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 (20)

• Search for New Physics with Atoms and Molecules
• Theory of Light Hydrogenlike Atoms
• The DIRAC code for relativistic molecular calculations
• QED calculation of the n=1 and n=2 energy levels in He-like ions
• Model operator approach to the Lamb shift calculations in relativistic many-electron atoms
• ${\alpha }^4$ Ry corrections to singlet states of helium
• Benchmarking theory with an improved measurement of the ionization and dissociation energies of H${}_2$
• Complete ${\alpha }^{6}m$ corrections to the ground state of H${}_2$
• Rotational spectroscopy of cold, trapped molecular ions in the Lamb-Dicke regime
• Relativistic corrections for the ground electronic state of molecular hydrogen
• Pre-Born-Oppenheimer Molecular Structure Theory
• Calculation of the relativistic Bethe logarithm in the two-center problem
• Nonadiabatic rotational states of the hydrogen molecule
• On the Calculation of Resonances in Pre-Born-Oppenheimer Molecular Structure Theory
• Complex scaled relativistic configuration-interaction study of the $LL$ resonances in helium-like ions: from Boron to Argon
• NRQED approach to the fine and hyperfine structure corrections of order $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ -- Application to the hydrogen atom
• QED corrections to the ${}^2{P}_{1/2}-{}^2{P}_{3/2}$ fine structure in fluorinelike ions: model Lamb shift operator approach
• Ro-vibrational states of H${}_2^{+}$. Variational calculations
• Precise computation of rovibronic resonances of molecular hydrogen: $EF{}^1{\Sigma }_{\mathrm{g}}^{+}$ inner-well rotational states
• Relativistic Kinetic-Balance Condition for Explicitly Correlated Basis Functions

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