Uniform electron gases. III. Low-density gases on three-dimensional spheres.

  title={Uniform electron gases. III. Low-density gases on three-dimensional spheres.},
  author={Davids Agboola and Anneke L Knol and Peter M. W. Gill and Pierre-François Loos},
  journal={The Journal of chemical physics},
  volume={143 8},
By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor… 

Figures and Tables from this paper

Transient uniform electron gases

The uniform electron gas (UEG), a hypothetical system with finite homogenous electron density composed by an infinite number of electrons in a box of infinite volume, is the practical pillar of

One-electron densities of freely rotating Wigner molecules

A formalism enabling computation of the one-particle density of a freely rotating assembly of identical particles that vibrate about their equilibrium positions with amplitudes much smaller than

The uniform electron gas

The uniform electron gas or UEG (also known as jellium) is one of the most fundamental models in condensed‐matter physics and the cornerstone of the most popular approximation—the local‐density

Two and three electrons on a sphere: A generalized Thomson problem

Generalizing the classical Thomson problem to the quantum regime provides an ideal model to explore the underlying physics regarding electron correlations. In this work, we systematically investigate

A weight-dependent local correlation density-functional approximation for ensembles.

A local, weight-dependent correlation density-functional approximation that incorporates information about both ground and excited states in the context of density functional theory for ensembles (eDFT) and automatically incorporates the infamous derivative discontinuity contributions to the excitation energies through its explicit ensemble weight dependence.

Natural occupation numbers in two-electron quantum rings.

The closed-form expression of the NOs of two-electron quantum rings are reported, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory.

Coulomb and Riesz gases: The known and the unknown

We review what is known, unknown, and expected about the mathematical properties of Coulomb and Riesz gases. Those describe infinite configurations of points in [Formula: see text] interacting with

Efficient Spherical Designs with Good Geometric Properties

Spherical t-designs on \(\mathbb {S}^{d}\subset \mathbb {R}^{d+1}\) provide N nodes for an equal weight numerical integration rule which is exact for all spherical polynomials of degree at most t.

Harmonium atoms at weak confinements: The formation of the Wigner molecules.

It is concluded that, like in two dimensions, the emergence of the Wigner molecules in Coulombic systems confined by spherically symmetric harmonic potentials is a complex and gradual process that takes place over a range of confinement strengths spanning several orders of magnitude.

Exchange functionals based on finite uniform electron gases.

It is shown how one can construct a simple exchange functional by extending the well-know local-density approximation (LDA) to finite uniform electron gases by forming a new family of "rung 3" meta-GGA (MGGA) functionals that are named factorizable MGGAs.



Generalized local-density approximation and one-dimensional finite uniform electron gases

We explicitly build a generalized local-density approximation (GLDA) correlation functional based on one-dimensional (1D) uniform electron gases (UEGs). The fundamental parameters of the GLDA

Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas

We have studied the spin-polarized three-dimensional homogeneous electron gas using the diffusion quantum Monte Carlo method, with trial wave functions including backflow and three-body correlations

Uniform electron gases. II. The generalized local density approximation in one dimension.

An explicit gLDA functional for the correlation energy of electrons that are confined to a one-dimensional space is presented and its accuracy with LDA, second- and third-order Møller-Plesset perturbation energies, and exact calculations for a variety of inhomogeneous systems are compared.

Correlation energy of two electrons in the high-density limit.

It is conjecture that for large D, the limiting correlation energy E(c) approximately -delta(2)/8 in any confining external potential, where delta = 1/(D-1).

Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

We report diffusion quantum Monte Carlo calculations of three-dimensional Wigner crystals in the density range rs=100–150. We have tested different types of orbital for use in the approximate wave

Hartree-Fock ground state of the three-dimensional electron gas.

Using numerical calculations for finite systems and analytic techniques, this work studies the unrestricted HF ground state of the three-dimensional electron gas and finds broken spin symmetry states with a nearly constant charge density at high density.

Accuracy of electronic wave functions in quantum Monte Carlo: The effect of high-order correlations

Compact and accurate wave functions can be constructed by quantum Monte Carlo methods. Typically, these wave functions consist of a sum of a small number of Slater determinants multiplied by a

Ground state of two electrons on a sphere

We have performed a comprehensive study of the singlet ground state of two electrons on the surface of a sphere of radius $R$. We have used electronic structure models ranging from restricted and

Effects of backflow correlation in the three-dimensional electron gas: Quantum Monte Carlo study

The correlation energy of the homogeneous three-dimensional interacting electron gas is calculated using the variational and fixed-node diffusion Monte Carlo methods, with trial functions that