Abstract
High-precision calculations of the ground-state energy of atoms He through Xe are performed in the algebraic approximation of the Hartree-Fock method. The orbital exponents of Slater-type basis functions are optimized using the second-order minimization methods, which allows the virial theorem to be fulfilled to within 10−15–10−17 for the first time. The energies of atoms calculated with rather limited basis sets are, in terms of accuracy, as good as the results obtained by using the numerical procedure for solving the Hartree-Fock equations.
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