Different Perturbed Uncoupled Hartree–Fock (PUCHF) Methods for Physical Properties. II. Dipole Shielding Factors

The dipole shielding factors for the He and Be isoelectronic sequences have been calculated by the three uncoupled Hartree–Fock (UCHF) methods, ${\gamma }_{\mathrm{UCHF}}{\mathrm{\hspace{0.17em}=\hspace{0.17em}\gamma }}_0$ , by the three UCHF methods with the first‐order perturbation correction (PUCHF methods), ${\gamma }_{\mathrm{PUCHF}}{\mathrm{\hspace{0.17em}=\hspace{0.17em}\gamma }}_0{\mathrm{\hspace{0.17em}+\hspace{0.17em}\gamma }}_1$ , and by the geometric approximation based on the three PUCHF methods, ${\gamma }_{\mathrm{geom}}{\mathrm{\hspace{0.17em}=\hspace{0.17em}\gamma }}_0{\text{(1\hspace{0.17em}−\hspace{0.17em}γ}}_1{\mathrm{\hspace{0.17em}/\hspace{0.17em}\gamma }}_0{)}^{\text{−1}}$ . The significance of the different amounts of self‐potential included in the three PUCHF methods is demonstrated by comparing the results with results from coupled Hartree–Fock (CHF) calculations and the theoretical values. For the He isoelectronic sequence the PUCHF Method C_1/2 is considered to be the best. The range of error of ${\gamma }_0$ compared with ${\gamma }_{\mathrm{CHF}}$ is 0.14%–0.49%. The range of error of ${\gamma }_0{\mathrm{\hspace{0.17em}+\hspace{0.17em}\gamma }}_1$ or of ${\gamma }_{\mathrm{geom}}$ compared with ${\gamma }_{\mathrm{CHF}}$ is 0.01%–0.13%. Larger errors in the Be series are attributed to the restricted forms of the Hartree–Fock wavefunction and the variational first‐order orbitals.