Oscillating Kernels in Electronic Structure Calculations
Heinz-Jürgen Flad (MPI Leipzig)
Due to Pauli's principle, electronic structure calculations have to deal with
various types of oscillations. Strong oscillations are restricted to
comparatively small regions around nuclei and can be efficiently treated, at
least approximately, by a variety of techniques which are briefly reviewed.
More severe are weak oscillations which extend over the whole system.
In our approach to electronic structure calculations, we separate the many-electron
problem into asymptotically smooth kernel functions, like the Coulomb interaction
and Jastrow factors, and an oscillating kernel
function corresponding to the one-particle density matrix. For insulators and
semiconductor like materials, the oscillations are damped by the exponential
decay of the density matrix. This is not the case for metals
where only an algebraic decay of the density matrices can be observed.
We discuss the interactions between these kernel functions in terms of Feynman like
diagrams. The possibility of sparse wavelet representations for certain types of
diagrams is considered for a simplified model problem
and the homogeneous electron gas.