On accuracy of the Hartree-Fock method in calculation of atoms and ions

Background. In a number of fields of physics it is necessary to know not only the properties of the neutral atoms, but also their highly ionized states. This is so due to some specific properties arising in multiply ionized systems. One of the main problems in the study of the properties of atoms and ions is calculation of total energy in stationary states. The energy of the ground state of an atom or an ion can be calculated by experimentally determining all of the ionization potentials of the atom. It is a very difficult experimental problem. Therefore, the theoretical calculation of atom and ion energy, which can be done for almost any atom and ion in the framework of the Hartree-Fock method, is of special topicality. The aim of this work is to establish the level of effectiveness of the Hartree-Fock method in calculation of the energy of atoms and ions. Materials and methods. Comparison of the theoretically calculated values of the energy for the atoms from H to Cu and all of their ions will allow to obtain objective assessment of the Hartree-Fock method's accuracy, which is initially approximate. In this paper, the authors calculated in the Hartree-Fock algebraic approximation the energy of atoms ($21 \leq Z \leq 29$) of the periodic system and all their ions to hydrogen atoms, inclusive. These numbers were compared with the experimental values of the energy obtained from the data for ionization potentials. The experimental values of the ionization potentials were taken from the known sources, which are linked in the text. Results. Due to the comparison of the theoretically calculated by the Hartree-Fock method energies of atoms from H to Cu, as well as atomic ions from Sc to Cu, the authors got the results characterizing the accuracy of the calculated values. For atoms ($5 <Z \leq 20$) the error of theoretically obtained values of energy by the Hartree-Fock method is only 0.3%-0.5%. For the isoelectronic series of Sc, Ti, V error of experimental calculations is around 0.6%. However, it starts to grow, and for Ni and Cu atoms is up to 1%. At the same for such atoms the accuracy of experimental data, used for comparison, falls. Conclusions. The results presented in this paper show that the use of the Hartree-Fock method in the calculation of atom and ion energy is quite effective. The error of the theoretical calculations, not exceeding 1 %, taking into account the uncertainty of the experimental data, allows to confirm the correctness of the approximations, that compile the base of the Hartree-Fock method.