Exact Schrodinger wave-function solutions of the fully-correlated few-electron gas and the uniform electron gas

TL;DR

This paper provides numerically exact solutions to the fully correlated few-electron and uniform electron gas models, revealing new oscillatory behaviors at low densities not captured by previous methods.

Contribution

It introduces a Sum-of-Products approach for solving the full-dimensional Schrödinger Equation in few-electron systems, enabling detailed analysis of exchange, correlation, and spin properties.

Findings

Exact solutions show oscillatory behavior at low densities.

New pure-spin exchange/correlation functionals are developed.

Differences observed between few-electron and uniform electron gas behaviors.

Abstract

We present numerically exact solutions to the full-dimensional Schrodinger Equation for the few-electron gas (few-EG) model of electronic structure theory. Our core methodology uses a Sum-of-Products (SOP) representation of singular potentials to make the fully correlated multi-particle quantum mechanical problem computationally tractable. With full access to periodic wave-functions, we analyze the exchange/correlation, spin symmetry, and thermodynamic ($T = 0$K) phases for few-EG systems with up to four explicit electrons per unit cell. We also present pure-spin exchange/correlation functionals for the same few-EG solutions. Finally, we consider the family of few-EG calculations in juxtaposition with the closely related uniform electron gas (UEG) system, for which previous calculations have been performed using density functional theory and quantum Monte Carlo methods. The exact few-EG solutions all display a similar oscillatory behavior at lower densities, which is not predicted by previous UEG simulations.