Implicit infinite lattice summations for real space ab initio correlation methods

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 explicitly 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.