Calculation of the energy of atoms in configurations with three open shells in the algebraic version of the Hartree-Fock method

According to the nuclear theory of Roothaan - Hartree - Fock theory (a method of Roothaan - Bagus) the authors have conducted high-precision calculations of analytical Hartree - Focks orbitals and energies of atoms in excited configurations with three open shells of different symmetry. Calculations have been performed in algebraic approach applying nuclear orbitals of Slater type as basic functions. Non-linear parameters (orbital exhibitors) have been optimised by means of methods of the first and second order with split-hair accuracy. Due to this method it is possible to reach precision in performance of the virial relation $10^{-14}-10^{-17}$, and the calculated energies of terms of atoms are close to Hartree - Fock limit.