Density-based perturbation theory within the Hohenberg-Kohn (HK) formalism of density functional theory (DFT), developed recently by us, is employed to calculate hyperpolarizabilities of helium-like ions from their ground-state densities obtained from their respective Hylleraas wavefunctions. The only approximation made is that of the local density (LDA) for exchange and correlation. Use of densities — instead of wavefunctions — in density-based perturbation theory together with simple approximate energy functionals makes our calculations much simpler than those based on wavefunctions. They lead, however, to accurate results.

In this paper we employ the hydrodynamic formulation of time-dependent density functional theory to obtain the van der Waals coefficientsC₆ andC₈ of alkali metal clusters of various sizes including very large clusters. Such calculations become computationally very demanding in the orbital-based Kohn-Sham formalism, but are quite simple in the hydrodynamic approach. We show that for interactions between the clusters of the same sizes,C₆ andC₈ scale as the sixth and the eighth power of the cluster radius, respectively, and approach their classically predicted values for the large size clusters.

We have theoretically studied the collective modes of a quasi-two-dimensional (Q2D) Bose condensate in the large gas parameter regime by using a formalism which treats the interaction energy beyond the mean-field approximation. The results show that incorporation of this higher order term leads to significant modifications in the mode frequencies.