Energies of K-Shell for Chemical Elements From (Ne to Si) By Hartree -Fock Method

Abstract

The energies of the K-shell, as well as the atomic characteristics of the (Ne, Na, Mg, Al, and Si) atoms were computed using the algebraic approximation of the Hartree-Fock method(HF) and compared to some experimental results from extensive studies. The calculated atomic energies for atomic number (10 ≤ Z ≤ 14) were assessed. The study demonstrated that the estimates used to calculate the atomic properties using this method were accurate. The function f(r₁₂) for the inter-particle distribution is one of the atomic characteristics. According to this approximation, the two techniques should yield values for the one-particle radial density distribution function D(r) ,( <r₁ⁿ> , <r₁₂ⁿ>), where n is an integer number from  -2 to 2, and the standard deviationand. The properties of the energies expectation values are repulsion potential energy < Vee >, attractive  potential energy< Ven > , total potential energy <V> , kinetic energy <T> and total energy <E>. In conclusion increasing the atomic number leads to an increase in all values studied energies. Finally, the equations were programmed in Mathematics 2015 and all calculations were calculated in atomic units.