Relativistic effect on total energies for determination of correlation energies of atoms from their experimental total energies

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Abstract
Relativistic effect Erel upon the total electronic energy of an atom is discussed with particular reference to obtaining the nonrelativistic total energy Eexact from the experimental total energy. Numerical values of this effect obtained by various authors by different nonempirical methods are compared for neutral atoms of rare-gas elements. It is shown that methods either of a Hartree–Fock-type or of a Dirac–Hartree–Fock-type give much the same Erel value for He through Ar. It is pointed out that Erel calculated with Hartree–Fock wave functions is not adequate for use in obtaining Eexact from the experimental total energy and that the Erel value calculated with wave functions including electron correlation should work well, although an actual demonstration can be done only for two-electron systems for lack of data. A semiempirical formula is therefore proposed, which is useful for least-squares fit of experimental total energies of isoelectronic series of atoms to extract nonrelativistic total energies along with the relativistic effect. From nonrelativistic energies thus derived, semiempirical values of correlation energies of atoms are obtained. The results thus obtained are in reasonable agreement with correlation energies derived by Clementi along somewhat different lines. The power series expansion in Z of the fitted formula for the He series shows that numerical values of expansion coefficients agree reasonably well with the corresponding values obtained by accurate relativistic and nonrelativistic Z expansion-type calculations.