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 η at each point in space. The gLDA reduces to the LDA when applied to the infinite homogeneous electron gas but, unlike the LDA, it 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 Møller-Plesset perturbation energies, and exact calculations for a variety of inhomogeneous systems.

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 Møller-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 3+ 2 , 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.

Following two recent papers [Phys. Chem. Chem. Phys. 2015, 17, 3196; Mol. Phys. 2015, 113, 1843, we perform a larger-scale study of chemical structure in one dimension (1D). We identify a wide, and occasionally surprising, variety of stable 1D compounds (from diatomics to tetra-atomics) as well as a small collection of stable polymeric structures. We define the exclusion potential, a 1D analogue of the electrostatic potential, and show that it can be used to rationalise the nature of bonding within molecules. This allows us to construct a small set of simple rules which can predict whether a putative 1D molecule should be stable.