A fast multipole algorithm for the efficient treatment of the Coulomb problem in electronic structure calculations of periodic systems with Gaussian orbitals

An efficient implementation of the Gaussian very fast multipole method (GvFMM) for periodic systems (pGvFMM) is presented. Relevant details of our algorithm are discussed and linear scaling properties with unit cell size demonstrated on benchmarks using minimum and double-zeta bases on solid NaCl, (5,5) and (10,10) carbon nanotubes containing up to 960 atoms in the unit cell.