I. A. Howard

Wave functions and low-order density matrices for a class of two-electron 'artificial atoms' embracing Hookean and Moshinsky models

Abstract A class of model two-electron ‘artificial atoms’ is proposed which embraces both Hookean and Moshinsky models. Particle densities and spinless first-order density matrices are obtained for this class of models. These quantities and the interacting system kinetic energy can be calculated using the ground-state solution of an explicit single-particle radial Schrodinger equation.

Pair function at coincidence and ground-state energy for interacting systems of two fermions with isotropic harmonic confinement and antiparallel spins

Abstract Harmonically confined isotropic two-dimensional fermion systems with different interparticle interactions are compared and contrasted. For a harmonic oscillator interparticle force, the pair correlation function n 2 ( r,r ′) at coincidence is determined analytically and is shown to uniquely fix the ground-state energy. The two-electron Hookean atom is cited for comparison.

Relativistic effects when many independent Fermions are confined in d dimensions

The study of the density of independent harmonically confined Fermions is of considerable current interest because of (a) quantum dots and (b) the experiments of DeMarco and Jin on some alkali metal vapours in magnetic traps. Our concern here is with relativistic effects, first in harmonically confined assemblies of electrons as in (a) above and secondly with a stronger type of Fermion confinement typified again by electrons but now in a quartic rather than quadratic potential. While our numerical illustrations are for dimensionalities d = 1 and 3, some analytical results are presented in d dimensions.

Surface charge model of a carbon nanotube: self-consistent field from Thomas-Fermi theory

Abstract A model of a C nanotube is set up and solved self-consistently by numerical methods using the Thomas–Fermi statistical approach to treat the C 2s and 2p valence electrons. In the model presented here the C 4+ ions are ‘smeared out’ uniformly over the surface of an infinitely long cylinder of radius R t . Analytic forms of the self-consistent field are also presented far from the axis of the infinite tube, and well into its interior.

Changes in nonlinear potential scattering theory in electron gases brought about by reducing dimensionality

Recent work has shown the essential equivalence of stopping power, force-force correlation function, and phase-shift analysis for nonlinear potential scattering in a three-dimensional electron gas. In the present study, we first demonstrate that the above situation is markedly different when the scattering occurs from a localized potential in a two-dimensional (2D) electron gas. Only to second order in the potential do the three methods referred to above precisely agree. However, all these methods can still be applied in 2D, some fully nonlinear evaluation proving possible. The one-dimensional case is also discussed, albeit more briefly. Scattering from a two-center modeling of the localized potential is also calculated, but now only in the Born approximation, due to the added complication of a noncentral potential.

Vibrational frequencies of (H2O) n and (D2O) n clusters for n = 2 and 8: possible relevance to inelastic neutron scattering of ice

Hartree-Fock plus MP2 corrections are reported for the vibrational frequencies in (H2O)2 and (D2O)2 and in the cubic octamers (H2O)8 and (D2O)8. The motivation was the inelastic incoherent neutron scattering of ice as studied experimentally by Li et al. (J.-C. Li, D. Londono, D.K. Ross, J.L. Finney, S.M. Bennington and A.D. Taylor (1992). J. Phys. Cond. Matter, 4, 2109). Some contact is made between our results and these experiments, and also with earlier infrared and Raman studies of Bertie and coworkers.

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.

Force -∂Vxc/∂r associated with the exchange-correlation potential Vxc(r) in the neutral Ne atom

Following an electrostatic interpretation of the force Fxc = −∂Vxc/∂r associated with the exchange-correlation potential Vxc(r), we present both analytical and numerical results for Fxc(r) in the Ne atom. The basic input is an existing quantum Monte Carlo (QMC) calculation of the ground-state electron density ρ(r) in this atom. The analytic form of ∂Vxc/∂r is in terms of the number of electrons Q(r) enclosed in a sphere of radius r centred on the nucleus, plus two phases needed to characterize the radial wavefunctions of density functional theory. Eigenvalue equations are presented for these phases, and used numerically. A brief discussion is added on the result of replacing the QMC ground-state density by its Hartree–Fock counterpart.

An exactly solvable model where properties of a fermion assembly are dominated by the highest occupied level: case of harmonic confinement in d dimensions

It is shown explicitly that the fermion particle density (r) in d dimensions for isotropic harmonic confinement and odd d is determined by the one-dimensional wavefunctions of the highest occupied state. Knowledge of the Dirac density matrices for d = 1 and 2 suffices to completely determine the general d-dimensional matrices.

Interaction of a hydrogen molecule with a water cage (H2O)8

We study the stability of a hydrogen molecule H2 interacting with an octamer water cage (H2O)8, both in the D 2d and in the S 4 configurations. The H2 molecule was allowed to approach the water cage along its main symmetry directions, resulting in physisorbed final configurations, with binding energy 0.01–0.06 eV, depending on the starting geometry and the level of approximation used. The vibrational spectra of all stable configurations show an increase of both IR intensity and Raman activity below 300 cm−1, due to dimer–octamer interaction. Finally, we have also considered an H2 dimer inside a water octamer cage. In this case, we confirm a sizeable blue-shift of the H2 frequency, as has been recently found also for the H2·(H2O)12 cluster.