Multipole polarizabilities and shielding factors of the hydrogen atom from the hydrodynamic analogy to quantum mechanics. II

Long‐Range interaction coefficients between H, He+, He, and Li+

“…Table I contains the values of effective oscillator strengths Z, and the effective transition energies wi for these systems. In Table I1 good agreement with that reported by Yousif et al [13]. Recently [15], we have shown that the variational calculation of dynamic multipole polarizabilities of atomic systems using the two schemes namely hydrodynamic analogy to quantum mechanics [ 161 and perturbation expansion of the energy in multipole [ 101 also follow from the conventional time-dependent perturbation scheme [15].…”

“…. ,-18 are in harmony with the best estimated values [13], so our formula is encouraging to calculate S l ( k ) , for k = -18,. . .…”

Why the Kirkwood-Pople-Schofield method works so well

“…Finally, we want to point out that a similar analysis can also be used to justify the KPS results for frequency dependent polarizabilities [2,7,31] and may provide additional arguments in favour of methods which are based on what is called the hydrodynamic analogy to quantum mechanics [3,6,8,9]. However, for both static and frequency dependent polarizabilities the final result of Downloaded by [University of California, San Diego] at 13: 14 29 June 2016 the KPS based on the SCF HF tF(~ is to some extent unpredictable.…”

“…In other words, one has the following inequality < (10) which can be used to discuss the validity of the KPS method for the HF unperturbed wavefunctions. The difference between the Karplus-Kolker and the KPS method is that in the latter case the variation functions [~ are assumed to be the same for all orbitals, that is f~=f, i=l, 2,...,N. (11) This restriction makes the total variation function less flexible and the second order energy functional of the KPS method will lead to the second order KPS energy EKes (2) which must be higher than the variational minimum for the functional (8), that is…”

Dispersion interaction between helium pair from hydrodynamic analogy to quantum mechanics

“…Recently, we generalized the Wiener, Askar, and Demiralp scheme [l, 21 for frequency-dependent dipole polarizability of hydrogen to the multipole of the hydrogen atom [3,4]. This has been successfully employed in working out the frequency-dependent multipole polarizabilities of lithium and lithium sequence in the frozen-core approximation [5,6].…”