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

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

Marital status and suicidal ideation among Australian older adults: the mediating role of sense of belonging

See also Corrigendum: Suzanne McLaren, Rapson Gomez, Peter Gill and Jessica Chesler (2015). Marital status and suicidal ideation among Australian older adults: the mediating role of sense of belonging – CORRIGENDUM. International Psychogeriatrics, 27, pp 155-155. doi:10.1017/S1041610214002166

INFRARED AND RAMAN SPECTROSCOPIC STUDY OF ION PAIRING OF STRONTIUM(II) AND BARIUM(II) BY THIOCYANATES IN LIQUID AMMONIA

Infrared and Raman spectroscopy techniques have been used to study the ionic interactions of strontium(II) and barium(II) with thiocyanate ion in liquid ammonia. A number of bands were observed in both n (CN) and n (CS) regions of infrared and Raman spectra and these were assigned to 1:1 contact ion pair, [M2+----NCS]+; band (B) to a triple-ion, SCN---- M2+----NCS; band (C) to solvent-shared ion pair, [(NH3)xM2+¬ NH3----NCS]+; band (D) to a ";free"; thiocyanate anion SCN- and band (E) to an upper stage transition arising from the excitation of a linear species already in a vibrational level above the ground state. (Received September 28, 2001; revised April 10, 2002) Bull. Chem. Soc. Ethiop. 2002, 16(1), 65-72

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

Aynak : a world-class sediment-hosted copper deposit, Afghanistan

The Aynak copper deposit, located 30 km south of Kabul in Afghanistan, was discovered by Soviet geologists in the 1970s. Extensive exploration undertaken in the area between 1974-80 included several hundred boreholes, seventy trenches and nine exploratory adits. This delineated several large ore bodies and smaller lenses with a total “drill-indicated resource” of 240 Mt at 2.3% Cu (ESCAP, 1995). The mineralisation at Aynak consists of disseminated bornite and chalcopyrite, mainly concentrated in a stratabound orebody in a cyclic succession of metamorphosed dolomites, marls, siltstones and carbonaceous pelites. A model proposes Cu was leached from underlying volcanic rocks and flowed up faults to deposit Cu sulphides into overlying sediments