Variational versus perturbative relativistic energies for small and light atomic and molecular systems

Abstract

Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called non-radiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac$-$Coulomb$-$Breit (DCB) equation to all orders of the $\alpha$ fine-structure constant. The analysis of the polynomial $\alpha$ dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the non-relativistic energy to high precision without regularization. Contributions from the Breit$-$Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The $\alpha$ dependence of the no-pair DCB energy shows that the higher-order (${\alpha }^4{E}_{\mathrm{h}}$) non-radiative QED correction is 5 % of the leading-order (${\alpha }^3{E}_{\mathrm{h}}$) non-radiative QED correction for $Z=2$ (He), but it is 40 % already for $Z=4$ (Be${}^{2+}$), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.

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Cited by in corpus (12)

• 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
• Relativistic two-electron atomic and molecular energies using $LS$ coupling and double groups: role of the triplet contributions to singlet states
• Pre-Born-Oppenheimer energies, leading-order relativistic and QED corrections for electronically excited states of molecular hydrogen
• Regularized relativistic corrections for polyelectronic and polyatomic systems with explicitly correlated Gaussians
• Lower bounds on par with upper bounds for few-electron atomic energies
• Pre-Born-Oppenheimer Dirac-Coulomb-Breit computations for two-body systems
• 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