Theory of electron-electron interaction effects on antishielding factors of negative ions

The influence of electron-electron interaction effects on nuclear quadrupole antishielding factors γ_∞ is studied for the negative halide ions F^-, Cl^-, and Br^-. Using a procedure developed earlier which utilizes the nuclear-quadrupole-moment-perturbed and external-point-charge-perturbed wave functions for the ions, obtained by the differential equation procedure for the zero-order antishielding factor (γ_∞)₀, we have computed the consistency contributions (γ_∞)₁ to be +2.28, -1.50, and -7.16 in F^-, Cl^-, and Br^-, respectively. The resulting values of γ_∞ correct to first order in electron-electron interaction are then -19.29, -56.58, and -140.83. The appearance of negative signs for (γ_∞)₁ in Cl^- and Br^- is seen to be due to large negative interactions between p electrons belonging to different shells. This intershell effect is not present in F^- (1s²2s²2p⁶). The contributions to (γ_∞)₁ for all three ions are analyzed in detail, and a comparison is made of (γ_∞)₁ for F^- and the isoelectronic positive ion Na⁺. An explanation is proposed for the comparable values of the ratio (γ_∞)₁(γ_∞)₀ found for these two ions, even though the F^- ion is substantially more deformable with a larger value of (γ_∞)₀. From the results of the present investigations, as well as earlier ones in related positive ions, it is felt that the consistency contribution (γ_∞)₁ should, in general, be less than 15% of (γ_∞)₀ for most ions.