Efficient O(N) Integration For All-Electron Electronic Structure Calculation Using Numeric Basis Functions

We consider the problem of developing O(N) scaling grid based operations needed in many central operations when performing electronic structure calculations with numeric atom-centered orbitals as basis functions. We outline the overall formulation of localized algo-rithms, and specifically the creation of localized grid batches. The choice of the grid parti-tioning scheme plays an important role in the performance and memory consumption of the grid based operations. Three different top-down partitioning methods are investigated, and compared with formally more rigorous yet much more expensive bottom-up algorithms. We show that a conceptually simple top-down grid partitioning scheme achieves essentially the same efficiency as the more rigorous bottom-up approaches. Key words: electronic structure theory, density functional theory, atom-centered basis functions, numerical integration grid, spatial partitioning PACS: 02.60.Jh, 71.15.Ap, 71.15.Dx