density matrix (DM) theory will be reviewed, following some brief comments on analogies with, and differences from, density functional theory (DFT). First, the local energy equation, involving first-to-third order DMs, will be set out and applied exactly to model spin-compensated two-electron atoms. Explicit relations known between low-order DMs for harmonic confinement and arbitrary interparticle interactions will be reported for such model atoms. Second, the March–Young proposal for use variationally, satisfyingN-representability, will be set out for spin-free systems such as a four-electron model in the quintet state. Third, the equation of motion for the correlated 1DM is summarised, and brief comments are made on its application to (a) the He atom and (b) crystalline Si. Finally, a model two-electron atom with Coulomb confinement plus ans-wave Coulomb repulsion modified by aδ-function radial correlation is reported as an exactly solvable example. [ABSTRACT FROM AUTHOR]

Quantum-chemical calculations are first reported on the building block Li2C2. Two low-lying isomers are predicted, and hence the equilibrium ground-state geometry by the coupled cluster method (CCSD). The ground-state is non-linear, contrasting with the other planar isomer. The dimer (Li2C2)2 is then examined by the Hartree–Fock plus second-order Møller–Plesset (HF+MP2) method. The ground-state geometry is predicted to have C4 on a linear chain. As to the trimer, the C6 atoms are predicted at the same ab initio level to lie on a hexagon. But the Li atoms prefer each to bond to two C atoms, rather than reproduce the geometry of benzene. Finally, some contact is made with a recent density functional theory study of solid lithium carbide under pressure. [ABSTRACT FROM PUBLISHER]

Motivated by current experimental interest in the interaction of H2O with nanographene, we have made a start on modelling the above system by reporting a Hartree-Fock calculation of H2O on coronene. The lowest energy configuration predicted has the H2O molecule perpendicular to the plane of the coronene molecule, with the oxygen atom away from the plane. The geometry of H2O in this adsorbed state is reported. The case of two H2O molecules interacting with anthracene is also considered, and compared with the structure of the free-space H2O dimer. [ABSTRACT FROM AUTHOR]

Using existing theoretical studies, we point out that the dominant variable in determining Lowdin correlation energies per electron Ec/N of isoelectronic series of molecules at equilibrium is the total number of electrons. This turns out to be Ec/N = -0.033 ± 0.003 a.u. for CH4, NH3, H2O and HF (N = 10), and Ec/N = -0.039 ± 0.007 for some 20 Si-containing molecules in the series SiXnYm. Following earlier work of March and Wind on atoms, some proposals are then made as to a possible explanation of such behaviour. A test is proposed, via low-order Møller-Plesset perturbation theory, as to whether the Lowdin correlation energy density εc(r) is, albeit approximately, a local functional εc(ρ) of the ground-state density for molecules at equilibrium. Such an LDA assumption would imply that εc(ρ) is quantitatively linear in ρ(r), for closed-shell molecules at equilibrium, at least for the light atomic components treated here. This, in turn implies that the dominant effect of the Lowdin correlation energy for closed-shell molecules at equilibrium is merely to shift the chemical potential. [ABSTRACT FROM AUTHOR]

Using a proposed generalisation of the pair distribution function for a gas of non-interacting particles obeying fractional exclusion statistics in arbitrary dimensionality, we derive the statistical correlations in the asymptotic limit of vanishing or low temperature. While Friedel-like oscillations are present in nearly all non-bosonic cases at T = 0, they are characterised by exponential damping at low temperature. We discuss the dependence of these features on dimensionality and on the value of the statistical parameter α. [ABSTRACT FROM AUTHOR]

It is known experimentally that the melting temperature Tm(p) of Na as a function of pressure p increases with p out to ∼20 GPa and then passes through a maximum. Here, we interpret the behavior as passing from classical Wigner-like bcc nuclear structure at low pressures to a structure out to about 60 GPa where the melting is mediated by topological defects. [ABSTRACT FROM AUTHOR]

Recent experiments on the suppression of ferromagnetism due to the spin-polarized electron liquid in half-metallic CrO2 are combined with existing band structure calculations. A semi-empirical form of the variation of Curie temperature with pressure P for P<12 GPa is thereby proposed, to be confirmed, or refined, following further high pressure experiments. [ABSTRACT FROM AUTHOR]

The free energy for superconducting electrons in the Bardeen–Cooper–Schrieffer (BCS) framework is first generalized to apply to superfluid anyons. By appropriate minimization of this free energy, the gap equation for superfluid anyons is then derived. As an application, the energy gap Δ (0), in reduced energy units k B T c , with T c the transition temperature, is obtained as a function of the anyon statistics parameter. [ABSTRACT FROM AUTHOR]

Anyons have been used earlier to interpret the oscillatory orbital magnetization in the Laughlin two-dimensional (2D) electron liquid, which is the seat of the fractional quantum Hall effect. Here, we examine first the anyon fractional statistics distribution function in some detail. Then, applications are treated to other 2D systems, namely (a) a vibrating lattice such as a graphene layer in crystalline graphite, and (b) 2D insulating ferromagnets. [ABSTRACT FROM AUTHOR]

