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

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.

References in corpus (5)

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• Complete ${\alpha }^{6}m$ corrections to the ground state of H${}_2$
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Cited by in corpus (16)

• Variational Dirac-Coulomb explicitly correlated computations for atoms and molecules
• On the Breit interaction in an explicitly correlated variational Dirac-Coulomb framework
• Variational versus perturbative relativistic energies for small and light atomic and molecular systems
• The Bethe-Salpeter QED wave equation for bound-state computations of atoms and molecules
• Evaluation of the Bethe logarithm: from atom to chemical reaction
• Bound-state relativistic quantum electrodynamics: a perspective for precision physics with atoms and molecules
• Regularized relativistic corrections for polyelectronic and polyatomic systems with explicitly correlated Gaussians
• Pre-Born-Oppenheimer energies, leading-order relativistic and QED corrections for electronically excited states of molecular hydrogen
• Relativistic two-electron atomic and molecular energies using $LS$ coupling and double groups: role of the triplet contributions to singlet states
• Pre-Born-Oppenheimer Dirac-Coulomb-Breit computations for two-body systems
• Lower bounds on par with upper bounds for few-electron atomic energies
• QED corrections to the correlated relativistic energy: one-photon processes
• One-particle operator representation over two-particle basis sets for relativistic QED computations
• Rovibrational computations for the He${}_2$ a ${}^3{\Sigma }_{\mathrm{u}}^{+}$ state including non-adiabatic, relativistic, and QED corrections
• Double-pair Coulomb and Breit photon correction to the correlated relativistic energy
• Deformed Explicitly Correlated Gaussians