O(NlogN) scaling method to evaluate the ion-electron potential of crystalline solids

We propose a simple O(NlogN) scaling expression in reciprocal space for evaluating the ion-electron potential of crystalline solids. The expression replaces the long-range ion-electron potential with an equivalent localized charge distribution and corresponding boundary conditions on the unit cell. Given that no quadratic scaling structure factor is required-as used in traditional methods-the expression shows the inherent O(NlogN) behavior, and is well suited to simulating large-scale systems within orbital-free density functional theory. The scheme is implemented in the ATLAS software package and benchmarked by using a solid Mg body-centered cubic lattice containing tens of thousands of atoms in the unit cell. The test results show that the method can efficiently simulate large scale crystals with high computational accuracy.