A linear scaling method to evaluate the ion-electron potential of crystalline solids

TL;DR

This paper introduces a linear scaling method for efficiently computing the ion-electron potential in large crystalline solids, replacing traditional long-range calculations with a localized charge approach suitable for large-scale orbital-free DFT simulations.

Contribution

The paper presents a novel linear scaling expression in reciprocal space that simplifies ion-electron potential calculations without requiring structure factors, enabling efficient large-scale simulations.

Findings

Efficiently models large crystals with tens of thousands of atoms.

Demonstrates high computational accuracy in benchmark tests.

Achieves linear computational scaling for ion-electron potential evaluation.

Abstract

We propose a simple linear 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 inherent linear 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 bcc lattice containing tens of thousands of atoms in the unit cell. The test results show that the method can efficiently model large crystals with high computational accuracy.