Analytical and Separable Representation of Coulomb-like Potentials

In this article, low-rank separable analytical representations of Coulomb-like potentials are presented. Cartesian coordinates are employed for the sake of generality. The original potential is regularized to avoid the numerical divergence associated with the coalescence region. Furthermore, a range-separation approach is adopted. The long-range part, being smooth and well-behaved, can be directly expressed in our functional sparse Tucker Finite Basis Representation (sparse Tucker FBR). On the other hand, the short-range part, which contains the tamed singularity, is expressed using a sparse spectral representation. The quality and accuracy of the full sparse Tucker expression is demonstrated by comparison to the two-interacting-electron-in-a-box model.