All-order relativistic computations for atoms and molecules using an explicitly correlated Gaussian basis

TL;DR

This paper presents a variational method for highly accurate relativistic calculations of atoms and molecules using explicitly correlated Gaussian basis functions, achieving near-ppb precision within the fixed nuclei approximation.

Contribution

It introduces a new variational approach for solving the no-pair Dirac-Coulomb-Breit Hamiltonian with extremely high convergence, applicable across a range of atomic numbers.

Findings

Achieved parts-per-billion convergence for atomic and molecular energies.

Observed deviations from perturbation theory are smaller than self-energy and vacuum polarization corrections.

Method tested successfully from hydrogen to iron (Z=1 to 28).

Abstract

A variational solution procedure is reported for the many-particle no-pair Dirac-Coulomb-Breit Hamiltonian aiming at a parts-per-billion (ppb) convergence of the atomic and molecular energies, described within the fixed nuclei approximation. The procedure is tested for nuclear charge numbers from $Z=1$ (hydrogen) to $28$ (iron). Already for the lowest $Z$ values, a significant difference is observed from leading-order Foldy-Woythusen perturbation theory, but the observed deviations are smaller than the estimated self-energy and vacuum polarization corrections.