Efficient algorithms for Hirshfeld-I charges.

A new viewpoint on iterative Hirshfeld charges is presented, whereby the atomic populations obtained from such a scheme are interpreted as such populations which reproduce themselves. This viewpoint yields a self-consistent requirement for the Hirshfeld-I populations rather than being understood as the result of an iterative procedure. Based on this self-consistent requirement, much faster algorithms for Hirshfeld-I charges have been developed. In addition, new atomic reference densities for the Hirshfeld-I procedure are presented. The proposed reference densities are N-representable, display proper atomic shell structure and can be computed for any charged species.