  We introduce two new approximation methods for the numerical evaluation of
the long-range Coulomb potential and the approximation of the resulting high
dimensional Two-Electron Integrals tensor (TEI) with long-range interactions
arising in molecular simulations. The first method exploits the tensorized
structure of the compressed two-electron integrals obtained through
two-dimensional Chebyshev interpolation combined with Gaussian quadrature. The
second method is based on the Fast Multipole Method (FMM). Numerical
experiments for different medium size molecules on high quality basis sets
outline the efficiency of the two methods. Detailed algorithmic is provided in
this paper as well as numerical comparison of the introduced approaches.
