Lower bounds on par with upper bounds for few-electron atomic energies

Abstract

The development of computational resources has made it possible to determine upper bounds for atomic and molecular energies with high precision. Yet, error bounds to the computed energies have been available only as estimates. In this paper, the Pollak-Martinazzo lower-bound theory, in conjunction with correlated Gaussian basis sets, is elaborated and implemented to provide sub-parts-per-million convergence of the ground- and excited-state energies for the He, Li, and Be atoms. The quality of the lower bounds is comparable to that of the upper bounds obtained from the Ritz method. These results exemplify the power of lower bounds to provide tight estimates of atomic energies.

References in corpus (10)

• Pre-Born-Oppenheimer Molecular Structure Theory
• Non-adiabatic, Relativistic, and Leading-order QED Corrections for Rovibrational Intervals of ${}^4$He${}_2^{+}$ ($X{}^2{\Sigma }_{\mathrm{u}}^{+}$)
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• Integrals for lower bounds to the exact energy

Cited by in corpus (3)

• Regularized relativistic corrections for polyelectronic and polyatomic systems with explicitly correlated Gaussians
• Pre-Born-Oppenheimer Dirac-Coulomb-Breit computations for two-body systems
• One-particle operator representation over two-particle basis sets for relativistic QED computations