Interactions on the Fermi Sphere in an All-Electron World: The Projector Augmented Wave Implementation of the Mott-Jones Hamilton Population and the Three Archetypal Sphere Packings.

The development of computational chemistry packages to translate the wavefunctions from a planewave DFT calculation to atom-centered functions has greatly contributed to the elucidation of bonding and stability in solid-state compounds. Fewer tools are available for the analysis of how nonlocalized, nearly-free electron character can be associated with stability, as proposed by the Mott-Jones (MJ) model. To bridge this divide, we developed the Mott-Jones Hamilton Population (MJHP) as a framework to extract the energetic contributions from interacting planewave pairs in a system's electronic structure. This method illustrates how the MJ effects can be tied to the overall energy of a system and the origins of an electronic pseudogap for a variety of intermetallic phases. However, its implementation has so far been limited to DFT calculations with norm-conserving pseudopotentials. In this article, we present the Projector Augmented Wave realization of the MJHP (PAW-MJHP), aiming to bypass the limitations, computational costs, and high barrier of use associated with the norm-conserving pseudopotentials. We begin by extending the original MJHP equations to the PAW-DFT method and testing its application with the PAW-MJHP analysis of elemental Zn. This test case illustrates the influence of the PAW atomic dataset on the MJHP results, where softer pseudo-wavefunctions lead to unintuitive splittings in the band energy from the MJ effect with destabilizing interactions occurring lower in energy than stabilizing interactions. Based on these results, we propose a series of guiding principles for the development of new atomic datasets optimized for use with the MJHP. After establishing this framework, we apply the PAW-MJHP analysis and optimized atomic datasets to three example systems: CsCl-type CuZn and AgCd, and AuCu3-type AlNi3. In each case, the PAW-MJHP analysis confirms the MJ origins of electronic stability. In the process, we demonstrate the role that MJ interactions can play in structures based on each of the three archetypal simple packings: body-centered cubic (CuZn and AgCd), face-centered cubic (AlNi3), and hexagonal close-packed (Zn).