  We suggest a local wave function based ab initio correlation method for
infinite periodic systems, which can describe both the near range as well as
the long range correlation effects coherently in the same scheme. Specifically,
this work introduces a formalism which allows to describe the long range
polarization cloud around a quasi particle in a solid explicitly in the
formalism of local wave function based ab initio descriptions. To this end we
reformulate the infinite lattice summation underlying the quantum chemistry
formula to second order in a closed analytic form employing the elliptic theta
function of the third kind. All formulas and manipulations are developed
explicitely in full detail and a first numeric example demonstrates the
principle idea. Good results for the long range polarization effects in LiH and
LiF are found in agreement with earlier estimates.
