Relation between the Z−1 type expansion of the total energy of isoelectronic atoms and the many-electron theory on the electron correlation by Sinanoǧlu

Abstract

By applying the economical formula for the total energies of isoelectronic atoms presented by the present authors [J. Chem. Phys. 84, 6895 (1986)] to both the nonrelativistic exact energy and the Hartree–Fock energy, an expression of the Z−1 expansion type for the correlation energy is obtained for isoelectronic series involving the first-row atoms. Based upon the expression obtained, the following conclusions are derived on the relation between the Z−1 type expansion theory and Sinanoǧlu’s many-electron theory (MET): (i) the Z2 term has nothing to do with the electron correlation; (ii) the term proportional to Z represents the internal correlation energy Eint in MET, at least when Z is large in comparison with the number of electrons N; (iii) the constant term in the Z−1 type expansion is the limiting value of the sum of the semi-internal and the all-external correlation energy (EF+Eu) when Z→∞ and its values for the ground-state atoms show a systematic trend when plotted against N; (iv) the sum of the Z−1 and the higher order terms in Z−1 represents the Z dependence of EF+Eu, although its small amount is attributable to a part of Eint when Z−N≲1.