 
Summary: Approximation free approach to dualscale problems :
Calculating the electronic structure of molecules using multigrid
techniques
Or Cohen
Weizmann Institute Of Science, Rehovot 70600 Israel
January 28, 2010
Since the dawn of quantum mechanical calculations for materials, describing the electronic
structure in the vicinity of the atom has been a major difficulty. In density functional the
ory (DFT), this problem is commonly avoided either by using atomic pseudo potentials, or by
spanning the electronic wavevectors in an atomic basis set. This approximation of the core
introduces errors. These errors are often below those related to the choice of approximate
exchangecorrelation functional. However, in light of recent developments for new types of
functionals, the effect of these core related errors has to be reevaluated. This brings about a
need to perform allelectron calculations that do not involve any approximation of the core.
In this work, I have developed a fully numerical allelectron solver that is meant to pro
vide bench mark computations for such functionals. High order realspace discretization, along
with advanced multigrid techniques, were implemented in order to achieve high accuracy and
efficiency. The KohnSham equations of DFT are solved on a set of locally refined Cartesian
grids that are adaptable to any type of geometry. The components of the nonlinear equa
tions are iterated together in a single, highly efficient multigrid cycle. Numerical results from
