Correlation energy of two electrons in the high-density limit

We consider the high-density-limit correlation energy \Ec in $D \ge 2$ dimensions for the $^1S$ ground states of three two-electron systems: helium (in which the electrons move in a Coulombic field), spherium (in which they move on the surface of a sphere), and hookium (in which they move in a quadratic potential). We find that the \Ec values are strikingly similar, depending strongly on $D$ but only weakly on the external potential. We conjecture that, for large $D$, the limiting correlation energy \Ec \sim -\delta^2/8 in any confining external potential, where $\delta = 1/(D-1)$.Comment: 4 pages, 0 figur

Chemistry in One Dimension

We report benchmark results for one-dimensional (1D) atomic and molecular systems interacting via the Coulomb operator $|x|^{-1}$. Using various wavefunction-type approaches, such as Hartree-Fock theory, second- and third-order M{\o}ller-Plesset perturbation theory and explicitly correlated calculations, we study the ground state of atoms with up to ten electrons as well as small diatomic and triatomic molecules containing up to two electrons. A detailed analysis of the 1D helium-like ions is given and the expression of the high-density correlation energy is reported. We report the total energies, ionization energies, electron affinities and other interesting properties of the many-electron 1D atoms and, based on these results, we construct the 1D analog of Mendeleev's periodic table. We find that the 1D periodic table contains only two groups: the alkali metals and the noble gases. We also calculate the dissociation curves of various 1D diatomics and study the chemical bond in H$_2^+$, HeH$^{2+}$, He$_2^{3+}$, H$_2$, HeH$^+$ and He$_2^{2+}$. We find that, unlike their 3D counterparts, 1D molecules are primarily bound by one-electron bonds. Finally, we study the chemistry of H$_3^+$ and we discuss the stability of the 1D polymer resulting from an infinite chain of hydrogen atoms.Comment: 27 pages, 7 figure

Uniform Electron Gases. II. The Generalized Local Density Approximation in One Dimension

We introduce a generalization (gLDA) of the traditional Local Density Approximation (LDA) within density functional theory. The gLDA uses both the one-electron Seitz radius \rs and a two-electron hole curvature parameter $\eta$ at each point in space. The gLDA reduces to the LDA when applied to the infinite homogeneous electron gas but, unlike the LDA, is is also exact for finite uniform electron gases on spheres. We present an explicit gLDA functional for the correlation energy of electrons that are confined to a one-dimensional space and compare its accuracy with LDA, second- and third-order M{\o}ller-Plesset perturbation energies and exact calculations for a variety of inhomogeneous systems.Comment: 26 pages, 2 figures, accepted for publication in Journal of Chemical Physic

Interplay of charge and spin correlations in nickel perovskites

Analyzing the motion of low--spin $(s=1/2)$ holes in a high--spin $(S=1)$ background, we derive a sort of generalized t--J Hamiltonian for the $\rm NiO_2$ planes of Sr--doped nickelates. In addition to the rather complex carrier--spin and spin--spin couplings we take into account the coupling of the doped holes to in--plane oxygen breathing modes by a Holstein--type interaction term. Because of strong magnetic confinement effects the holes are nearly entirely prelocalized and the electron--phonon coupling becomes much more effective in forming polarons than in the isostructural cuprates. In the light of recent experiments on $\rm La_{2-x}Sr_xNiO_4$ we discuss how the variety of the observed transport and charge/spin--ordering phenomena can be qualitatively understood in terms of our model Hamiltonian.Comment: 2 pages, LTpaper.sty, Proc. XXI Int. Conf. on Low Temp. Phys. Prague 9

High-density correlation energy expansion of the one-dimensional uniform electron gas

We show that the expression of the high-density (i.e small-$r_s$) correlation energy per electron for the one-dimensional uniform electron gas can be obtained by conventional perturbation theory and is of the form \Ec(r_s) = -\pi^2/360 + 0.00845 r_s + ..., where $r_s$ is the average radius of an electron. Combining these new results with the low-density correlation energy expansion, we propose a local-density approximation correlation functional, which deviates by a maximum of 0.1 millihartree compared to the benchmark DMC calculations.Comment: 7 pages, 2 figures, 3 tables, accepted for publication in J. Chem. Phy

Effective one-band electron-phonon Hamiltonian for nickel perovskites

Inspired by recent experiments on the Sr-doped nickelates, $La_{2-x}Sr_xNiO_4$, we propose a minimal microscopic model capable to describe the variety of the observed quasi-static charge/lattice modulations and the resulting magnetic and electronic-transport anomalies. Analyzing the motion of low-spin (s=1/2) holes in a high-spin (S=1) background as well as their their coupling to the in-plane oxygen phonon modes, we construct a sort of generalized Holstein t-J Hamiltonian for the $NiO_2$ planes, which contains besides the rather complex ``composite-hole'' hopping part non-local spin-spin and hole-phonon interaction terms.Comment: 12 pages, LaTeX, submitted to Phys. Rev.

Ground state of two electrons on concentric spheres

We extend our analysis of two electrons on a sphere [Phys. Rev. A {\bf 79}, 062517 (2009); Phys. Rev. Lett. {\bf 103}, 123008 (2009)] to electrons on concentric spheres with different radii. The strengths and weaknesses of several electronic structure models are analyzed, ranging from the mean-field approximation (restricted and unrestricted Hartree-Fock solutions) to configuration interaction expansion, leading to near-exact wave functions and energies. The M{\o}ller-Plesset energy corrections (up to third-order) and the asymptotic expansion for the large-spheres regime are also considered. We also study the position intracules derived from approximate and exact wave functions. We find evidence for the existence of a long-range Coulomb hole in the large-spheres regime, and infer that unrestricted Hartree-Fock theory over-localizes the electrons.Comment: 10 pages, 10 figure

Invariance of the correlation energy at high density and large dimension in two-electron systems

We prove that, in the large-dimension limit, the high-density correlation energy \Ec of two opposite-spin electrons confined in a $D$-dimensional space and interacting {\em via} a Coulomb potential is given by \Ec \sim -1/(8D^2) for any radial confining potential $V(r)$. This result explains the observed similarity of \Ec in a variety of two-electron systems in three-dimensional space.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let