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

TL;DR

This paper demonstrates that the Pollak-Martinazzo lower-bound theory, combined with correlated Gaussian basis sets, can produce highly accurate lower bounds for atomic energies, matching the precision of upper bounds and enabling tight energy estimates.

Contribution

It elaborates and implements the Pollak-Martinazzo lower-bound theory with correlated Gaussian basis sets to achieve highly precise bounds for atomic energies.

Findings

Achieved sub-parts-per-million convergence for He, Li, and Be atoms.

Lower bounds are comparable in quality to Ritz upper bounds.

Demonstrated the power of lower bounds for tight atomic energy estimates.

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.