We review what is known, unknown, and expected about the mathematical properties of
Coulomb and Riesz gases. Those describe infinite configurations of points in R d interacting …

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 …

Spherical t-designs on 𝕊 d⊂ ℝ d+ 1 S^ d ⊂ 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 …

We report a local, weight-dependent correlation density-functional approximation that
incorporates information about both ground and excited states in the context of density …

The formation of the Wigner molecules in three-dimensional assemblies of equicharged
particles upon weakening of harmonic confinements with spherical symmetry is investigated …

We show how one can construct a simple exchange functional by extending the well-know
local-density approximation (LDA) to finite uniform electron gases. This new generalized …

Natural orbitals (NOs) are central constituents for evaluating correlation energies through
efficient approximations. Here, we report the closed-form expression of the NOs of two …

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 …

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 …

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 …