This repository implements numerical integration of arbitrary functions over an atom-centered molecular grid using Becke partitioning. Becke’s crucial discovery allows for the subdivision of space into individual atom-centered grids so that nuclear cusps can be accurately integrated, while simultaneously respecting normalization over all space. This is accomplished by using a weighting function for each atom that decays rapidly in the interatomic regions, thus dividing space into Voronoi cells in a smooth fashion. You can see the cool way that the weight functions for two hydrogen molecules partition the grid points between them in the image below, where the red points have non-negligible weight values with respect to the lower hydrogen and the blue points have non-negligible weight values with respect to the upper hydrogen (this is with an Euler-Maclaurin radial grid and a product angular grid):
