Variational Dirac-Coulomb explicitly correlated computations for atoms and molecules

Abstract

The Dirac-Coulomb equation with positive-energy projection is solved using explicitly correlated Gaussian functions. The algorithm and computational procedure aims for a parts-per-billion convergence of the energy to provide a starting point for further comparison and further developments in relation with high-resolution atomic and molecular spectroscopy. Besides a detailed discussion of the implementation of the fundamental spinor structure, permutation and point-group symmetries, various options for the positive-energy projection procedure are presented. The no-pair Dirac-Coulomb energy converged to a parts-per-billion precision is compared with perturbative results for atomic and molecular systems with small nuclear charge numbers. The subsequent paper [Paper II: D. Ferenc, P. Jeszenszki, and E. Mátyus (2022)] describes the implementation of the Breit interaction in this framework.

References in corpus (15)

• On the eigenvalues of operators with gaps. Application to Dirac operators
• ${\alpha }^4$ Ry corrections to singlet states of helium
• QED and relativistic corrections in superheavy elements
• Benchmarking theory with an improved measurement of the ionization and dissociation energies of H${}_2$
• Nonrelativistic QED approach to the bound-electron g factor
• Complete ${\alpha }^{6}m$ corrections to the ground state of H${}_2$
• Many-electron QED corrections to the g factor of lithiumlike ions
• QED calculation of the ground-state energy of berylliumlike ions
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• Electron-correlation effects in the $g$-factor of light Li-like ions
• Precision Measurements in Few-Electron Molecules: The Ionization Energy of Metastable ${}^4$He${}_2$ and the First Rotational Interval of ${}^4$He${{}_2}^{+}$
• All-order relativistic computations for atoms and molecules using an explicitly correlated Gaussian basis
• Radiative ${\mathbf{\alpha }}^7\mathbf{m}$ QED contribution to the helium Lamb shift
• On the Breit interaction in an explicitly correlated variational Dirac-Coulomb framework
• Orientational decoherence within molecules and emergence of the molecular shape

Cited by in corpus (15)

• 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
• Vibronic mass computation for the $EF$-$GK$-$H\bar{H}$ ${}^1{\Sigma }_{\text{g}}^{+}$ manifold of molecular hydrogen
• Relativistic two-electron atomic and molecular energies using $LS$ coupling and double groups: role of the triplet contributions to singlet states
• 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
• 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