New set of rules of the Slater type on the screening constants and the effective principal quantum numbers

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Abstract
The screening constants (si→j's) and the effective principal quantum numbers (ni's) have been re‐examined for the atoms and the ions with electron configurations of the 1s22sm2pn (m=0, 1, 2; n=0, 1, ⋯ , 6) type. The method used is to derive the expression of the total energy of the 1s22sm2pn atom in its average of the configuration in terms of si→j's and ni's by using the virial theorem and to fit this expression to the experimental or the Hartree‐Fock (HF) values of the total energies of various 1s22sm2pn atoms. As the basis AO's, both the hydrogenic AO (HAO) and the (single) Slater‐type AO (STO) have been tried. The orthogonalized HAO (OHAO) and the orthogonalized STO (OSTO) have also been tried. These minimal basis AO's, in which the orbital exponents are determined with the ``new Slater rules'' thus derived, are compared with the HF AO's to see to what extent we are able to resemble minimal basis AO's to the correspondong HF AO's. It is concluded that the OSTO can behave reasonably closely to the HF AO as far as the 1s and the 2s orbital are concerned. As for the 2p AO, it is found that a minimal basis AO of the Slater type cannot approximate the HF AO, no matter what value of the orbital exponent is taken. The occurence of the nonintegral value of the effective quantum number is discussed and a concept called orbital contraction factor is proposed.
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