Multipole Polarizabilities and Shielding Factors from Hartree-Fock Wave Functions

Abstract

Electric dipole, quadrupole, and octupole polarizabilities and shielding factors are calculated for a large number of two- to twenty-electron $S$-state atoms and ions. The calculations are carried out within the framework of an uncoupled Hartree-Fock approximation, subject to the proviso that the exchange part of the Fock potential be expressable as a multiplicative function. All zeroth-order functions used are of the anayltical Hartree-Fock type. The resulting numerical values are found to be strongly sensitive to the quality of the Hartree-Fock function used in the calculation, in agreement with Sternheimer's previous conclusion. This point proves to be of special importance in the case of the negative ions. In addition, it is shown that the variational method pioneered by Das and Bersohn, if carried out under proper orthogonality conditions, is equivalent to the present uncoupled Hartree-Fock approximation. Finally, it is noted that the variational method used in this work is less accurate than the Sternheimer numerical method; however, use of the variational method allows some simplification in the computational procedure.