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

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