Efficient projector expansion for the ab initio LCAO method

A projector expansion method is presented for an efficient and accurate implementation of the first-principles electronic structure calculations using pseudopotentials and atomic basis functions. By expressing the rapidly varying local potential in the vicinity of nuclei by a separable projector expansion, the difficulty involved in the grid integration using the regular real-space grid is remarkably reduced without increasing the computational effort. To illustrate the capability, it is shown that the proposed method significantly suppresses not only a spurious oscillation in the energy curve for the atomic displacement involved in a weak interaction such as hydrogen bonding, but also the dependence of optimized structure on relative position to the real-space grid in the geometry optimization within a modest grid fineness.