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We propose a simple linear scaling expression in reciprocal space forevaluating the ion--electron potential of crystalline solids. The expressionreplaces the long-range ion--electron potential with an equivalent localizedcharge distribution and corresponding boundary conditions on the unit cell.Given that no quadratic scaling structure factor is required---as used intraditional methods---the expression shows inherent linear behavior, and iswell suited to simulating large-scale systems within orbital-free densityfunctional theory. The scheme is implemented in the ATLAS software package andbenchmarked by using a solid Mg bcc lattice containing tens of thousands ofatoms in the unit cell. The test results show that the method can efficientlymodel large crystals with high computational accuracy.

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