Thinking inside the box: Novel linear scaling algorithm for Coulomb potential evaluation

Abstract Beginning with the Poisson equation, and expanding the electronic potential in terms of sine functions, the natural orbitals for describing the particle‐in‐a‐box problem, we find that simple analytic forms can be found for the evaluation of the Coulomb energy for both the interacting and non‐interacting system of N ‐electrons in a box. This method is reminiscent of fast‐Fourier transform and scales linearly. To improve the usefulness …