Article 11114

Title of the article

ON ACCURACY OF THE HARTREE-FOCK METHOD IN CALCULATION OF ATOMS AND IONS

Authors

Malykhanov Yuriy Borisovich, Doctor of physical and mathematical sciences, professor, sub-department of physics and physics teaching technique, Mordovia State Pedagogical Institute named after M. E. Evsevyev
(11a Studencheskaya street, Saransk, Russia), malykhanov@mail.ru
Gorshunov Maksim Vladimirovich, Postgraduate student, Mordovia State Pedagogical Institute named after M. E. Evsevyev (11a Studencheskaya street, Saransk, Russia), malykhanov@mail.ru

Index UDK

539.184

Abstract

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≤Z≤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 ≤ 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.

Key words

energy, atom, ion, Hartree-Fock method, one-electron approximation.

Download PDF
References

1. Lide D. R. Handbook of Chemistry and Physics. 84th edition. New York: CRS Press, 2004, 2475 p.
2. Moore C. E. Natl. Stand. Ref. Data Ser., Natl. Bur. Stand. 1970, no. 34, 22 p.
3. Malykhanov Yu. B., Gorshunov M. V., Evseev S. V., Eremkin I. N., Romanov S. A., Chadin R. M. Tablitsy vysokotochnykh analiticheskikh khartri-fokovskikh funktsiy ato-mov [Tables of highprecision analytical Hartree-Fock functions of atoms]. Saransk: Izd-vo Mord. gos. ped. inst-ta, 2012, 233 p.
4. Malykhanov Yu. B., Gorshunov M. V., Evseev S. V., Eremkin I. N., Chadin R. M. Optika i spektroskopiya [Optics and spectroscopy]. 2013, vol. 114, no. 3, pp. 335–362.
5. Malykhanov Yu. B., Evseev S. V., Gorshunov M. V. Zhurnal prikladnoy spektroskpii [Journal of applied spectroscopy]. 2012, vol. 79, no. 1, pp. 5–14.
6. Malykhanov Yu. B., Evseev S. V., Eremkin I. N. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki [University proceedings. Vol-ga region. Physical and mathematical sciences]. 2011, no. 3 (19), pp. 120–130.
7. Frose-Fisher C. The Hartree-Fock Method for Atoms. New York: Wiley, 1977, 309 p.
8. Bunge C. F., Barrientos J. A., Bunge A. V. At. Data and Nucl. Data Tables. 1993, vol. 53, pp. 113–162.
9. Koga T., Tatewaki H., Thakkar A. J. Phys. Rev. A. 1993, vol. 47, no. 5, pp. 4510–4512.
10. Koga T., Seki Y., Thakkar A. J., Tatewaki H. J. Phys. B.: At. Mol. Opt. Phys. 1993, vol. 26, pp. 2529–2532.
11. Malykhanov Yu. B., Gorshunov M. V. Zhurnal prikladnoy spektroskopii [Journal of applied spectroscopy]. 2013, vol. 80, no. 5, pp. 649–654.
12. Roothaan C. C. J., Bagus P. S. Methods in Computational Physics. New York: Academic Press Inc. 1963, vol.2, pp. 47–94.
13. Mendl C. B., Friesecke G. J. Chem. Phys. 2010, vol. 133, no. 18, pp. 1–14.

 

Дата создания: 18.07.2014 13:35
Дата обновления: 23.07.2014 11:17