Self-Consistent Chemical Pressure Analysis: Resolving Atomic Packing Effects through the Iterative Partitioning of Space and Energy

Abstract

While planewave DFT methods offer capabilities to calculate the relative stabilities and many physical properties exhibited by solid state structures, their detailed numerical output does not easily map onto the often empirical concepts and parameters used by synthetic chemists or materials scientists. The DFT-chemical pressure (CP) method is an approach to bridging this divide by explaining or anticipating a variety of structural phenomena in terms of atomic size and packing effects, but its reliance on adjustable parameters has limited the method’s predictive potential. In this article, we present the self-consistent (sc)-DFT-CP analysis, in which the criterion of self-consistency is used to automatically solve these parameterization issues. We begin by illustrating the need for this improved method with the results for a series of CaCu5-type/MgCu2-type intergrowth structures, where unphysical trends emerge that have no clear structural origin. To address these challenges, we derive iterative treatments for assigning ionicity and for the partitioning of the E Ewald + E α terms in the DFT total energy into homogeneous and localized terms. In this method, self-consistency is achieved between the input and output charges from a variation of the Hirshfeld charge scheme, while the partitioning of the E Ewald + E α terms is adjusted to create equilibrium between the net atomic pressures calculated within atomic regions and from the interatomic interactions. The behavior of the sc-DFT-CP method is then tested using electronic structure data for several hundred compounds from the Intermetallic Reactivity Database. Finally, we return to the CaCu5-type/MgCu2-type intergrowth series with the sc-DFT-CP approach, showing that trends in the series are now easily traced to changes in the thicknesses of the CaCu5-type domains and lattice mismatch at the interface. Through this analysis and the complete update to the CP schemes in the IRD, the sc-DFT-CP method is demonstrated as a theoretical tool for the investigation of atomic packing issues across intermetallic chemistry.

Toward Predicting the Assembly of Modular Intermetallics from Chemical Pressure Analysis: The Interface Nucleus Approach

“…In this way, the formation of the YNi 3 intergrowth has served to soothe the strongest CP features experienced by the interface nuclei in the parent structures without significantly intensifying CPs elsewhere. These conclusions align with our previous findings from a detailed CP analysis of a series of Laves/CaCu 5 -type intergrowths in the Y–Ni system . This time we have framed the story in terms of a visual language suited for analyzing modular intermetallicscomplex phases derived from fragments of simpler structures via construction principles that allow for further variationsmore broadly.…”

“…In the generation of the CP maps, the core unwarping procedure was applied, based on free ion electron densities derived from an iterative binary Hirshfeld analysis and atomic calculations carried out with the Atomic Pseudo-potentials Engine . The mapping of the E Ewald + E α terms was accomplished with the self-consistency criterion for the net atomic pressures as determined from atomic cells and Hirshfeld-inspired contact volumes . The CP maps were interpreted in terms of the interatomic pressures using the Hirshfeld-inspired contact volume scheme and the iterative binary Hirshfeld free ion densities .…”

Entropic Control of Bonding, Guided by Chemical Pressure: Phase Transitions and 18-n+m Isomerism of IrIn3

“…Single-point calculations were then performed on the equilibrium, slightly expanded, and slightly contracted geometries (linear scale ±0.5%) to obtain the kinetic energy densities, electron densities, and local components of the Kohn–Sham potentials . Contributions from the Ewald energy and E α components were spatially distributed to achieve self-consistency between net pressures obtained from the contact volumes and atomic cells, as obtained from the iterative binary Hirschfeld scheme . CP maps were constructed using the core-unwarping procedure and pressures within contact volumes were averaged and projected onto spherical harmonics centered on the atomic sites.…”

“…It remains unclear, however, why under certain conditions the IrIn 3 -type is preferred. Here, we combine DFT-reversed approximation Molecular Orbital (DFT-raMO) analysis and DFT-Chemical Pressure (DFT-CP) analysis − to determine how the electronic structure and atomic packing interact to shape the structural preferences in these systems. We will see that the different ( n , m ) configurations for the two polymorphs have distinct spatial requirements and are adapted for different T/E atomic size ratios.…”

The Zintl Concept Applied to Intergrowth Structures: Electron‐Hole Matching, Stacking Preferences, and Chemical Pressures in Pd5InAs

“…Single point electronic structure calculations for each phase were then performed for the equilibrium geometry plus slightly expanded and contracted versions (total volume range: 98.5 -101.5 %) to yield the electron densities, kinetic energy densities, wavefunctions, and Kohn-Sham potential components needed for CP analysis. DFT-CP maps were calculated using the self-consistent procedure, [46] employing core-unwarping, and were analyzed through the integration of interatomic pressures in Hirshfeldinspired contact volumes, which were projected onto spherical harmonics (l max = 4) for visualization. Further computational details, including the original input files, have been deposited on the Intermetallic Reactivity Database.…”