Towards dft calculations of metal clusters in quantum fluid matrices

This paper reports progress on the simulation of metallic clusters embedded in a quantum uid matrix such as 4He. In previous work we have reported progress developing a real–space density functional method. The core of the method is a diffusion algorithm that extracts the low-lying eigenfunctions of the Kohn-Sham Hamiltonian by propagating the wave functions (which are represented on a real–space grid) in imaginary time. Due to the difusion character of the kinetic energy operator in imaginary time, algorithms developed so far are at most fourth order in the time–step. The first part of this paper discusses further progress, in particular we show that for a grid based algorithm, imaginary time propagation of any even order can be devised on the basis of multi–product splitting. The new propagation method is particularly suited for modern parallel computing environments. The second part of this paper addresses a yet unsolved problem, namely a consistent description of the interaction between helium atoms and a metallic cluster that can bridge the whole range from a single atom to a metal. Using a combination of DFT calculations to determine the response of the valence electrons, and phenomenological acounts of Pauli repulsion and short-ranged correlations that are poorly described in DFT, we show how such an interaction can be derived.