Achieving linear scaling in exchange-correlation density functional quadratures

We present a new set of atomic partition functions (weight scheme) for density functional quadratures that yields similar accuracy but is substantially faster than the widely used algorithm of Becke. Employing efficient screening techniques, we have achieved near-linear scaling with molecular size in both weight schemes. Furthermore, using microbatches of grid points that have similar sets of significant basis functions, we have also achieved near-linear scaling at modest molecular sizes in the evaluation of the density (and other quantities of interest). We demonstrate the near-linear scaling properties of our numerical integration method in benchmark calculations of graphitic sheets and diamond chunks that contain up to 400 atoms and 3500 contracted Gaussians.