Two complementary mechanisms have been proposed for relatively high temperature superconductor MgB 2 . While the first is the electron–phonon mechanism of BCS theory, advocated strongly by Pickett and co-workers, the second, by Bianconi et al ., invokes Feshbach shape resonances. While we cannot presently discount the second mechanism, and while both proposals exploit the multiband nature of the electronic structure of MgB 2 , we show here that five body-centred cubic (bcc) transition metals, whose superconducting transition temperature correlate intimately with elastic constants and therefore are plainly BCS-like in character, lie on a curve which has MgB 2 at the high T c end. Any alternative mechanism to electron–phonon interaction in MgB 2 will need to account quantitatively for this circumstance. [ABSTRACT FROM AUTHOR]

In earlier work, we have been concerned with the scaling properties of some classes of superconductors, specifically with heavy Fermion materials and with five bcc transition metals of BCS character. Both of these classes of superconductors were three-dimensional but here we are concerned solely with quasi-two-dimensional high- T c cuprates in the underdoped region of their phase diagram. A characteristic feature of this part of the phase diagram is the existence of a pseudogap (pg). We therefore build our approach around the assumption that is the basic dimensionless ratio on which to focus, where the energy E pg introduced above is a measure of the pseudogap. Since anyon fractional statistics apply to two-dimensional assemblies, we expect the fractional statistics parameter allowing ‘interpolation’ between Fermi-Dirac and Bose-Einstein statistical distribution functions as limiting cases to play a significant role in determining and experimental data are analyzed with this in mind. [ABSTRACT FROM AUTHOR]

In the Thomas–Fermi (TF) regime, S. Stringari [Phys. Rev. Lett., 77, 2360 (1996)] established the hydrodynamic normal modes of an interacting dilute Bose-condensed fluid confined in an isotropic harmonic trap. Here, we extend this treatment beyond the TF condensate using the work of B. Hu, G. Huang and Y. Ma [Phys. Rev. A, 69, 063608 (2004)] as a starting point. Both numerical results for low-lying eigenfrequencies, for various angular momentum quantum numbers?l?and n?=?0, and also samples of corresponding eigenfunctions, are presented. Finally, eigenfrequencies are also given for some collective excitations in an axially symmetrical trap. [ABSTRACT FROM AUTHOR]

Recent ab initio predictions concerning the metal-insulator (MI) transition in rings of the light alkali atoms, Li and Na, are compared and contrasted with experimental facts concerning diluted Rb and Cs alkalis. The main focus here is on the local coordination number as a function of density as these two heavy alkali metallic fluids are taken along the liquid-vapour coexistence curve towards the critical point, which in these cases coincides with the MI transition. Also recorded are the results of experiments in which Cs chains are observed at large interatomic spacing outside semiconducting substrates of InSb and GaAs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

After a quite brief discussion of the quantal liquids 4 He, 3 He and H, 'classical' elemental liquids which are treated in turn are C, P, Se and S. Phase boundaries in the ( p , T ) plane exist for each of these liquids, characterized by a change in local coordination number across these boundaries. Corresponding changes in other physical properties are briefly noted. Finally, following this review of elemental liquids, some liquids with two types of atom are briefly considered, the most important but also the most controversial being water. [ABSTRACT FROM AUTHOR]

Superconductors, classified by materials, embrace at least four broad groups: (i) BCS metals and alloys; (ii) heavy Fermion materials; (iii) high- T c cuprates and (some) organic compounds, and (iv) fullerides. Broadly speaking, in classes (i) and (iv), with (i) possibly embracing the recent discovery of superconductivity in MgB 2 with T c ∼ 40 K, electron liquids flow through essentially non-magnetic lattices and the electron-phonon interaction is a key component of the mechanism for Cooper pairing. In classes (ii) and (iii), plus the low- T c material Sr 2 RuO 4 , electron or hole liquids flow through assemblies with magnetic spin fluctuations. The nature of the normal state in class (iii) is not yet universally agreed, both Fermi or Luttinger liquids remaining viable to date, the former, however, with the formation of precursor 2 e Bosons somewhat above T c . Our own studies reveal some common ground between classes (ii) and (iii), involving coherence lengths and effective masses, as well as non- s -wave pairing, though the interactions leading to pairing almost certainly have different physical origins in these two groups. Finally, topological superconductivity is reviewed. It is argued that such a treatment of a topological superfluid could eventually deepen the understanding of the class (iv) fullerides. Resonating valence bond theory, used by Anderson and co-workers as an, of course, approximate strongly-correlated electron technique for high- T c cuprates, can itself be re-written in the form of topological superconductivity, as discussed especially by Wiegmann and collaborators. [ABSTRACT FROM AUTHOR]