Many-body approximations for atomic binding energies

TL;DR

This paper compares three many-body approximation methods for atomic binding energies against exact configuration-interaction calculations, finding the random phase approximation to be the most accurate among them.

Contribution

It provides a direct benchmark of Hartree-Fock, projected Hartree-Fock, and random phase approximations against full configuration-interaction results for atoms from Li to Ne.

Findings

RPA has the smallest overall errors among the tested methods.

All methods overestimate the ground state binding energy.

RPA may be useful for efficient basis function optimization.

Abstract

We benchmark three standard approximations for the many-body problem -- the Hartree-Fock, projected Hartree-Fock, and random phase approximations -- against full numerical configuration-interaction calculations of the electronic structure of atoms, from Li through to Ne. These configuration-interaction calculations used up to $2 \times 10^8$ uncoupled basis states, equivalent to $ 10^7$ coupled basis states (configuration state functions.) Each method uses exactly the same input, i.e., the same single-particle basis and Coulomb matrix elements, so any differences are strictly due to the approximation itself. Although it consistently overestimates the ground state binding energy, the random phase approximation has the smallest overall errors; furthermore, we suggest it may be useful as a method for efficient optimization of single-particle basis functions.