This work presents an updated strategy for computing Coulomb matrix elements directly on a regular grid superimposed on the underlying crystal lattice. It removes the need for an auxiliary basis transfer while retaining near-linear practical scaling.
Keywords: Coulomb integrals, linear scaling, silicon dopants
Main result: Coulomb matrix elements for multi-million-atom systems can be computed with O(N log N) scaling while remaining numerically consistent with direct summation. This substantially expands the feasible size of atomistic many-body calculations.