Optimization of basis sets for isoelectronic series of closed-shell atoms in Hartree-Fock-Roothaan calculations

Optimization of the nonlinear parameters (orbital exponents) of basis functions in Hartree-Fock-Roothaan calculations may be canied out with a high degree of accuracy. A scheme using second-order methods is suggested for optimization of the orbital exponents of Slater type basis functions defining the ground state of closed-shell atoms. An exact fomula is derived for calculating the partial second derivatives of energy with respect to nonlinear parameters in temis of the density matrix. In bases of isoelectronic series, the orbital exponents are shown to be the linear functions of the charge of the ion nucleus. Optimization calculations are reported for He, Be, Ne, and Mg atoms and their isoelectronic series.