Thinking outside the box: the uniform electron gas on a hypersphere

Abstract

We discuss alternative homogeneous electron gas systems in which a finite number $n$ of electrons are confined to a $D$-dimensional sphere. We derive the first few terms of the high-density ($r_s\to 0$, where $r_s$ is the Seitz radius) energy expansions for these systems and show that, in the thermodynamic limit ($n\to \infty$), these terms become identical to those of $D$-dimensional jellium.

5 pages, 2 figures, 2 tables, accepted for publication in J. Chem. Phys

References in corpus (10)

• Nearsightedness of Electronic Matter
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• Ground state of two electrons on a sphere
• Ground-state energy of the electron liquid in ultrathin wires
• Excited states of spherium
• Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid
• Hooke's law correlation in two-electron systems
• Correlation energy of the spin-polarized uniform electron gas at high density
• Ground state of two electrons on concentric spheres
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• Uniform electron gases. I. Electrons on a ring
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• Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems
• High-density correlation energy expansion of the one-dimensional uniform electron gas
• Uniform Electron Gases. II. The Generalized Local Density Approximation in One Dimension
• Exchange functionals based on finite uniform electron gases
• Generalized local-density approximation and one-dimensional finite uniform electron gases
• Nodal surfaces and interdimensional degeneracies
• Complex Adiabatic Connection: a Hidden Non-Hermitian Path from Ground to Excited States
• Uniform electron gases: III. Low-density gases on three-dimensional spheres
• Understanding excitons using spherical geometry
• Basis functions for electronic structure calculations on spheres
• Harmonically trapped jellium
• Symmetry-broken local-density approximation for one-dimensional systems
• Two and three electrons on a sphere: A generalized Thomson problem
• Excited States of the Uniform Electron Gas
• Temperature dependence of the surface plasmon resonance in small electron gas fragments, self consistent field approximation
• Transient Uniform Electron Gases