  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.
