Agradecimentos: The authors would like to thank the reviewers of this papers for suggestions, comments, and criticism. Financial support is also acknowledged: from FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo - Center for Computational Engineering and Sciences, Grant 2013/08293-7 and Grant 2017/11485-6), and FAEPEX-UNICAMP (Fundo de Apoio ao Ensino, à Pesquisa e à Extensão da UNICAMP). The National Center of High Performance Computing in São Paulo (CENAPAD-SP) is acknowledged for access to their computational facilities. GSTM wishes to thank CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) for a scholarship Ver menos

A grid-based variational method was proposed and applied to the ground state energies of atoms from the first to the third period of the periodic table. The nonuniform grid in the radial coordinate was defined by a q-exponential sequence. Some unusual properties between the optimum q-parameters and the electronic energies or atomic numbers are described. The behavior of the electronic energy, with respect to the q-parameter, yields near Hartree-Fock accuracy with a relatively small number of integration points. A simple relationship between the optimum q-parameters and the atomic numbers was found, which allowed the determination of the optimum q-parameters for atoms of the same period from two results. The remarkable results provide a simple alternative route to reach accurate results. The consistent results also suggest that this is not a random or accidental effect, but some optimum condition achieved by using a q-exponential mesh grid Ver menos