Methods of density functional theory in one dimension

Density functional theory is formally justified by an existence proof. As such, the need for computational methods to study the theory is a useful route to understanding the full theory. In this paper, we discuss the numerical strategies to efficiently evaluate computations for Kohn-Sham systems in one dimension and also methods for determining exact properties, including time-dependence. An accompanying library is also available for computing one-dimensional density functional theory and publicly available. The expressions used to implement the density functional in one-dimension are surveyed. An alternative justification for a gradient-based technique is also shown that can be applied to time-dependent evolution of the exact Kohn-Sham potential.